SFM Qbook

1.
Time Value of Money

Study Session 1
LOS 1 : Introduction
 Time value of Money is the first and the most important chapter of Finance.
 Anything connected with Finance is based on the “TIME VALUE OF MONEY”
 ` 100 today is Not Equal to ` 100 a year later.
 Three Factors determines the Time Value of Money:
Expected Inflation Rate

+
Real Rate of Return on Risk free Investment
+
Risk Premium
LOS 2 : Future Value of a Single Cash Flow
n
FV = PV × (1 + r)
Example:
You invest ` 15,000 for two years that pays you 12% p.a. how much will you have at the end of two
years?
Solution:
FV = PV × (1 + r) n
2
= 15,000 × (1 + 0.12)
= 18,816
1.2
LOS 3 : Present Value of a Single Cash Flow
𝐅𝐕
FV = PV × (1 + r) n or PV =
( 𝟏 𝐫)𝐧
Example:
You need ` 10,000 for buying a mobile next year. You can earn 10% on your money. How much do
you need to invest today?
Solution:
FV = 10,000
r = 10%
n = 1 year
,
PV =   9090.91
( ) ( . )
LOS 4 : Future Value of a Multiple Unequal Cash Flow

Example:
Suppose you receive ` 1000 today, another ` 1200 a year later and ` 1300 two year later. How much
will you have three years from today? Interest Rate @ 10%
Solution:
1000 × (1 + 0.10) 3 = 1331

1200 × (1 + 0.10) 2 = 1452
1300 × (1 + 0.10) 1 = 1430
4213
LOS 5 : Present Value of a Multiple Unequal Cash Flow

Example:
Mr. X receives ` 1000, 1500, 1100, 1400 & 400 at the end of year 1, 2, 3, 4 & 5. Rate = 10%,
Calculate PV.
+ + + +
( . ) ( . ) ( . ) ( . ) ( . )
PV = 4179.30
LOS 6 : Present Value of a Multiple Equal Cash Flow (Period Defined)

1.3
a) Present Value of Multiple Equal Cash Flow (Period Defined) :- (at the end of each year)
Example:
Mr. X will receive ` 1000 at the end of each year upto 5 years, Rate = 10%. Find Present Value.
+ + + +
( . ) ( . ) ( . ) ( . ) ( . )
Or
PV = 1000 [ PVAF @ 10% for 5 years]  1000 × 3.791  3791
b) Present Value of Multiple Equal Cash Flow (Period Defined) :- (at the Beginning of each year)
Example:
Mr. X will receive ` 1000 starts from today upto 5 years, Rate = 10%. Find Present Value.
+ + + +
( . ) ( . ) ( . ) ( . ) ( . )
Or
PV = 1000 [1 + PVAF @ 10%, (5 – 1) years]
= 1000 × [1 + 3.17]  4170
Note: If question is silent always assume Deferred Annuity.
LOS 7 : Present Value of Equal Cash Flow upto infinity (Perpetuity/

Indefinite): (Series of equal Cash Flow arising upto infinite or forever)
𝐀𝐧𝐧𝐮𝐚𝐥 𝐂𝐚𝐬𝐡 𝐅𝐥𝐨𝐰
PV =
𝐃𝐢𝐬𝐜𝐨𝐮𝐧𝐭 𝐑𝐚𝐭𝐞
Example:
Mr. X will receive ` 1000 at the end of each year upto infinity, Rate = 10%. Find Present Value.
Solution:
PV =  10,000
.
LOS 8: Present Value of Growing Cash Flow upto Infinity (Growing Perpetuity)
𝐂𝐅𝟏
PV =
𝐃𝐢𝐬𝐜𝐨𝐮𝐧𝐭 𝐑𝐚𝐭𝐞 𝐆𝐫𝐨𝐰𝐭𝐡 𝐑𝐚𝐭𝐞
Where CF1 = Cash Flow at the end of year 1.

Example:
Mr. X will receive ` 1000 at the end of year 1, thereafter cash flow will grow by 8% every year upto
infinity, Rate = 10%. Find Present Value.
Solution:
PV =  50,000
. .
1.4
2.1
Security Valuation
Study Session 2
Note: Total Earnings mean Earnings available to equity share holders

Income Statement
Sales
Less: Variable cost
Contribution
Less: Fixed cost excluding Dep.
EBITDA
Less: Depreciation and Amortization
EBIT
Less: Interest
EBT
Less: Tax
EAT
Less: Preference Dividend
Earnings Available to Equity Share holders
Less: Equity Dividend
T/F to R&S
LOS 2 : SOME BASIC RATIOS

𝐓𝐨𝐭𝐚𝐥 𝐞𝐚𝐫𝐧𝐢𝐧𝐠 𝐚𝐯𝐚𝐢𝐥𝐚𝐛𝐥𝐞 𝐭𝐨 𝐞𝐪𝐮𝐢𝐭𝐲 𝐬𝐡𝐚𝐫𝐞𝐡𝐨𝐥𝐝𝐞𝐫𝐬
 EPS =
𝐓𝐨𝐭𝐚𝐥 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐞𝐪𝐮𝐢𝐭𝐲 𝐬𝐡𝐚𝐫𝐞𝐬
𝐓𝐨𝐭𝐚𝐥 𝐝𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐩𝐚𝐢𝐝 𝐭𝐨 𝐞𝐪𝐮𝐢𝐭𝐲 𝐬𝐡𝐚𝐫𝐞𝐡𝐨𝐥𝐝𝐞𝐫𝐬

 DPS =
𝐓𝐨𝐭𝐚𝐥 𝐌𝐚𝐫𝐤𝐞𝐭 𝐕𝐚𝐥𝐮𝐞/ 𝐌𝐚𝐫𝐤𝐞𝐭 𝐂𝐚𝐩𝐢𝐭𝐚𝐥𝐢𝐳𝐚𝐭𝐢𝐨𝐧/ 𝐌𝐚𝐫𝐤𝐞𝐭 𝐂𝐚𝐩

 MPS =
𝐓𝐨𝐭𝐚𝐥 𝐑𝐞𝐭𝐚𝐢𝐧𝐞𝐝 𝐞𝐚𝐫𝐧𝐢𝐧𝐠𝐬

 REPS =
OR
 REPS = EPS - DPS

𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞
 Dividend Yield = × 100
𝐌𝐚𝐫𝐤𝐞𝐭 𝐩𝐫𝐢𝐜𝐞 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞
2.2
 Dividend pay-out Ratio = × 100
𝐄𝐚𝐫𝐧𝐢𝐧𝐠 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞

 Dividend Rate = × 100
𝐅𝐚𝐜𝐞 𝐯𝐚𝐥𝐮𝐞 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞

 Earning Yield = × 100
𝐌𝐚𝐫𝐤𝐞𝐭 𝐏𝐫𝐢𝐜𝐞 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞
𝐌𝐏𝐒
 P/E Ratio =
𝐄𝐏𝐒
𝐑𝐞𝐭𝐚𝐢𝐧𝐞𝐝 𝐄𝐚𝐫𝐧𝐢𝐧𝐠 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞
 Retention Ratio = × 100
𝐄𝐏𝐒 𝐃𝐏𝐒
=
𝐄𝐏𝐒
× 100
OR
 Retention Ratio = 1 – Dividend Payout Ratio
Note :
 Relationship Between DPR & RR:
RR + DPR = 100% or 1
 Dividend yield and Earning Yield is always calculated on annual basis.
 Dividend is 1st paid to preference share holder before any declaration of dividend to equity
shareholders.
 Dividend is always paid upon FV(Face Value) not on Market Value.
LOS 3 : Define Cash Dividends, Stock Dividend ,Stock Split

Cash Dividends: As the name implies, are payments made to shareholders in cash. They come in 3
forms:
(i) Regular Dividends: Occurs when a company pays out a portion of profits on a consistent basis.
E.g. Quarterly, Yearly, etc.
(ii) Special Dividends: They are used when favourable circumstances allow the firm to make a one-
time cash payment to shareholders, in addition to any regular dividends. E.g. Cyclical Firms
(iii) Liquidating Dividends: Occurs when company goes out of business and distributes the proceeds
to shareholders.
Stock Dividends (Bonus Shares) :
 Stock Dividend are dividends paid out in new shares of stock rather than cash. In this case, there
will be more shares outstanding, but each one will be worth less.
 Stock dividends are commonly expressed as a percentage. A 20% stock dividend means every
shareholder gets 20% more stock.
Stock Splits :
 Stock Splits divide each existing share into multiple shares, thus creating more shares. There are
now more shares, but the price of each share will drop correspondingly to the number of shares
created, so there is no change in the owner’s wealth.
 Splits are expressed as a ratio. In a 3-for-1 stock split, each old share is split into three new shares.
 Stock splits are more common today than stock dividends.
Effects on Financial ratios:
 Paying a cash dividend decreases assets (cash) and shareholders’ equity (retained earnings).
Other things equal, the decrease in cash will decrease a company’s liquidity ratios and increase
2.3
its debt-to-assets ratio, while the decrease in shareholders’ equity will increase its debt-to-equity
ratio.
 Stock dividends, stock splits, and reverse stock splits have no effect on a company’s leverage ratio
or liquidity ratios or company’s assets or shareholders’ equity.
LOS 4 : RETURN CONCEPTS
 A sound investment decision depends on the correct use and evaluation of the rate of return.
Some of the different concepts of return are given as below:
Required Rate of Return:

An asset's required return is the minimum return an investor requires given the asset's risk. A more
risky asset will have a higher required return. Required return is also called the opportunity cost for
investing in the asset. If expected return is greater (less) than required return, the asset is undervalued
(overvalued).
Price Convergence
If the expected return is not equal to required return, there can be a "return from convergence of
price to intrinsic value."
Letting V0 denote the true intrinsic value, and given that price does not equal that value
𝑽𝟎 𝑷𝟎
(i.e., V0 ≠ P0), then the return from convergence of price to intrinsic value is .
𝑷𝟎
If an analyst expects the price of the asset to converge to its intrinsic value by the end of the horizon,
𝑽𝟎 𝑷𝟎
then is also the difference between the expected return on an asset and its required return:
𝑷𝟎
𝑽𝟎 𝑷𝟎
Expected Return= Required Return +
𝑷𝟎
Example:
Suppose that the current price of the shares of ABC Ltd. is ₹30 per share. The investor estimated the
intrinsic value of ABC Ltd.’s share to be ₹35 per share with required return of 8% per annum. Estimate
the expected return on ABC Ltd.
Solution :
Intel's expected convergence return is (35 - 30)/30 * 100 = 16.67%, and let's suppose that the
convergence happens over one year. Thus, adding this return with the 8% required return, we obtain
an expected return of 24.67%.
Discount Rate
Discount Rate is the rate at which present value of future cash flows is determined. Discount rate
depends on the risk free rate and risk premium of an investment.
Internal Rate of Return
Internal Rate of Return is defined as the discount rate which equates the present value of future cash
flows to its market price. The IRR is viewed as the average annual rate of return that investors earn
over their investment time period assuming that the cash flows are reinvested at the IRR.
LOS 5 : Ex – Dividend and Cum – Dividend Price of a share

 If Question is Silent, always Assume Ex- Dividend price of share.
 If cum-dividend price is given, we must deduct dividend from it.
 It may be noted that in all the formula, we consider Ex-Dividend & not Cum-Dividend.
2.4
LOS 6 : Valuation Models based on Earnings & Dividends

Walter’s Model :
Walter’s supports the view that the dividend policy plays an important role in determining the market
price of the share.
He emphasis two factors which influence the market price of a share:-
(i) Dividend Payout Ratio.
(ii) The relationship between Internal return on Retained earnings (r) and cost of equity capital (Ke)
Walter classified all the firms into three categories:-
a) Growth Firm:
 If (r > K e). In this case, the shareholder’s would like the company to retain maximum amount
i.e. to keep payout ratio quite low.
 In this case, there is negative correlation between dividend and market price of share.
 If r > Ke, Lower the Dividend Pay-out Ratio Higher the Market Price per Share & vice-versa.
b) Declining Firm:
 If (r < Ke). In this case, the shareholder’s won’t like the firm to retain the profits so that they
can get higher return by investing the dividend received by them.
 In this case, there is positive correlation between dividend and market price of share.
 If r < Ke, Higher the Dividend Pay-out Ratio, Higher the Market Price per Share & vice-versa.
c) Constant Firm:
 If rate of return on Retained earnings (r) is equal to the cost of equity capital (Ke) i.e.(r = Ke).
In this case, the shareholder’s would be indifferent about splitting off the earnings between
dividend & Retained earnings.
 If r = Ke, Any Retention Ratio or Any Dividend Payout Ratio will not affect Market Price of share.
MPS will remain same under any Dividend Payout or Retention Ratio.
Note: Walter concludes:-
 The optimum payout ratio is NIL in case of growth firm.
 The optimum payout ratio for declining firm is 100%
 The payout ratio of constant firm is irrelevant.
Summary: Optimum Dividend as per Walter’s
Category of r Vs. Ke Correlation between Optimum Payout Optimum
the Firm DPS & MPS Ratio Retention Ratio
Growth r >Ke Negative 0% 100 %
Constant r = Ke No Correlation Every payout is Every retention is
Optimum Optimum
Decline r <Ke Positive 100% 0%
Valuation of Equity as per Walter’s
Current market price of a share is the present value of two cash flow streams:-
a) Present Value of all dividend.
b) Present value of all return on retained earnings.
In order to testify the above, Walter has suggested a mathematical valuation model i.e.,
𝒓
𝑫𝑷𝑺 (𝑬𝑷𝑺 𝑫𝑷𝑺)
P0 = 𝑲𝒆
+ 𝑲𝒆
𝑲𝒆
2.5
When
P0 = Current price of equity share (Ex-dividend price)/ Fair or Theoretical or Intrinsic or
Equilibrium or present Value Price per Share
DPS = Dividend per share paid by the firm
r = Rate of return on investment of the firm / IRR / Return on equity
Ke = Cost of equity share capital / Discount rate / expected rate of return/opportunity
cost / Capitalization rate
EPS = Earnings per share of the firm
EPS – DPS = Retained Earning Per Share
Assumptions :
 DPS & EPS are constant.
 Ke & r are constant.
 Going concern assumption, company has infinite life.
 No external Finance
QUESTION NO. 1A
Sahu & Co. earns ₹ 6 per share having capitalization rate of 10% and has a return on investment at the
rate of 20%. According to Walter's Model, what should be the price per share at 30% dividend payout
ratio? Is this the optimum payout ratio as per Walter?
QUESTION NO. 1B
Following figures are collected from annual report of A Ltd.
Net Profit ₹ 30.00 Lacs
Outstanding 12% Preference Shares ₹ 100.00 Lacs
Number of Equity Shares 3,00,000
Return on Investment 20%
Ke 16%
What should be the approximate dividend payout ratio so as to keep share price at ₹ 42, use Walter
Model?
QUESTION NO. 1C
The following information pertains to M/s XY Ltd.
Earnings of the Company Rs, 5,00,000
Dividend Payout Ratio 60%
No. of Shares Outstanding 1,00,000
Equity Capitalization Rate 12%
Rate of Return on Investment 15%
a) What would be the market value per share as per Walter's model?
b) What is the optimum dividend payout ratio according to Walter's model and the market value of
Company's share at that payout ratio?
QUESTION NO. 1D
Goldilocks Ltd. was started a year back with equity capital of ₹ 40 lakhs. The other details are as
under:
Earnings of the company ₹ 4,00,000
Price Earnings ratio 12.5
Dividend paid ₹ 3,20,000
Number of Shares 40,000
Find the current market price of the share. Use Walter's Model.
Find whether the company's D/ P ratio is optimal, use Walter's formula.
2.6
LOS 7 : Gordon’s Model/Growth Model/ Dividend discount Model

 Gordon’s Model suggest that the dividend policy is relevant and can effect the value of the share.
 Dividend Policy is relevant as the investor’s prefer current dividend as against the future uncertain
Capital Gain
 Current Market price of share = PV of future Dividend, growing at a constant rate
𝐃𝟎 (𝟏 𝐠) 𝐃𝟏 (𝐧𝐞𝐱𝐭 𝐞𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐝𝐢𝐯𝐢𝐝𝐞𝐧𝐝) 𝑬𝑷𝑺𝟏 ( 𝟏 𝒃)

P0 = OR P0 = OR P0 =
𝐊𝐞 𝐠𝐜 𝐊𝐞 𝐠𝐜 𝑲𝒆 𝒃𝒓
P0 = Current market price of share.

Ke = Cost of equity capital / Discount rate / expected rate of return / Opportunity cost/
Capitalization rate.
g = Growth rate
D1 = DPS at the end of year / Next expected dividend / Dividend to be paid
D0 = Current year dividend / dividend as on today / last paid dividend
EPS1 = EPS at the end of the year
b = Retention Ratio
1-b = Dividend payout Ratio
Note:
Watch for words like ‘ Just paid ’ or ‘ recently paid ’, these refers to the last dividend D0 and words
like ‘ will pay ’ or ‘ is expected to pay ’ refers to D1 .
Assumptions:
(i) No external finance is available.
(ii) K e & r are constant.
(iii) ‘g’ is the product of its Retention Ratio ‘b’ and its rate of return ‘r’
g = b × r OR g = RR × ROE
(iv) K e > g
(v) g & RR are constant.
(vi) Firm has an infinite life
Applications
1. EPS1 (1-b) = DPS1
Proof :
EPS1 (1-b) = EPS1 × Dividend payout Rate
= EPS1 ×
= DPS1
We know that DPR + RR = 1 or 100%
2. If EPS = DPS, RR = 0 then g = 0

( )
P0 =
P0 = as g = 0
𝐄𝐏𝐒
P0 = (˙.˙ EPS = DPS)
𝑲𝒆
2.7
3. Calculation of P1 (Price at the end of year 1)
Price at the beginning = PV of Dividend at end + PV of market price at end

𝑫𝟏 𝑷𝟏
P0 =
(𝟏 𝑲𝒆 )
𝟏
4. K e =
𝐏.𝐄 𝐑𝐚𝐭𝐢𝐨
Note:
The above equation for calculating Ke should only be used when no other method of calculation
is available.
QUESTION NO. 2A
A share of T Ltd. is currently quoted at a price-earnings ratio of 7.5 times. The retained earnings per
share being 37.5% is ₹ 3 per share. Compute:
a) The company's cost of equity if investors expect annual growth rate of 12%
b) If anticipated growth rate is 13% p.a., calculate indicated market price with same cost of equity.
c) If the company's cost of Equity is 18% and anticipated growth rate is 15% p.a., calculate the market price
per share assuming other conditions remain the same.
QUESTION NO. 2B
Shares of Volga Ltd. are being quoted at a price-earnings ratio of 8 times. The company retains 50% of its
Earnings Per Share. The Company's EPS is 10.
You are required to determine:
1) The cost of equity to the company if the market expects a growth rate of 15% p.a.
2) The indicative market price with the same cost of capital and if the anticipated growth rate is 16%p.a.
3) The market price per share if the company's cost of capital is 20% p.a. and the anticipated growth
rate is 18% p.a.
QUESTION NO. 2C
A firm had been paid dividend at ₹ 2 per share last year. The estimated growth of the dividends from
the company is estimated to be 5% p.a. Determine the estimated market price of the equity share if the
estimated growth rate of dividends (i) rises to 8%, and (ii) falls to 3%.Also find out the present market price of
the share, given that the required rate of return of the equity investors is 15.5%.
QUESTION NO. 2D
Amal Ltd. has been maintaining a growth rate of 12% in dividends. The company has paid dividend @ 3
per share. The rate of return on market portfolio is 15% and the risk-free rate of return in the market has
been observed as 10% . The beta co-efficient of the company's share is 1.2. You are required to calculate
the expected rate of return on the company's shares as per CAPM model and the equilibrium price per
share by dividend growth model.
QUESTION NO. 2E
With the help of following figures calculate the market price of a share of a company by using
(i) Walter's Formula, (ii) Dividend Growth Model (Gordon's Formula)
Earnings per Share (EPS) ₹ 10

Dividend per Share (DPS) ₹6
Cost of Capital (K) 20%
Internal Rate of Return on Investment 25%
Retention Ratio 40%
2.8
QUESTION NO. 2F
A company pays a dividend of ₹ 2/- per share with a growth rate of 7%. The risk free rate is 9% and the
market rate is 13%. The company has a beta factor of 1.50. However, due to a decision of the finance
manager, Beta is likely to increase to 1.75. Find out the present as well as the likely value of share after the
decisions.
QUESTION NO. 2G
In December, 2011 AB Co.’s share was sold for ₹ 146 per share. A long term earnings growth rate
of 7.5% is anticipated. AB Co. is expected to pay dividend of ₹ 3.36 per Share.
a) What rate of return an investor can expect to earn assuming that dividends are expected to grow
along with earnings at 7.5% per year in perpetuity?
b) It is expected that AB Co. will earn about 10%on book Equity and shall retain 60% of earnings. In
this case, whether, there would be any change in growth rate and Cost of Equity?
QUESTION NO. 2H
Abinash is holding 5,000 shares of Future Group Limited. Presently the rate of dividend being paid by
the company is ₹ 5 per share and the share is being sold at ₹ 50 per share in the market. However,
several factors are likely to change during the course of the year as indicated below:
Existing Revised
Risk free rate 12.5% 10%
Market risk premium 6% 4.8%
Expected growth rate 5% 8%
Beta value 1.5 1.25
In view of the above factors whether Abinash should buy, hold or sell the shares? Narrate the reason
for the decision to be taken.
QUESTION NO. 2I
An investor is holding 5,000 shares of X Ltd. Current year dividend rate is ₹ 3/ share. Market price of
the share is ₹ 40 each. The investor is concerned about several factors which are likely to change
during the next financial year as indicated below:
Current Year Next Year
Dividend paid /anticipated per share (₹) 3 2.5
Risk free rate 12% 10%
Market Risk Premium 5% 4%
Beta Value 1.3 1.4
Expected growth 9% 7%
In view of the above, advise whether the investor should buy, hold or sell the shares.
QUESTION NO. 2J
Following Financial Data for Platinum Ltd. are available for the year 2011:
(₹ In lacs)
Equity Shares (₹ 10 each) 100
8% Debentures 125
10% Bonds 50
Reserve and Surplus 200
Total Assets 500
Assets Turnover Ratio 1.1
Effective Tax Rate 30%
Operating Margin 10%
2.9
Required rate of return of investors 15%

Dividend payout ratio 20%
Current market price of shares ₹ 13
You are required to:
a) Draw income statement for the year
b) Calculate the sustainable growth rate
c) Compute the fair price of the company's share using dividend discount model, and
d) Draw your opinion on investment in the company's share at current price.
QUESTION NO. 2K
Following Financial data are available for PQR Ltd. for the year 2008:
(₹ in lakh)
8% debentures 125
10% bonds (2007) 50
Equity shares (₹ 10 each) 100
Reserves and Surplus 300
Total Assets 600
Assets Turnovers ratio 1.1
Effective interest rate 8%
Effective tax rate 40%
Operating margin 10%
Dividend payout ratio 16.67%
Current market Price of Share ₹14
Required rate of return of investors 15%
(i) Draw income statement for the year
(ii) Calculate its sustainable growth rate of earnings
(iii) Calculate the fair price of the Company's share using dividend discount model, and
(iii) What is your opinion on investment in the company's share at current price?
QUESTION NO. 2L
Following financial information’s are available of XP Ltd. for the year 2018:
Equity Share Capital (₹ 10 each) ₹ 200 Lakh
Reserves and Surplus ₹ 600 Lakh
10% Debentures (₹ 100 each) ₹ 350 Lakh
Total Assets ₹ 1200 Lakh
Assets Turnover Ratio 2 times
Tax Rate 30%
Current Market Price per Equity Share ₹ 28
Required Rate of Return of Investors 18%
(i) Prepare Income Statement for the year 2018.
(ii) Determine its Sustainable Growth Rate.
(iii) Determine the fair price of the company's share using Dividend Discount Model.
(iv) Give your opinion on investment in the company's share at current price. (8 Marks)
2.10
QUESTION NO. 2M
A company has an EPS of ₹ 2.5 for the last year and the DPS of ₹ 1. The earnings is expected to grow
at 2% a year in long run. Currently it is trading at 7 times its earnings. If the required rate of return
is 14%, compute the following:
(i) An estimate of the P/E ratio using Gordon growth model.
(ii) The Long-term growth rate implied by the current P/E ratio.
LOS 8 : Determination of Growth rate

The sustainable growth rate is the rate at which equity, earnings and dividends can continue to grow
indefinitely assuming that ROE is constant, the dividend payout ratio is constant, and no new equity
is sold.
Method 1: Sustainable growth (g) = (1 - Dividend payout Ratio ) × ROE
Or g = RR × ROE
Method 2 : D n = D0 (1 + g )n-1
D0 = Base year dividend
Dn = Latest (Current year dividend)
n-1 = No. Of times D0 increases to Dn
LOS 9: Calculation of Ke in case of Floating cost is given

Floating Cost are costs associated with the issue of new equity. E.g. Brokerage, Commission,
underwriting expenses etc.
 If issue cost is given in question, we will take P0 net of issue cost (Net Proceeds).
 If floating Cost is expressed in % i.e. P0 (1 – f) =
 If floating Cost is expressed in Absolute Amount i.e. P0 – f =

Note:
 K e of new equity will always be greater than K e of existing equity.
 Floatation Cost is only applicable in case of new equity and not on existing equity (or retained
earnings).
QUESTION NO. 3A
A company is contemplating an issue of new equity shares. The current market price is ₹ 125 per share.
The dividend per share for last five years, has been as follows:
2012 2013 2014 2015 2016
10 11 11 12 14
The floating costs are expected to be 4% of issue price which is ₹ 125.
Determine (i) growth rate in dividends, (ii) cost of existing equity share (iii) cost of new equity.
QUESTION NO. 3B
SRK Ltd. is a listed company and it has just announced annual dividend for the year ending 2013-
14. Earning Per Share (EPS) and Dividend Per Share (DPS) for 5 years is as follows:
2013-14 2012-13 2011-12 2010-11 2009-10
EPS (₹) 14.00 13.60 13.10 12.70 12.20
DPS (₹) 8.20 8.10 7.90 7.80 7.70
In the opinion of MD of SRK Ltd., if current dividend policy is maintained annual growth in Earning
and Dividends will be no better than the annual growth in earnings over the past years.
2.11
Since the Board of SRK Ltd. is reluctant to take debt to finance growth it is considering changing its
dividend policy by retaining 50% of its earnings for investment in various projects having a post-tax
rate of return of 15%. The beta of SRK Ltd. is 1.5, market risk premium is 4% and Risk Free Rate of
Return is 6%.
You are required to calculate expected market price of share, if
(1) SRK Ltd. does not announce a change in its Dividend Policy.
(2) SRK Ltd. does announce a change in its Dividend Policy by retaining 50% of its earnings.
Note: Growth Rate can be assumed to be remain stable.
LOS 10 : Return on Equity (ROE) and Book Value Per Share (BVPS)
EPS = BVPS × ROE
Note : Calculate P / E Ratio at which Dividend payout will have no effect on the value of the
share.
When r = Ke , dividend payout ratio will not affect value of share.
Example:
If r = 10% then Ke = 10% and Ke = => 0.10 =
/ /
=> P/E Ratio = 10 times
QUESTION NO. 4A
The firm was started a year ago with an equity capital of ₹ 20 Lacs
Earning of the firm ₹ 2,00,000 Dividend paid ₹ 1,50,000 P/E Ratio 12.5
Number of the shares outstanding, 20,000 @ ₹ 100 each. The firm is expected its current rate of earning
on investment.
a) Ascertain whether the company's D/P ratio is optimal according to Walter.
b) What should be the P/E ratio at which the dividend pay-out ratio will have no effect on the value of
the share?
c) Will your decision change if the P/E ratio is 8, instead of 12.5?
QUESTION NO. 4B
A Ltd. has a book value per share of ₹ 137.80. Its return on equity is 15% and it follows a policy of
retaining 60% of its earnings. If the opportunity cost of capital is 18%, what is price of share today.
2.12
QUESTION NO. 4C
X Ltd has an internal rate of return @ 20%. It has declared dividend @18% on its equity shares, having
face value of ₹ 10 each. The payout ratio is 36% and Price Earnings Ratio is 7.25. Find the cost of equity
according to Walter’s Model and hence determine the limiting value of its shares in case the payout
ratio is varied as per the said model.
LOS 11 : Over – Valued & Under – Valued Shares

Cases Value Decision
PV Market Price < Actual Market Price Over – Valued Sell
PV Market Price > Actual Market Price Under – Valued Buy
PV Market Price = Actual Market Price Correctly Valued Buy / Sell
LOS 12 : Holding Period Return (HPR)
(𝐏𝟏 𝐏𝟎 ) 𝐃𝟏
HPR =
𝐏𝟎
𝐏 𝟏 𝐏𝟎 𝐃𝟏
HPR =
𝐏𝟎
+ 𝐏𝟎
(Capital gain Yield / Return) (Dividend Yield / Return)

QUESTION NO. 5A
Tata is to pay dividend of ₹ 2.15 at the end of the year and it is expected to grow at 11.2% per year
forever, and the required rate of return on Tata stock is 15.2% per annum
What is its intrinsic value?
If the current stock price of Tata is equal to its intrinsic value, what is the next years expected price?
If an investor wants to buy Tata stock now and sell it after receiving ₹ 2.15 dividend a year from now,
what is the expected capital gain in % terms? What is the dividend yield and what is the holding period
return?
QUESTION NO. 5B
Om Tech Ltd. engaged in the manufacturing of engineering goods, expects a moderate growth in coming
years dividend for the last year has just been paid and the company is contemplating to pay a dividend of ₹
18 after one year. The equity shares are currently traded at ₹ 200 per share. If the equity capitalization rate is
14% then what would be the market price of the share after one year. Assume that Capital gains tax rate
applicable to an investor is 20%. He buys one share today and sells after one year after dividend receipt. What
is his after tax rate of return or Holding Period Return.
2.13
LOS 13 : Multi-stage Dividend discount Model [ If g >K e ]/ Variable Growth

Rate Model
 Growth model is used under the assumption of g = constant.
 When more than one growth rate is given, then we will use this concept.
or
If g > K e
 A firm may temporarily experience a growth rate that exceeds the required rate of return on firm’s
equity but no firm can maintain this relationship indefinitely.
Value of a dividend- paying firm that is experiencing temporarily high growth =
PV of dividends expected during high growth period.
+
PV of the constant growth value of the firm at the end of the high growth period.
𝑫𝟏 𝑫𝟐 𝑫𝒏 𝑷𝒏
Value = + +..................+ +
(𝟏 𝒌𝒆 )𝟏 (𝟏 𝒌𝒆 )𝟐 (𝟏 𝒌𝒆 )𝒏 (𝟏 𝒌𝒆 )𝒏
𝑫𝒏 ( 𝟏 𝒈𝒄 )
When Pn =
𝑲𝒆 𝒈𝒄
QUESTION NO. 6A
MNP Ltd. has declared and paid annual dividend of ₹ 4 per share. It is expected to grow @ 20% for
the next two years and 10% thereafter. The required rate of return of equity investors is 15%. Compute
the current price at which equity shares should sell.
Present Value Interest Factor (PVIF) @ 15%: For year 1 = 0.8696, For year 2 = 0.7561
QUESTION NO. 6B
The shares of G Ltd. we currently being traded at ₹46. The company published its results for the year ended
31st March 2019 and declared a dividend of ₹5. The company made a return of 15% on its capital and
expects that to be the norm in which it operates. G Ltd. Also expects the dividends to grow at 10% for the
first three years and thereafter at 5%. You are required to advise whether the share of the company is
being traded at a premium or discount.
PVIF @ 15% for the next 3 years is 0.870, 0.756 and 0.658 respectively.
QUESTION NO. 6C
X Limited, just declared a dividend of ₹14.00 per share. Mr. B is planning to purchase the share of X
Limited, anticipating increase in growth rate from 8% to 9%, which will continue for three years He
also expects the market price of this share to be ₹ 360.00 after three years
a) The maximum amount Mr. B should pay for shares, if he requires a rate of return of 13% per
annum.
b) The maximum price Mr. B will be willing to pay for share, if he is of the opinion that the 9% growth
can be maintained indefinitely and require 13% rate of return per annum.
c) The price of share at the end of three years, if 9% growth rate is achieved and assuming other
conditions remaining same as in (ii) above.
Calculate rupee amount up to two decimal points.
Year-1 Year-2 Year-3
FVIF @ 9% 1.09 1.188 1.295
FVIF @ 13% 1.13 1.277 1.443
PVIF @ 13% 0.885 0.783 0.693
2.14
QUESTION NO. 6D
X Ltd. is a Shoes manufacturing company. It is all equity financed and has a paid-up Capital
₹10,00,000 (₹10 per share)
X Ltd. has hired Swastika consultants to analyze the future earnings. The report of Swastika
consultants states as follows :
1. The earnings and dividend will grow at 25% for the next two years.
2. Earnings are likely to grow at the rate of 10% from 3rd year and onwards.
3. Further, if there is reduction in earnings growth, dividend payout ratio will increase to 50%.
The other data related to the company are as follows :
Year EPS(₹) Net Dividend per share(₹) Share Price (₹)
2010 6.30 2.52 63.00
2011 7.00 2.80 46.00
2012 7.70 3.08 63.75
2013 8.40 3.36 68.75
2014 9.60 3.84 93.00
You may assume that the tax rate is 30% (not expected to change in future) and post-tax cost of capital
is 15%.
By using the Dividend Valuation Model, calculate
a) Expected Market Price per share
b) P/E Ratio.
QUESTION NO. 6E
Seawell Corporation, a manufacturer of do-it-yourself hardware and housewares, reported earnings
per share of € 2.10 in 2003, on which it paid dividends per share of €0.69. Earnings are expected to
grow 15% a year from 2004 to 2008, during this period the dividend payout ratio is expected to
remain unchanged. After 2008, the earnings growth rate is expected to drop to a stable rate of 6%,
and the payout ratio is expected to increase to 65% of earnings. The firm has a beta of 1.40 currently,
and is expected to have a beta of 1.10 after 2008. The market risk premium is 5.5%. The Treasury
bond rate is 6.25%.
(a) What is the expected price of the stock at the end of 2008?
(b) What is the value of the stock, using the two-stage dividend discount model?
QUESTION NO. 6F
SAM Ltd. has just paid a dividend of ₹ 2 per share and it is expected to grow @ 6% p.a. After paying
dividend, the Board declared to take up a project by retaining the next three annual dividends. It is
expected that this project is of same risk as the existing projects.
The results of this project will start coming from the 4th year onward from now. The dividends will then
be ₹ 2.50 per share and will grow @ 7% p.a.
An investor has 1,000 shares in SAM Ltd. and wants a receipt of at least ₹ 2,000 p.a. from this
investment.
Show that the market value of the share is affected by the decision of the Board. Also show as to how
the investor can maintain his target receipt from the investment for first 3 years and improved income
thereafter, given that the cost of capital of the firm is 8%.
QUESTION NO. 6G
An investor is considering purchasing the equity shares of LX Ltd., whose current market price (CMP)
is 150. The company is proposing a dividend of ₹ 6 for the next year. LX is expected to grow @ 18
per cent per annum for the next four years. The growth will decline linearly to 14 per cent per annum
after first four years. Thereafter, it will stabilize at 14 per cent per annum infinitely. The required rate
of return is 18 per cent per annum.
2.15

(i) The intrinsic value of one share
(ii) Whether it is worth to purchase the share at this price
t 1 2 3 4 5 6 7 8
PVIF (18, t) 0.847 0.718 0.609 0.516 0.437 0.370 0.314 0.266
QUESTION NO. 6H
A company had paid a dividend of ₹2.50 per share last year and its required rate of return for
equity investors is 20%. What will be the market price of the share at the end of the year, if
(i) there is no growth in dividend ?
(ii) dividend grows at constant rate of 5% per annum in perpetuity?
(iii) constant dividend for first five years and then grows at constant rate of 5% per annum in
perpetuity?
(iv) constant dividend for first five years and then share is sold at the price of ₹20?
QUESTION NO. 6I
The current EPS of M/s VEE Ltd. is ₹ 4. The company has shown an extraordinary growth of 40% in its
earnings in the last few year This high growth rate is likely to continue for the next 5 years after which
growth rate in earnings will decline from 40% to 10% during the next 5 years and remain stable at
10% thereafter. The decline in the growth rate during the five year transition period will be equal
and linear. Currently, the company' s pay-out ratio is 10%. It is likely to remain the same for the next
five years and from the beginning of the sixth year till the end of the 10th year, the pay-out will
linearly increase and stabilize at 50% at the end of the 10th year. The post tax cost of capital is 17%
and the PV factors are given below:
Years 1 2 3 4 5 6 7 8 9 10
PVIF 0.855 0.731 0.625 0.534 0.456 0.390 0.333 0.285 0.244 0.209
@17%
You are required to calculate the intrinsic value of the company's stock based on expected dividend.
If the current market price of the stock is ₹ 125, suggest if it is advisable for the investor to invest in
the company's stock or not.
LOS 14 : IRR Technique & Growth Model

IRR is the discount rate that makes the present values of a project’s estimated cash inflows equal to
the Present value of the project’s estimated cash outflows.
 At IRR Discount Rate => PV (inflows) = PV (outflows)
 The IRR is also the discount rate for which NPV of a project is equal to Zero.
 IRR technique is used when, K e is missing in the Question.
𝐋𝐨𝐰𝐞𝐫 𝐑𝐚𝐭𝐞𝐍𝐏𝐕
 IRR = Lower Rate + × Difference in Rate
𝐋𝐨𝐰𝐞𝐫 𝐑𝐚𝐭𝐞 𝐍𝐏𝐕 𝐇𝐢𝐠𝐡𝐞𝐫 𝐑𝐚𝐭𝐞𝐍𝐏𝐕
QUESTION NO. 7
Piyush Ltd presently pay a dividend of Re. 1.00 per share and has a share price of ₹ 20.00.
a) If this dividend were expected to grow at a rate of 12% per annum forever, what is the firm's
expected or required Cost of Equity using a dividend-discount model approach?
b) Instead of this situation in part (i), suppose that dividend were expected to grow at a rate of 20%
p.a. for 5 years and 10% per year thereafter. Now what is the firm's expected, or Cost of Equity?
2.16
LOS 15 : Price at the end of each year

𝐏𝟏 𝐃 𝟏
P0 =
(𝟏 𝐊 𝐞 )𝟏
𝐏𝟐 𝐃 𝟐
P1=
(𝟏 𝐊 𝐞 )𝟏
𝐏𝟑 𝐃 𝟑
P2=
(𝟏 𝐊 𝐞 )𝟏
𝐏𝟒 𝐃 𝟒
P3=
(𝟏 𝐊 𝐞 )𝟏
.
.
So on
QUESTION NO. 8
P Ltd. Industries has been growing at the rate of 15% per year and this trend is expected to continue for
5 more years. Thereafter it is likely to grow at the rate of 8% which is the industry average. The investors
expect return of 12%. The dividend paid per share last year (D0) corresponding to period 0 (t0) is ₹ 5.
Determine at what price an investor at period t0 be ready to buy the shares of the company at the end
of period t0 (now) and simultaneously price he is going to pay at t1, t2, t3,t4 and t5.
Present value of Re. 1 at 12%
Year 1 2 3 4 5
P.V. 0.893 0.797 0.712 0.636 0.567
Los 16 : Negative Growth

𝐃𝟎 ( 𝟏 𝐠)
If Positive Growth, then P0 =
𝐊𝐞 𝐠
𝐃𝟎 ( 𝟏 𝐠)
If Negative Growth, then P0 =
𝐊𝐞 𝐠
Note: We Know g = RR × ROE
Case I EPS > DPS Retention is Positive g = Positive
Case II EPS < DPS Retention is Negative g = Negative
Case III EPS = DPS No Retention g=0
QUESTION NO. 9A
On the basis of the following information:
Current dividend (Do) ₹ 2.50
Discount rate (ke) 10.5%
Growth rate (g) 2%
a) Calculate the present value of stock of ABC Ltd.
b) Is this stock overvalued if stock price is ₹ 35, ROE= 9% and EPS = ₹2.25?
Show detailed calculation.
QUESTION NO. 9B
Given the following information:
Current dividend ₹ 5.00
Discount rate 10%
Growth rate 2%
2.17
a) Calculate the present value of the stock.

b) Is the stock over valued if the price is ₹ 40, ROE = 8% and Current EPS = ₹ 3.00. Show your
calculations under the PE Multiple approach and Earnings Growth model.
LOS 17 : Valuation Using the H-Model

The earnings growth of most firms does not abruptly change from a high rate to a low rate as in the
two-stage model but tends to decline over time as competitive forces come into play. The H-model
approximates the value of a firm assuming that an initially high rate of growth declines linearly over
a specified period. The formula for this approximation is:
𝑫𝟎 × (𝟏 + 𝒈𝑳 ) 𝑫𝟎 × 𝑯 × (𝒈𝑺 − 𝒈𝑳 )
𝑷𝟎 = +
𝐊 𝐞 − 𝒈𝑳 𝐊 𝐞 − 𝒈𝑳
where:
H= = half-life (in years) of high-growth period
t = length of high growth period
gS = short-term growth rate
gL = long-term growth rate
r = required return
QUESTION NO. 10
Omega Foods currently pays a dividend of €2.00. The growth rate, which is currently 20%, is expected
to decline linearly over the next ten years to a stable rate of 5% thereafter. The required return is 12%.
Calculate the current value of Omega.
LOS 18 : Preference Dividend Coverage Ratio & Equity Dividend Coverage Ratio
𝐄𝐚𝐫𝐧𝐢𝐧𝐠 𝐁𝐞𝐟𝐨𝐫𝐞 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐚𝐧𝐝 𝐓𝐚𝐱
Interest Coverage Ratio =
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭
𝐏𝐫𝐨𝐟𝐢𝐭 𝐀𝐟𝐭𝐞𝐫 𝐓𝐚𝐱
Preference Dividend Coverage Ratio =
𝐏𝐫𝐞𝐟𝐞𝐫𝐞𝐧𝐜𝐞 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝
𝐏𝐫𝐨𝐟𝐢𝐭 𝐀𝐟𝐭𝐞𝐫 𝐓𝐚𝐱 – 𝐏𝐫𝐞𝐟𝐞𝐫𝐞𝐧𝐜𝐞 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝
Equity Dividend Coverage Ratio =
𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐩𝐚𝐲𝐚𝐛𝐥𝐞 𝐭𝐨 𝐞𝐪𝐮𝐢𝐭𝐲 𝐬𝐡𝐚𝐫𝐞 𝐡𝐨𝐥𝐝𝐞𝐫𝐬
Note:
The Higher the Better. These Ratios indicates the surplus profit left after meeting all the fixed
obligation.
QUESTION NO. 11
Tiger Ltd. is presently working with an Earning Before Interest and Taxes (EBIT) of ₹ 90 lacs. Its present
borrowings are as follows:
₹ In lacs
12% term loan 300
Working capital borrowings:
From Bank at 15% 200
Public Deposit at 11 % 100
The sales of the company are growing and to support this, the company proposes to obtain additional
borrowing of ₹ 100 lacs expected to cost 16%.The increase in EBIT is expected to be 15%.
Calculate the change in interest coverage ratio after the additional borrowing is effected and
comment on the arrangement made.
2.18
LOS 19 : Calculation of Maximum price of a share

QUESTION NO. 12
Mr. A is thinking of buying shares at ₹ 500 each having face value of ₹ 100. He is expecting a bonus at
the ratio of 1:5 during the fourth year. Annual expected dividend is 20% and the same rate is expected
to be maintained on the expanded capital base. He intends to sell the shares at the end of seventh year
at an expected price of ₹ 900 each. Incidental expenses for purchase and sale of shares are estimated
to be 5% of the market price. He expects a minimum return of 12% per annum. Should Mr. A buy the
share? If so, what maximum price should he pay for each share? Assume no tax on dividend income
and capital gain.
LOS 20 : Cash Flow Base Models
Calculation of FCFF
EBITDA xxx
Less : Depreciation & Amortisation (NCC) xxx
EBIT xxx
Less : Tax xxx
NOPAT xxx
Add : Depreciation (NCC) xxx
Less : Increase in Working Capital (WCInv) xxx
Less : Capital Expenditure (FCInv) xxx
Free Cash Flow For Firm (FCFF) xxx
a) Based on its Net Income:

FCFF= Net Income + Interest expense *(1-tax) + Depreciation -/+ Capital Expenditure –/+
Change in Non-Cash Working Capital
b) Based on Operating Income or Earnings Before Interest and Tax (EBIT):
FCFF= EBIT *(1 - tax rate) + Depreciation -/+ Capital Expenditure –/+ Change in Non-Cash
Working Capital
c) Based on Earnings before Interest, Tax , Depreciation and Amortisation (EBITDA):
FCFF = EBITDA* (1-Tax) +Depreciation* (Tax Rate) -/+ Capital Expenditure – /+Change in Non-
Cash Working Capital
2.19
d) Based on Free Cash Flow to Equity (FCFE):

FCFF = FCFE + Interest* (1-t) + Principal Prepaid - New Debt Issued + Preferred Dividend
e) Based on Cash Flows:
FCFF = Cash Flow from Operations (CFO) + Interest (1-t) -/+ Capital Expenditure
Calculation of FCFE
Method 1 : If Debt financing ratio is given:
EBITDA xxx
Less : Depreciation & Amortisation xxx
EBIT xxx
Less : Interest xxx
EBT xxx
Less : Tax xxx
PAT xxx
Add : Depreciation × % Equity Invested xxx
Less: Increase in Working Capital × % Equity Invested xxx
Less: Capital Expenditure × % Equity Invested xxx
Free Cash Flow for Equity (FCFE) xxx
Method 2 : If Debt financing ratio is not given:
EBITDA xxx
EBIT xxx
Less : Interest xxx
EBT xxx
Less : Tax xxx
PAT xxx
Less: Increase in Working Capital (WCInv) xxx
Less: Capital Expenditure (FCInv) xxx
Add : Net Borrowings xxx
a) Calculating FCFE from FCFF

FCFE = FCFF - [ Interest ( 1- tax rate) ] + Net borrowing
b) Calculating FCFE from net income
FCFE = NI + NCC - FCInv - WCInv + net borrowing
c) Calculating FCFE from CFO
FCFE = CFO - FCInv + net borrowing
QUESTION NO. 13A : Calculating FClnv with no long-term asset sales
Airbrush, Inc. financial statements for 2009 include the following information:
Selected Financial Data
2009 2008
Gross PP&E $5000 $4150
Accumulated depreciation $1500 $1200
Net PP&E $3500 $2950
There were no sales of PP&E during the year; depreciation expense was $300. Calculate
Airbrush's FCInv for 2009.
2.20
QUESTION NO. 13B : Calculation of FCFF & FCFE

EBITDA $1,000
Depreciation expense $400
Interest expense $150
Tax rate 30%
Purchases of fixed assets $500
Change in working capital $50
Net borrowing $80
Common dividends $200
QUESTION NO. 13C : Calculating FCFF and FCFE
Anson Ford, CFA, is analysing the financial statements of Sting's Delicatessen. He has a 2009 income
statement and balance sheet, as well as 2010 income statement & balance sheet (as shown in the
tables below). Assume there will be no sales of long-term assets in 2010. Calculate forecasted free
cash flow to the firm (FCFF) and free cash flow to equity (FCFE) for 2010.
Sting's Income Statement
Income Statement 2010 Forecast 2009 Actual
Sales $300 $250
Cost of goods sold 120 100
Gross profit 180 150
SG&A 35 30
Depreciation 50 40
EBIT 95 80
Interest expense 15 10
Pre-tax earnings 80 70
Taxes (at 30%) 24 21
Net income 56 49
Sting's Balance Sheet
Balance Sheet 2010 Forecast 2009 Actual
Cash $10 $5
Account Receivable 30 15
Inventory 40 30
Current Assets $80 $50
Gross property, plant and equipment 400 300
Accumulated depreciation 190 140
Total Assets $290 $210
Account Payable $20 $20

Short Term Debt 20 10
Current Liabilities $40 $30
Long Term Debt 114 100
Common Stock 50 50
Retained earnings 86 30
Total liabilities and owners’ equity $290 $210
2.21
LOS 21 : Valuation Based on Multiples
1. P/E Multiple Approach MPS = EPS × P/E Ratio

𝑬𝑽
2. Enterprise Value to Sales =
𝑺𝒂𝒍𝒆𝒔
𝑬𝑽
3. Enterprise Value to EBITDA =
𝑬𝑩𝑰𝑻𝑫𝑨
EV = market value of common stock + market value of preferred equity + market value
of debt + minority interest – cash & cash equivalents and Equity investments,
investment in any co. & also Long term investments.
EBITDA = EBIT + depreciation + amortization
QUESTION NO. 14
An analyst gathered the following data for Boulevard Industries
Recent share price ₹ 22.50
Shares outstanding 40 Lakhs
Market value of debt ₹ 137 Lakhs
Cash and marketable securities ₹ 62.30 Lakhs
Investments ₹ 327 Lakhs
Net income ₹ 137.50 Lakhs
Interest expense ₹ 6.90 Lakhs
Depreciation and amortization ₹ 10.40 Lakhs
Taxes ₹ 95.90 Lakhs
Based on this information, calculate the EV/EBITDA ratio for Boulevard Industries.
2.22
PRACTICE QUESTION
QUESTION NO. 15
The following information pertains to Golden Ltd:
Profit before tax ₹ 75 crore
Tax rate 30%
Equity capitalization rate 15%
Return on investment (ROI) 18%
Retention ratio 80%
Number of shares outstanding 75,00,000
The market price of the share of the company in the bull market was somewhere around
₹ 2100 per share. Advice, whether the share of the Golden Ltd. should be purchased or not.
Further, also suggest the form of Market prevalent as per EMH Theory.
Note: Use Gordon’s Growth Model.
QUESTION NO. 16
An investor is considering to purchase the equity shares of LX Ltd., whose current market price (CMP)
is ₹ 112. The company is proposing a dividend of ₹ 4 for the next year. LX Ltd. is expected to grow @
20 per cent per annum for the next four years. The growth will decline linearly to 16 per cent per
annum after first four years. Thereafter, it will stabilise at 16 per cent per annum infinitely. The investor
requires a return of 20 per cent per annum.
You are required
(i) To calculate the intrinsic value of the share of LX Ltd.
(ii) Whether it is worth to purchase the share at this price.
Period 1 2 3 4 5 6 7
PVIF (20%, n) 0.833 0.694 0.579 0.482 0.402 0.335 0.279
QUESTION NO. 17
Summit Ltd., an All Equity Company, has a PAT of ₹ 300 Crores and 15,00,000 Shares of ₹ 10 each
outstanding at the end of financial year. Its Cost of Capital is 13% and Rate of Return is 17%. Ascertain
the value of the Company under Walter’s Model, if payout ratio is (a) 15%, (b) 30%, (c) 60%, and (d)
90%. Also draw out the inference from the values obtained under different cases.
QUESTION NO. 18
M/s. B Ltd. has declared dividend of ₹ 2.50 per share on the EPS of ₹ 7. Earnings of the company are
expected to grow at the rate of 10% for the next 3 years and to be stabilized at 3% thereafter.
The pay-out ratio is expected to remain at the same level during 3 years and then will increase to
60%. If required rate of return is 16% calculate:
(i) The current price of the share.
(ii) The expected price of share of B Ltd. At the end of 3rd year. Following table may be used for
calculations.
Present Values t1 t2 t3 t4 t5
PVIF0.16,t 0.862 0.743 0.641 0.553 0.477
3.1
Corporate Valuation
Study Session 3
LOS 2 : Dividend Yield Valuation Method

𝐃𝐏𝐒
Dividend Yield =
𝐌𝐏𝐒
𝐃𝐏𝐒
MPS =
𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐘𝐢𝐞𝐥𝐝
Note:
𝐓𝐨𝐭𝐚𝐥 𝐝𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐩𝐚𝐢𝐝
DPS =
Total Market Value = MPS × Total Number of Equity share
QUESTION NO. 1
ABC Ltd has an issued and paid up capital of 5,00,000 shares of ₹10 each. The company declared a
dividend of ₹12.50 Lakhs p.a. during the last five years and expects to maintain the same level of
dividends in the future. The control and ownership of the company is lying in the few hands of Directors
and their family members. The average dividend yield for listed companies in the same line of business
is 18%.Calculate the value of 3000 shares in the company.
LOS 3 : Earning Yield Valuation Method

𝐄𝐏𝐒
Earning Yield =
𝐌𝐏𝐒
𝐄𝐏𝐒
MPS =
𝐄𝐚𝐫𝐧𝐢𝐧𝐠 𝐘𝐢𝐞𝐥𝐝
𝐄𝐚𝐫𝐧𝐢𝐧𝐠 𝐚𝐯𝐚𝐢𝐥𝐚𝐛𝐥𝐞 𝐭𝐨 𝐄𝐪𝐮𝐢𝐭𝐲 𝐒𝐡𝐚𝐫𝐞 𝐡𝐨𝐥𝐝𝐞𝐫𝐬
Therefore, EPS =
3.2
LOS 4 : P/E Ratio Valuation Model

𝐌𝐏𝐒
P / E Ratio =
𝐄𝐏𝐒
MPS = EPS × P/E Ratio
LOS 5 : Value Based on Future Maintainable Profits (FMP’s)
𝐅𝐮𝐭𝐮𝐫𝐞 𝐌𝐚𝐢𝐧𝐭𝐚𝐢𝐧𝐚𝐛𝐥𝐞 𝐏𝐫𝐨𝐟𝐢𝐭

Value of Business =
𝐑𝐞𝐥𝐞𝐯𝐚𝐧𝐭 𝐂𝐚𝐩𝐢𝐭𝐚𝐥𝐢𝐬𝐚𝐭𝐢𝐨𝐧 𝐑𝐚𝐭𝐞
Value of Business – Market Value of Debt = Value of Equity

Calculation of Future Maintainable Profits:
Average Past Year Profits before tax xxx
Add : All Profit likely to arise in Future xxx
All Actual Expenses & Losses not likely to occur in future xxx
Less : All Profit not likely to occur in Future xxx
All Actual Expenses & Losses likely to occur in future xxx
Future Maintainable Profits (FMP’s) before tax xxx
Less : Tax xxx
FMP’s after tax xxx
Note:
Treatment of Sunk Cost
Sunk Cost are those cost which are not relevant for decision making. These cost must be totally
ignored. Example: Allocated Fixed Cost, R & D cost already incurred.
QUESTION NO. 2A
In the current year, a corporate firm has reported a profit of ₹ 65 lakh, after paying taxes@ 35 percent Current
year's income includes:
(i) extraordinary income of ₹ 10 lakh and
(ii) extraordinary loss of ₹ 3 lakh.
Apart from existing operations, which are normal in nature and are likely to continue in the future,
the company expects to launch a new product in the coming year. Revenue and cost estimates in
respect of the new product are as follows:
₹ (lakhs)
Sales 60
Material Cost 15
Labour cost (additional) 10
Allocated fixed costs 5
Additional fixed costs 8
a) From the above information compute the value of the business, given that capitalization rate
applicable to such business in the market is 15%.
b) Determine the Market Price per equity share on the basis of FMP calculated above, with X Ltd.
share capital being consists of 1,00,000, 11% preference shares of ₹ 100 each and 40,00,000
equity shares of ₹ 10 each and the P/E Ratio being 8 times.
QUESTION NO. 2B
XN Ltd. reported a profit of ₹ 100.32 lakhs after 34% tax for the financial Year 2015- 2016. An
analysis of the accounts reveals that the income included extraordinary items of ₹ 14 lakhs and an
3.3
extraordinary loss of ₹ 5 lakhs. The existing operations, except for the extraordinary items, are
expected to continue in future. Further, a new product is launched and the expectations are as
under:
Particulars Amount ₹ in lakhs
Sales 70
Material Costs 20
Labour Costs 16
Fixed Costs 10
The company has 50,00,000 Equity Shares of ₹ 10 each and 80,000, 9% Preference Shares of ₹ 100
each with P/E Ratio being 6 times.
(i) compute the value of the business. Assume cost of capital to be 12% (after tax) and
(ii) determine the market price per equity share.
QUESTION NO. 2C
The closing price of LX Ltd. is ₹ 24 per share as on 31st March, 2019 on NSE Ltd. The Price Earnings
Ratio was 6. It was found that an amount of ₹ 24 Lakhs as income and an extra ordinary loss of ₹ 9
lakhs were included in the books of accounts. The existing operations except for the extraordinary
items are expected to continue in future. Further the company has launched a new product during
the year with the following expectations:
(₹ in Lakhs)
Sales 150
Material Cost 40
Labour Cost 34
Fixed Cost 24
The company has 500,000 equity shares of ₹ 10 each and 100,000 9% Preference Shares of ₹ 100
each. The Price Earnings Ratio is 6 times. Post tax cost of capital is 10 per cent per annum. Tax rate
is 34 per cent.
(i) Existing Profit from old operations
(ii) The value of business
LOS 6 : Net Asset Valuation Method (For Equity)
𝐓𝐨𝐭𝐚𝐥 𝐀𝐬𝐬𝐞𝐭𝐬 𝐓𝐨𝐭𝐚𝐥 𝐄𝐱𝐭𝐞𝐫𝐧𝐚𝐥 𝐋𝐢𝐚𝐛𝐢𝐥𝐢𝐭𝐲

NAV per Share =
Note:
1. The following external liabilities should be deducted

 All short term (Current Liabilities) and Long Term Liabilities (Debenture, Loans, etc) including
outstanding and accrued interest.
 Provision for Taxation
 Liabilities not provided for in the accounts i.e. Contingent Liabilities which have crystallized
now.
 Liabilities arising out of prior period adjustment
 Preference Share Capital including Arrears of dividend and proposed preferred Dividend
 Proposed Equity Dividend (If the objective is to determine ex-dividend value of equity share).
2. Total assets doesn’t include Miscellaneous Expenditure to the extend not yet written-off, fictitious
assets, accumulated losses, profit & Loss (Dr.) Balance.
3.4
3. NAV may be calculated by using

a) Book Value (BV): The BV of an asset is an accounting concept based on the historical data
given in the balance sheet of the firm.
b) Market Value (MV): The MV of an asset is defined as the price which is prevailing on the
market.
c) Liquidating Value (LV): The LV refers to the net difference between the realizable value of
all assets and the sum total of external liabilities. This net difference belongs to the owners/
shareholders and is known as LV.
4. If question is silent always prefer Market Value weights.
QUESTION NO. 3A
Liabilities ₹ in Asset ₹ in
Lakhs Lakhs
Share Capital (₹ 10 FV) 100 Land & Building 40
Reserve & Surplus 40 Plant & Machinery 80
Long term Loans 30 Investment 10
Stock 20
Debtors 15
Cash at Bank 5
Total 170 170
You are required to work out the value of the Company's shares on the basis of Net Assets Method
and Profit-Earning capacity (capitalization) method and arrive at the fair price of the shares, by
considering the following information:
(i) Profit before tax for the current year ₹ 64 Lakhs includes ₹ 4 Lakhs extraordinary income and ₹ 1
lakh income from investments of surplus funds; such surplus funds are unlikely to recur.
(ii) In subsequent years, additional advertisement expenses of ₹ 5 Lakhs are expected to be incurred
each year.
(iii) Market value of Land and Building and Plant and Machinery have been ascertained at ₹ 96 Lakhs
and ₹ 100 Lakhs respectively. This will entail additional depreciation of ₹ 6 Lakhs each year.
(iv) Effective Income-tax rate is 30%.
(v) The capitalization rate applicable to similar businesses is 15%.
QUESTION NO. 3B
T Ltd. Recently made a profit of ₹ 50 crore and paid out ₹ 40 crore (slightly higher than the average
paid in the industry to which it pertains). The average PE ratio of this industry is 9. As per Balance
Sheet of T Ltd., the shareholder’s fund is ₹ 225 crore and number of shares is 10 crore. In case
company is liquidated, building would fetch ₹ 100 crore more than book value and stock would realize
₹ 25 crore less.
The other data for the industry is as follows:
Projected Dividend Growth 4%
Risk Free Rate of Return 6%
Market Rate of Return 11%
Average Dividend Yield 6%
The estimated beta of T Ltd. is 1.2. You are required to calculate valuation of T Ltd. using
(i) P/E Ratio
(ii) Dividend Yield
(iii) Valuation as per:
(a) Dividend Growth Model
(b) Book Value
(c) Net Realizable Value
3.5
LOS 7 : Economic Value Added (EVA)

It is excess return over minimum return which is expected by the company on its Capital employed.
EVA = NOPAT – K0 × Average Capital Invested
Calculation of NOPAT:
 NOPAT means, Net Operating Profit After Tax but before any distribution of Interest, Preference
Dividend and Equity Dividend.
i.e. NOPAT = EBIT (1 – Tax Rate)
Note: It excludes non-operating income & expenses/losses like
 Profit/Loss on Sale of Fixed Assets
 Interest on non-trade investment
 Profit/Loss on trading in shares & bonds
 Interest income from Loans & Advances
Calculation of Cost of Overall Capital:
K0 = Cost of Overall Capital = WACC = Weighted Average Cost of Capital
K e W e + K r W r + KDWD + KPWP
Note:
1. K d = Interest (1- Tax Rate)
2. K e = R f + β (R m –Rf) Or K e = +g
3. K p = Preference Dividend (1 + CDT)
4. Calculation of Average Capital Invested:
𝐂𝐚𝐩𝐢𝐭𝐚𝐥 𝐚𝐭 𝐭𝐡𝐞 𝐛𝐞𝐠𝐢𝐧𝐧𝐢𝐧𝐠 + 𝐂𝐚𝐩𝐢𝐭𝐚𝐥 𝐚𝐭 𝐭𝐡𝐞 𝐄𝐧𝐝 𝐨𝐟 𝐘𝐞𝐚𝐫
𝟐
5. Calculation of Capital Invested:
Equity share capital
Add Preference share capital
Reserve & Surplus
Debenture/Bonds
Long-Term Loan
Less P/L (Dr. Balance)
Preliminary Expenses
Miscellaneous Expenditure
Note: It excludes:
 Investment in Equity shares & Bonds
 Loans & Advances
 Non-Trade Investment
𝐄𝐁𝐈𝐓 𝐄𝐁𝐈𝐓
6. Financial Leverage = Or =
𝐄𝐁𝐓 𝐄𝐁𝐈𝐓 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭
7. EBIT = EBT + Interest
EBIT = + Interest
( )
EBIT = + Interest
( )
Note :
 Operating profits may have to be adjusted using matching concept.
3.6
 There might be some intangible assets such as patents, trademark etc. which is not shown in
balance sheet, we need to include that in invested capital.
 The balance sheet figures of assets & liabilities are at book value. If replacement cost is provided,
take invested capital at replacement cost instead of Book Value.
QUESTION NO. 4A
Calculate Economic Value Added (EVA) with the help of the following information of A Limited:
Financial leverage 1.4 times
Capital Structure
Equity Capital ₹ 170 Lakhs
Reserves and Surplus ₹ 130 Lakhs
10% Debentures ₹ 400 Lakhs
Cost of Equity 17.5%
Income Tax Rate 30%
QUESTION NO. 4B
Consider the following operating information gathered from 3 companies that are identical except
for their capital structures:
P Ltd. Q Ltd. R Ltd.
Total invested capital ₹ 100,000 ₹100,000 ₹100,000
Debt/assets ratio 0.80 0.50 0.20
Shares outstanding 6100 8300 10000
Before-tax cost of debt 14% 12% 10%
Cost of equity 26% 22% 20%
Operating income, (EBIT) ₹ 25,000 ₹ 25,000 ₹ 25,000
Net Income ₹ 8,970 12,350 14,950
Tax rate 35% 35% 35%
a) Compute the weighted average cost of capital, WACC, for each firm.
b) Compute the Economic Value Added, EVA, for each firm.
c) Based on the results of your computations in part b, which firm would be considered the best
investment? Why?
d) Assume the industry P/E ratio generally is 15.Using the industry norm, estimate the price for each
share.
e) Calculate the estimated market capitalization for each of the firm.
QUESTION NO. 4C
Associated Advertising Agency (AAA) just announced that the current financial year's income
statement reports its net income to be ₹ 12,00,000. AAA's marginal tax rate is 40 percent and its
interest expense for the year was ₹ 15,00,000. The company has ₹80,00,000 of invested capital, of
which 60 percent is debt. In addition, AAA tries to maintain a weighted average cost of capital (WACC)
near 12 percent.
a) Compute the operating income, or EBIT, AAA earned in the current year.
b) What is AAA's Economic Value Added (EVA) for the current year?
c) AAA has 5,00,000 equity share outstanding. According to the EVA value you computed in part b,
how much can AAA pay in dividends per share before the value of the firm would start to
decrease? If AAA does not pay any dividends, what would you expect to happen to the value of
the firm?
3.7
QUESTION NO. 4D
RST Ltd.’s current financial year's income statement reported its net income as ₹25,00,000. The
applicable corporate income tax rate is 30%.
Following is the capital structure of RST Ltd. at the end of current financial year:
₹
Debt (Coupon rate = 11%) 40 lakhs
Equity (Share Capital + Reserves & Surplus) 125 lakhs
Invested Capital 165 lakhs
Following data is given to estimate cost of equity capital:
Beta of RST Ltd. 1.36
Risk -free rate i.e. current yield on Govt. bonds 8.5%
Average market risk premium (i.e. Excess of return 9%
on market portfolio over risk-free rate)
Required:
a) Estimate Weighted Average Cost of Capital (WACC) of RST Ltd.; and
b) Estimate Economic Value Added (EVA) of RST Ltd.
QUESTION NO. 4E
H Ltd. is a small but profitable producer of beauty cosmetics using the plant Aloe Vera. This is not a high-
tech business, but H Ltd. 's earnings have averaged around ₹ 12 lakh after tax, largely on the strength
of its patented beauty cream for removing the pimples. The patent has eight years to run, and H Ltd. has
been offered ₹ 40 Lakhs for the patent rights. H Ltd's assets include ₹ 20 Lakhs of working capital and ₹
80 Lakhs of property, plant, and equipment. The patent is not shown on Herbal's books. Suppose H Ltd's
cost of capital is 15 percent. What is its Economic Value Added (EVA)?
QUESTION NO. 4F
Constant Engineering Ltd. has developed a high tech product which has reduced the Carbon emission
from the burning of the fossil fuel. The product is in high demand. The product has been patented and
has a market value of ₹ 100 Crore, which is not recorded in the books. The Net Worth (NW) of Constant
Engineering Ltd. is ₹ 200 Crore. Long term debt is ₹ 400 Crore. The product generates a revenue of ₹
84 Crore. The rate on 365 days Government bond is 10 percent per annum. Bond portfolio generates a
return of 12 percent per annum. The stock of the company moves in tandem with the market. Calculate
Economic Value added of the company.
QUESTION NO. 4G
ABC Ltd. has divisions A,B & C. The division C has recently reported on annual operating profit of ₹
20,20,00,000. This figure arrived at after charging ₹3 crores full cost of advertisement expenditure for
launching a new product. The benefits of this expenditure is expected to be lasted for 3 years.
The cost of capital of division C is ₹11% and cost of debt is 8%.
The Net Assets (Invested Capital) of Division C as per latest Balance Sheet is ₹60 crore, but replacement cost
of these assets is estimated at ₹84 crore.
You are required to compute EVA of the Division C.
QUESTION NO. 4H
Compute Economic Value Added (EVA) of Good luck Ltd. from the following information:
Profit & Loss Statement
Particulars (₹ in Lakh)
(a) Income -
Revenue from Operations 2000
(b) Expenses -
3.8
Direct Expenses 800

Indirect Expenses 400
(c) Profit before interest & tax(a-b) 800
(d) Interest 30
(e) Profit before tax (c - d) 770
(f) Tax 231
(g) Profit after tax (e - f) 539
Balance Sheet
Particulars (₹ in Lakh)
Equity and Liabilities :
(a) Shareholder's Fund -
Equity Share Capital 1000
(b) Non- Current Liabilities -
Long Term Borrowings 200
(c) Current Liabilities 800
Total 2600
Assets :
(a) Non - Current Assets 2000
b) Current Assets 600
Total 2600
Other Information:
(1) Cost of Debts is 15%.
(2) Cost of Equity (i.e. shareholders' expected return) is 12%.
(3) Tax Rate is 30%.
(4) Bad Debts Provision of ₹ 40 lakhs is included in indirect expenses and ₹ 40 lakhs reduced from
receivables in current assets.
LOS 8 : Value of Business using EVA Method

Valuation of Business using EVA Method (Assume Constant growth after 2 years):
𝐄𝐕𝐀 𝟐 (𝟏 𝐠)
𝐄𝐕𝐀𝟏 𝐄𝐕𝐀𝟐 𝐊𝐨 𝐠
MVA = + +
( 𝟏 𝐊 𝟎 )𝟏 ( 𝟏 𝐊 𝟎 )𝟐 ( 𝟏 𝐊 𝐨 )𝟐
MVA = Value of Business – Total Capital Employed

Value of Business = Total Capital Employed + MVA
QUESTION NO. 5
From the following data compute the value of business using EVA method.
Current Period Projected Periods
2010 2011 2012
Total Invested Capital ₹ 90,00,000 ₹ 1,00,00,000 ₹ 1,10,00,000
Adjusted NOPAT ₹ 12,60,000 ₹ 14,00,000 ₹ 16,00,000
WACC 8.42%
Capital Growth (g) is projected = 6.5% per year after 2012.
3.9
LOS 9 : Discounted Cash Flow approach or Free Cash Flow Approach or Value
of Business using FCFE & FCFF
Under this approach, we will calculate value of business by discounting the future cash flows.
Steps Involved:
Step 1: Calculation of Free Cash Flow of each Year.
Step 2: Calculate Terminal Value at the end of forecast period.
Step 3: Compute Discount Rate
Step 4: Calculate Present Value of Business/ Equity by discounting the Cash Flows & Terminal Value.
Calculation of Terminal Value / Continuing Value / Salvage Value
Terminal Value is calculated at the end of the Project Life or at the end of the forecasted period.
Note:
 Given in the Question.
 Assumption of Growth Model (Let’s assume Growing Cash Flow after 3 Years)
𝐂𝐅𝟑 (𝟏 𝐠)
𝐂𝐅𝟏 𝐂𝐅𝟐 𝐂𝐅𝟑 𝐊𝐨 𝐠
P0 = + + +
(𝟏 𝐊 𝟎 )𝟏 (𝟏 𝐊 𝟎 )𝟐 (𝟏 𝐊 𝟎 )𝟑 (𝟏 𝐊 𝟎 )𝟑
 Assumption of Constant Model/ Perpetuity Approach (Let’s assume Constant Cash Flow
after 3 Years)
𝐂𝐅𝟑
𝐂𝐅𝟏 𝐂𝐅𝟐 𝐂𝐅𝟑 𝐊𝐨
P0 = + + +
(𝟏 𝐊 𝟎 )𝟏 (𝟏 𝐊 𝟎 )𝟐 (𝟏 𝐊 𝟎 )𝟑 (𝟏 𝐊 𝟎 )𝟑
 Continuing value/ Terminal Value is calculated because it is not easy to estimate realistic cash
flows, so we take uniform assumption of Constant Model or Growth Model.
Calculation of FCFF
EBITDA xxx
Less : Depreciation(NCC) xxx
EBT xxx
Less : Tax xxx
NOPAT xxx
Less : Increase in Working Capital (WCInv) xxx
Less : Capital Expenditure (FCInv) xxx
Free Cash Flow For Firm (FCFF) xxx
3.10
Calculation of FCFE
Method 1 : When Debt-financing ratio is given:
EBITDA xxx
EBIT xxx
Less : Interest xxx
EBT xxx
Less : Tax xxx
PAT xxx
Add : Depreciation × % Equity Invested xxx
Less: Increase in Working Capital × % Equity Invested xxx
Less: Capital Expenditure × % Equity Invested xxx
Method 2 : When Debt-financing ratio is not given:
EBITDA xxx
EBIT xxx
Less : Interest xxx
EBT xxx
Less : Tax xxx
PAT xxx
Less: Increase in Working Capital (WCInv) xxx
Less: Capital Expenditure (FCInv) xxx
Add : Net Borrowings xxx
QUESTION NO. 6A
Following information’s are available in respect of XYZ Ltd. which is expected to grow at a higher rate
for 4 years after which growth rate will stabilize at a lower level:
Base year information:
Revenue ₹ 2,000 crores
EBIT ₹ 300 crores
Capital expenditure ₹ 280 crores
Depreciation ₹ 200 crores
Information for high growth and stable growth period are as follows:
High Growth Stable Growth
Growth in Revenue & EBIT 20% 10%
Growth in capital expenditure and 20% Capital Expenditure are offset by
depreciation depreciation
Risk Free Rate 10% 9%
Equity Beta 1.15 1
Market Risk Premium 6% 5%
Pre Tax Cost of debt 13% 12.86%
Debt equity ratio 1:1 2:3
For all time, working capital is 25% of revenue and corporate tax rate is 30%. What is the value of
the firm?
3.11
QUESTION NO. 6B
Following information is given in respect of WXY Ltd., which is expected to grow at a rate of 20% p.a.
for the next three years, after which the growth rate will stabilize at 8% p.a. normal level, in perpetuity.
For the year ended
March 31, 2014
Revenues ₹ 7,500 Crores
Cost of Goods Sold (COGS) ₹ 3,000 Crores
Operating Expenses ₹ 2,250 Crores
Capital Expenditure ₹ 750 Crores
Depreciation (included in COGS & Operating Expenses) ₹ 600 Crores
During high growth period, revenues & Earnings before Interest & Tax (EBIT) will grow at 20% p.a.
and capital expenditure net of depreciation will grow at 15% p.a. From year 4 onwards, i.e. normal
growth period revenues and EBIT will grow at 8% p.a. and incremental capital expenditure will be
offset by the depreciation. During both high growth & normal growth period, net working capital
requirement will be 25% of revenues.
The Weighted Average Cost of Capital (WACC) of WXY Ltd. is 15%.
Corporate Income Tax rate will be 30%.
Required:
Estimate the value of WXY Ltd. using Free Cash Flows to Firm (FCFF) & WACC methodology.
The PVIF @ 15 % for the three years are as below:
Year t1 t2 t3
PVIF 0.8696 0.7561 0.6575
QUESTION NO. 6C
ABC Co. is considering a new sales strategy that will be valid for the next 4 years. They want to know
the value of the strategy. Following information relating to the year which has just ended, is available:
Income Statement: ₹
Sales 20,000
Gross Margin (20%) 4,000
Administration, Selling & Distribution Expense
2,000
(10%)
PBT 2,000
Tax @ 30% 600
PAT 1,400
Balance Sheet Information:
Fixed Assets 8,000
Current Assets 4,000
Equity 12,000
If it adopts the new strategy, sales will grow at the rate of 20% per year for three years. The Gross
Margin Ratio, Assets Turnover Ratio, the Capital Structure Ratio and the Income Tax rate will remain
unchanged.
Depreciation would be at 10% of net fixed assets at the beginning of the year. The company's target
rate of return is 15%. Determine the incremental value due to adoption of the strategy. Ignore
Depreciation on existing strategy.
QUESTION NO. 6D
Following details are available for X Ltd.
Income Statement for the year ended 31st March, 2018
3.12
Particulars Amount
Sales 40,000
Gross Profit 12,000
Administrative Expenses 6,000
Profit Before tax 6,000
Tax @ 30% 1,800
Profit After Tax 4,200
Balance sheet as on 31st March, 2018
Particulars Amount
Fixed Assets 10,000
Total Assets 16,000
Equity Share Capital 15,000
Sundry Creditors 1,000
Total Liabilities 16,000
The Company is contemplating for new sales strategy as follows :
(i) Sales to grow at 30% per year for next four years.
(ii) Assets turnover ratio, net profit ratio and tax rate will remain the same.
(iii) Depreciation will be 15% of value of net fixed assets at the beginning of the year.
(iv) Required rate of return for the company is 15%
Evaluate the viability of new strategy.
QUESTION NO. 6E
Calculate the value of share from the following information;
Profit of the company or Earning for Equity ₹ 290crores
Equity capital of company ₹ 1,300 crores
Par value of share ₹ 40 each
Debt ratio of company 27
Long run growth rate of the company 8%
Beta 0.1, risk free interest rate 8.7%
Market return 10.3%
Capital expenditure per share ₹ 47
Depreciation per share ₹ 39
Change in Working capital per share ₹ 3.45 per share
QUESTION NO. 6F
Calculate the value of share of Avenger Ltd. from the following information:
Equity capital of company ₹ 1,200 crores
Profit of the company ₹ 300 crores
Par value of share ₹ 40 each
Debt ratio of company 25
Long run growth rate of the company 8%
Beta 0.1; risk free interest rate 8.7%
Market returns 10.3%
Change in working capital per share ₹ 4
Depreciation per share ₹ 40
Capital expenditure per share ₹ 48
3.13
QUESTION NO. 6G
BRS Inc deals in computer and IT hardwares and peripherals. The expected revenue for the next 8
years is as follows:
Years Sales Revenue ($ Million)
1 8
2 10
3 15
4 22
5 30
6 26
7 23
8 20
Summarized financial position as on 31 March 2012 was as follows:
Liabilities Amount Assets Amount
($ ($
Million) Million)
Equity Stocks 12 Fixed Assets (Net) 17
12% Bonds 8 Current Assets 3
20 20
Additional Information:
a) Its variable expenses is 40% of sales revenue and fixed operating expenses (cash) are estimated
to be as follows:
Period Amount ($ Million)
1- 4 years 1.6
5-8 years 2
b) An additional advertisement and sales promotion campaign shall be launched requiring
expenditure as per following details:
1 year 0.50
2-3 years 1.50
4-6 years 3.00
7-8 years 1.00
c) Fixed assets are subject to depreciation at 15% as per WDV method.
d) The company has planned additional capital expenditures (in the beginning of each year) for the
coming 8 years as follows:
1 0.50
2 0.80
3 2.00
4 2.50
5 3.50
6 2.50
7 1.50
8 1.00
e) Investment in Working Capital is estimated to be 20% of Revenue.
f) Applicable tax rate for the company is 30%.
3.14
g) Cost of Equity is estimated to be 16%.

h) The Free Cash Flow of the firm is expected to grow at 5% per annum after 8 years.
With above information you are require to determine the:
(i) Value of Firm
(ii) Value of Equity
QUESTION NO. 6H
ABC (India) Ltd., a market leader in printing industry, is planning to diversify into defense
equipment businesses that have recently been partially opened up by the GOI for private
sector. In the meanwhile, the CEO of the company wants to get his company valued by a
leading consultants, as he is not satisfied with the current market price of his scrip.
He approached consultant with a request to take up valuation of his company with the following data
for the year ended 2009:
Share Price ₹ 66 per share
Outstanding debt 1934 lakh
Number of outstanding shares 75 lakh
Net income (PAT) 17.2 lakh
EBIT 245 lakh
Interest expenses 218.125 lakh
Capital expenditure 234.4 lakh
Depreciation 234.4 lakh
Working capital 44 lakh
Growth rate 8% (from 2010 to 2014)
Growth rate 6% (beyond 2014)
Free cash flow 240.336 lakh (year 2014 onwards)
The capital expenditure is expected to be equally offset by depreciation in future and the debt is
expected to decline by 30% in 2014.
Required:
Estimate the value of the company and ascertain whether the ruling market price is undervalued as
felt by the CEO based on the foregoing data. Assume that the cost of equity is 16%, and 30% of debt
repayment is made in the year 2014.
LOS 10 : Calculation of Range of Valuation

The range of valuation means we have to calculate minimum & maximum value of business by using
more than one method as indicated in question.
QUESTION NO. 7
ABC Company is considering acquisition of XYZ Ltd. which has 1.5 crores shares outstanding and
issued. The market price per share is ₹ 400 at present. ABC's average cost of capital is 12%. Available
information from XYZ indicates its expected cash accruals for the next 3 years as follows:
Year ₹ Cr.
1 250
2 300
3 400
Calculate the range of valuation that ABC has to consider. (PV factors at 12% for years 1 to 3
respectively: 0.893, 0.797 and 0.712)
3.15
LOS 11 : Basis of Allocation for Fully & Partly paid shareholders

QUESTION NO. 8
AB Ltd. is planning to acquire and absorb the running business of XY Ltd. The valuation is to be based
on the recommendation of merchant bankers and the consideration is to be discharged in the form
of equity shares to be issued by AB Ltd.
As on 31.3.2006, the paid up capital of AB Ltd. consists of 80 Lakhs shares of ₹ 10 each. The highest
and the lowest market quotation during the last 6 months were ₹ 570 and ₹ 430.
For the purpose of the exchange, the price per share is to be calculated as the average of the highest
and lowest market price during the last 6 months ended on 31.3.06.
XY Ltd's Balance Sheet as at 31.3.2006 is summarized below: ₹ Lakhs
Sources
Share Capital
20 Lakhs equity shares of ₹ 10 each, fully paid 200
10 Lakhs equity shares of ₹ 10 each, ₹ 5 paid 50
Loans 100
Total 350
Uses
Fixed Assets (Net) 150
Net Current Assets 200
Total 350
An independent firm of merchant bankers engaged for the negotiation, have produced the following
estimates of cash flows from the business of XY Ltd.:
Year ended By way of ₹ Lakhs
31.03.2007 after tax earnings for equity 105
31.03.2008 — do — 120
31.03.2009 — do — 125
31.03.2010 — do — 120
31.03.2011 — do — 100
31.03.2011 Terminal Value Estimate 200
It is the recommendation of the merchant banker that the business of XY Ltd. may be valued on the
basis of the average of:
(i) Aggregate of discounted cash flows at 8% and
(ii) Net Assets Value.
Year 1 Year 2 Year 3 Year 4 Year 5
PVF at 8% 0.93 0.86 0.79 0.74 0.68
You are required to
a) Calculate the total value of the business of XY Ltd.
b) The number of shares to be issued by AB Ltd; and
c) The basis of allocation of the shares among the shareholders of XY Ltd.
3.16
LOS 12 : Valuation with NPV decision
𝐓𝐨𝐭𝐚𝐥 𝐍𝐏𝐕
Revised MPS = Existing MPS ±
𝐓𝐨𝐭𝐚𝐥 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 𝐒𝐡𝐚𝐫𝐞𝐬
QUESTION NO. 9A
DEF Ltd has been regularly paying a dividend of ₹ 19,20,000 per annum for several years and it is
expected that same dividend would continue at this level in near future. There was 12,00,000 equity
shares of ₹ 10 each and the share is traded at par.
The company has an opportunity to invest ₹ 8,00,000 in one year’s time as well as further ₹ 8,00,000 in
two years’ time in a project as it is estimated that the project will generate cash inflow of ₹ 3,60,000 per
annum in three years’ time which will continue forever. This investment is possible if dividend is reduced
for next two years
Whether the company should accept the project? Also analyse the effect on the market price of the share,
if the company decides to accept the project.
QUESTION NO. 9B
Rahim Enterprises is a manufacturer and exporter of woollen garments to European countries. Their
business is expanding day by day and in the previous financial year the company has registered a 25%
growth in export business. The company is in the process of considering a new investment project. It is
an all equity financed company with 10,00,000 equity shares of face value of ₹ 50 per share. The current
issue price of this share is ₹ 125 ex-divided. Annual earning are ₹ 25 per share and in the absence of
new investments will remain constant in perpetuity. All earnings are distributed at present. A new
investment is available which will cost ₹ 1,75,00,000 in one year’s time and will produce annual cash
inflows thereafter of ₹ 50,00,000. Analyse the effect of the new project on dividend payments and the
share price.
QUESTION NO. 9C
Two companies A Ltd. and B Ltd. paid a dividend of ₹3.50 per share. Both are anticipating that
dividend shall grow @ 8%. The beta of A Ltd. and B Ltd. are 0.95 and 1.42 respectively.
The yield on GOI Bond is 7% and it is expected that stock market index shall increase at an annual rate of
13%. You are required to determine:
(a) Value of share of both companies.
(b) Why there is a difference in the value of shares of two companies.
(c) If current market price of share of A Ltd. and B Ltd. are ₹74 and ₹55 respectively. As an investor what
course of action should be followed?
LOS 13 : Market Value Added (MVA)

From Equity Point of View
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 – 𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐄𝐪𝐮𝐢𝐭𝐲
MVA = for equity shareholders
𝐚𝐬 𝐩𝐞𝐫 𝐦𝐚𝐫𝐤𝐞𝐭 𝐚𝐬 𝐩𝐞𝐫 𝐁𝐨𝐨𝐤𝐬 𝐨𝐟 𝐀/𝐜′𝐬
= MPS × No. of Equity share – Equity Shareholder’s Fund.
Note:
Add Reserve & Surplus
3.17
From Overall company’s Point of View
MVA = Value of the company based on Free Cash Flows – Total Capital Employed
Note: Total Capital Employed

Add Preference share capital
Reserve & Surplus
Debenture/Bonds
Long-Term Loan
QUESTION NO. 10A
Nappp.com plc is a closely held company based Lincolnshire in B2B business offering logistic services
mainly to small and medium sized companies through internet, who cannot afford sophisticated
logistics practices. Company is planning to go for public issue in the coming year and is interested to
know what the company's share will be worth. The company engaged a consultant based in
Leicestershire. The consultant evaluated company's future prospects and made following estimates of
future free cash flows.
Years 1 2 3 4
Sales £100,000.00 £115,000,00 £ 132,250.00 £132,250.00
Operating income £16,000.00 £18,400.00 £21,160.00 £21,160.00
(earnings before interest
and taxes)
Less: Cash tax payments (£4,800.00) (£5,520.00) (£6,348.00) (£6,348.00)
Net operating profits after £11,200.00 £ 12,880.00 £ 14,812.00 £ 14,812.00
taxes (NOPAT)
Less: Investments in net (£1,695.65) (£1,950.00) (£2,242.50) —
working capital
Capital expenditures (£2,347.83) (£2,700.00) (£3,105.00) —
(CAPEX)
Total investments (£4,043.48) (£4,650.00) (£5,347.50) —
Free cash flow £7,156.52 £8,230.00 £ 9,464.50 £14,812.00
Further, the company's investment banker had done a study of the company's cost of capital and
estimated WACC to be 12%. You are required to determine,
a) Value of Nappp.com plc based on these estimates.
b) Market Value Added (MVA) by company supposing that invested capital in the year 0 was
£31,304.05.
c) Value of per share, if company has 2,000 common equity share outstanding and debt amounting
to £ 4,000.
QUESTION NO. 10B
The following data pertains to XYZ Inc. engaged in software consultancy business as on 31 December
2010
$ Million
Income from consultancy 935.00
EBIT 180.00
3.18
Less : Interest on Loan 18.00

EBT 162.00
Tax @ 35% 56.70
105.30
Balance Sheet
Liabilities Amount ($ Asset Amount
Million) ($ Million)
Equity Stock (10 million share @ $ 100 Land and Building 200
10 each)
Reserves & Surplus 325 Computers & Software 295
Loans 180 Current Assets:
Current Liabilities 180 Debtors 150
Bank 100
Cash 40 290
785 785
With the above information and following assumption you are required to compute
a) Economic Value Added
b) Market Value Added. Assuming that:
(i) WACC is 12%.
(ii) The share of company currently quoted at $ 50 each
LOS 14 : Determination of Correct Value of the Firm

QUESTION NO. 11A
Suppose you are verifying a valuation done on an established company by a well-known analyst has
estimated a value of ₹ 750 Lakhs, based upon the expected free cash flow next year, of ₹ 30 Lakhs,
and with an expected growth rate of 5%. You found that, he has made the mistake of using the book
values of debt and equity in his calculation. While you do not know the book value weights he used,
you have been provided following information:
a) Company has a cost of equity of 12%.
b) After-tax cost of debt of 6%.
c) The market value of equity is three times the book value of equity, while the market value of debt
is equal to the book value of debt. You are required to estimate the correct value of company.
QUESTION NO. 11B
The valuation of Hansel Limited has been done by an investment analyst. Based on an expected free
cash flow of ₹ 54 lakhs for the following year and an expected growth rate of 9 percent, the analyst
has estimated the value of Hansel Limited to be ₹ 1800 lakhs. However, he committed a mistake of
using the book values of debt and equity.
The book value weights employed by the analyst are not known, but you know that Hansel Limited
has a cost of equity of 20 percent and post-tax cost of debt of 10 percent.
The value of equity is thrice its book value, whereas the market value of its debt is nine-tenths of its
book value. What is the correct value of Hansel Ltd?
QUESTION NO. 11C
An established company is going to be de merged in two separate entities. The valuation of the
company is done by a well-known analyst. He has estimated a value of ₹ 5,000 lakhs, based on the
expected free cash flow for next year of ₹ 200 lakhs and an expected growth rate of 5%. While going
through the valuation procedure, it was found that the analyst has made the mistake of using the book
3.19
values of debt and equity in his calculation. While you do not know the book value weights he used, you
have been provided with the following information:
(i) The market value of equity is 4 times the book value of equity, while the market value of debt is
equal to the book value of debt,
(ii) Company has a cost of equity of 12%,
(iii) After tax cost of debt is 6%.
You are required to advise the correct value of the company.
LOS 15 : Calculation of Value of Equity

QUESTION NO. 12A
Capital structure of Sun Ltd., as at 31.3.2003 was as under: (₹ in Lacs)
Equity share capital 80
8% Preference share capital 40
12% Debentures 64
Reserves 32
Sun Ltd., earns a profit of ₹ 32 Lacs annually on an average before deduction of income-tax, which
works out to 35%, and interest on debentures.
Normal return on equity shares of companies similarly placed is 9.6% provided:
a) Profit after tax covers fixed interest and fixed dividends at least 3 times.
b) Capital gearing ratio is 0.75.
c) Yield on share is calculated at 50% of profits distributed and at 5% on undistributed profits.
Sun Ltd., has been regularly paying equity dividend of 8%.
Compute the value per equity share of the company, taken
(i) 1 % for every one time of difference for Interest and Fixed Dividend Coverage Ratio,
(ii) 2% for every one time of difference for Capital Gearing Ratio.
QUESTION NO. 12B
The director of D Ltd. wish to make an equity issue to invest $ 80,00,000, which has an expected NPV
of $ 11,00,000 and to refund an existing $ 50, 00,000 15% Bond that is due for Maturity in 5 years’
time. For early redemption of these bonds there is a $ 3,50,000 penalty charges. The company will
issue new shares of $ 1,50,00, 000.
It is estimated that the flotation cost of the issue to be 4% of Gross proceeds. As on date the capital
structure of D Ltd. is as follows: $’000
Ordinary Shares (25 per share) 8,000
Free reserves 11,200
Security Premium 23,100
42,300
15% term Bonds 5,000
11% Debentures 9,000
56,300
The entity’s current share price is $ 190. D Ltd. can raise debenture or medium-term bank finance at
10% p.a., which can be treated as discount rate. You are required to estimate D Ltd. expected value
of equity.
QUESTION NO. 12C
The directors of Implant Inc. wishes to make an equity issue to finance a $10 m (million) expansion
scheme which has an excepted Net Present Value of $2.2m and to re-finance an existing $6 m 15%
Bonds due for maturity in 5 year’s time. For early redemption of these bonds there is a $3,50,000
penalty charges. The Co. has also obtained approval to suspend these pre-emptive rights and make
3.20
a $15 m placement of shares which will be at a price of $0.5 per share. The floatation cost of
issue will be 4% of Gross proceeds. Any surplus funds from issue will be invested in IDRs which is
currently yielding 10% per year.
The Present capital structure of Co. is as under:
’000
Ordinary Share ($1 per share) 7,000
Share Premium 10,500
Free Reserves 25,500
43,000
15% Term Bonds 6,000
11% Debenture (2012-2020) 8,000
57,000
Current share price is $2 per share and debenture price is $ 103 per debenture. Cost of capital of
Co. is 10%. It may be further presumed that stock market is semi-strong form efficient and no
information about the proposed use of funds from the issue has been made available to the public.
You are required to calculate expected share price of company once full details of the placement and
to which the finance is to be put, are announced.
3.21
PRACTICE QUESTIONS
QUESTION NO. 13
There are two companies ABC Ltd. and XYZ Ltd. are in same in industry. On order to increase its size
ABC Ltd. made a takeover bid for XYZ Ltd.
Equity beta of ABC and XYZ is 1.2 and 1.05 respectively. Risk Free Rate of Return
is 10% and Market Rate of Return is 16%. The growth rate of earnings after tax of ABC Ltd. in recent
years has been 15% and XYZ’s is 12%. Further both companies had continuously followed constant
dividend policy.
Mr. V, the CEO of ABC requires information about how much premium above the current market
price to offer for XYZ’s shares.
Two suggestions have forwarded by merchant bankers.
(i) Price based on XYZ’s net worth as per B/S, adjusted in light of current value of assets and
estimated after tax profit for the next 5 years.
(ii) Price based on Dividend Valuation Model, using existing growth rate estimates. Summarised
Balance Sheet of both companies is as follows.
(₹ In lacs)
ABC Ltd. XYZ Ltd. ABC Ltd. XYZ Ltd.
Equity Share Capital 2,000 1,000 Land & Building 5,600 1,500
General Reserves 4,000 3,000 Plant & Machinery 7,200 2,800
Share Premium 4,200 2,200
Long Term Loans 5,200 1,000
Current Liabilities Current Assets
Sundry Creditors 2,000 1,100 Accounts Receivable 3,400 2,400
Bank Overdraft 300 100 Stock 3,000 2,100
Tax Payable 1,200 400 Bank/Cash 200 400
Dividend Payable 500 400 - -
19,400 9,200 19,400 9,200
Profit & Loss A/c
(₹ In lacs)
ABC XYZ ABC XYZ
Ltd. Ltd. Ltd. Ltd.
To Net Interest 1,200 220 By Net Profit 7,000 2,550
To Taxation 2,030 820
To Distributable Profit 3,770 1,510 - -
7,000 2,550 7,000 2,550
To Dividend 1,130 760 By Distributable Profit 3,770 1,510
To Balance c/d 2,640 750 - -
3,770 1,510 3,770 1,510
Additional information
(1) ABC Ltd.’s land & building have been recently revalued. XYZ Ltd.’s have not been revalued for 4
years, and during this period the average value of land & building have increased by 25% p.a.
(2) The face value of share of ABC Ltd. is ₹ 10 and of XYZ Ltd. is ₹ 25 per share.
(3) The current market price of shares of ABC Ltd. is ₹ 310 and of XYZ Ltd.’s ₹ 470 per share.
With the help of above data and given information you are required to calculate the premium per
share above XYZ’s current share price by two suggested valuation methods. Discuss which of these
two values should be used for bidding the XYZ’s shares.
3.22
State the assumptions clearly, you make.

QUESTION NO. 14
MS Stones has different divisions of home interiors products. Recently, due to economic slowdown,
the Managing Director of the Company expressed it desire to divestiture its ceramic tile business. The
relevant financial details of this business are as follows:
Estimated Pre Tax Cash Flow Next Year = ₹ 200 Crore
Book Value of Liabilities = ₹ 780 Crore
In an order to increase its share in the ceramic tile market, the Tripati Tiles Ltd. showed its interest in
the acquisition of this unit and offered a proceed of ₹ 950 Crore for the same to MS Stones.
The other data pertaining to the business are as follows:
Tax Rate 30%
Growth Rate 4%
Applicable Discount Rate for Tile Business 12%
If market value of liabilities are ₹ 40 Crore more than book value, you are required to advice MD
whether she should go for divestiture of the tile business or not.
QUESTION NO. 15
XY Ltd., a Cement manufacturing Company has hired you as a financial consultant of the company. The
Cement Industry has been very stable for some time and the cement companies SK Ltd. & AS Ltd. are
similar in size and have similar product market mix characteristic. Use comparable method to value the
equity of XY Ltd. In performing analysis, use the following ratios:
(i) Market to book value
(ii) Market to replacement cost
(iii) Market to sales
(iv) Market to Net Income
The following data are available for your analysis:
(Amount in ₹)
SK Ltd. AS Ltd. XY Ltd.
Market Value 450 400
Book Value 400 300 250
Replacement Cost 600 550 500
Sales 550 450 500
Net Income 18 16 14
QUESTION NO. 16
You are interested in buying some equity stocks of RK Ltd. The company has 3 divisions operating in
different industries. Division A captures 10% of its industries sales which is forecasted to be ₹ 50 crore
for the industry. Division B and C captures 30% and 2% of their respective industry's sales, which are
expected to be ₹ 20 crore and ₹ 8.5 crore respectively. Division A traditionally had a 5% net income
margin, whereas divisions B and C had 8% and 10% net income margin respectively. RK Ltd. has
3,00,000 shares of equity stock outstanding, which sell at ₹ 250.
The company has not paid dividend since it started its business 10 years ago. However from the market
sources you come to know that RK Ltd. will start paying dividend in 3 years time and the pay-out ratio is
30%. Expecting this dividend, you would like to hold the stock for 5 year. By analysing the past financial
statements, you have determined that RK Ltd.'s required rate of return is 18% and that P/E ratio of 10
for the next year and on ending P/E ratio of 20 at the end of the fifth year are appropriate.
Required:
(i) Would you purchase RK Ltd. equity at this time based on your one year forecast?
(ii) If you expect earnings to grow @ 15% continuously, how much are you willing to pay for the stock
of RK Ltd ?
Ignore taxation.
3.23
PV factors are given below :

Years 1 2 3 4 5
PVIF@ 18% 0.847 0.718 0.609 0.516 0.437
QUESTION NO. 17
The shares of G Ltd. we currently being traded at ₹ 46. The company published its results for the year
ended 31st March 2019 and declared a dividend of ₹ 5. The company made a return of 15% on its
capital and expects that to be the norm in which it operates. G Ltd. Also expects the dividends to grow
at 10% for the first three years and thereafter at 5%.
You are required to advise whether the share of the company is being traded at a premium or discount.
3.24
4.1
Mergers, Acquisition & Corporate Restructuring

Study Session 4
Merger & Acquisition
MERGER (A + B = A)
ACQUISITION (Stake Buyout)
AMALGAMATION (A + B = C)
Reasons for Merger & Acquisition

 Economies of Scale
 Efficiency Improvement
 Power of Market Share – Reduced Competition
 Tax Consideration
 Combining resources that are complementary.
LOS 2 : Share Exchange Ratio/ Swap Ratio

Swap Ratio may be defined as No. of equity shares issued by Acquiring Company to Target Company
for every one share held by Target Company.
Example:
If Swap Ratio = 2, it means that for every 1 share held by Target company, Acquiring Company will
issue 2 shares.
Methods of Calculating the Swap Ratio:
𝐌𝐏𝐒 𝐨𝐟 𝐓𝐚𝐫𝐠𝐞𝐭 𝐂𝐨𝐦𝐩𝐚𝐧𝐲
1. On the basis of MPS Swap Ratio =
𝐌𝐏𝐒 𝐨𝐟 𝐀𝐜𝐪𝐮𝐢𝐫𝐢𝐧𝐠 𝐂𝐨𝐦𝐩𝐚𝐧𝐲
𝐄𝐏𝐒 𝐨𝐟 𝐓𝐚𝐫𝐠𝐞𝐭 𝐂𝐨𝐦𝐩𝐚𝐧𝐲

2. On the basis of EPS Swap Ratio =
𝐄𝐏𝐒 𝐨𝐟 𝐀𝐜𝐪𝐮𝐢𝐫𝐢𝐧𝐠 𝐂𝐨𝐦𝐩𝐚𝐧𝐲
𝐍𝐀𝐕 𝐨𝐟 𝐓𝐚𝐫𝐠𝐞𝐭 𝐂𝐨𝐦𝐩𝐚𝐧𝐲

3. On the basis of NAV per Share Swap Ratio =
𝐍𝐀𝐕 𝐨𝐟 𝐀𝐜𝐪𝐮𝐢𝐫𝐢𝐧𝐠 𝐂𝐨𝐦𝐩𝐚𝐧𝐲
𝐁𝐕𝐏𝐒 𝐨𝐟 𝐓𝐚𝐫𝐠𝐞𝐭 𝐂𝐨𝐦𝐩𝐚𝐧𝐲

4. On the basis of Book Value per share Swap Ratio =
𝐁𝐕𝐏𝐒 𝐨𝐟 𝐀𝐜𝐪𝐮𝐢𝐫𝐢𝐧𝐠 𝐂𝐨𝐦𝐩𝐚𝐧𝐲
𝐏/𝐄 𝐑𝐚𝐭𝐢𝐨 𝐨𝐟 𝐓𝐚𝐫𝐠𝐞𝐭 𝐂𝐨𝐦𝐩𝐚𝐧𝐲

5. On the basis of P/E Ratio Swap Ratio =
𝐏/𝐄 𝐑𝐚𝐭𝐢𝐨 𝐨𝐟 𝐀𝐜𝐪𝐮𝐢𝐫𝐢𝐧𝐠 𝐂𝐨𝐦𝐩𝐚𝐧𝐲
Note:
EPS =
NAV =
P / E Ratio =
Note:
If question is silent regarding the basis of calculation of swap ratio, Swap Ratio may be calculated
using EPS or MPS as per the requirement of the question.
4.2
Negative SWAP Ratio

.
Swap Ratio =
.
.
e.g. Swap Ratio =
.
QUESTION NO. 1
A Ltd. wants to take over B Ltd. and the financial details of both are as follows:
A Ltd. (₹) B Ltd. (₹)
Fixed Assets 1,22,000 35,000
Current Assets 51,000 26,000
Total 1,73,000 61,000
Preference Share Capital 20,000 —
Equity Share Capital of ₹ 10 each 1,00,000 50,000
Securities Premium — 2,000
Profit and Loss A/c 38,000 4,000
10% Debentures 15,000 5,000
Total 1,73,000 61,000
Profit After Tax and Preference Dividend 24,000 15,000
Market Price 24 27
What should be share exchange ratio to be offered to the shareholders of B Ltd. based on:
(i) Net Assets Value,
(ii) EPS, and
(iii) Market Price.
Which should be preferred from the points of view of A Ltd.?
LOS 3 : Some Basic Concepts
1. Total Number of Equity Shares after Merger
Number of Shares A+B = NA + NB × ER

Example:
A Ltd. B Ltd.
No. of Shares 100000 50000
Calculate total no. of Equity Shares after Merger if Swap Ratio/ Exchange Ratio = 0.50?
Solution:
Number of Shares A+B (T A+B) = NA + NB × ER
= 1,00,000 + 50,000 × 0.50
= 1,00,000 + 25,000 = 1,25,000 shares
2. EPS after Merger or EPSA + B or EPS of a Merged Firm/ Combined Firm
𝐄𝐀 𝐄𝐁 𝐒𝐲𝐧𝐞𝐫𝐠𝐲 𝐆𝐚𝐢𝐧
EPSA+B =
𝐍𝐀 𝐍𝐁 × 𝐄𝐑
Example:
A Ltd. B Ltd.
Earnings 5,00,000 2,00,000
No. of Shares 100000 50000
Synergy Gain 1,00,000
E/R 0.50
4.3
Calculate:
a) EPS of A Ltd. before Merger.
b) EPS of B Ltd. before Merger.
c) Total Earnings after Merger.
d) Total No. of Equity Shares after Merger.
e) EPS after Merger or EPS A+B.
Solution:
, ,
a) EPS A Ltd. = = ₹ 5 per share
, ,
, ,
b) EPS B Ltd. = = ₹ 4 per share
,
c) Total Earnings A+B = 5,00,000 + 2,00,000 + 1,00,000 = 8,00,000
d) Total No. of Shares A+B = 1,00,000 + 50,000 × 0.50 = 1,25,000

, , , , , ,
e) EPSA+B = = 6.40
, , , × .
3. MPS after Merger or MPSA + B or MPS of a Merged Firm

Alternative 1: If P/E Ratio is given
MPS A+B = EPS A+B × P/E A+B
Alternative 2: If P/E Ratio is not given
𝐓𝐨𝐭𝐚𝐥 𝐌𝐕 𝐚𝐟𝐭𝐞𝐫 𝐌𝐞𝐫𝐠𝐞𝐫

MPSA+B =
𝐓𝐨𝐭𝐚𝐥 𝐍𝐨.𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 𝐒𝐡𝐚𝐫𝐞𝐬 𝐚𝐟𝐭𝐞𝐫 𝐌𝐞𝐫𝐠𝐞𝐫
Or
𝐌𝐕𝐀 𝐌𝐕𝐁 𝐒𝐲𝐧𝐞𝐫𝐠𝐲 𝐆𝐚𝐢𝐧
MPSA+B =
Note:
 Answer by both alternative will be different.
 Alternative 1 should be preferred whenever any hint regarding P/E after merger is given in
question.
4. Market Value of Merged Firm or MVA + B
Alternative 1:
MV A+B = MPS A+B × [NA + NB × ER]
Alternative 2:
MV A+B = MV A + MV B + Synergy
Note:
 Answer by both alternative will be different.
 Alternative 1 should be preferred
5. Equivalent EPS of Target Co. in Merged Firm
Equivalent EPS of Target Co. in Merged Firm = EPS A+B × ER

4.4
Example:
EPS A+B = 15; E/R (given to B Ltd.) = 0.40
Calculate Equivalent EPS of B Ltd. in Merged Firm?
Solution:
Equivalent EPS of B Ltd. in Merged Firm = 15 × 0.40 = ₹ 6 per share
6. Equivalent MPS of Target Co. in Merged Firm
Equivalent MPS of Target Co. in Merged Firm = MPS A+B × ER
QUESTION NO. 2A
A Ltd. wants to acquire B Ltd. and has offered a swap ratio of 1:2 (0.5 shares for everyone share of B
Ltd.). Following information is provided:
A Ltd. B Ltd.
Profit After Tax ₹ 18,00,000 ₹ 3,60,000
Equity Shares Outstanding (Nos.) 6,00,000 1,80,000
EPS ₹3 ₹2
P/E Ratio 10 times 7 times
Market Price per Share ₹ 30 ₹ 14
Required:
a) The number of equity shares to be issued by A Ltd. for acquisition of B Ltd.
b) What is the EPS of A Ltd. after the acquisition?
c) Determine the equivalent earnings per share of B Ltd.
d) What is the expected market price per share of A Ltd. after the acquisition, assuming its PE multiple
remains unchanged?
e) Determine the market value of the merged firm.
QUESTION NO. 2B
B Ltd. is a highly successful company and wishes to expand by acquiring other firms. Its expected high
growth in earnings and dividends is reflected in its PE ratio of 17. The Board of Directors of B Ltd. has
been advised that if it were to take over firms with a lower PE ratio than it own, using a share-for-share
exchange, then it could increase its reported earnings per share. C Ltd. has been suggested as a possible
target for a takeover, which has a PE ratio of 10 and 1,00,000 shares in issue with a share price of ₹ 15.
B Ltd. has 5,00,000 shares in issue with a share price of ₹ 12.
Calculate the change in earnings per share of B Ltd. if it acquires the whole of C Ltd. by issuing shares
at its market price of ₹12. Assume the price of B Ltd. shares remains constant.
LOS 4 : Gain or Loss

 Merger may result into Gain/Loss for acquiring company & target Company.
 On the basis of EPS/MPS/Market Value (MV)
A Ltd. B Ltd.
MPS / EPS / MV after Merger XXX XXX
MPS / EPS / MV before Merger XXX XXX
Gain/ Loss XXX XXX
QUESTION NO. 3A
The following information is provided related to the acquiring Firm A Limited and the target Firm B
Limited:
4.5
Firm A Limited Firm B Limited

Earning after tax (₹) 2,000 Lakhs 400 Lakhs
Number of shares outstanding 200 Lakhs 100 Lakhs
P/E ratio (times) 10 5
Required:
a) What is the Swap Ratio based on current market prices?
b) What is the EPS of A Limited after acquisition?
c) What is the expected market price per share of A Limited after acquisition, assuming P/E ratio of
A Limited remains unchanged?
d) Determine the market value of the merged firm
e) Calculate gain/ loss for shareholders of the two independent companies after acquisition.
QUESTION NO. 3B
Company X is contemplating the purchase of Company Y. Company X has 3,00,000 shares having a
market price of ₹ 30 per share, while Company Y has 2,00,000 shares selling at ₹ 20 per share. The
EPS are ₹ 4.00 and ₹ 2.25 for Company X and Y respectively. Managements of both companies are
discussing two alternative proposals for exchange of shares as indicated below:
(i) In proportion to the relative earnings per share of two companies.
(ii) 0.5 share of Company X for one share of Company Y (0.5 : 1).
You are required:
a) To calculate the Earnings Per Share (EPS) after merger under two alternatives; and
b) To show the impact on EPS for the shareholders of two companies under both the alternatives.
QUESTION NO. 3C
You have been provided the following Financial data of two companies:
Krishna Ltd. Rama Ltd.
Earnings after taxes ₹ 7,00,000 ₹ 10,00,000
No. of Equity shares (outstanding) 2,00,000 4,00,000
EPS 3.5 2.5
P/E ratio 10 times 14 times
Market price per share ₹ 35 ₹ 35
Company Rama Ltd. is acquiring the company Krishna Ltd., exchanging its shares on a one- to-one
basis for company Krishna Ltd. The exchange ratio is based on the market prices of the shares of the
two companies.
Required:
1. What will be the EPS subsequent to merger?
2. What is the change in EPS for the shareholders of companies Rama Ltd. and Krishna Ltd.?
3. Determine the market value of the post-merger firm. PE ratio is likely to remain the same.
4. Ascertain the profits accruing to shareholders of both the companies.
QUESTION NO. 3D
ABC Ltd. is a company operating in the software industry. It is considering the acquisition of XYZ Ltd.
which is also into software industry. The following information are available for the companies:
ABC Ltd. XYZ Ltd.
Earnings after tax (₹) 9,00,000 2,40,000
Number of equity shares 1,50,000 60,000
P/E ratio (no. of times) 14 10
4.6
ABC Ltd. is planning to offer a premium of 25% over the market price of XYZ Ltd. Required:
(i) What is the swap ratio based on current market price?
(ii) Find the number of shares to be issued by ABC Ltd. to the shareholders of XYZ Ltd.
(iii) Compute the new EPS of ABC Ltd. after merger and comment on the impact of merger.
(iv) Determine the market price of the share when P/E ratio remains unchanged.
(v) Compute the market price when P/E declines to 12 and comment on the results. Figures are to
be rounded off to 2 decimals.
QUESTION NO. 3E
Following information is provided relating to the acquiring company Mani Ltd. and the target
company Ratnam Ltd:
Mani Ltd. Ratnam Ltd.
Earnings after tax (₹ lakhs) 2,000 4,000
No. of shares outstanding (lakhs) 200 1,000
P/E ratio (No. of times) 10 5
Required:
(i) What is the swap ratio based on current market prices?
(ii) What is the EPS of Mani Ltd. after the acquisition?
(iii) What is the expected market price per share of Mani Ltd. after the acquisition, assuming its
P/E ratio is adversely affected by 10%?
(iv) Determine the market value of the merged Co.
(v) Calculate gain/loss for the shareholders of the two independent entities, due to the merger.
LOS 5 : Maximum Exchange Ratio and Minimum Exchange Ratio

A= Acquiring Company  will try to keep exchange ratio as low as possible. Hence, we calculate
maximum ER for acquiring company.
B= Target Company  will try to keep exchange ratio as high as possible. Hence, we calculate
minimum ER for Target Company.
4.7
Case 1: On the basis of EPS:
a) Maximum Exchange ratio for A Ltd.
EPS before Merger = EPS after Merger

EPSA = EPSA + B
EPSA =
𝐍𝐀 𝐍𝐁 × 𝐄𝐱𝐜𝐡𝐚𝐧𝐠𝐞 𝐑𝐚𝐭𝐢𝐨 𝐄𝐑
Solve for ER
b) Minimum Exchange ratio for B Ltd.
EPS before Merger = Equivalent EPS after Merger

EPSB = EPSA + B× ER
ESPB =
× ER
Solve for ER
Case 2: On the basis of MPS (If P/E Ratio after merge is given i.e. P/E(A+B) is given)
MPS before Merger = MPS after Merger

MPSA = MPSA + B
MPSA = EPSA + B× P/E (A+B)
MPSA = × P/E (A+B)
Solve for ER
MPS before Merger = Equivalent MPS after Merger

MPSB = MPSA + B × ER
MPSB = [EPSA + B× P/E(A+B) ] × ER
MPSB = × P/E(A+B)× ER
Solve for ER
4.8
Case 3: On the basis of MPS (If P/E Ratio after merge is not given):
MPS before merger = MPS after merger

MPSA = MPSA + B
MPSA =
Solve for ER
MPS before merger = Equivalent MPS after merger

MPSB = MPSA + B × ER
MPSB = × ER
Solve for ER
QUESTION NO. 4A
A Ltd. is considering merger with B Ltd. A Ltd. shares are currently traded at ₹ 20. It has 2,50,000
shares outstanding and its earnings after taxes (EAT) amount to ₹ 5,00,000. B Ltd. has 1,25,000
shares outstanding; its current market price is ₹ 10 and its EAT are ₹ 1,25,000. The merger will be
effected by means of a stock swap (exchange). B Ltd. has agreed to a plan under which A Ltd. will
offer the current market value of B Ltd. shares:
a) What is the pre-merger Earnings Per Share (EPS) and P/E Ratios of both the companies?
b) If B Ltd's P/E ratio is 6.4, what is its current market price? What is the exchange ratio? What will
A Ltd's post-merger EPS be?
c) What should be the exchange ratio, if A Ltd's pre-merger & post-merger EPS are to be same?
QUESTION NO. 4B
M Co. Ltd. is studying the possible acquisition of N Co. Ltd. by way of merger. The following data are
available in respect of the companies:
Particulars M Co. Ltd. N Co. Ltd.
Earning after tax (₹) 80,00,000 24,00,000
No. of equity shares 1600000 400000
Market value per share (₹) 200 160
a) If the merger goes through by exchange of equity and the exchange ratio is based on the current
market price, what is the new earning per share for M Co. Ltd.?
b) N. Co. Ltd. wants to be sure that the earnings available to its shareholders will not be diminished
by the merger. What should be the exchange ratio in that case?
4.9
QUESTION NO. 4C
Longitude Limited is in the process of acquiring Latitude Limited on a share exchange basis. Following
relevant data are available:
Longitude Latitude
Limited Limited
Profit after Tax (PAT) ₹ in Lakhs 140 60
Number of Shares Lakhs 15 16
Earning per Share (EPS) ₹ 8 5
Price Earnings Ratio (P/E Ratio) 15 10
(Ignore Synergy)
(i) Pre-merger Market Value per Share, and
(ii) The maximum exchange ratio Longitude Limited can offer without the dilution of
a) EPS and
b) Market Value per Share
Calculate Ratio/s up to four decimal points and amounts and number of shares up to two decimal
points.
QUESTION NO. 4D
XYZ Ltd. wants to purchase ABC Ltd. by exchanging 0.7 of its share for each share of ABC Ltd. Relevant
financial data are as follows :
Equity shares outstanding 1000000 400000
EPS (₹) 40 28
Market price per share (₹) 250 160
a) Illustrate the impact of merger on EPS of both the companies.
b) The management of ABC Ltd. has quoted a share exchange ratio of 1 : 1 for the merger. Assuming
that P/E ratio of XYZ Ltd. will remain unchanged after the merger, what will be the gain from
merger for ABC Ltd.?
c) What will be the gain / loss to shareholders of XYZ Ltd. ?
d) Determine the maximum exchange ratio acceptable to shareholders of XYZ Ltd.
QUESTION NO. 4E
C Ltd. & D Ltd. are contemplating a merger deal in which C Ltd. will acquire D Ltd. The relevant
information about the firms are given as follows:
C Ltd. D Ltd.
Total Earnings (E) (in millions) ₹ 96 ₹ 30
Number of outstanding shares (S) (in millions) 20 14
Earnings per share (EPS) (₹) 4.8 2.143
Price earnings ratio (P/E) 8 7
Market Price per share (P)(₹) 38.4 15
(i) What is the maximum exchange ratio acceptable to the shareholders of C Ltd., if the P/E ratio
of the combined firm is 7?
(ii) What is the minimum exchange ratio acceptable to the shareholders of D Ltd., if the P/E ratio of
the combined firm is 9?
QUESTION NO. 4F
R Ltd. and S Ltd. operating in same industry are not experiencing any rapid growth but providing a steady
stream of earnings. R Ltd.'s management is interested in acquisition of S. Ltd. due to its excess plant
capacity. Share of S Ltd. is trading in market at ₹ 3.20 each. Other data relating to S Ltd. is as follows:
4.10
Balance Sheet of S Ltd.

Liabilities Amount (₹) Assets Amount (₹)
Current Liabilities 1,59,80,000 Current Assets 2,48,75,000
Long Term Liabilities 1,28,00,000 Other Assets 94,00,000
Reserve & Surplus 2,79,95,000 Property Plants & 3,45,00,000
Share Capital Equipment
(80 Lakhs shares of ₹ 1.5 each) 1,20,00,000
Total 6,87,75,000 Total 6,87,75,000
Particulars R Ltd. (₹) S Ltd. (₹) Combined Entity (₹)

Profit after Tax 86,50,000 49,72,000 1,21,85,000
Residual Net Cash Flows per year 90,10,000 54,87,000 1,85,00,000
Required return on equity 13.75% 13.05% 12.5%
You are required to compute the following:
(i) Minimum price per share S Ltd. should accept from R Ltd.
(ii) Maximum price per share R Ltd. shall be willing to offer to S Ltd.
(iii) Floor Value of per share of S Ltd., whether it shall play any role in decision for its acquisition by R Ltd.
QUESTION NO. 4G
AXE Ltd. is interested to acquire PB Ltd. AXE has 50,00,000 shares of ₹ 10 each, which are presently being
quoted at ₹ 25 per share. On the other hand PB has 20,00,000 share of ₹ 10 each currently selling at ₹
17. AXE and PB have EPS of ₹ 3.20 and ₹ 2.40 respectively.
(a) Show the impact of merger on EPS, in case if exchange ratio is based on relative proportion of EPS.
(b) Suppose, if AXE quote an offer of share exchange ratio of 1:1, then should PB accept the offer or
not, assuming that there will be no change in PE ratio of AXE after the merger.
(c) The maximum ratio likely to be acceptable to management of AXE.
QUESTION NO. 4H
K. Ltd. is considering acquiring N. Ltd., the following information is available :
Company Profit after Tax Number of Equity shares Market value per share
K. Ltd. 50,00,000 10,00,000 200.00
N. Ltd. 15,00,000 2,50,000 160.00
Exchange of equity shares for acquisition is based on current market value as above. There is no synergy
advantage available:
Find the earning per share for company K. Ltd. after merger.
Find the exchange ratio so that shareholders of N. Ltd. would not be at a loss.
4.11
LOS 6 : Calculation of % of Holding in New Company
𝐓𝐨𝐭𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐬𝐡𝐚𝐫𝐞𝐬 𝐨𝐟 𝐀 𝐋𝐭𝐝.

For A Ltd. =
𝐓𝐨𝐭𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐬𝐡𝐚𝐫𝐞 𝐨𝐟 𝐀 𝐋𝐭𝐝. 𝐓𝐨𝐭𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐒𝐡𝐚𝐫𝐞𝐬 𝐢𝐬𝐬𝐮𝐞𝐝 𝐭𝐨 𝐁 𝐋𝐭𝐝.
𝐓𝐨𝐭𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐒𝐡𝐚𝐫𝐞𝐬 𝐢𝐬𝐬𝐮𝐞𝐝 𝐭𝐨 𝐁 𝐋𝐭𝐝
For B Ltd. =
𝐓𝐨𝐭𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐬𝐡𝐚𝐫𝐞 𝐨𝐟 𝐀 𝐋𝐭𝐝. 𝐓𝐨𝐭𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐒𝐡𝐚𝐫𝐞𝐬 𝐢𝐬𝐬𝐮𝐞𝐝 𝐭𝐨 𝐁 𝐋𝐭𝐝.
Example:
A Ltd. B Ltd.
No. of Shares 200000 50000
E/R 0.50
Calculate % of holding of A Ltd. & B Ltd. after Merger.
Solution:
New No. of Equity shares issued to B Ltd. = 50,000 × 0.50  25,000 shares
Total No. of equity shares after Merger = 2,00,000 + 25,000 2,25,000 shares
𝟐,𝟎𝟎,𝟎𝟎𝟎
% of Holding A Ltd. in merged entity = × 100  88.89%
𝟐,𝟐𝟓,𝟎𝟎𝟎
𝟐𝟓,𝟎𝟎𝟎
% of Holding B Ltd. in merged entity = × 100  11.11%
𝟐,𝟐𝟓,𝟎𝟎𝟎
LOS 7 : Free Float Market Capitalization (Value)

 “Free Float” means shares which are freely available or freely tradable in the market. Shares held
by promoters are not freely tradable in the market. There shares are subject to certain restrictions
as placed by SEBI.
 A Firm’s market float is the total value of the shares that are actually available to the investing
public and excludes the value of shares held by controlling shareholders because they are unlikely
to sell their shares.
 Sensex and Nifty is based on Free-Float market Capitalization.
Free Float Mkt Capitalization = Free float No. of equity shares ×MPS
Total No. of Equity Shares

(-)
× MPS
Promotors Holding / Management
Holding / Govt. Holding / Strategic
Holding
Example:
Total number of equity shares of X Ltd. is 5 Lacs. Promoters’ holding is 20%. MPS is ₹ 25. Calculate
the Market Value and free float market value of X Ltd.
Solution:
Total Market Value = 5, 00,000 × 25 = 1,25,00,000
Total Free Float Market Value = 5, 00,000 × 80% × 25 = 1,00,00,000
QUESTION NO. 5
The following information relating to the acquiring Company A Ltd. and the target Company B Ltd.
are available. Both the Companies are promoted by Multinational Company, Trident Ltd.
The promoter's holding is 50% and 60% respectively in A Ltd. and B Ltd.:
4.12
A Ltd. B Ltd.
Share Capital (₹) 200 Lakhs 100 Lakhs
Free Reserves and Surplus (₹) 800 Lakhs 500 Lakhs
Paid up Value per share (₹) 100 10
Free Float Market Capitalization (₹) 400 Lakhs 128 Lakhs
P/E Ratio (times) 10 4
Trident Ltd. is interested to do justice to the shareholders of both the Companies. For the swap ratio
weights are assigned to different parameters by the Board of Directors as follows:
Book Value: 25%
EPS (Earning per share): 50%
Market Price: 25%
a) What is the swap ratio based on above weights?
b) What is the Book Value, EPS and expected Market price of A Ltd. after acquisition of B Ltd.
(assuming P/E. ratio of A Ltd. remains unchanged and all assets and liabilities of B Ltd. are taken
over at book value).
c) Calculate:
(i) Promoter's revised holding in the A Ltd.
(ii) Free float market capitalization,
(iii) Also calculate No. of Shares, Earning per Share (EPS) and Book Value (B.V.), if after acquisition
of B Ltd., A Ltd. decided to:
1. Issue Bonus shares in the ratio of 1:2; and
2. Split the stock (share) as ₹5 each fully paid
LOS 8 : Calculation of EPSA+B and MPSA+B in case of CASH TAKOVER
1. EPS A+B in case of cash take-over & cash is paid out of borrowed money
𝐄𝐀 𝐄𝐁 𝐒𝐲𝐧𝐞𝐫𝐠𝐲 𝐆𝐚𝐢𝐧 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 (𝟏 𝐭𝐚𝐱)

EPSA+B =
𝐍𝐀
2. EPS A+B in case of cash take-over & money is arranged from Business itself
𝐄𝐀 𝐄𝐁 𝐒𝐲𝐧𝐞𝐫𝐠𝐲 𝐆𝐚𝐢𝐧 𝐂𝐚𝐬𝐡 𝐏𝐚𝐢𝐝×𝐎𝐩𝐩𝐨𝐫𝐭𝐮𝐧𝐢𝐭𝐲 𝐜𝐨𝐬𝐭 𝐨𝐟 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭

EPSA+B =
𝐍𝐀
4.13
3. MPS A+B (If P/E ratio after merger is given)
= EPSA+B × P/EA+B
4. MPS A+B (If P/E ratio after merger is NOT given)
𝑴𝑽𝑨 𝑴𝑽𝑩 𝑺𝒚𝒏𝒆𝒓𝒈𝒚 𝑮𝒂𝒊𝒏 𝑪𝒂𝒔𝒉 𝑷𝒂𝒊𝒅

MPSA+B =
𝑵𝑨
QUESTION NO. 6A
The chief executive of a company thinks that shareholders always look for the earnings per share.
Therefore, he considers maximization of the earnings per share as his company's objective. His
company's current net profits are ₹ 80 lakh and EPS is ₹ 4. The current market price is ₹ 42. He wants
to buy another firm which has current income of ₹ 15.75 lacs, EPS of ₹ 10.50 and the market price
per share of ₹ 85.
a) What is the maximum exchange ratio which the chief executive should offer so that he could keep
EPS at the current level?
b) If the chief executive borrows funds at 15% rate of interest and buys out another company by
paying cash, how much should he offer to maintain his EPS? Assume Tax Rate to be 52%.
QUESTION NO. 6B
A Ltd. wanted to acquire B Ltd. The shares issued by the two companies are 10,00,000 and 5,00,000
respectively:
(i) Calculate the increase in the total value of B Ltd. resulting from the acquisition on the basis of the
following conditions:
Current Expected Growth Rate of B Ltd. 7%
Expected Growth Rate under control of A Ltd. 8%
(without any additional capital investment & without any change in risk of
operations)
Current Market Price Per Share of A Ltd. ₹100
Current Market Price Per Share of B Ltd. ₹20
Expected Dividend Price Per Share of B Ltd. ₹0.60
(ii) On the basis of aforesaid conditions calculate the gain or loss to shareholders of both the
companies, If A Ltd. was to offer one of its shares for every four shares of B Ltd.
(iii) Calculate the gain to the shareholders of both the companies, if A Ltd. pays ₹22 for each share of
B Ltd. assuming the P/E Ratio of A Ltd. does not change after the merger. EPS of A Ltd. is ₹8 and
that of B is ₹2.50. It is assumed that A Ltd. invests its cash to earn 10%.
QUESTION NO. 6C
The CEO of a company thinks that shareholders always look for EPS. Therefore he considers
maximization of EPS as his company's objective. His company's current Net Profits are ₹ 80.00 lakhs
and P/E multiple is 10.5. He wants to buy another firm which has current income of ₹ 15.75 lakhs
& P/E multiple of 10.
What is the maximum exchange ratio which the CEO should offer so that he could keep EPS at the
current level, given that the current market price of both the acquirer and the target company are ₹
42 and ₹ 105 respectively?
4.14
If the CEO borrows funds at 15% and buys out Target Company by paying cash, how much should
he offer to maintain his EPS? Assume tax rate of 30%.
LOS 9 : Purchase Price Premium

𝐎𝐟𝐟𝐞𝐫 𝐏𝐫𝐢𝐜𝐞 𝐭𝐨 𝐭𝐚𝐫𝐠𝐞𝐭 𝐂𝐨.– 𝐌𝐏𝐒 𝐨𝐟 𝐭𝐚𝐫𝐠𝐞𝐭 𝐂𝐨.𝐛𝐞𝐟𝐨𝐫𝐞 𝐌𝐞𝐫𝐠𝐞𝐫
Purchase Price Premium =
𝐌𝐏𝐒 𝐨𝐟 𝐭𝐚𝐫𝐠𝐞𝐭 𝐂𝐨.𝐛𝐞𝐟𝐨𝐫𝐞 𝐌𝐞𝐫𝐠𝐞𝐫
Example:
MPS of B Ltd. = ₹ 80
A Ltd. has offered ₹120 to B Ltd. for the purpose of exchange.
Calculate Purchase Price Premium?
–
Solution: Purchase Price Premium = × 100 = 50%
QUESTION NO. 7
Acquiring company is considering the acquisition of Target Company in a stock-for-stock transaction
in which Target Company would receive ₹ 85 for each share of its common stock. The Acquiring
Company does not expect any change in its price/earnings ratio multiple after the merger and
chooses to value the target company conservatively by assuming no earnings growth due to synergy.
Additional information:
Acquiring Target
Earnings ₹ 2,50,000 ₹ 72,500
Number of Shares 1,10,000 20,000
Market price per Share ₹ 52 ₹ 64
Calculate:
(i) The purchase price premium
(ii) The exchange ratio
(iii) The number of new shares issued by acquiring company.
(iv) Post-merger EPS of the combined firms
(v) Pre-merger EPS of the Acquiring Company
(vi) Pre-merger P/E ratio.
(vii) Post-merger share price
(viii) Post-merger equity ownership distribution
LOS 10 : Purchase Consideration / Cost of Acquisition
 PC = Net Payment made by Acquiring Co. to Target Co.
Calculation of PC/ COA

Market Value of Equity Shares Issued by A Ltd. to B Ltd. XXX
(+) Debentures, Preference shares Capital Issued by A Ltd. to B Ltd. XXX
(+) Current Liability paid or Taken over XXX
(+) Any other expenses incurred XXX
(-) Cash in hand or Bank XXX
(-) Sale of any other asset not required in business XXX
Cost of Acquisition / Purchase Consideration XXX
Note:
 Cash and current Liabilities must be taken, even if question is Silent.
 Sale of any other asset not required should be taken only if clear indication in the Question.
4.15
QUESTION NO. 8A
A Ltd. is investigating the merger of B Ltd. Balance Sheet of B Ltd. is given below:
10% Cumulative Preference Capital 100
Ordinary Share Capital (30 Crore shares at ₹ 10 per share) 300
Reserves and Surplus 150
14% Debentures 80
Current Liabilities 100
Total 730
Net Fixed Assets 275
Investments 50
Current Assets
Stock 190
Book Debts 150
Cash and Bank Balance 65
Total 730
A Ltd. proposed to offer the following to B Ltd.:
a) 10% convertible preference shares of ₹100 Crore in A Ltd. for paying 10% cumulative preference
capital of B Ltd.;
b) 12% convertible debentures of ₹ 84 Crore in A Ltd. to redeem 14% debentures of B Ltd.;
c) One ordinary share of A Ltd. for every three shares held by B Ltd's shareholders, the market
price per share being ₹ 42 for A Ltd's shares and ₹ 20 for B Ltd's shares.
After acquisition, A Ltd. is expected to dispose of B Ltd's stock (inventory) for ₹ 150 Crore, book debts
for ₹ 102 Crore and investments for ₹ 55 Crore. It would pay entire current liabilities,
(i) What is the cost of acquisition to A Ltd?
(ii) If A Ltd's required rate of return is 20% how much should be the annual after-tax cash flows
from B Ltd's acquisition to justify merger assuming a time horizon of eight years and a zero
salvage value?
(iii) Would your answer change if there is a salvage value of ₹30 Crore after 8 years?
QUESTION NO. 8B
M/s Tiger Ltd. wants to acquire M/s Leopard Ltd. The balance sheet of Leopard Ltd. as on 31st March,
2012 is as follows:
Liabilities ₹ Assets ₹
Equity Capital 7,00,000 Cash 50,000
(70000 Shares)
Retained Earnings 3,00,000 Debtors 70,000
12% Debentures 3,00,000 Inventories 2,00,000
Creditors and Other liabilities 3,20,000 Plant & Equipment 13,00,000
16,20,000 16,20,000
1. Shareholders of Leopard Ltd will get one share in Tiger Ltd. for every two shares. External liabilities
are expected to be settled at ₹ 5,00,000. Shares of Tiger Ltd would be issued at its current price
of ₹ 15 per share. Debentures will get 13% convertible debentures in the purchasing Company
for the same amount. Debtors and inventories are expected to realize ₹ 2,00,000.
2. Tiger Ltd. has decided to operate the business of Leopard Ltd. as a separate division. The division
is likely to give cash flows (after tax) to the extent of ₹5,00,000 per year for 6 years. Tiger Ltd has
planned that after 6 years, this division would be demerged and disposed of for ₹ 2, 00,000.
3. The Company’s cost of capital is 16 %
4.16
Make a report to the Board of the Company advising them about the financial feasibility of this
acquisition.
Net Present Values for 16 % for Re. 1 are as follows:
Years 1 2 3 4 5 6
PV 0.862 0.743 0.641 0.552 0.476 0.410
LOS 11: Calculation of Net Consideration Payable

QUESTION NO. 9
A Ltd and B Ltd. are in the same industry. The former is in the negotiation for acquisition of the
later. Important information about the two companies as per their latest financial statements is given
below:
A Ltd. B Ltd.
₹ 10 equity shares outstanding 12 Lakhs 6 Lakhs
Debt: 10%debentures ₹ lacs 580 —
12.5%Institutional Loan ₹ Lacs — 240
EBIDT* ₹ Lacs 400.86 115.71
Market price/share (₹) 220 110
* Earning Before Interest, Depreciation and tax.
A Ltd is planning to offer a price for B Ltd., business as a whole which will be 7 times EBIDT reduced
by the outstanding debt, to be discharged by own shares at market price.
B Ltd. is planning to seek one share in A Ltd for every two shares in B Ltd. based on the market price.
Tax rate for the two companies may be assumed as 30%.
Calculate and show the following under both alternatives- A Ltd offer and B Ltd's plan:
(i) Net consideration payable.
(ii) No. of shares to be issued by A Ltd
(iii) EPS of A Ltd after acquisition
(iv) Expected market price per share of A Ltd after acquisition Assume PE Ratio of A Ltd. After Merger
is same.
(v) State briefly the advantages to A Ltd from the acquisition.
Calculations (except EPS) may be rounded off to two decimal places in Lacs
LOS 12 : Evaluation when Acquiring Company acquire more than one Company
QUESTION NO. 10
Following data is available in respect of Good Ltd., Better Ltd. and Best Ltd. In order to diversify and
expand operations. Best Ltd. is on a look out for smaller companies. It has shortlisted Good Ltd. &
Better Ltd. Swap Ratio to be offered is to be determined on the basis of PE ratio.
Best Ltd. Better Ltd. Good Ltd.
No. of Equity Shares 90000 36000 18000
Earnings per Share ₹2 ₹1 ₹2
PE ratio 30 37 23
Find out the EPS of Best Ltd. after merger with Better Ltd., Good Ltd., and both. Which one would you
suggest, Best Ltd. should go for?
4.17
LOS 13 : Components of MPS
QUESTION NO. 11A

Following are the financial statement for A Ltd. and B Ltd. for the current financial year. Both the
company operate in the same industry:
Balance Sheet
Particulars A Ltd. B Ltd.
Total Current Assets 14,00,000 10,00,000
Total Fixed Assets (net) 10,00,000 5,00,000
Total 24,00,000 15,00,000
Equity Capital (of ₹ 10 each) 10,00,000 8,00,000
Retained Earnings 2,00,000 —
4% Long-term Debt 5,00,000 3,00,000
Total Current Liabilities 7,00,000 4,00,000
Total 24,00,000 15,00,000
INCOME STATEMENT
Net sales 34,50,000 17,00,000
Less : Cost of Goods Sold 27,60,000 13,60,000
Gross Profit 6,90,000 3,40,000
Operating Expenses 2,00,000 1,00,000
Interest 70,000 42,000
Earnings Before Taxes 4,20,000 1,98,000
Taxes (50%) 2,10,000 99,000
Earnings after taxes (EAT) 2,10,000 99,000
Number of Equity Shares 100000 80000
Dividend Payment Ratio (D/P) 40% 60%
Market Price Per Share (MPS) ₹ 40 ₹ 15
Assume that the two firms are in the process of negotiating a merger through an exchange of equity
shares. You have been asked to assist in establishing equitable exchange terms, and are required to-
4.18
(i) Decompose share prices of both companies into EPS & P/E components, & also segregate their
EPS figures into return on equity (ROE) & book value/intrinsic value per share (BVPS) components.
(ii) Estimate future EPS growth rates for each firm.
(iii) Based on expected operating synergies A Ltd. estimates that the intrinsic value of B's equity share
would be ₹ 20 per share on its acquisition .Assume A Ltd. Intrinsic Value to be equal to its Market
Price. You are required to develop a range of justifiable equity share exchange ratio based on
Intrinsic Value and MPS that can be offered by A Ltd. to B Ltd's shareholders. Based on your
analysis in parts (i) and (ii) would you expect the negotiated terms to be closer to the upper, or
the lower exchange ratio limits? Why?
(iv) Calculate the post-merger EPS based on an exchange ratio of 0.4:1 being offered by A Ltd.
Indicate the immediate EPS accretion or dilution, if any, that will occur for each group of
shareholders.
(v) Based on a 0.4:1 exchange ratio, and assuming that A's pre-merger P/E ratio will continue after
the merger estimate the post-merger market price. Show the resulting accretion or dilution in pre-
merger market price.
QUESTION NO. 11B
R Ltd. and S Ltd. are companies that operate in the same industry. The financial statements of both
the companies for the current financial year are as follows:
Balance Sheet
Particulars R. Ltd. (₹ ) S. Ltd (₹ )
Equity & Liabilities
Shareholders Fund
Equity Capital (₹ 10 each) 20,00,000 16,00,000
Retained earnings 4,00,000 -
Non-current Liabilities
16% Long term Debt 10,00,000 6,00,000
Current Liabilities 14,00,000 8,00,000
Total 48,00,000 30,00,000
Assets
Non-current Assets 20,00,000 10,00,000
Current Assets 28,00,000 20,00,000
Total 48,00,000 30,00,000
Income Statement
Particulars R. Ltd. (₹ ) S. Ltd. (₹ )
A. Net Sales 69,00,000 34,00,000
B. Cost of Goods sold 55,20,000 27,20,000
C. Gross Profit (A-B) 13,80,000 6,80,00
D. Operating Expenses 4,00,000 2,00,000
E. Interest 1,60,000 96,000
F. Earnings before taxes [C-(D+E)] 8,20,000 3,84,000
G. Taxes @ 35% 2,87,000 1,34,400
H. Earnings After Tax (EAT) 5,33,000 2,49,600
No. of equity shares 2,00,000 1,60,000
Dividend payment Ratio (D/P) 20% 30%
4.19
Assume that both companies are in the process of negotiating a merger through exchange of Equity
shares:
(i) Decompose the share price of both the companies into EPS & P/E components. Also segregate
their EPS figures into Return On Equity (ROE) and Book Value/Intrinsic Value per share
components.
(ii) Estimate future EPS growth rates for both the companies.
(iii) Based on expected operating synergies, R Ltd. estimated that the intrinsic value of S Ltd. Equity
share would be ₹ 25 per share on its acquisition. You are required to develop a range of
justifiable Equity Share Exchange ratios that can be offered by R Ltd. to the shareholders of S Ltd.
Based on your analysis on parts (i) and (ii), would you expect the negotiated terms to be closer
to the upper or the lower exchange ratio limits and why?
LOS 14 : Maximum MPS & Minimum MPS
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 𝐨𝐟 𝐁 𝐋𝐭𝐝.

Minimum MPS offered by A Ltd. To B Ltd. =
𝐍𝐨. 𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 𝐒𝐡𝐚𝐫𝐞𝐬 𝐨𝐟 𝐁 𝐋𝐭𝐝.
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 𝐨𝐟 𝐁 𝐋𝐭𝐝. 𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐒𝐲𝐧𝐞𝐫𝐠𝐲

Maximum MPS offered by A Ltd. To B Ltd. =
𝐍𝐨. 𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 𝐒𝐡𝐚𝐫𝐞𝐬 𝐨𝐟 𝐁 𝐋𝐭𝐝.
QUESTION NO. 12A

In 2000 A Ltd. acquired B Ltd. after a hotly contested takeover for approximately $ 110 per share.
The free cash flows of the two firms—before and after merger - were projected as follows:
Free Cash flow ($ millions)
Year/firm 1 2 3 4 5 Terminal value *
A Ltd. 4684 4918 5164 5422 5693 82756
B ld. 471 509 550 594 641 8102
Combined 5195 5558 5948 6364 6809 97672
(Post-Merger)
* Terminal value as at the end of the 5th year.
Cost of equity and debt of the individual firms and the combined firm (after merger) were estimated
as given under:
A Ltd. B Ltd. Combined
Cost of equity 14.23% 15.33% 14.34%
Cost of debt 5.40% 6.00% 5.42%
Debt/ (Debt +Equity) 21% 9% 20%
At the time of merger deal B Ltd. had 70.6 million outstanding shares and $537 million worth of
outstanding debt.
a) Calculate the value of A Ltd. & B Ltd. before Merger? Also Calculate the value of Synergy?
b) What is the Minimum price per share A Ltd. could have offered to B Ltd.?
c) What is the Maximum price per share A Ltd. could have offered to B Ltd.?
d) Do you think that the price of $ 110 paid by A Ltd. was justifiable?
QUESTION NO. 12B
The equity shares of XYZ Ltd. are currently being traded at ₹ 24 per share in the market. XYZ Ltd. has
total 10,00,000 equity shares outstanding in number; and promoters' equity holding in the company
is 40%.
4.20
PQR Ltd. wishes to acquire XYZ Ltd. because of likely synergies. The estimated present value of these
synergies is ₹ 80,00,000.
Further PQR feels that management of XYZ Ltd. has been over paid. With better motivation, lower
salaries and fewer perks for the top management, will lead to savings of ₹ 4,00,000 p.a. Top
management with their families are promoters of XYZ Ltd. Present value of these savings would add
₹ 30,00,000 in value to the acquisition.
Following additional information is available regarding PQR Ltd.:
Earnings per share: ₹4
Total number of equity shares outstanding: 15,00,000
Market price of equity share: ₹ 40
Required:
(i) What is the maximum price per equity share which PQR Ltd. can offer to pay for XYZ Ltd.?
(ii) What is the minimum price per equity share at which the management of XYZ Ltd. will be willing
to offer their controlling interest?
LOS 15 : Valuation + Merger

QUESTION NO. 13A
H Ltd. agrees to buy over the business of B Ltd. effective 1st April, 2012.The summarized Balance
Sheets of H Ltd. and B Ltd. as on 31st March 2012 are as follows:
Balance sheet as at 31st March, 2012 (In Crores of Rupees)
Liabilities: H Ltd. B Ltd.
Paid up Share Capital
Equity Shares of ₹ 100 each 350.00 —
Equity Shares of ₹ 10 each — 6.50
Reserve & Surplus 950.00 25.00
Total 1,300.00 31.50
Assets:
Net Fixed Assets 220.00 0.50
Net Current Assets 1020.00 29.00
Deferred Tax Assets 60.00 2.00
Total 1,300.00 31.50
H Ltd. proposes to buy out B Ltd. and the following information is provided to you as part of the
scheme of buying:
(i) The weighted average post tax maintainable profits of H Ltd. and B Ltd. for the last 4 years are ₹
300 Crores and ₹ 10 Crores respectively.
(ii) Both the companies envisage a capitalization rate of 8%.
(iii) H Ltd. has a contingent liability of ₹ 300 Crores as on 31st March, 2012.
(iv) H Ltd. to issue shares of ₹100 each to the shareholders of B Ltd. in terms of the
exchange ratio as arrived on a Fair Value basis. (Please consider weights of 1 and 3 for the value
of shares arrived on Net Asset basis and Earnings capitalization method respectively for both H
Ltd. and B Ltd.)
You are required to arrive at the value of the shares of both H Ltd. and B Ltd. under:
a) Net Asset Value Method
b) Earnings Capitalization Method
Exchange ratio of shares of H Ltd. to be issued to the shareholders of B Ltd. on a Fair value basis
(taking into consideration the assumption mentioned in point 4 above.)
4.21
QUESTION NO. 13B

Yes Ltd. wants to acquire No Ltd. and the cash flows of Yes Ltd. and the merged entity are given
below:
(₹ In lacs)
Year 1 2 3 4 5
Yes Ltd. 175 200 320 340 350
Merged Entity 400 450 525 590 620
Earnings would have witnessed 5% constant growth rate without merger and 6% with merger on
account of economies of operations after 5 years in each case. The cost of capital is 15%.
The number of shares outstanding in both the companies before the merger is the same
and the companies agree to an exchange ratio of 0.5 shares of Yes Ltd. for each share of
No Ltd.
PV factor at 15% for years 1-5 are 0.870, 0.756; 0.658, 0.572, 0.497 respectively. You are required
to:
(i) Compute the Value of Yes Ltd. before and after merger.
(ii) Value of Acquisition and
(iii) Gain to shareholders of Yes Ltd.
LOS 16 : Calculation of Bonus Ratio

QUESTION NO. 14
Trupti Co. Ltd. promoted by a Multinational group “ INTERNATIONAL INC” is listed on stock exchange
holding 84 % i.e. 63 Lakhs shares.
Profit after Tax is ₹ 4.80 Crores
Free Float Market Capitalization is ₹ 19.20 Crores
As per the SEBI guidelines promoters have to restrict their holding to 75 % to avoid delisting from the
stock exchange. Board of Directors has decided not to delist the share but to comply with the SEBI
guidelines by issuing Bonus shares to minority shareholders while maintaining the same P/E ratio.
Calculate:
a) P/E ratio
b) Bonus Ratio
c) Market price of share before and after the issue of bonus shares.
d) Free Float Market Capitalization of the Company after the bonus shares.
LOS 17 : Calculation of EPS A+B when Synergy Gain is Given in Question
1. EPSA+B when Synergy Gain is Expressed in %
(𝐄𝐀 𝐄𝐁 ) ( 𝟏 𝐒𝐲𝐧𝐞𝐫𝐠𝐲 𝐆𝐚𝐢𝐧)

ESPA+B =
4.22
2. EPSA+B when Synergy Gain is Expressed in Absolute Amount
ESPA+B =
Note:
If question is silent regarding Synergy Gain, assume it to be NIL.
Synergy Gain – In terms of Earnings & Market Value
Synergy means extra – benefit/ advantage.
1. Synergy In terms of Earnings
Synergy = E A+B – (E A + E B)
2. Synergy In terms of Market Value
Synergy = MV A+B – (MV A + MV B)
LOS 18 : True Cost & True Benefit of Merger

Case 1: When Merger is Financed by Case 2: When Merger is Financed by Stock
Cash
For Acquiring company (A Ltd.) For Acquiring company (A Ltd.)
Cost to A Ltd. Cost to A Ltd.
= Cash paid to B Ltd. – MVB Ltd received = MVA+B × % Holding of B Ltd. – MVB Ltd. received
Benefit of Merger (Synergy Gain) Benefit of Merger (Synergy Gain)
= MVA+B – (MVA Ltd. + MVB Ltd.) = MVA+B – (MVA Ltd. + MVB Ltd.)
Net Benefit (NPV) = Benefit – Cost Net Benefit (NPV) = Benefit – Cost
For Target Company (B Ltd.) For Target Company (B Ltd.)
Benefit (Net Benefit) Benefit (Net Benefit)
= Cash Received – MVB Ltd. sacrificed = MVA+B × % Holding of B Ltd.– MVB Ltd. sacrificed
Note:
Cost of A Ltd. = Benefit for B Ltd.
QUESTION NO. 15A
Firm A is planning to acquire Firm B. The relevant financial details of the two firms prior to merger
announcement are as follows:
Firm A Firm B
Market price per share (₹) 75 30
Number of Shares 1000000 500000
Market value of the firm (₹) 750,00,000 150,00,000
The merger is expected to bring gains which have present value of ₹ 1.50 crores. Firm A offers
2,50,000 shares in exchange for 5 lacs shares to the shareholders of firm B.
You are required to calculate:
(i) True cost of firm A for acquiring firm B; and
(ii) Net present value (or net benefit) of the merger to Firm A and Firm B.
4.23
QUESTION NO. 15B

Elrond Limited plans to acquire Doom Limited. The relevant financial details of the two firms prior to
the merger announcement are:
Elrond Limited Doom Limited
Number of outstanding shares 20 lakhs 10 Lakhs
The merger is expected to generate gains, which have a present value of ₹ 200 lakhs. The exchange
ratio agreed to is 0.5.
What is the true cost of the merger from the point of view of Elrond Limited?
QUESTION NO. 15C
Given is the following information:
Day Ltd. Night Ltd.
Net Earnings ₹ 5 crores ₹ 3.5 crores
No. of Equity Shares 10,00,000 7,00,000
The shares of Day Ltd. and Night Ltd. trade at 20 and 15 times their respective P/E ratios.
Day Ltd. considers taking over Night Ltd. By paying ₹ 55 crores considering that the market price of
Night Ltd. reflects its true value. It is considering both the following options:
I. Takeover is funded entirely in cash.
II. Takeover is funded entirely in stock.
You are required to calculate the cost of the takeover and advise Day Ltd. on the best alternative.
LOS 19 : Expected value of Equity and Debt.

QUESTION NO. 16
Simple Ltd. and Dimple Ltd. are planning to merge. The total value of the companies are dependent
on the fluctuating business conditions. The following information is given for the total value (debt +
equity) structure of each of the two companies.
Business Condition Probability Simple Ltd. ₹ Lakhs Dimple Ltd. ₹ Lakhs
High Growth 0.20 820 1050
Medium Growth 0.60 550 825
Slow Growth 0.20 410 590
The current debt of Dimple Ltd. is ₹ 65 lacs and of Simple Ltd. is ₹ 460 lacs. Calculate the expected
value of debt and equity separately for the merged entity.
LOS 20 : Financial Restructuring/ Internal Re-Construction

 Financial restructuring refers to a kind of internal changes made by the management in Assets
and Liabilities of a company with the consent of its various stakeholders This is a suitable mode
of restructuring for corporate entities who have suffered from sizeable losses over a period of
time. Consequent upon losses the share capital or net worth of such companies get substantially
eroded. In fact, in some cases, the accumulated losses are even more than the share capital and
thus leading to negative net worth, putting the firm on the verge of liquidation.
 In order to revive such firms, financial restructuring is one of the techniques to bring into health
such firms who are having potential and promise for better financial performance in the years to
come. To achieve this desired objective, such firms need to re-start with a fresh balance sheet free
from losses and fictitious assets and show share capital at its real true worth.
 Impact of Financial Restructuring
1. Benefits to XYZ Ltd.
4.24
a) Reduction in Liabilities
b) Revaluation of Assets
Total Benefits
2. Amount of Benefit will be utilized to Written Off Fictitious Assets, Profit & Loss Dr. Bal., Provision
for Doubtful Debts and over-valued Assets.
QUESTION NO. 17
The following is the Balance-sheet of XYZ Company Ltd as on March 31st, 2006. (₹ in lacs)
6 lacs equity shares of ₹100/- each 600 Land & Building 200
2 lacs 14% Preference shares of ₹ 100/- each 200 Plant & Machinery 300
13% Debentures 200 Furniture & Fixtures 50
Debenture Interest accrued and Payable 26 Inventory 150
Loan from Bank 74 Sundry debtors 70
Trade Creditors 300 Cash at Bank 130
Preliminary Expenses 10
Cost of Issue of debentures 5
Profit & Loss A/c 485
Total 1400 1400
The XYZ Company did not perform well and has suffered sizable losses during the last few
years. However, it is now felt that the company can be nursed back to health by proper
financial restructuring and consequently the following scheme of reconstruction has been
devised:
a) Equity shares are to be reduced to ₹25/- per share, fully paid up;
b) Preference shares are to be reduced (with coupon rate of 10%) to equal number of shares of ₹50
each fully paid up.
c) Debenture holders have agreed to forego interest accrued to them. Beside this, they have agreed
to accept new debentures carrying a coupon rate of 9%.
d) Trade creditors have agreed to forgo 25 per cent of their existing claim; for the balance sum they
have agreed to convert their claims into equity shares of ₹25/- each.
e) In order to make payment for bank loan and augment the working capital, the company issues 6
lakh equity shares at ₹25/- each; the entire sum is required to be paid on application. The existing
shareholders have agreed to subscribe to the new issue.
f) While Land and Building is to be revalued at ₹250 lacs, Plant & Machinery is to be written down
to ₹104 lacs. A provision amounting to ₹5 lacs is to be made for bad and doubtful debts.
You are required to show the impact of financial restructuring/re-construction. Also, prepare the new
balance sheet assuming the scheme of re-construction is implemented in letter and spirit.
LOS 21 : Demerger
 A Corporate strategy to sell-off subsidiaries or divisions of a company. The act of splitting off a
part of an existing company to become a new company, which operates completely separate from
the original company.
 Shareholders of the original company are usually given an equivalent stake of ownership in the
new company.
 A demerger is often done to help each of the segments operate more smoothly, as they can now
focus on a more specific task.
4.25
QUESTION NO. 18
The following information is relating to Fortune India Ltd. having two division, viz. Pharma Division
and Fast Moving Consumer Goods Division (FMCG Division). Paid up share capital of Fortune India
Ltd. is consisting of 3,000 Lacs equity shares of Re. 1 each. Fortune India Ltd. decided to de merge
Pharma Division as Fortune Pharma Ltd. w.e.f. 1.4.2005. Details of Fortune India Ltd. as on
31.3.2005 and of Fortune Pharma Ltd. as on 1.4.2005 are given below:
Particulars Fortune Pharma Ltd. Fortune India Ltd.
(₹ in Lakhs) (₹ in Lakhs)
Outside Liabilities
Secured Loans 400 3,000
Unsecured Loans 2,400 800
Current Liabilities & Provisions 1,300 21,200
Assets
Fixed Assets 7,740 20,400
Investments 7,600 12,300
Current Assets 8,800 30,200
Loans & Advances 900 7,300
Deferred Tax 60 —
Miscellaneous Expenses Outstanding — (200)
Board of Directors of the Company has decided to issue necessary equity shares of Fortune Pharma
Ltd. of Re. 1 each, without any consideration to the shareholders of Fortune India Ltd. For that
purposes following points are to be considered
1. Transfer of Liabilities & Assets at Book value.
2. Estimated Profit for the year 2005-06 is ₹ 11,400 Lakh for Fortune India Ltd. &₹ 1,470 lacs for
Fortune Pharma Ltd.
3. Estimated Market Price of Fortune Pharma Ltd. is ₹ 24.50 per share.
4. Average P/E Ratio of FMCG sector is 42 &Pharma sector is 25, which is to be expected for both
the companies.
Calculate:
a) The Ratio in which shares of Fortune Pharma are to be issued to the shareholders of Fortune India
Ltd.
b) Expected Market price of Fortune India Ltd.
c) Book Value per share of both the Companies immediately after Demerger.
LOS 22 : Banking Merger & Acquisition

QUESTION NO. 19
Bank 'R' was established in 2005 and doing banking in India. The bank is facing DO OR DIE situation.
There are problems of Gross NPA (Non-Performing Assets) at 40% & CAR/CRAR (Capital Adequacy
Ratio/ Capital Risk Weight Asset Ratio) at 4%. The net worth of the bank is not good. Shares are not
traded regularly. Last week, it was traded @₹ 8 per share.
RBI Audit suggested that bank has either to liquidate or to merge with other bank.
Bank 'P' is professionally managed bank with low gross NPA of 5%.It has Net NPA as 0% and CAR at
16%. Its share is quoted in the market @ ₹128 per share. The board of directors of bank 'P' has
submitted a proposal to RBI for takeover of bank 'R' on the basis of share exchange ratio.
The Balance Sheet details of both the banks are as follows:
4.26
Bank ‘R’ Bank ‘P’

Amt. in ₹ lakhs Amt. in ₹ lakhs
Paid up share capital(₹10) 140 500
Reserves & Surplus 70 5,500
Deposits 4,000 40,000
Other liabilities 890 2,500
Total Liabilities 5,100 48,500
Cash in hand & with RBI 400 2,500
Balance with other banks — 2,000
Advances 3,500 27,000
Other Assets 100 2,000
Total Assets 5,100 48,500
It was decided to issue shares at Book Value of Bank 'P' to the shareholders of Bank 'R'.
All assets and liabilities are to be taken over at Book Value.
For the swap ratio, weights assigned to different parameters are as follows:
Gross NPA 30%
CAR 20%
Market price 40%
Book value 10%
a) What is the swap ratio based on above weights?
b) How many shares are to be issued?
c) Prepare Balance Sheet after merger.
d) Calculate CAR & Gross NPA % of Bank 'P' after merger.
4.27
PRACTICE QUESTIONS
QUESTION NO. 20
The following is the Balance-sheet of Grape Fruit Company Ltd as on March 31st 2011.
Liabilities Assets (₹ in lacs)
6 lacs equity shares of ₹100/- each 600 Land & Building 200
2 lacs 14% Preference shares of 200 Plant & Machinery 300
₹100/- each
13% Debentures 200 Furnitures & Fixtures 50
Debenture Interest accrued and 26 Inventory 150
Payable
Loan from Bank 74 Sundry debtors 70
Trade Creditors 340 Cash at Bank 130
Preliminary Expenses 10
Cost of Issue of debentures 5
Profit & Loss A/c 525
1440 1440
The Company did not perform well and has suffered sizable losses during the last few years. However,
it is now felt that the company can be nursed back to health by proper financial restructuring and
consequently the following scheme of reconstruction has been devised:
(i) Equity shares are to be reduced to ₹ 25/- per share, fully paid up;
(ii) Preference shares are to be reduced (with coupon rate of 10%) to equal number of shares of ₹50
each fully paid up.
(iii) Debenture holders have agreed to forego interest accrued to them. Beside this, they have agreed
to accept new debentures carrying a coupon rate of 9%.
(iv) Trade creditors have agreed to forgo 25 per cent of the amount due to them.
(v) The company issues 6 lac of equity shares at ₹25/- each and the entire sum was to be paid on
application. The existing shareholders have agreed to subscribe to the new issue.
(vi) While Land and Building is to be revalued at ₹450 lacs, Plant & Machinery is to be written down
to ₹120 lacs. A provision amounting to ₹15 lacs is to be made for bad and doubtful debts.
You are required to
a) Show the impact of financial restructuring/re-construction
b) Prepare the fresh balance sheet after the reconstructions is completed on the basis of the above
proposals.
QUESTION NO. 21
During the audit of the Weak Bank (W), RBI has suggested that the Bank should either merge with
another bank or may close down. Strong Bank (S) has submitted a proposal of merger of Weak Bank
with itself. The relevant information and Balance Sheets of both the companies are as under:
Particulars Weak Bank Strong Assigned
(W) Bank (S) Weights (%)
Gross NPA (%) 40 5 30
Capital Adequacy Ratio (CAR) Total Capital/ 5 16 28
Risk Weight Asset
Market price per Share (MPS) 12 96 32
Book value 10
Trading on Stock Exchange Irregular Frequent
4.28
Balance Sheet (₹ in Lakhs)

Particulars Weak Bank (W) Strong Bank (S)
Paid up Share Capital (₹ 10 per share) 150 500
Reserves & Surplus 80 5,500
Deposits 4,000 44,000
Other Liabilities 890 2,500
Cash in Hand & with RBI 400 2,500
Balance with Other Banks - 2,000
Advances 3,500 27,000
Preliminary Expenses 50 -
You are required to
(a) Calculate Swap ratio based on the above weights:
(b) Ascertain the number of Shares to be issued to Weak Bank;
(c) Prepare Balance Sheet after merger; and
(d) Calculate CAR and Gross NPA of Strong Bank after merger.
QUESTION NO. 22
The following information is provided relating to the acquiring company E. Ltd. and the target
company
H Ltd.
Particulars E. ltd. (₹) H Ltd. (₹)
Number of shares (Face value ₹10 each) 20 Lakhs 15 Lakhs
Market Capitalization 1000 Lakhs 1500 Lakhs
P/E Ratio (times) 10.00 5.00
Reserves and surplus in ₹ 600.00 Lakhs 330.00 Lakhs
Promoter's Holding (No. of shares) 9.50 Lakhs 10.00 Lakhs
The Board of Directors of both the companies have decided to give a fair deal to the shareholders.
Accordingly, the weights are decided as 40%, 25% and 35% respectively for earnings, book value and
market price of share of each company for swap ratio.
Calculate the following :
(i) Market price per share, earnings per share and Book Value per share :
(ii) Swap ratio
(iii) Promoter's holding percentage after acquisition ;
(iv) EPS of E Ltd. after acquisitions of H Ltd.
(v) Expected market price per share and market capitalization of E Ltd.; after acquisition, assuming
P/E ratio of E Ltd. remains unchanged; and
(vi) Free float market capitalization of the merged firm.
QUESTION NO. 23
Personal Computer Division of Distress Ltd., a computer hardware manufacturing company has started
facing financial difficulties for the last 2 to 3 years. The management of the division headed by Mr. Smith
is interested in a buyout on 1 April 2013. However, to make this buy-out successful there is an urgent
need to attract substantial funds from venture capitalists.
4.29
Ven Cap, a European venture capitalist firm has shown its interest to finance the proposed buy-out.
Distress Ltd. is interested to sell the division for ₹ 180 crore and Mr. Smith is of opinion that an additional
amount of ₹ 85 crore shall be required to make this division viable. The expected financing pattern shall
be as follows:
Source Mode Amount (₹
Crore)
Management Equity Shares of ₹ 10 each 60.00
VenCap VC Equity Shares of ₹ 10 each 22.50
9% Debentures with attached warrant of ₹ 100 each 22.50
8% Loan 160.00
Total 265.00
The warrants can be exercised any time after 4 years from now for 10 equity shares @ ₹ 120 per
share.
The loan is repayable in one go at the end of 8th year. The debentures are repayable in equal annual
installment consisting of both principal and interest amount over a period of 6 years.
Mr. Smith is of view that the proposed dividend shall not be kept more than 12.5% of distributable
profit for the first 4 years. The forecasted EBIT after the proposed buyout is as follows:
Year 2013-14 2014-15 2015-16 2016-17
EBIT (₹ crore) 48 57 68 82
Applicable tax rate is 35% and it is expected that it shall remain unchanged at least for 5-6 years. In
order to attract VenCap, Mr. Smith stated that book value of equity shall increase by 20% during above
4 years. Although, VenCap has shown their interest in investment but are doubtful about the projections
of growth in the value as per projections of Mr. Smith. Further VenCap also demanded that warrants
should be convertible in 18 shares instead of 10 as proposed by Mr. Smith.
You are required to determine whether or not the book value of equity is expected to grow by 20% per
year. Further if you have been appointed by Mr. Smith as advisor then whether you would suggest to
accept the demand of VenCap of 18 shares instead of 10 or not.
QUESTION NO. 24
The Nishan Ltd. has 35,000 shares of equity stock outstanding with a book value of ₹20 per share. It
owes debt ₹ 15,00,000 at an interest rate of 12%. Selected financial results are as follows.
Income and Cash Flow Capital
EBIT ₹ 80,000 Debt ₹ 1,500,000
Interest 1,80,000 Equity 7,00,000
EBT (₹ 1,00,000) ₹ 2,200,000
Tax 0
EAT (₹ 1,00,000)
Depreciation ₹ 50,000
Principal repayment (₹ 75,000)
Cash Flow (₹ 1,25,000)
Restructure the financial line items shown assuming a composition in which creditors agree to convert
two thirds of their debt into equity at book value. Assume Nishan will pay tax at a rate of 15% on income
after the restructuring, and that principal repayments are reduced proportionately with debt. Who will
control the company and by how big a margin after the restructuring?
QUESTION NO. 25
Tatu Ltd. wants to takeover Mantu Ltd. and has offered a swap ratio of 1:2 (0.5 shares for everyone
share of Mantu Ltd.). Following information is provided
4.30
Tatu Ltd. Mantu Ltd.

Profit after tax ₹ 24,00,000 ₹ 4,80,000
Equity shares outstanding (Nos.) 8,00,000 2,40,000
EPS ₹3 ₹2
PE Ratio 10 times 7 times
Market price per share ₹30 ₹ 14
(i) The number of equity shares to be issued by Tatu Ltd. for acquisition of Mantu Ltd.
(ii) What is the EPS of Tatu Ltd. after the acquisition?
(iii) Determine the equivalent earnings per share of Mantu Ltd.
(iv) What is the expected market price per share of Tatu Ltd. after the acquisition, assuming its PE
multiple remains unchanged? Determine the market value of the merged firm.
QUESTION NO. 26
XML bank was established in 2001 and doing banking business in India. The bank is facing very critical
situation. There are problems of Gross NPA (Non-Performing Assets) at 40% & CAR/CRAR (Capital
Adequacy Ratio/Capital. Risk Weight Asset Ratio) at 2%. The net worth of the bank is not good. Shares
are not traded regularly. Last week, it was traded @ ₹ 4 per share.
RBI Audit suggested that bank has either to liquidate or to merge with other bank.
ZML Bank is professionally managed bank with low gross NPA of 5%. I t has net NPA as 0% and CAR at
16%. Its share is quoted in the market @ ₹ 64 per share. The Board of Directors of ZML Bank has
submitted a proposal to RBI for takeover of bank XML on the basis of share exchange ratio.
The Balance Sheet details of both the banks are as follows:
PARTICULARS XML Bank (₹) (Amount ZML Bank (₹)
in Crores) (Amount in Crores)
Liabilities
Paid up share capital (₹ 10) 70 250
Reserve and Surplus 35 2,750
Deposits 2,000 20,000
Other Liabilities 445 1,250
Assets
Cash in hand and with RBI 200 1,250
Balance with other banks 0 1,000
Investments 550 7,500
Advances 1,750 13,500
It was decided to issue shares at Book Value of ZML Bank to the shareholders of XML Bank. All Assets &
Liabilities are to be taken over at Book Value.
For the Swap Ratio, weights assigned to different parameters are as follows:
You are required to :
(i) Calculate swap ratio based on above rates.
(ii) Calculate number of shares are to be issued.
(iii) Prepare Balance Sheet after Merger.
QUESTION NO. 27
Hanky Ltd. and Shanky Ltd. operate in the same field, manufacturing newly born babies’ s clothes.
Although Shanky Ltd. also has interests in communication equipments, Hanky Ltd. is planning to take
over Shanky Ltd. and the shareholders of Shanky Ltd. do not regard it as a hostile bid.
4.31
The following information is available about the two companies.

Hanky Ltd. Shanky Ltd.
Current earnings ₹ 6,50,00,000 ₹ 2,40,00,000
Number of shares 50,00,000 15,00,000
Percentage of retained earnings 20% 80%
Return on new investment 15% 15%
Return required by equity shareholders 21% 24%
Dividends have just been paid and the retained earnings have already been reinvested in new projects.
Hanky Ltd. plans to adopt a policy of retaining 35% of earnings after the takeover and expects to achieve
a 17% return on new investment.
Saving due to economies of scale are expected to be ₹ 85,00,000 per annum. Required return to equity
shareholders will fall to 20% due to portfolio effects.
Requirements
(i) Calculate the existing share prices of Hanky Ltd. and Shanky Ltd.
(ii) Find the value of Hanky Ltd. after the takeover
(iii) Advise Hanky Ltd. on the maximum amount it should pay for Shanky Ltd.
QUESTION NO. 28
A Ltd. (Acquirer company’s) equity capital is ₹ 2,00,00,000. Both A Ltd. and T Ltd. (Target Company)
have arrived at an understanding to maintain debt equity ratio at 0.30 : 1 of the merged company. Pre-
merger debt outstanding of A Ltd. stood at ₹ 20,00,000 and T Ltd at ₹ 10,00,000 and marketable
securities of both companies stood at ₹ 40,00,000.
You are required to determine whether liquidity of merged company shall remain comfortable if A Ltd.
acquires T Ltd. against cash payment at mutually agreed price of ₹ 65,00,000.
QUESTION NO. 29
Two companies Bull Ltd. and Bear Ltd. recently have been merged. The merger initiative has been taken
by Bull Ltd. to achieve a lower risk profile for the combined firm in spite of fact that both companies
belong to different industries and disclose a little co- movement in their profit earning streams. Though
there is likely to synergy benefits to the tune of ₹ 7 crore from proposed merger. Further both companies
are equity financed and other details are as follows:
Market Capitalization Beta
Bull Ltd. ₹1000 crore 1.50
Bear Ltd. ₹500 crore 0.60
Expected Market Return and Risk Free Rate of Return are 13% and 8% respectively. Shares of merged
entity have been distributed in the ratio of 2:1 i.e. market capitalization just before merger.
(a) Calculate return on shares of both companies before merger and after merger.
(b) Calculate the impact of merger on Mr. X, a shareholder holding 4% shares in Bull Ltd. and 2%
share of Bear Ltd.
QUESTION NO. 30
Simpson Ltd. is considering a merger with Wilson Ltd. The data below are in the hands of both Board of
Directors. The issue at hand is how many shares of Simpson should be exchanged for Wilson Ltd. Both
boards are considering three possibilities 20,000, 25,000 and 30,000 shares. You are required to
construct a table demonstrating the potential impact of each scheme on each set of shareholders:
Simpson Ltd. Wilson Ltd. Combined
Post merger
Firm ‘A’
1. Current earnings per year 2,00,000 1,00,000 3,50,000
2. Shares outstanding 50,000 10,000 ?
4.32
3. Earnings per share (₹ ) (1÷ 2) 4 10 ?

4. Price per share (₹ ) 40 100 ?
5. Price-earning ratio [4  3] 10 10 10
6. Value of firm (₹ ) 20,00,000 10,00,000 35,00,000
7. Expected Annual growth rate in
earnings in foreseeable future 0 0 0
QUESTION NO. 31
Teer Ltd. is considering acquisition of Nishana Ltd. CFO of Teer Ltd. is of opinion that Nishana Ltd. will
be able to generate operating cash flows (after deducting necessary capital expenditure) of ₹ 10 crore
per annum for 5 years.
The following additional information was not considered in the above estimations.
(i) Office premises of Nishana Ltd. can be disposed of and its staff can be relocated in Teer Ltd.’s office
not impacting the operating cash flows of either businesses. However, this action will generate an
immediate capital gain of ₹ 20 crore.
(ii) Synergy Gain of ₹ 2 crore per annum is expected to be accrued from the proposed acquisition.
(iii) Nishana Ltd. has outstanding Debentures having a market value of ₹ 15 crore. It has no other debts.
(iv) It is also estimated that after 5 years if necessary, Nishana Ltd. can also be disposed of for an
amount equal to five times its operating annual cash flow.
Calculate the maximum price to be paid for Nishana Ltd. if cost of capital of Teer Ltd. is 20%. Ignore any
type of taxation.
QUESTION NO. 32
Mr. X, a financial analyst, intends to value the business of PQR Ltd. in terms of the future cash generating
capacity. He has projected the following after tax cash flows :
Year : 1 2 3 4 5
Cash flows (₹ in lakh) 1,760 480 640 860 1,170
It is further estimated that beyond 5th year, cash flows will perpetuate at a constant growth rate of 8%
per annum, mainly on account of inflation. The perpetual cash flow is estimated to be ₹ 10,260 lakh at
the end of the 5th year.
Required:
(i) What is the value of the firm in terms of expected future cash flows, if the cost of capital of the firm
is 20%.
(ii) The firm has outstanding debts of ₹ 3,620 lakh and cash/bank balance of ₹ 2,710 lakh. Calculate
the shareholder value per share if the number of outstanding shares is 151.50 lakh.
(iii) The firm has received a takeover bid from XYZ ltd. of ₹ 225 per share. Is it a good offer?
[Given: PVIF at 20% for year 1 to Year 5: 0.833, 0.694, 0.579, 0.482, 0.402]
QUESTION NO. 33
ICL is proposing to take over SVL with an objective to diversify. ICL’s profit after tax (PAT) has grown
@ 18 per cent per annum and SVL’s PAT is grown @ 15 per cent per annum. Both the companies
pay dividend regularly. The summarised Profit & Loss Account of both the companies are as follows:
₹ in Crores
Particulars ICL SVL
Net Sales 4,545 1,500
PBlT 2,980 720
Interest 750 25
Provision for Tax 1,440 445
PAT 790 250
Dividends 235 125
4.33
ICL SVL
Fixed Assets
Land & Building (Net) 720 190
Plant & Machinery (Net) 900 350
Furniture & Fixtures (Net) 30 1,650 10 550
Current Assets 775 580
Less: Current Liabilities
Creditors 230 130
Overdrafts 35 10
Provision for Tax 145 50
Provision for dividends 60 470 50 240
Net Assets 1,955 890
Reserves and Surplus 1,050 1,300 660 785
Borrowing 655 105
Capital Employed 1,955 890
Market Price Share (₹) 52 75

ICL’s Land & Buildings are stated at current prices. SVL’s Land & Buildings are revalued three years
ago. There has been an increase of 30 per cent per year in the value of Land & Buildings.
SVL is expected to grow @ 18 per cent each year, after merger.
ICL’s Management wants to determine the premium on the shares over the current market price
which can be paid on the acquisition of SVL. You are required to determine the premium using:
(i) Net Worth adjusted for the current value of Land & Buildings plus the estimated average profit
after tax (PAT) for the next five years.
(ii) The dividend growth formula.
(iii) ICL will push forward which method during the course of negotiations?
Period (t) 1 2 3 4 5
FVIF (30%, t) 1.300 1.690 2.197 2.856 3.713
FVIF (15%, t) 1.15 2.4725 3.9938 5.7424 7.7537
QUESTION NO. 34
The following are the financial statements of A Ltd., and B Ltd. for the financial year ended 31st
March, 2020. Both the companies are working in the same industry.
Balance Sheets (₹)
Total Net Fixed Assets 12,00,000 6,00,000
Total Assets 27,00,000 18,00,000
Equity Capital (Face Value ₹ 10) 10,00,000 8,00,000
Retained Earnings 3,00,000 ---
14% Long Term Debt 7,00,000 5,00,000
Total Liabilities 27,00,000 18,00,000
4.34
Income Statement (₹)

Net Sales 33,10,000 16,60,000
Gross Profit 6,90,000 3,40,000
Interest 98,000 70,000
EBT 3,92,000 1,70,000
Tax @ 30% 1,17,600 51,000
PAT 2,74,400 1,19,000
Additional information :
Dividend Pay-out Ratio 40% 60%
Market Price per Share 40 15
(i) Earnings Per share (EPS), Profit Earning Ratio (PER), Return on Equity (ROE) and Book Value Per
Share (BVPS) for both the firms.
(ii) Estimate future EPS growth rate for both the firms.
(iii) If on acquisition of B Ltd. by A Ltd., intrinsic value of B Ltd., will be ₹ 20 per share, develop range
of justifiable Exchange Ratio (ER) that can be offered by A Ltd., to shareholders of B Ltd.
(iv) Based on your analysis in (i) and (ii) whether the negotiated ratio will be close to upper or lower
range. Justify.
(v) Post-merger EPS on an ER of 0.4: 1. What will be immediate accretion or dilution to EPS to the
shareholders of both the firms?
(vi) Post-Merger MPS on the basis of ER of 0.4 : 1
QUESTION NO. 35
M/s. Roly Ltd. wants to acquire M/s. Poly Ltd. The following is the Balance Sheet of Poly Ltd. as on
31st March, 2020 :
Equity Capital (₹ 10 per share) 10,00,000 Cash 20,000
Creditors and other liability 3,20,000 Plant & Machinery 16,50,000
Total 19,20,000 Total 19,20,000
Shareholders of Poly Ltd. will get one share of Roly Ltd. at current Market price of ₹ 20 for every two
shares. External liabilities are expected to be settled at a discount of ₹ 20,000. Sundry debtors and
Inventories are expected to realise ₹ 2,00,000.
Poly Ltd. will run as an independent unit. Cash Flow After Tax is expected to be ₹ 4,00,000 per annum
for next 6 years. Assume the disposal value of the plant after 6 years will be ₹ 1,50,000.
Poly Ltd. requires a return of 14%
n 1 2 3 4 5 6
PVIF (14%, n) 0.877 0.769 0.675 0.592 0.519 0.456
Advise the Board of Directors on the financial feasibility of the Proposal.
QUESTION NO. 36
B Ltd. wants to acquire S Ltd. and has offered a swap ratio of 2 : 3 (2 shares for every 3 share of S Ltd.)
Following information is available:
Particulars B Ltd. S Ltd.
Profit after tax (in ₹) 21,00,000 4,50,000
4.35
EPS (in ₹) 3.5 2.5

Price quoting per share on BSE before the merger
35 17.5
announcement
Required:
(i) The number of equity shares to be issued by B Ltd. for acquisition of S Ltd.
(ii) What is the EPS of B Ltd. after the acquisition?
(iii) Determine the equivalent earnings per share of S Ltd. and calculate per share gain or loss to
shareholders of S Ltd.
(iv) What is the expected market price per share of B Ltd. after the acquisition, assuming its PE Multiple
remains unchanged?
(v) Determine the market value of the merged firm.
(vi) After the announcement of merger, price of shares of S Ltd. rose by 10% on BSE. Mr. X, an investor,
having 10,000 shares of S Ltd. is having another investment opportunity, which yields annual return
of 14% is seeking your advise whether he needs to offload the shares in the market or accept the
shares from B Ltd.
QUESTION NO. 37
C Ltd. and P Ltd. both companies operating in the same industry decided to merge and form a new entity
S Ltd. The relevant financial details of the two companies prior to merger announcement are as follows:
C Ltd. P Ltd.
Annual Earnings after Tax (Rs. lakh) 10000 5800
No. Shares Outstanding (lakh) 4000 1000
PE Ratio (No. of Times) 8 10
The merger will be affected by means of stock swap (exchange) of 3 shares of C Ltd. for 1 share of P Ltd.
After the merger it is expected that due to synergy effects, Annual Earnings (Post Tax) are expected to be
8% higher than sum of the earnings of the two companies individually. Further, it is expected that P/E
Ratio of S Ltd. shall be average of P/E Ratios of two companies before the merger.
Evaluate the extent to which shareholders of P Ltd. will be benefitted per share from the proposed
merger.
4.36
5.1
Mutual Funds
Study Session 5
A mutual fund is a common pool of money into which investors place their contributions that are to
be invested in accordance with a stated objective.
A Mutual Fund is the most suitable investment for the cautious investors as it offers an opportunity to
invest in a diversified professionally managed basket of securities at a relatively low cost.
Mutual fund is a type of passive investment. If investors directly investment in market is known as
active investment.
LOS 2 : NAV (Net Asset Value) per unit

As per SEBI Regulation, every mutual fund company should calculate its NAV on a daily basis
(excluding holidays)
𝐍𝐞𝐭 𝐀𝐬𝐬𝐞𝐭𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐒𝐜𝐡𝐞𝐦𝐞

NAV =
𝐍𝐨.𝐎𝐟 𝐮𝐧𝐢𝐭𝐬 𝐎𝐮𝐭𝐬𝐭𝐚𝐧𝐝𝐢𝐧𝐠
Net Assets i.e. Total Assets – Total External Liabilities

= [Market Value of Investments + Receivables + Accrued Income + Other Assets]
–
[Accrued Expenses + Payables + Other liabilities]
5.2
Note:
 NAV signifies the realizable value that the investor will get for each unit that one is holding, if the
scheme is liquidated on that date.
 NAV is calculated for each Scheme & not for whole Company.
 While using NAV, we should always give preference to market value, If market value is not given
then use book value.
QUESTION NO. 1A
Cinderella Mutual Fund has the following assets in Scheme Rudolf at the close of business on 31st March,
2014.
Company No. of Shares Market Price Per Share
Nairobi Ltd. 25000 ₹ 20
Dakar Ltd. 35000 ₹ 300
Senegal Ltd. 29000 ₹ 380
Cairo Ltd. 40000 ₹ 500
The total number of units of Scheme Rudolf are 10 lacs. The Scheme Rudolf has accrued expenses of
₹ 2,50,000 and other liabilities of ₹ 2,00,000. Calculate the NAV per unit of the Scheme Rudolf.
QUESTION NO. 1B
Based on the following data, determine the NAV of a Income Scheme
Particulars ₹ in Lacs
Listed shares at cost (ex-dividend) 20.00
Cash in hand 1.23
Bonds & Debentures at cost (ex-interest) 4.30
Of these, bonds not listed & not quoted 1.00
Other fixed interest securities at cost 4.50
Dividend accrued 0.80
Amount payable on shares 6.32
Expenditure accrued 0.75
Number of Units (₹ 10 FV each) 2.4 lakhs
Current realizable value of fixed income securities of FV of ₹ 100 106.50
All listed shares were purchased at a time when index was 1200. On NAV date, the index is ruling at
2120. Listed bonds and debentures carry a market value of ₹ 5 lacs on NAV date.
QUESTION NO. 1C
Based on the following data, estimate the Net Asset Value (NAV) on per unit basis of a Regular Income
Scheme of a Mutual Fund:
Particulars ₹ in Lacs
Listed shares at cost (ex-dividend) 40.00
Cash in hand 2.76
Number of Units (₹ 10 FV each) 2.75 lakhs
5.3
Current realizable value of fixed income securities of FV of ₹ 100 is 96.50

All the listed equity shares were purchased at a time when market portfolio index was 12,500.
On NAV date, the market portfolio index is at 19,975.
There has been a diminution of 15% in unlisted bonds and debentures valuation.
Listed bonds and debentures carry a market value of ₹ 7.5 lakhs, on NAV date.
Operating expenses paid during the year amounted to ₹ 2.24 lakhs.
QUESTION NO. 1D
Calculate the NAV of a regular income scheme on per unit basis of Red Bull mutual fund from the
following information:
Particulars ₹ in crores
Listed shares at cost (ex-dividend) 30
Cash in hand 0.75
Value of listed bonds & debentures at NAV date 10
Number of units (₹10 face value) 30 lakhs
Current realizable value of fixed income securities of face value of ₹ 100 is 106.50
The listed shares were purchased when index was 7100 and the Present index is 9000
Unlisted bonds and debentures are at cost. Other fixed interest securities are also at cost.
QUESTION NO. 1E
Templan Mutual Fund had ₹ 10,00,00,000 as on Jan. 1,2007.The fund had issued 1,00,00,000 units
of ₹ 10 each.
It made following investments. (₹)
5,00,000 Equity Shares of ₹ 100 each @ ₹ 160/- 8,00,00,000
8% Central Government Securities 80,00,000
9% Debentures (unlisted) 50,00,000
10% Debentures (Listed) 50,00,000
Total 9,80,00,000
During the year, dividends of ₹ 120,00,000 were received on equity shares. Interest on all types of
debt securities was received as and when due. At the end of the year, the equity shares and 10%
debentures are quoted at ₹ 175 and ₹ 90 respectively. Find out the NAV per unit given that operating
expenses incurred during the year amounted to ₹50,00,000.
Also find out the NAV, if the mutual fund had distributed a dividend of ₹0.80 per unit during the year
to the unit holders. Assume that no load was charged.
QUESTION NO. 1F
On 1st April 2009 Fair Return Mutual Fund has the following assets and prices at 4.00 p.m.
Shares No. of Shares Market Price Per Share (₹)
A Ltd. 10000 19.70
B Ltd. 50000 482.60
C Ltd. 10000 264.40
5.4
D Ltd. 100000 674.90

E Ltd. 30000 25.90
No. of units of funds = 800000
Please calculate:
a) NAV of the Fund on 1st April 2009.
b) Assuming that on 1st April 2009, Mr. X, a HNI, send a cheque of ₹ 50,00,000 to the Fund and
Fund Manager immediately purchases 18000 shares of C Ltd. and balance is held in bank. Then
what will be position of fund.
c) Now suppose on 2 April 2009 at 4.00 p.m. the market price of shares is as follows:
Shares (₹)
A Ltd. 20.30
B Ltd. 513.70
C Ltd. 290.80
D Ltd. 671.90
E Ltd. 44.20
Then what will be new NAV.
LOS 3 : Calculation of Return (HPR)

Investors derive three type of Return :-
(i) Cash Dividend
(ii) Capital Gain Disbursements
(iii) Change in the Fund’s NAV per unit (Unrealized Capital Gain) [Closing NAV – Opening NAV]
𝐂𝐥𝐨𝐬𝐢𝐧𝐠 𝐍𝐀𝐕 – 𝐎𝐩𝐞𝐧𝐢𝐧𝐠 𝐍𝐀𝐕 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐫𝐞𝐜𝐞𝐢𝐯𝐞𝐝 𝐂𝐚𝐩𝐢𝐭𝐚𝐥 𝐆𝐚𝐢𝐧 𝐑𝐞𝐜𝐞𝐢𝐯𝐞𝐝

Return = × 𝟏𝟎𝟎
𝐎𝐩𝐞𝐧𝐢𝐧𝐠 𝐍𝐀𝐕
QUESTION NO. 2A
A mutual fund that had a net asset value of ₹ 20 at the beginning of month made income and capital
gain distribution of ₹ 0.0375 and Re. 0.03 per unit respectively during the month, and then ended the
month with a Net Asset Value of ₹ 20.06. Calculate monthly and annual rate of return.
QUESTION NO. 2B
Kaamat has invested in three mutual fund schemes as per details given below:
Mutual Fund A B C
Date of investment 1.12.2003 1.1.2004 1.3.2004
Amount of investment (₹) 50,000 1,00,000 50,000
NAV at entry date (₹) 10.50 10.00 10.00
Dividend received upto 31.3.2004 (₹) 950 1,500 Nil
NAV as on 31.3.2004 (₹) 10.40 10.10 9.80
Required:
What is the effective yield on per annum basis in respect of each of the three schemes to Kaamat up to
31.3.04?
QUESTION NO. 2C
5.5
Mr. A has invested in three Mutual Fund (MF) schemes as per the details given below:
Mutual Fund A B C
Date of investment 1.11.2015 1.02.2016 1.3.2016
Amount of investment (₹) 1,00,000 2,00,000 2,00,000
NAV at entry date (₹) 10.30 10.00 10.10
Dividend received upto 31.3.2016 (₹) 2,850 4,500 Nil
NAV as on 31.3.2016 (₹) 10.25 10.15 10.00
Assume 1 year = 365 days. Show the amount of rupees upto two decimal points.
You are required to find out the effective yield (upto three decimal points) on per annum
basis in respect of each of the above three Mutual Fund (MF) schemes upto 31-3-2016.
QUESTION NO. 2D
Mr. Y has invested in the three mutual funds (MF) as per the following details:
Particulars MF ‘X’ MF ‘Y’ MF ‘Z’
Amount of Investment (₹) 2,00,000 4,00,000 2,00,000
Net Assets Value (NAV) at the time of purchase (₹) 10.30 10.10 10
Dividend Received up to 31.03.2018 (₹) 6,000 0 5,000
NAV as on 31.03.2018 (₹) 10.25 10 10.20
Effective Yield per annum as on 31.03.2018 (percent) 9.66 -11.66 24.15
Assume 1 Year =365 days
Mr. Y has misplaced the documents of his investment. Held him in finding the date of his original
investment after ascertaining the following:
(i) Number of units in each scheme;
(ii) Total NAV;
(iii) Total Yield; and
(iv) Number of days investment held.
QUESTION NO. 2E
A Mutual Fund raised ₹ 100 lacs on April 1, 2009 by issue of 10 lakh units of ₹ 10 per unit. The fund
invested in several capital market instruments to build a portfolio of ₹ 90 lacs. The initial expenses
amounted to ₹ 7 lacs. During April 2009, the fund sold certain securities of cost ₹ 38 lacs for ₹ 40 lacs
and purchased certain other securities for ₹ 28.20 lacs. The fund management expenses for the month
amounted to ₹ 4.50 lacs of which ₹ 0.25 lacs in arrears The dividend earned was ₹ 1.20 lacs. 75% of the
realized earnings are distributed. The market value of the portfolio on 30.04.2009 was ₹ 101.90 lacs.
Determine NAV per unit. An investor subscribed to 1 unit on April 1, and disposed of it at closing NAV
on April 30. Determine his annual rate of earnings.
QUESTION NO. 2F
A mutual fund raised ₹ 150 lakhs on April 1, 2018 by issue of 15 lakh units at ₹ 10 per unit. The fund
invested in several capital market instruments to build a portfolio of ₹ 140 lakhs, Initial expenses
amounted to ₹ 8 lakhs. During the month of April, the fund sold certain instruments costing ₹ 44.75
lakhs for ₹ 47 lakhs and used the proceeds to purchase certain other securities for ₹ 41.6 Iakhs. The fund
management expenses for the month amounted to ₹ 6 lakhs of which ₹ 50,000 was in arrears. The fund
earned dividends amounting to ₹ 1.5 lakhs and it distributed 80% of the realized earnings. The market
value of the portfolio on 30th April, 2018 was ₹ 147.85 Iakhs.
An investor subscribed to 1000 units on April 1 and disposed it off at closing NAV on 30th April.
Determine his annual rate of earnings.
LOS 4 : Different Plans Under Mutual Fund

5.6
1. Dividend Payout Plan : Under this plan, Mutual Fund Co. declares & distributes dividend to its
unitholders on regular basis.
Impact : NAV will fall & no. of units will remain same.
2. Bonus Plan : Free units are distributed to the unitholders like bonus shares.
Impact : NAV will fall & no. of units will increase.
3. Growth Plan : Neither dividend is distributed nor are bonus units given. NAV will be increase to
the extent of growth.
Impact : NAV will change according to the mkt only & no. of units will remain same.
4. Dividend Re–investment Plan : Although dividend is declared but it is not paid. Amount of
dividend is again re-invested at the ex-Dividend NAV price prevailing at the time of declaration.
Impact : NAV will fall & no. of units will increase.

QUESTION NO. 3A
A Mutual Fund having 300 units has a NAV of ₹ 8.75 and ₹ 9.45 at the beginning and at the end of
the year respectively. The Mutual Fund has given two options:
(i) Pay ₹ 0.75 per unit as dividend and ₹ 0.60 per unit as a capital gain, or
(ii) These distributions are to be reinvested at an average NAV of ₹ 8.65 per unit.
What difference it would make in terms of return available and which option is preferable?
QUESTION NO. 3B
Mr. X, an investor purchased 200 units of ABC Mutual Fund at rate of ₹ 8.50 per unit one year ago.
Over the year Mr. X received ₹ 0.90 as dividend and had received a capital gains distribution of ₹
0.75 per unit. You are required to find out:
(i) Mr. X's holding period return assuming that this no load fund has a NAV of ₹ 9.10 as on today.
(ii) Mr. X's holding period return, assuming all the dividends and capital gains distributions are
reinvested into additional units as at average price of ₹ 8.75 per unit.
QUESTION NO. 3C
Moon Mutual Fund (Approved Mutual Fund) sponsored open-ended equity oriented scheme
"Chanakya Opportunity Fund". There were three plans viz. 'A'-Dividend Re-investment Plan, 'B'-Bonus
Plan & 'C'-Growth Plan. At the time of Initial Public Offer on 1.4.1995, Mr. Anand, Mr. Bacchan &
Miss Cham, three investors invested ₹1,00,000 each & selected 'B\ 'C & 'A' Plan respectively. The
History of the Fund is as follows:
Date Dividend % Bonus Ratio Net Asset Value per unit (F.V. ₹ 10)
Plan A Plan B Plan C
28-07-1999 20 30.70 31.40 33.42
31-03-2000 70 5:4 58.42 31.05 70.05
31-10-2003 40 42.18 25.02 56.15
05-03-2004 25 46.45 29.10 64.28
31-03-2004 1:3 42.18 20.05 60.12
24-03-2005 40 1:4 48.10 19.95 72.40
31-07-2005 53.75 22.98 82.07
st
On 31 July, 2005 all three investors redeemed all the balance units. Calculate annual rate of return
to each of the investors. Consider :
1. Long Term capital Gain is exempt from Income Tax.
2. Short term Capital Gain is subject to 10% income tax
5.7
3. Security Transaction Tax 0.2% only on sale/redemption of units.

4. Ignore Education Cess.
QUESTION NO. 3D
T Ltd. has promoted an open-ended equity oriented scheme in 999 with two plans -Dividend
Reinvestment Plan (Plan-A) and a Bonus Plan (Plan-B); the face value of the units was ₹ 10 each. X
and Y invested ₹ 5,00,000 each on 1.4.2001 respectively in Plan-A and Plan-B, when the NAV was ₹
42.18 for Plan A and ₹ 35.02 for Plan-B, X and Y both redeemed their units on 31.3.2008. Particulars
of dividend and bonus declared on the units over the period were as follows:
Date Dividend Ratio Bonus NAV
Plan A Plan B
15.09.2001 15 — 46.45 29.10
28.07.2002 — 1:6 42.18 30.05
31.03.2003 20 — 48.10 34.95
31.10.2003 — 1:8 49.60 36.00
15.03.2004 18 — 52.05 37.00
24.03.2005 — 1:11 53.05 38.10
27.03.2006 16 — 54.10 38.40
28.02.2007 12 1:12 55.20 39.10
31.03.2008 — — 50.10 34.10
You are required to calculate the annual return for X and Y after taking into consideration the
following information:
(i) Securities transaction tax @ 2% on redemption,
(ii) Liability of capital gains to income tax
a. Long-term capital gain-exempt; and
b. Short-term capital gains at 10% plus education cess at 3%.
QUESTION NO. 3E
The following information is extracted from Steady Mutual Fund’s Scheme:
Asset Value at the beginning of the month ₹ 65.78
Annualized return 15 %
Distributions made in the nature of Income Capital gain (per unit ₹ 0.50 and ₹ 0.32
respectively).
a) Calculate the month end net asset value of the mutual fund scheme (limit your answers to two
decimals).
b) Provide a brief comment on the month end NAV.
QUESTION NO. 3F
Mr. X on 1.7.2000, during the initial offer of some Mutual Fund invested in 10,000 units having face
value of ₹ 10 for each unit. On 31.3.2001 the dividend operated by the MF was 10% and Mr. X found
that his annualized yield was 153.33%. On 31.12.2002, 20% dividend was given. On 31.3.2003 Mr.
X redeemed all his balance of 11,296.11 units when his annualized yield was 73.52 %. What are the
NAVs on 31.3.2001, 31.12.2002 and 31.03.2003?
QUESTION NO. 3G
Mr. X on 1.7.2012, during the initial public offer of a Mutual Fund (MF) invested ₹ 1,00,000 at Face
Value of ₹ 10. On 31.3.2013, the MF declared a dividend of 10% when Mr. X calculated that his holding
period return was 115%. On 31.3.2014, MF again declared a dividend of 20%. On 31.3.2015, Mr. X
5.8
redeemed all his investment which had accumulated to 11,296.11 units when his holding period return
was 202.17%. Calculate the NAVs as on 31.3.2013, 31.3.2014 and 31.3.2015.
QUESTION NO. 3H
On 01-07-2010, Mr. X Invested ₹ 50,000/- at initial offer in Mutual Funds at a face value of ₹ 10 each
per unit. On 31-03-2011, a dividend was paid @ 10% and annualized yield was 120%. On 31-03-
2012, 20% dividend and capital gain of ₹ 0.60 per unit was given. Mr. X redeemed all his 6271.98 units
when his annualized yield was 71.50% over the period of holding. Calculate NAV as on 31-03-2011,
31-03-2012 and 31-03-2013.
For calculations consider a year of 12 months.
LOS 5 : Expense Ratio

𝐄𝐱𝐩𝐞𝐧𝐬𝐞 𝐈𝐧𝐜𝐮𝐫𝐫𝐞𝐝 𝐩𝐞𝐫 𝐮𝐧𝐢𝐭
Expense ratio =
𝐀𝐯𝐞𝐫𝐚𝐠𝐞 𝐍𝐀𝐕
Note:
𝐎𝐩𝐞𝐧𝐢𝐧𝐠 𝐍𝐀𝐕 𝐂𝐥𝐨𝐬𝐢𝐧𝐠 𝐍𝐀𝐕
Average NAV =
𝟐
QUESTION NO. 4
A mutual fund's opening NAV is ₹ 20 and its closing NAV is ₹ 24. If the expense per unit is ₹ 0.5 what
is the expense ratio?
LOS 6: Relationship between Return of Mutual fund, Recurring Expenses, Issue

Expenses & Return Desire by Investors (Indifference Point)
Required return by investors

= (Return of Mutual fund – Recurring Expenses) (1 – Issue Expenses)
QUESTION NO. 5A
Mr. A can earn a return of 16% by investing in equity shares by his own. Now he is considering a recently
announced equity based mutual fund scheme in which the initial expenses are 5.5 percent and annual
recurring expenses are 1.5 %. How much should the mutual fund earn to provide Mr. A return of 16
percent?
QUESTION NO. 5B
Mr. X earns 10% on his investments in equity shares. He is considering a recently floated scheme of a
mutual Fund where the initial expenses are 6% and annual recurring expenses are expected to be 2%.
How much the mutual fund scheme should earn to provide a return of 10% to Mr. X?
5.9
LOS 7: Entry Load & Exit Load

Entry Load is paid by the investor at the time of purchase of Mutual Fund unit.
Sale Price of NAV = NAV (1 + Entry Load)
Exit Load is paid by the investor at the time of selling of mutual fund units.
Realized value of NAV = NAV (1 – Exit Load)
QUESTION NO. 6A
Opening NAV = 50 Entry Load = 2% Exit Load =1%. Closing NAV=52
If Mr. Mohan wants to invest ₹ 1,00,000 in above fund what is the no. of units he will get and What is
the realized amount?
QUESTION NO. 6B
Following particulars are related to Mr. Tirupati:
On 1st Jan 06, he purchased 1 unit of Tata Mutual Fund. NAV as on 1st Jan 06-₹ 100. Entry Load- 2%.
What amount he will pay to purchase one unit of Tata Mutual Fund.
At the end of year 31st Dec 2006, he wants to exit from this Mutual Fund. NAV as on this date: ₹ 150.
Exit Load 1%. What amount he will receive after selling his unit?
QUESTION NO. 6C
An Investor holds 1000 units in a bond fund. The current NAV is ₹ 12.45. He would like to switch his
holdings to an equity fund whose NAV is ₹ 15.65. If the exit load for the bond fund is 0.50% and the
entry load for the equity fund is 0.75%, what is the value of his holding in the equity fund, after the
switch?
QUESTION NO. 6D
The unit price of Equity Linked Savings Scheme (ELSS) of a mutual fund is ₹ 10/-. The public offer price
(POP) of the unit is ₹ 10.204 and the redemption price is ₹ 9.80.
Calculate:
(i) Front-end Load
(ii) Back end Load
QUESTION NO. 6E
During the year 2017 an investor invested in a mutual fund. The capital gain and dividend for the year
was ₹ 3.00 per unit, which were re-invested at the yearend NAV of ₹ 23.75. The investor had total units
of 26,750 as at the end of the year. The NAV had appreciated by 18.75% during the year and there was
an entry load of ₹ 0.05 at the time when the investment was made.
The investor lost his records and wants to find out the amount of investment made and the entry load in
the mutual fund.
LOS 8: Dividend Equalization under Mutual Fund

QUESTION NO. 7
On 1st April, an open ended scheme of mutual fund had 300 lakh units outstanding with Net Assets
Value (NAV) of ₹ 18.75. At the end of April, it issued 6 Lakh units at opening NAV plus 2% load,
adjusted for dividend equalization. At the end of May, 3 Lakh units were repurchased at opening NAV
less 2% exit load adjusted for dividend equalization. At the end of June, 70% of its available income
was distributed.
5.10
In respect of April - June quarter, the following additional information are available :
₹ in lakh
Portfolio value appreciation 425.470
Income of April 22.950
Income of May 34.425
Income of June 45.450
You are required to calculate :
a) Income available for distribution;
b) Issue price at the end of April,
c) Repurchase price at the end of May, and
d) Net asset value (NAV) as on 30th June.
5.11
PRACTICE QUESTIONS
QUESTION NO. 8
A Mutual Fund Company introduces two schemes - Dividend Plan and Bonus Plan. The face value of
the Unit is ₹10 on 1-4-2014. Mr. R invested ₹ 5 lakh in Dividend Plan and
₹ 10 lakh in Bonus Plan. The NAV of Dividend Plan is ₹ 46 and NAV of Bonus Plan is
₹ 42. Both the plans matured on 31-03-2019. The particulars of Dividend and Bonus declared over the
period are as follows:
Date Dividend % Bonus Ratio NAV of Dividend NAV of Bonus Plan
Plan
(₹) (₹)
31-12-2014 12% - 47.0 42.0
30-09-2015 - 1:4 48.0 43.0
31-03-2016 15% - 49.5 41.5
30-09-2017 - 1:6 50.0 44.0
31-03-2018 10% - 48.0 43.5
31-03-2019 - - 49.0 44.0
You are required to calculate the effective yield per annum in respect of the above two plans.
QUESTION NO. 9
The following particulars relating to Vishnu Fund Schemes:
Particulars Value ₹ in Crores
1. Investment in Shares (at cost)
a. Pharmaceuticals companies 79
b. Construction Industries 31
c. Service Sector Companies 56
d. IT Companies 34
E. Real Estate Companies 10
2. Investment in Bonds (Fixed Income)
a. Listed Bonds (8000, 14% Bonds of ₹ 15,000 each) 12
b. Unlisted Bonds 7
3. No. of Units outstanding (crores) 4.2
4. Expenses Payable 3.5
5. Cash and Cash equivalents 1.5
6. Market expectations on listed bonds 8.842%
Particulars relating to each sector are as follows:
Sector Index on Purchase date Index on Valuation date
Pharmaceutical companies 260 465
Construction Industries 210 450
Service Sector Companies 275 480
IT Companies 240 495
Real Estate Companies 255 410
The fund has incurred the following expenses:
Consultancy and Management fees ₹ 480 Lakhs
Office Expenses ₹ 150 Lakhs
Advertisement Expenses ₹ 38 Lakhs
5.12
You are required to calculate the following:

(i) Net Asset Value of the fund
(ii) Net Asset Value per unit
(iii) If the period of consideration is 2 years, and the fund has distributed ₹ 3 per unit per year as cash
dividend, ascertain the Net return (Annualized).
(iv) Ascertain the Expenses ratio.
QUESTION NO. 10
A mutual fund has two schemes i.e. Dividend plan (Plan-A) and Bonus plan (Plan-B). The face value of
the unit is ₹ 10. On 01/04/2016 Mr. Anand invested ₹ 5,00,000 each in Plan- A and Plan-B when the
NAV was ₹ 46.00 and ₹ 43.50 respectively, Both the Plans matured on 31/03/2019.
Particulars of dividend and bonus declared over the period are as follows:
Date Dividend (%) Bonus ratio Net Assets Value (₹)
Plan – A Plan – B
30-06-2016 15% 46.80 44.00
31-08-2016 1:6 47.20 45.40
31-03-2017 10% 48.00 46.60
17-09-2017 1:8 48.40 47.00
21-11-2017 14% 49.60 47.20
25-02-2018 15% 50.00 47.80
31-03-2018 1:10 50.50 48.80
30-06-2018 12% 51.80 49.00
31-03-2019 52.40 50.00
You are required to calculate the Effective Yield Per annum in respect of the above two plans.
QUESTION NO. 11
Based on the following data, estimate the Net Asset Value (NAV) 1st July 2016 on per unit basis of a
Debt Fund:
Name of Face Purchase Maturity No. of Coupon Date(s) Duration
Security Value Price Date Securities of Bonds
₹ ₹
10.71% 100 104.78 31st March, 100000 31st March 7.3494
GOI 2028 2028
10 % 100 100.00 31st March, 50000 31st March & 5.086
GOI 2023 2023 30th September
9.5 % GOI 100 97.93 31st 40000 30th June & 31st 4.3949
2021 December, December
2021
8.5% 100 91.36 30th June 20000 30th June 6.5205
SGL 2025 2025
Number of Units (₹ 10 face value each): 100000
All securities were purchased at a time when applicable Yield to Maturity (YTM) was 10%. On NAV
date, the required yield increased by 75 basis point and Cash in hand and accrued expenses were ₹
6,72,800 and ₹ 2,37,400 respectively.
QUESTION NO. 12
The NAV of per unit of XYZ Mutual Fund (a Close Ended Funds) on 1.1.2014 was ₹ 28. The value on
31.12.2014 comes to ₹ 28.80. On the same date unit was trading in market at a premium of 3% though
5.13
on 1.1.2014 same was trading at a discount at 5%. On 31.12.2014, XYZ distributed a sum of ₹ 2.80 as
incomes and capital gains. You are required to compute rate of return to the investor during the year.
QUESTION NO. 13
SG Mutual Fund Company has the following assets under it on the close of business as on:
1st August 2017 2nd August 2017
Company No. of Shares Market price per share (₹) Market price per share (₹)
Q Ltd. 2,000 200.00 205.00
R Ltd. 30,000 312.40 360.00
S Ltd. 40,000 180.60 191.55
T Ltd. 60,000 505.10 503.90
Total No. of Units issued by the Mutual Fund is 6,00,000.
(i) Calculate Net Assets Value (NAV) of the Fund.
(ii) Following information is also given:
Assuming that Mr. Zubin, an investor, submits a cheque of ₹ 30,00,000 to the Mutual Fund and the
Fund Manager of this entity purchases 8,000 shares of R Ltd; and the balance amount is held in
Bank. In such a case, what would be the position of the Fund?
(iii) Calculate new NAV of the Fund as on 2nd August 2017.
QUESTION NO. 14
Mr. Alex, a practicing Chartered Accountant, can earn a return of 15 percent by investing in equity
shares on his own. He is considering a recently announced equity based mutual fund scheme in which
initial expenses are 6 percent and annual recurring expenses are 2 percent.
(i) How much should the mutual fund earn to provide Mr. Alex a return of 15 percent per annum?
(ii) Mr. Alex's current Annual Professional Income is ₹ 40 Lakhs. His portfolio value is ₹ 50 Lakhs and
now he is spending 10% of his time to manage his portfolio. If he spends this time on profession,
his professional income will go up in same proportion. He is thinking to invest his entire portfolio
into a Multicap Fund, assuming the fund's NAV will grow at 13% per annum (including dividend).
You are requested to advise Mr. Alex, whether he can invest the portfolio into Multicap Funds ? If so,
what is the net financial benefit?
QUESTION NO. 15
Cinderella Mutual Fund, an approved mutual fund, sponsored open-ended equity oriented scheme
"Rudolf Opportunity Fund". There are three plans under the scheme viz. 'A' - Dividend Re-investment
plan, 'B' - Bonus plan and 'C' - Growth plan.
At the time of initial public offer on 1-4-2009, Mr. Amit, Mr. Ashish and Mr. Arun, three investors invested
₹ 2,00,000 each at face value of ₹ 10 per unit and chosen plan 'B', 'C' and 'A' respectively.
The particulars of the fund over the period are as follows:
Date Dividend % Bonus Ratio Net Asset Value per unit (₹)
31.07.2013 10 - 30.70 31.20 35.40
31.03.2014 35 5:4 58.42 31.05 58.25
30.10.2017 20 - 42.18 26.45 56.45
15.03.2018 12.50 - 46.45 27.72 62.78
31.03.2018 - 1:3 45.20 20.05 67.12
25.03.2019 20 1:4 48.10 19.95 71.42
31.07.2019 - - 53.75 22.98 82.07
On 31st July, 2019, all the three investors redeemed all the balance units.
5.14
1. Consider the following:

(a) Long-term capital gain is exempt from Income-tax.
(b) Short-term capital gain is subject to 10% Income-tax.
(c) Security Transaction Tax is 0.2% only on sale/ redemption of units.
(d) Ignore Education Cess.
2. You are required:
(i) To calculate the Effective Yield per annum (annual rate of return) of each of the investors.
(ii) To suggest the name of investor with the highest Effective Yield per annum with the difference
to his nearest investor.
(Show your calculations up to two decimal points)
QUESTION NO. 16
M/S. Corpus an AMC, on 1.04.2015 has floated two schemes viz. Dividend Plan and Bonus Plan. Mr.
X, an investor has invested in both the schemes. The following details (except the issue price) are
available:
Date Dividend (%) Bonus Ratio NAV
Dividend Plan Bonus Plan
1.04.2015 ? ?
31.12.2016 1 :4 (One unit on 4 units 47 40
held)
31.03.2017 12 48 42
31.03.2018 10 50 39
31.12.2018 1 :5 (One unit on 5 units 46 43
held)
31.03.2019 15 45 42
31.03.2020 - - 49 44
Additional details
Investment (₹) ₹ 9,20,000 ₹ 10,00,000
Average Profit (₹) ₹ 27, 748.60
Average Yield (%) 6.40
You are required to calculate the issue price of both the schemes as on 1.04.2015.
QUESTION NO. 17
On 1st January, 2020, an open ended scheme of mutual fund had outstanding units of 300 lakhs
with a NAV of ₹ 20.25. At the end of January 2020, it had issued 5 lakhs units at an opening NA V
plus a load of 2%, adjusted for dividend equalisation. At the end of February 2020, it had repurchased
2.5 lakhs units at an opening NAV less 2% exit load adjusted for dividend equalisation. At the end of
March 2020, it had distributed 70 per cent of its available income.
In respect of January - March quarter, the following additional information is available:
Value appreciation of the portfolio ₹ 460 lakhs
Income for January ₹ 24 lakhs
Income for February ₹ 36 lakhs
Income for March ₹ 47 lakhs
(i) Income available for distribution
(ii) Issue price at the end of January
(iii) Repurchase price at the end of February
(iv) Closing Value of Net Assets at the end of March.
6.1
Derivatives Analysis & Valuation (Futures)

Study Session 6
Define Forward Contract, Future Contract.

 Forward Contract, In Forward Contract one party agrees to buy, and the counterparty to sell, a
physical asset or a security at a specific price on a specific date in the future. If the future price of
the assets increases, the buyer(at the older, lower price) has a gain, and the seller a loss.
 Futures Contract is a standardized and exchange-traded. The main difference with forwards are
that futures are traded in an active secondary market, are regulated, backed by the clearing house
and require a daily settlement of gains and losses.
Future Contracts differ from Forward Contracts in the following ways:
Future Contracts Forward Contracts
Organized Exchange Private Contracts
Highly Standardized Customized Contracts
 Lot size requirement
 Expiry Date
 MTM
No Counterparty default risk Counterparty default risk exists
Government Regulated Usually not Regulated
6.2
LOS 2 : Position to be taken under Future Market
How to settle / square-off / covering / closing out a position to calculate Profit / Loss
Long Position To Square Off Short position

Short Position To Square Off Long position
LOS 3 : Gain or Loss under Future Market

Position If Price on Maturity/ Settlement Price Gain/ Loss
Increase Gain
Long Position
Decrease Loss
Increase Loss
Short Position
Decrease Gain
Note:
 Gain/Loss is net of brokerage charge. Brokerage is paid on both buying & selling.
 Security Deposit is not considered while calculating Profit & Loss A/c.
 Interest paid on borrowed amount must be deducted while calculating Profit & Loss.
 A Future contract is ZERO-SUM Game. Profit of one party is the loss of other party.
6.3
LOS 4 : How Future Contract can be terminated at or prior to expiration?
 A short can terminate the contract by delivering the goods, and a long can terminate the Contract
by accepting delivery and paying the contract price to the short. This is called Delivery. The
location for delivery (for physical assets), terms of delivery, and details of exactly what is to be
delivered are all specified in the contract.
 In a cash-settlement contract, delivery is not an option. The futures account is marked-to-
market based on the settlement price on the last day of trading.
 You may make a reverse, or offsetting, trade in the future market. With futures, however, the
other side of your position is held by the clearinghouse- if you make an exact opposite
trade(maturity, quantity, and good) to your current position, the clearinghouse will net your
positions out, leaving you with a zero balance. This is how most futures positions are settled.
QUESTION NO. 1A
Ram buys 10,000 shares of x Ltd. At ₹ 22 and obtains a complete hedge selling 400 Nifty at ₹ 1100
each. He closes out his position at the closing price of the next day at which point, the share of X Ltd.
has dropped 2% and the Nifty future has dropped 1.5%. What is the overall profit/loss of this set of
transaction?
QUESTION NO. 1B
An investor buys a NIFTY Futures contract for ₹ 2,80,000 (lot size 200 futures). On the settlement date,
the NIFTY closes at 1378. Find out his profit or loss, if he pays ₹ 1000 as brokerage.
What would be his position, if he has sold the futures contract?
LOS 5 : Difference between Margin in the cash market and Margin in the
future markets and Explain the role of initial margin, maintenance
margin
In Cash Market, margin on a stock or bond purchase is 100% of the market value of the asset.
 Initially, 50% of the stock purchase amount may be borrowed and the remaining amount must
be paid in cash (Initial margin).
 There is interest charged on the borrowed amount.
In Future Markets, margin is a performance guarantee i.e. security provided by the client to the
exchange. It is money deposited by both the long and the short. There is no loan involved and
consequently, no interest charges.
 The exchange requires traders to post margin and settle their account on a daily basis.
6.4
Note:
 Any amount, over & above initial margin amount can be withdrawn.
 If Initial Margin is not given in the question, then use:
Initial Margin = Daily Absolute Change + 3 Standard Deviation
QUESTION NO. 2A
The settlement price of December Nifty futures contract on particular day was ₹ 1310. The minimum
trading lot on Nifty futures is 100. The initial margin is 8% and the maintenance margin is 6%. The index
closed at the following levels on the next five days.
Day 1 2 3 4 5
Closing Price 1340 1360 1300 1280 1305
a) Calculate the mark to market cash flows and daily closing balance in the a/c of
(i) An investor who has gone long at 1310 and
(ii) An investor who has gone short at 1310.
b) Calculate the net profit or loss on each of the contracts.
QUESTION NO. 2B
Sensex futures are traded at a multiple of 50. Consider the following quotations of Sensex futures in
the 10 trading days during February, 2009:
Day’s High Low Closing
4-2-09 3306.40 3290.00 3296.50
5-2-09 3298.00 3262.50 3294.40
6-2-09 3256.20 3227.00 3230.40
7-2-09 3233.00 3201.50 3212.30
10-2-09 3281.50 3256.00 3267.50
11-2-09 3283.50 3260.00 3263.80
12-2-09 3315.00 3286.30 3292.00
14-2-09 3315.00 3257.10 3309.30
17-02-09 3278.00 3249.50 3257.80
18-02-09 3118.00 3091.40 3102.60
Abhishek bought one Sensex futures contract on February, 04 .The average daily absolute change in
the value of contract is ₹ 10,000 and standard deviation of these changes is ₹2,000. The maintenance
margin is 75% of initial margin.
You are required to determine the daily balances in the margin account and payment on margin
calls, if any.
6.5
LOS 6 : Concept of Compounding
Example: Computing EAR for Range of compounding frequency.

Using a stated rate of 6%, compute EARs for semi-annual, quarterly, monthly and daily compounding.
Solution:
EAR with :
Semi-annual Compounding = (1+0.03) 2 – 1 = 1.06090 – 1 = 0.06090 = 6.090%
4
Quarterly compounding = (1+0.015) – 1 = 1.06136 – 1 = 0.06136 = 6.136%
12
Monthly Compounding = (1+0.005) – 1 = 1.06168 – 1 = 0.06168 = 6.168%
365
Daily Compounding = (1+0.00016438) – 1 = 1.06183 – 1 = 0.06183 = 6.183%
Notice here that the EAR increases as the compounding frequency increases.
Concept of e rt & e –rt (Continuous Compounding)
Most of the financial variable such as Stock price, Interest rate, Exchange rate, Commodity price
change on a real time basis. Hence, the concept of Continuous compounding comes in picture.
Continuous Compounding means compounding every moment. Instead of (1 + r) we will use ert
Calculation of ab Calculation of eb
1. √𝒂 12 Times 1. √𝒆 12 Times
2. -1 2. - 1
3. ×b 3. × b
4. +1 4. + 1
5. × = 12 Times 5. × = 12 Times
Hint : e1 = 2.71828
How to Calculate e rt & e –rt

Example:
e0 = 1 e.25 = 1.28403
e-.25 = 0.77880 e .205 = ?
or e .20 = 1.22140
= 0.77880 e.21 = 1.23368
. . .
 1.22754
6.6
e .357 = ?
e .35 = 1.41907
e .36 = 1.43333
Since 3rd digit is not 5, in this case we have to use interpolation
technique: - .357
e
when power of e increases by 0.01, then value increase by 0.01426
[1.43333 – 1.41907] = = 0.69977
.
.
when power of e increases by 1, then value increases by
.
.
when power of e increases by 0.007, then value increases by
.
× 0.007 = 0.00998
Value of e .357 = 1.41907 + 0.00998 = 1.42905
LOS 7 : Fair future price of security with no income

In case of Normal Compounding
Fair future price = Spot Price (1+r)n
In case of Continuous Compounding

rt
Fair future price = Spot Price × e
Where
r = risk free interest p.a. with Continuous Compounding.
t = time to maturity in years/ days. (No. of days / 365) or (No. of months / 12)
QUESTION NO. 3A
Current NIFTY is 1800 and minimum lot is 100. Risk free rate is 8%p.a.c.c and the futures period is 3
months. What is the fair value of 3 months NIFTY future?
QUESTION NO. 3B
The 6-months forward price of a security is ₹ 208.18. The borrowing rate is 8% per annum payable with
monthly interests. What should be the spot price?
6.7
LOS 8 : Fair Future Price of Security with Dividend Income
Fair Future Price = [Spot Price – PV of Expected Dividend ] ( 1+r)n

rt
Fair Future Price = [Spot Price – PV of Expected Dividend ] × e
–rt
PV of DI = Present Value of Dividend Income = Dividend × e
Where t = period of dividend payments
QUESTION NO. 4A
Determine value of 6 months future on B Ltd. shares from following data:
Current Price = ₹ 80 Dividend (after 3 months) = ₹ 3 r = 10% p.a.c.c
QUESTION NO. 4B
A share is selling at ₹ 900. Dividend of ₹ 40 is expected after 6 months and 12 months. The risk free rate
is 9% p.a.c.c. What is the price of the 12 months futures?
QUESTION NO. 4C
Suppose that there is a future contract on a share presently trading at ₹ 1000. The life of future
contract is 90 days and during this time the company will pay dividends of ₹ 7.50 in 30 days, ₹
8.50 in 60 days and ₹ 9.00 in 90 days.
Assuming that the Compounded Continuously Risk free Rate of Interest (CCRRI) is 12%
p.a. you are required to find out:
(a) Fair Value of the contract if no arbitrage opportunity exists.
(b) Value of Cost to Carry.
[Given e-0.01 = 0.9905, e-0.02 = 0.9802, e-0.03 = 0.97045 and e0.03 = 1.03045]
QUESTION NO. 4D
A future contract is available on R Ltd. that pays an annual dividend of ₹ 4 and whose stock is
currently priced at ₹ 125. Each future contract calls for delivery of 1,000 shares to stock in one year,
daily marking to market. The corporate treasury bill rate is 8%.
Required:
(i) Given the above information, what should the price of one future contract be ?
(ii) If the company stock price decreases by 6%, what will be the price of one futures contract ?
(iii) As a result of the company stock price decrease, will an investor that has a long position in one
futures contract of R Ltd. realizes a gain or loss ? What will be the amount of his gain or loss ?
(Ignore margin and taxation, if any)
6.8
LOS 9 : Fair Future Price of security when income is expressed in

percentage or when dividend yield is given

n
Fair Future Price = Spot Price [1+(r-y)]
Fair Future Price = Spot Price × e(r-y) ×t
Where y = income expressed in % or dividend Yield

QUESTION NO. 5A
Compute value of index future from following data:
Current value of index = 1200 Dividend yield = 8%,
CCRRI = 10% Future period = 3 months
QUESTION NO. 5B
On 31.8.2011, the value of Stock Index was ₹ 2,200. The risk free rate of return has been 8% per
annum. The dividend yield on this Stock Index is as under:
Month Dividend paid
January 3%
February 4%
March 3%
April 3%
May 4%
June 3%
July 3%
August 4%
September 3%
October 3%
November 4%
December 3%
Assuming that interest is continuously compounded daily, find out the future price of contract
deliverable on 31-12-2011. Given: e0.01583 = 1.01593
LOS 10 : Fair Future Price of Commodity with storage cost

n
Fair Future Price = [Spot Price + PV of S.C ] ( 1+r)
rt
Fair Future Price = [Spot Price + PV of S.C ] × e
6.9
Where PV of S.C = Present Value of Storage Cost

Note: Fair Future Price when Storage Cost is given in percentage(%).
(r + s) × t
FFP = Spot Price × e
Where S = Storage cost expressed in percentage.
QUESTION NO. 6
Consider a 6 month gold futures contract of 100 grams. If the spot price is ₹ 480 per gram and that it
costs ₹ 3 per gram for the 6 monthly period to store gold and that the cost is incurred at the end of the
period .If the continuously compounded Risk Free rate (CCRRI) is 10% per annum. Compute future price.
If future are available at ₹ 520 per gram what action would be suggested? If futures are available at ₹
490 per gram what action would be suggested? Do not Calculate Arbitrage Profit.
LOS 11 : Fair Future Price of commodities with Convenience yield expressed in

% (Similar to Dividend Yield)
The benefit or premium associated with holding an underlying product or physical good rather than
contract or derivative product i.e. extra benefit that an investor receives for holding a commodity.
Fair Future Price = Spot Price × e(r-c)×t
Note: Fair Future Price when convenience income is expressed in Absolute Amount.
rt
Fair Future Price = [Spot Price - PV of Convenience Income] × e
QUESTION NO. 7A
The spot price of steel scrap is ₹ 5000 per Ton. The one year futures price is ₹ 5802. The interest rate
is 15 % p.a.c.c. The present value of storage cost is ₹ 250 p.a. Compute the convenience yield.
Assuming that the futures are fairly priced.
QUESTION NO. 7B
The following information about copper scrap is given:
Spot price: $10,000 per ton Futures price: $10,800 for a one year contract
Interest rate: 12 % PV (storage costs): $500-per year
What is the PV (convenience yield) of copper scrap?
LOS 12 : Arbitrage Opportunity between Cash and Future Market

 Arbitrage is an important concept in valuing (Pricing) derivative securities. In its Purest sense,
arbitrage is riskless.
 Arbitrage opportunities arise when assets are mispriced. Trading by Arbitrageurs will continue
until they effect supply and demand enough to bring asset prices to efficient( no arbitrage) levels.
 Arbitrage is based on “Law of one price”. Two securities or portfolios that have identical cash flows
in future, should have the same price. If A and B have the identical future pay offs and A is priced
lower than B, buy A and sell B. You have an immediate profit.
Difference between Actual Future Price and Fair Future Price?
Fair Future Price is calculated by using the concept of Present Value & Future Value.
Actual Future Price is actually prevailing in the market.
Case Value Future Market Cash Market Borrow/ Invest
FFP < AFP Over-Valued Sell or Short Position Buy Borrow
FFP > AFP Under-Valued Buy or Long Position Sell # Investment
6.10
# Here we assume that Arbitrager already hold shares

QUESTION NO. 8A
The following data related to ABC Ltd. share prices:
Current Market Price per Share ₹ 180
Price in Futures Market for 6 month ₹ 195
It is possible to borrow money for securities transactions at the rate of 12% p.a.
Required:
a) Calculate the Fair / theoretical minimum price of a 6 month forward (future) contract,
b) Explain, if any, arbitrage opportunities exist.
QUESTION NO. 8B
The share of X Ltd. is currently selling for ₹ 300. Risk free interest rate is 0.8% per month. A three months
futures contract is selling for ₹ 312. Develop an arbitrage strategy and show what your riskless profit will
be 3 month hence assuming that X Ltd. will not pay any dividend in the next three months.
QUESTION NO. 8C
Calculate the price of a 6 months futures contract on a share that is currently priced at ₹ 75. The share
is expected to pay a ₹ 2 dividend four months from today. The continuously compounded risk free rate
is 12% per annum. The contract size is 100. If the contract value is ₹ 7400 what steps (action) would
follow. In case it is ₹ 7800. What would you do?
QUESTION NO. 8D
Suppose current price of an index is 13,800 and yield on index is 4.8% p.a. A 6 months future contract
on index is trading at 14,340. Assuming the risk free rate of interest is 12% p.a. Show how Mr. X can
earn arbitrage profit irrespective of outcome of the 6 months.
You can assume that after 6 months index closes at 10,200 and 15,600 and 50% of stock included
in index shall pay dividend in next 6 months. Also, calculate implied risk free rate.
QUESTION NO. 8E
The NSE-50 Index futures are traded with rupee value being ₹ 100 per index point. On 15th
September, the index closed at 1195, and December futures (last trading day December 15) were
trading at 1225. The historical dividend yield on the index has been 3% per annum and the
borrowing rate was 9.5% per annum.
(i) Determine whether on September 15, the December futures were under priced or overpriced?
(ii) What arbitrage transaction is possible to gain out this mispricing?
(iii) Calculate the gains and losses if the index on 15th December closes at (a) 1260 (b) 1175.
Assume 365 days in a year for your calculations.
LOS 13: Complete Hedging by using Index Futures & Beta

Hedging is the process of taking an opposite position in order to reduce loss caused by Price
fluctuation.
 The objective of Hedging is to reduce Loss.
 Complete Hedging means profit/ Loss will be Zero.
Position to be taken:
a) Long Position should be hedged by Short Position.
b) Short Position should be hedged by Long Position.
6.11
Value of Position to be taken:

Value of Position for Complete hedge should be taken on the basis of Beta through index futures.
Value of Position for Complete Hedge = Current Value of Portfolio × Existing Stock Beta
QUESTION NO. 9A
The beta of the SBI is 0.8. A person has a long SBI position of ₹ 2,00,000 coupled with a Short Nifty
position of ₹ 1,00,000. Is he hedged against fluctuation of Nifty?
QUESTION NO. 9B
Which position on the index futures gives a speculator a complete hedge against the following
transactions?
a) The share of Right Ltd. is going to fall. He has a long position on the cash market of ₹ 50 lacs on
the Right Ltd. The beta of the Right Ltd. is 1.25.
b) The share of Wrong Ltd. is going to rise. He has a short position on the cash market of ₹ 25 lacs
on the Wrong Ltd. The beta of the Wrong Ltd. is 0.9.
c) The share of Fair Ltd. is going to stagnate (constant). He has a short position on the cash market
of ₹ 20 lacs of Fair Ltd. The beta of the Fair Ltd. is 0.75.
LOS 14: Value of Position for Increasing & Reducing Beta to a Target Level
Alternative 1 (Hedging Using Index Future)

Step 1 : Decide Position
Case 1 : To Reduce Risk
Long Position Short Index Future
Short Position Long Index Future
Case 2 : To Increase Risk
Long Position Long Index Future
Short Position Short Index Future
Step 2 : Value of Position
Case I: When Existing Beta > Target Beta
Objective: Reducing Risk
Value of Index Position = Value of Existing Portfolio × [Existing Beta – Desired Beta]
Action: Take Short Position in Index & keep your current position unchanged.
Case II: When Existing Beta < Target Beta
Objective: Increase Risk
Value of Index Position = Value of Existing Portfolio × [Desired Beta – Existing Beta]
6.12
Action: Take Long Position in Index & keep your current position unchanged
Step 3 : No. of future contracts to be sold or purchased for increasing or reducing Beta to
a Desired Level using Index Futures.
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐈𝐧𝐝𝐞𝐱 𝐏𝐨𝐬𝐢𝐭𝐢𝐨𝐧
No. of Future Contract to be taken =
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐨𝐧𝐞 𝐅𝐮𝐭𝐮𝐫𝐞 𝐂𝐨𝐧𝐭𝐫𝐚𝐜𝐭
QUESTION NO. 10A

A portfolio manager owns 3 stocks
Stock Shares owned Stock Price Beta
1 1 Lakh 400 1.1
2 2 Lakh 300 1.2
3 3 Lakh 100 1.3
The Spot Nifty Index is at 1350 and Futures Price is 1352 .Use stock index futures to
a) Decrease the portfolio beta to .8 and
b) Increase the portfolio beta to 1.5. Assume the index factor is 100.
Find out the number of contracts to be bought/ sold of stock index futures.
Alternative 2 (Hedging Using Risk free Investment or Borrowing)

Case 1: Reducing Risk
SELL SOME SECURITIES AND REPLACE WITH RISK-FREE INVESTMENT
Step1: Equate the weighted Average Beta formulae to the new desired Beta
Target Beta = Beta1 × W1 + Beta2 × W2 ( Beta of Risk free investment is Zero)
Step2: Use the weights and decide
Case 2: Increasing Risk
BUY SOME SECURITIES AND BORROW AT RISK-FREE RATE
Step1: Equate the weighted Average Beta formulae to the new desired Beta
Target Beta = Beta1 × W1 + Beta2 × W2 ( Beta of Risk free investment is Zero)
Step2: Use the weights and decide
QUESTION NO. 10B
A Portfolio Manager (PM) has the following four stocks in his portfolio:
Security No. of Shares Market Price per share (₹) Beta
VSL 10000 50 0.9
CSL 5000 20 1.0
SML 8000 25 1.5
APL 2000 200 1.2
Compute the following:
a) Portfolio beta.
b) If the PM seeks to reduce the beta to 0.8, how much risk free investment should he bring in?
c) If the PM seeks to increase the beta to 1.2, how much risk free investment should he bring in?
6.13
QUESTION NO. 10C

On January 1, 2013 an investor has a portfolio of 5 shares as given below:
Security Price No. of Shares Beta
A 349.30 5,000 1.15
B 480.50 7,000 0.40
C 593.52 8,000 0.90
D 734.70 10,000 0.95
E 824.85 2,000 0.85
The cost of capital to the investor is 10.5% per annum.
a) The beta of his portfolio.
b) The theoretical value of the NIFTY futures for February 2013.
c) The number of contracts of NIFTY the investor needs to sell to get a full hedge until February for
his portfolio if the current value of NIFTY is 5900 and NIFTY futures have a minimum trade lot
requirement of 200 units. Assume that the futures are trading at their fair value.
d) The number of future contracts the investor should trade if he desires to reduce the beta of his
portfolios to 0.6.
No. of days in a year be treated as 365.
Given: In (1.105) = 0.0998, e(0.015858) = 1.01598
QUESTION NO. 10D
Details about portfolio of shares of an investor is as below:
Shares No. of shares (lakh) Price Per Share (₹) Beta
A Ltd. 3.00 500 1.40
B Ltd. 4.00 750 1.20
C Ltd. 2.00 250 1.60
The investor thinks that the risk of portfolio is very high and wants to reduce the portfolio beta to
0.91. He is considering two below mentioned alternative strategies:
a) Dispose off a part of his existing portfolio to acquire risk free securities, or
b) Take appropriate position on Nifty Futures which are currently traded at ₹ 8125 and each Nifty
points is worth ₹200. You are required to determine:
(i) portfolio beta,
(ii) the value of risk free securities to be acquired,
(iii) the number of shares of each company to be disposed off,
(iv) the number of Nifty contracts to be bought/sold; and
(v) the value of portfolio beta for 2% rise in Nifty.
QUESTION NO. 10E
Mr. A has a portfolio of ₹ 5 crore consisting of equity shares of X Ltd. and Y Ltd. with beta of 1.15.
Other information is as follows:
Spot Value of Index Future = 21000
Multiplier = 150
You are requested to reduce beta of portfolio to 0.85 and increase beta to 1.45 by using:
(a) Change in composition through Risk Free securities
(b) Index futures
6.14
QUESTION NO. 10F

On April 1, 2019, Kasi has a portfolio consisting of four securities as shown below:
Security A K S P
Market Price ₹ 48.5 ₹ 332.68 ₹ 13.99 ₹ 292.82
No. of Shares 673 480 721 358
β Value 0.74 1.28 0.54 0.46
Cost of Capital is 16% p.a. compounded continuously. Kasi fears a fall in prices of shares in future.
Accordingly, he approaches you for the advice to protect the interest of his Portfolio.
You can make use of the following information:
(i) The current NIFTY Value is 9380.
(ii) NIFTY Futures can be traded in units of 25 only.
(iii) Futures for September are currently quoted at 9540 and Futures for October are being quoted
at 9820.
1. The Beta of his Portfolio.
2. Theoretical Value of Futures for contracts expiring in September & October.
Given (e0.067 = 1.0693, e0.08 = 1.0833, e0.093 = 1.0975)
3. The number of NIFTY Contract that he would have to sell, if he desires to hedge 150% of the
Portfolio until October.
LOS 15 : Partial Hedge
Value of position in Index Future =

Value of existing Portfolio × Existing beta × percentage (%) to be Hedge
 It result into Over-Hedged or Under-Hedged Position

 There may be profit or loss depending upon the situation.
QUESTION NO. 11
On April 1, 2015, an investor has a portfolio consisting of eight securities as shown below :
Security Market Price No. of Shares Beta Value
A 29.40 400 0.59
B 318.70 800 1.32
C 660.20 150 0.87
D 5.20 300 0.35
E 281.90 400 1.16
F 275.40 750 1.24
G 514.60 300 1.05
H 170.50 900 0.76
The cost of capital for the investor is 20% p.a. continuously compounded. The investor fears
a fall in the prices of the shares in the near future. Accordingly, he approaches you for the advice to
protect the interest of his portfolio.
You can make use of the following information :
a) The current NIFTY value is 8500.
b) NIFTY futures can be traded in units of 25 only.
c) Futures for May are currently quoted at 8700 and Futures for June are being quoted at 8850.
(i) the beta of his portfolio.
6.15
(ii) the theoretical value of the futures contract for contracts expiring in May and June.
Given (e0.03 = 1.03045, e0.04 = 1.04081, e0.05 = 1.05127)
(iii) the number of NIFTY contracts that he would have to sell if he desires to hedge until June in each
of the following cases :
A. His total portfolio
B. 50% of his portfolio
C. 120% of his portfolio
LOS 16 : Beta of a Cash and Cash Equivalent

Beta of a cash and Risk free security is Zero.
QUESTION NO. 12A
A Mutual Fund is holding the following assets in ₹ Crores:
Investments in diversified equity shares 90.00
Cash and Bank Balances 10.00
100.00
The Beta of the portfolio is 1.1. The index future is selling at 4300 level. The Fund Manager
apprehends that the index will fall at the most by 10%. How many index futures he should short for
perfect hedging? One index future consists of 50 units.
Substantiate your answer assuming the Fund Manager's apprehension will materialize.
QUESTION NO. 12B
Current value of BSE Index (SR) 5000
Value of portfolio ₹ 10,10,000
Risk free interest rate 9% p.a.
Dividend yield on Index 6% p.a
Beta of portfolio 1.5
We assume that a future contract on the BSE index with four months maturity is used to hedge the
value of portfolio. One future contract is for delivery of 50 times the index. Based on the above
information.
Calculate:
a) Fair Future Price of Future Contract.
b) Calculate the gain on short futures position after 4 months with the help of index if it turns out to
be 4,500 in three months.
QUESTION NO. 12C
Ram buys 10000 shares of X Ltd. at a price of ₹ 22 per share whose Beta value is 1.5 and sells 5000
shares of A Ltd. at a price of ₹ 40 per share having a Beta value of 2. He obtains a complete hedge
by Nifty futures at ₹ 1000 each. He closes out position at the closing price of the next day when the
share of X Ltd dropped by 2%, share of A Ltd. appreciated by 3 % and Nifty futures dropped by 1.5%.
What is the overall profit / Loss to Ram?
QUESTION NO. 12D
A trader is having in its portfolio shares worth ₹ 85 Lakhs at current price and cash ₹ 15 Lakhs. The
Beta of the share portfolio is 1.6. After 3 months the price of shares dropped by 3.2 %.
Determine:
a) Current portfolio beta.
b) Portfolio beta after 3 Months if the trader on current date goes long position on ₹ 100 Lakhs Nifty
Futures.
6.16
QUESTION NO. 12E

A is an investor and having in its Portfolio Shares worth ₹ 1,20,00,000 at current price and Cash ₹
10,00,000. The Beta (β) of Share Portfolio is 1.4. After four months the price of shares dropped by
1.8%.
(i) Current Portfolio Beta and
(ii) Portfolio Beta after four months-if A on current date goes for long position on ₹ 1,30,00,000
Nifty futures.
QUESTION NO. 12F
Mr. X, is a Senior Portfolio Manager at ABC Asset Management Company. He expects to purchase a
portfolio of shares in 90 days. However he is worried about the expected price increase in shares in
coming day and to hedge against this potential price increase he decides to take a position on a 90-
day forward contract on the Index. The index is currently trading at 2290. Assuming that the
continuously compounded dividend yield is 1.75% and risk free rate of interest is 4.16%, you are
required to determine:
(a) Calculate the justified forward price on this contract.
(b) Suppose after 28 days of the purchase of the contract the index value stands at 2450 then
determine gain/ loss on the above long position.
(c) If at expiration of 90 days the Index Value is 2470 then what will be gain on long position.
Note: Take 365 days in a year and value of e0.005942 = 1.005960, e0.001849 = 1.001851.
QUESTION NO. 12G
Miss K holds 10,000 shares of IBS Bank @ 2,738.70 when 1 month Index Future was trading @ 6,086
The share has a Beta (β) of 1.2. How many Index Futures should she short to perfectly hedge his
position. A single Index Future is a lot of 50 indices.
Justify your result in the following cases:
(i) when the Index zooms by 1%
(ii) when the Index plummets by 2%.
LOS 17 : Hedging Commodity Risk Through Futures
QUESTION NO. 13A

A wheat trader has planned to sell 440000 kgs of wheat after 6 months from now. The spot price of
wheat is ₹ 19 per kg and 6 months future on same is trading at ₹ 18.50 per kg (Contract Size= 2000
kg). The price is expected to fall to as low as ₹ 17.00 per kg 6 month hence.
6.17
What trader can do to mitigate its risk of reduced profit? If he decides to make use of future market
what would be effective realized price for its sale when after 6 months is spot price is ₹ 17.50 per kg
and future contract price for 6 months is ₹ 17.55 per kg?
QUESTION NO. 13B
A Rice Trader has planned to sell 22000 kg of Rice after 3 months from now. The spot price of the
Rice is ₹ 60 per kg and 3 months future on the same is trading at ₹ 59 per kg. Size of the contract is
1000 kg. The price is expected to fall as low as ₹ 56 per kg, 3 months hence. What the trader can do
to mitigate its risk of reduced profit? If he decides to make use of future market, what would be the
effective realized price for its sale when after 3 months, spot price is ₹ 57 per kg and future contract
price for 3 months is ₹ 58 per kg?
LOS 18 : Calculation of Rate of Return

Increase or Decrease in Stock Price (P1 – P0)
(+) Dividend Received
(-) Transaction Cost
(-) Interest Paid on Borrowed Amount
Net Amount Received
𝐍𝐞𝐭 𝐀𝐦𝐨𝐮𝐧𝐭 𝐑𝐞𝐜𝐞𝐢𝐯𝐞𝐝
Rate of return = × 𝟏𝟎𝟎
𝐓𝐨𝐭𝐚𝐥 𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐄𝐪𝐮𝐢𝐭𝐲 𝐈𝐧𝐯𝐞𝐬𝐭𝐦𝐞𝐧𝐭
QUESTION NO. 14
Mr. V decides to sell short 10000 shares of ABC plc, when it was selling at yearly high of £5.60. His
broker requested him to deposit a margin requirement of 45% and commission of £1550 while Mr.
V was short the share, the ABC paid a dividend of £0.25 per share. At the end of one year Mr. V buys
10,000 shares of ABC plc at £4.50 to close out position and was charged a commission of £1450.
You are required to calculate the return on investment of Mr. V.
LOS 19 : Hedge Ratio

The Optional Hedge Ratio to minimize the variance of Hedger’s position is given by:-
𝛔𝐒
Hedge Ratio = Corr. (r)
𝛔𝐅
σS = S.D of Δ S
σF = S.D of Δ F
r = Correlation between Δ S and Δ F
Δ S = Change in Spot Price
Δ F = Change in Future Price
QUESTION NO. 15
A company is long on 10 MT of copper @ ₹ 474 per kg (spot) and intends to remains so for the
ensuing quarter. The standard deviation of changes of its spot and future prices are 4% and 6%
respectively, having correlation coefficient of 0.75.
What is its hedge ratio? What is the amount of the copper future it should short to achieve a perfect
hedge?
6.18
PRACTICE QUESTION
QUESTION NO. 16
Mr. SG sold five 4-Month Nifty Futures on 1st February 2020 for ₹ 9,00,000. At the time of closing of
trading on the last Thursday of May 2020 (expiry), Index turned out to be 2100. The contract multiplier
is 75.
Based on the above information calculate:
(i) The price of one Future Contract on 1st February 2020.
(ii) Approximate Nifty Sensex on 1st February 2020 if the Price of Future Contract on same date
was theoretically correct. On the same day Risk Free Rate of Interest and Dividend Yield on Index
was 9% and 6% p.a. respectively.
(iii) The maximum Contango/ Backwardation.
(iv) The pay-off of the transaction.
Note: Carry out calculation on month basis.
QUESTION NO. 17
The Following data relate to A Ltd.’s Portfolio:
Shares X Ltd. Y Ltd. Z Ltd.
No. of Shares (lakh) 6 8 4
Price per share (₹) 1000 1500 500
Beta 1.50 1.30 1.70
The CEO is of opinion that the portfolio is carrying a very high risk as compared to the market risk
and hence interested to reduce the portfolio’s systematic risk to 0.95. Treasury Manager has
suggested two below mentioned alternative strategies:
(i) Dispose off a part of his existing portfolio to acquire risk free securities, or
(ii) Take appropriate position on Nifty Futures, currently trading at 8250 and each Nif ty points
multiplier is ₹ 210.
(a) Interpret the opinion of CEO, whether it is correct or not.
(b) Calculate the existing systematic risk of the portfolio,
(c) Advise the value of risk-free securities to be acquired,
(d) Advise the number of shares of each company to be disposed off,
(e) Advise the position to be taken in Nifty Futures and determine the number of Nifty contracts to
be bought/sold; and
(f) Calculate the new systematic risk of portfolio if the company has taken position in Nifty Futures
and there is 2% rise in Nifty.
Note: Make calculations in ₹ lakh and upto 2 decimal points.
QUESTION NO. 18
The price of March Nifty Futures Contract on a particular day was 9170. The minimum trading lot on
Nifty Futures is 50. The initial margin is 8 and the maintenance margin is 6%. The index closed at the
following levels on next five days:
Day 1 2 3 4 5
Settlement Price (₹) 9380 9520 9100 8960 9140
(i) Mark to market cash flows and daily closing balances on account of
(a) An investor who has taken a long position at 9170
(b) An investor who has taken a short position at 9170
(ii) Net profit/ loss on each of the contracts
6.19
QUESTION NO. 19
Shyam buys 10,000 shares of X Ltd., @ ₹ 25 per share and obtains a complete hedge of shorting 400
Nifty at ₹ 1,100 each. He closes out his position at the closing price of the next day when the share
of X Ltd., has fallen by 4% and Nifty Future has dropped by 2.5%.
What is the overall profit or loss from this set of transaction?
6.20
7.1
Derivatives Analysis & Valuation (Options)

Study Session 7
Definition of Option Contract:

An option contract give its owner the right, but not the legal obligation, to conduct a transaction
involving an underlying asset at a pre-determined future date( the exercise date) and at a pre-
determined price (the exercise price or strike price)
There are four possible options position
1) Long call : The buyer of a call option  has the right to buy an underlying asset.
2) Short call : The writer (seller) of a call option has the obligation to sell the underlying asset.
3) Long put : The buyer of a put option  has the right to sell the underlying asset.
4) Short put : The writer (seller) of a put option  has the obligation to buy the underlying asset.
Note:
Meaning of Long position & Short position under Option Contract
Note:
 If question is silent always assume Long Position.
 Exercise Price/ Strike Price:
The fixed price at which buyer of the option can exercise his option to buy/ sell an underlying asset.
It always remain constant throughout the life of contract period.
7.2
 Option Premium:
 To acquire these rights, owner of options must buy them by paying a price called the Option
premium to the seller of the option.
 Option Premium is paid by buyer and received by Seller.
 Option Premium is non-refundable, non-adjustable deposit.
Note:
 The option holder will only exercise their right to act if it is profitable to do so.
 The owner of the Option is the one who decides whether to exercise the Option or not.
LOS 2 : Call Option

When Call Option Contract are exercised:
 When CMP > Strike Price  Call Buyer Exercise the Option.
 When CMP < Strike Price  Call Buyer will not Exercise the Option.
Right to Buy reliance share @ 1000 after 3 Obligation to Sell reliance share @ 1000 after
months 3 months if buyer approaches to do so.
LONG CALL SHORT CALL
OP Paid OP Received
Note :
 The call holder will exercise the option whenever the stock’s price exceeds the strike price at the
expiration date.
 The sum of the profits between the Buyer and Seller of the call option is always Zero. Thus, Option
trading is ZERO-SUM GAME. The long profits equal to the short losses.
 Position of a Call Seller will be just opposite of the position of Call Buyer.
 In this chapter, we first see whether the Buyer of Option opt or not & then accordingly we will
calculate Profit & Loss
PAY-OFF DIAGRAM
7.3
LOS 3 : Put Option

When Put Option Contract are exercised:
 When CMP > Strike Price  Put Buyer will not Exercise the Option.
 When CMP < Strike Price  Put Buyer will Exercise the Option.
Right to Sell reliance share @ 1000 after Obligation to Buy reliance share @ 1000 after 3
3 months months if buyer approaches to do so.
LONG PUT SHORT PUT
OP Paid OP Received
Note:
 Put Buyer will only exercise the option when actual market price is less the exercise price.
 Profit of Put Buyer = Loss of Put Seller & vice-versa. Trading Put Option is a Zero-Sum Game.
PAY-OFF DIAGRAM
Profit or Loss/ Pay off of call Option & Put Option

While calculating profit or loss, always consider option Premium,
Call Buyers (Long Call)
If S – X > 0 If S – X < 0
Exercise the option Not Exercise
Net Profit = S – X – OP Loss = Amount of Premium
Put Buyers (Long Put)
If X – S >0 If X – S < 0
Exercise the option Not Exercise
Net Profit = X – S –OP Loss = Amount of Premium
7.4
Calculation of Maximum Loss, Maximum Gain, Breakeven Point for Call & Put Option
Call Option
Maximum Loss Maximum Gain
Buyer (Long) Option Premium Unlimited
Seller (Short) Unlimited Option Premium
Breakeven X + Option Premium
Put Option
Maximum Loss Maximum Gain
Buyer (Long) Option Premium X – Option Premium
Seller (Short) X – Option Premium Option Premium
Breakeven X - Option Premium
Example:
Suppose that both a Call an a Put option have been written on a stock with an exercise price of $ 40.
The current stock price is $ 42, and the call and put premiums are $ 3 and $ 0.75, respectively.
Calculate the profit to the long and short positions for both the put and the call with an expiry day
stock price of $ 35 and with a price at expiration of $ 43.
Solution: Profit will be computed as ending option valuation- initial option cost.
Stock at $ 35:
 Long Call: $0 - $3 = - $3. The option finished out-of-the-money, so the premium is lost.
 Short Call: $3 - $0 = $3. Since the option finished out-of-the-money, the call writer’s gain equals
the premium.
 Long Put: $5 - $0.75 = $4.25. You paid $0.75 for an option that is now worth $5
 Short Put: $0.75 - $5 = -$4.25. you received $0.75 for writing the option but you face a $5 loss
because the option is in-the-money.
Stock at $ 43:
 Long Call: - $3 + $3 =$0. You paid $3 for the option, and it is now worth $3. Hence, your net
profit is Zero.
 Short Call: $3 - $3 = $0. You received $3 for writing the option and now face a -$3 valuation for
net profit of Zero.
 Long Put: -$0.75 - $0 = - $0.75. You paid $0.75 for the put option and the option is now
worthless. Your net profit is - $0.75
 Short Put: $0.75 - $0 = $0.75. You received $0.75 for writing the option and keep the premium
because the option finished out-of-the-money.
QUESTION NO. 1A
The shares of TATA power are selling at ₹ 104 per share. Ravi wants to chip in with buying three months
call option at premium of ₹ 5 per option. Exercise price is ₹ 105. Six possible prices per share on expiration
date ranging from 95 to 120, with interval of ₹ 5 are possible.
a) What is Ravi's pay off as call option holder on expiration?
b) What is the call writer's payoff on expiration?
QUESTION NO. 1B
The current market price of XYZ Ltd. is ₹ 30. Miss Namita buys three months put option at a premium of
₹ 5 per option. The exercise price is ₹ 33. Six possible prices per share on the expiration date ranging
from ₹ 25 to ₹ 50 with intervals of ₹ 5 are possible.
a) What is Namita's pay-off as a put holder on expiration?
b) What is the put writer's pay off on expiration?
7.5
QUESTION NO. 1C
The equity share of VCC Ltd is quoted at ₹ 210. A 3-month call option is available at a premium
of ₹ 6 per Share and a 3-month put option is available at a premium of ₹ 5 per share. Ascertain the net
pay offs to the option holder of a call option and a put option, given that:
(i) The strike price in both cases is ₹ 220; and
(ii) The share price on the Exercise day is ₹ 200, 210, 220, 230, 240.
Also indicate the price range at which the call and the put options maybe gainfully exercised.
QUESTION NO. 1D
A call and put exist on the same stock each of which is exercisable at ₹ 60. They now trade for:
Market price of Stock or stock index ₹ 55
Market price of call ₹9
Market price of put ₹1
Calculate the expiration date cash flow, investment value(Gross Profit),and net profit from:
(i) Buy 1.0 call
(ii) Write 1.0 call
(iii) Buy 1.0 put
(iv) Write 1.0 put
For expiration date stock prices of ₹ 50, ₹ 55, ₹ 60, ₹ 65, ₹ 70
QUESTION NO. 1E
The market received rumour about ABC Corporation’s tie-up with a multinational company. This has
induced the market price to move up. If the rumour is false the ABC corporation stock price will probably
fall dramatically. To protect from this an investor has bought the call and put options.
He purchase one 3 months call with a striking price of ₹ 42 for ₹ 2 premium and paid Re. 1 per share
premium for a3 months put with striking price of ₹ 40.
a) Determine the Investor's position if the tie up offer bids the price of ABC Corporation's stock up to ₹
43 in 3 months.
b) Determine the Investor's ending position, if the tie up program fails and the price of the stocks falls
to ₹ 36 in 3 months.
[Assume lot size =100 shares]
QUESTION NO. 1F
Mr. A purchased a 3-month call option for 100 shares in XYZ Ltd at a premium of ₹ 30per share, with
an exercise price of ₹ 550. He also purchased a 3-month put option for 100 shares of the same company
at a premium of ₹ 5 per share with an exercise price of ₹ 450. The Market price of the share on the date
of Mr. A's purchase of options is.₹ 500. Calculate the profit or loss that Mr. A would make assuming that
the market price falls to ₹ 350 at the end of 3 months.
QUESTION NO. 1G
Mr. X established the following spread on the Delta Corporation's stock
(i) Purchased one 3-month call option with a premium of ₹ 30 and an exercise price of ₹ 550.
(ii) Purchased one 3-month put option with a premium of ₹ 5 and an exercise price of ₹ 450.
Delta Corporation's stock is currently selling at ₹ 500. Determine profit or loss, if the price of Delta
Corporation’s:
(i) Remains at ₹ 500 after 3 months.
(ii) Falls at ₹ 350 after 3 months.
(iii) Rises to ₹ 600. Assume the size option is 100 shares of Delta Corporation.
QUESTION NO. 1H
7.6
Fresh Bakery Ltd.' s share price has suddenly started moving both upward and downward on a rumour
that the company is going to have a collaboration agreement with a multinational company in bakery
business. If the rumour turns to be true, then the stock price will go up but if the rumour turns to be false,
then the market price of the share will crash. To protect from this an investor has purchased the following
call and put option:
(i) One 3 months call with a striking price of ₹ 52 for ₹ 2 premium per share.
(ii) One 3 months put with a striking price of ₹ 50 for ₹ 1 premium per share.
Assuming a lot size of 50 shares, determine the followings:
a) The investor's position, if the collaboration agreement push the share price to ₹ 53 in 3 months.
b) The investor's ending position, if the collaboration agreement fails and the price crashes to ₹ 46 in 3
months’ time.
QUESTION NO. 1I
Mr. KK purchased a 3-month call option for 100 shares in PQR Ltd. at a premium of
₹ 40 per share, with an exercise price of ₹ 560. He also purchased a 3-month put option for 100 shares
of the same company at a premium of ₹ 10 per share with an exercise price of ₹ 460. The market price
of the share on the date of Mr. KK's purchase of options, is ₹ 500. Compute the profit or loss that Mr. KK
would make assuming that the market price falls to ₹ 360 at the end of 3 months.
QUESTION NO. 1J
Ram holding shares of Reliance Industries Ltd. which is currently selling at ₹ 1000. He is expecting that
this price will further fall due to lower than expected level of profits to be announced after one month.
As on following option contract are available in Reliance Share.
Strike Price (₹) Option Premium (₹)
1030 Call 40
1010 Call 35
1000 Call 30
990 Put 35
970 Put 20
950 Put 8
930 Put 5
Ram is interested in selling his stock holding as he cannot afford to lose more than 5% of its value.
RECOMMEND a hedging strategy with option and show how his position will be protected.
LOS 4 : Concept of Moneyness of an Option

Moneyness refers to whether an option is In-the money or Out- of the money.
Case I : If immediate exercise of the option would generate a positive pay-off, it is in the money
Case II : If immediate exercise would result in loss (negative pay-off), it is out of the money.
Case III : When current Asset Price = Exercise Price, exercise will generate neither gain nor loss
and the option is at the money.
Call Option Put Option
Case 1 S–X>0 In-the-Money X-S>0
Case 2 S–X<0 Out-of- the-Money X - S < 0
Case 3 S=X At-the-Money X=S
Note:
Do not consider option premium while Calculating Moneyness of the Option.
LOS 5 : European & American Options

7.7
American Option : American Option may be exercised at any time upto and including the contract’s
expiration date.
European Option : European Options can be exercised only on the contract’s expiration date.
The name of the Option does not imply where the option trades – they are just names.
LOS 6 : Action to be taken under Option Market
LOS 7 : Intrinsic Value & Time Value of Option

Option value (Premium) can be divided into two parts:-
(i) Intrinsic Value
(ii) Time Value of an Option (Extrinsic Value)
Option Premium = Intrinsic Value + Time Value of Option
Intrinsic Value:
 An Option’s intrinsic Value is the amount by which the option is In-the-money. It is the amount
that the option owner would receive if the option were exercised.
 Intrinsic Value is the minimum amount charged by seller from buyer at the time of selling the
right.
 An Option has ZERO Intrinsic Value if it is At-the-Money or Out-of-the-Money, regardless of
whether it is a call or a Put Option.
 The Intrinsic Value of a Call Option is the greater of (S – X) or 0. That is
C = Max [0, S –X]
 Similarly, the Intrinsic Value of a Put Option is (X - S) or 0. Whichever is greater. That is:
P = Max [0, X - S]
Time Value of an Option (Extrinsic Value):
 The Time Value of an Option is the amount by which the option premium exceeds the intrinsic
Value.
 Time Value of Option = Option Premium – Intrinsic Value
 When an Option reaches expiration there is no “Time” remaining and the time value is ZERO.
 The longer the time to expiration, the greater the time value and, other things equal, the greater
the option’s Premium (price).
QUESTION NO. 2
Mr. Ganesh is considering to buy put and call options on ITC shares with spot price ₹ 800. From the
following data determine intrinsic and time values:
Calls Puts
7.8
Option Strike Premium Strike Premium

1 790 25 810 28
2 800 15 800 18
3 810 5 790 8
Option Valuation
LOS 8 : Fair Option Premium/ Fair Value/ Fair Price of a Call on Expiration
Fair Premium of Call on Expiry

1 = Maximum of [(S – X), 0]
Note:
Option Premium can never be Negative. It can be Zero or greater than Zero.
QUESTION NO. 3
Determine value of call option at their expiration date.
Company Market price per share at Expiration Date Exercise price of option
HLL 170 150
RIL 200 240
ITC 480 520
MTNL 250 210
LOS 9 : Fair Option Premium/ Fair Value/ Fair Price of a Put on Expiration
Fair Premium of Put on Expiry = Maximum of [(X – S), 0]
QUESTION NO. 4
Find out value of PUT option at their expiration date.
Company Market price per share at Expiration Date Exercise price of option
ACC 150 170
BSES 200 210
TISCO 130 120
VSNL 115 140
7.9
LOS 10 : Fair Option Premium/ Theoretical Option Premium/ Price of a Call

before Expiry or at the time of entering into contract or As on Today
𝐗
Fair Premium of Call = 𝐒 − , 0 Max
(𝟏 𝐑𝐅𝐑)
Or
= S– ,0 Max
RFR (r) = Risk-free rate

T = Time to expiration
QUESTION NO. 5
Given the following: Strike Price = ₹ 180, Current Price of one share = 200, Risk free rate of interest -
10% p.a. Calculate theoretical minimum price of a European call option expiring after one year.
LOS 11 : Fair Option Premium/ Theoretical Option Premium/ Price of a Put

before Expiry or at the time of entering into contract or As on Today
𝐗
Fair Premium of Put = – 𝐒, 𝟎 Max
(𝟏 𝐑𝐅𝐑)𝐓
Or
= – 𝐒, 𝟎 Max
QUESTION NO. 6
Given the following: Strike Price = ₹ 400,Current stock price= ₹ 370,Time until expiration = 6 months,
Risk free rate of interest = 5% p.a. Calculate theoretical minimum price of a European put option.
LOS 12 : Expected Value of an Option on expiry

Under this approach, we will calculate the amount of Option premium on the basis of Probability.
Expected value of an option at Expiry = ∑ Value of Option at expiry × Probability
QUESTION NO. 7A
You as an investor had purchased a 4 month call option on the equity shares of X Ltd. of ₹ 10, of which
the current market price is ₹ 132 and the exercise price ₹ 150. You expect the price to range between ₹
120 to ₹ 190.
The expected share price of X Ltd. and related probability is given below:
Expected Price (₹) 120 140 160 180 190
Probability .05 .20 .50 .10 .15
Compute the following:
a) Expected Share price at the end of 4 months.
b) Value of Call Option at the end of 4 months, if the exercise price prevails.
c) In case the option is held to its maturity, what will be the expected value of the call option?
QUESTION NO. 7B
Equity share of PQR Ltd. is presently quoted at ₹ 320. The Market Price of the share after 6 months has
the following probability distribution:
7.10
Market Price (₹) 180 260 280 320 400

Probability 0.1 0.2 0.5 0.1 0.1
A put option with a strike price of ₹ 300 can be written. You are required to find out Expected value of
Option at maturity (i.e. 6 months)
QUESTION NO. 7C
A call option has been entered into by Arnav for delivery of share of X Ltd. at ₹ 460. The expected future
prices at the time of expiry of contract are as follows:
Price (₹) Prob.
470 0.20
450 0.25
480 0.35
490 0.05
500 0.15
Determine the premium at which Arnav will break even.
LOS 13 : Risk Neutral Approach for Call & Put Option(Binomial Model)
 Under this approach, we will calculate Fair Option Premium of Call & Put as on Today.
 The basic assumption of this model is that share price on expiry may be higher or may be lower
than current price.
Step 1: Calculate Value of Call or Put as on expiry at high price & low price
Value of Call as on expiry = Max [( S – X),0]
Value of Put as on expiry = Max [(X – S), 0]
Step 2: Calculate Probability of High Price & Low Price
( )
Probability of High Price = 𝐨𝐫 Probability of High Price =
Step 3: Calculate expected Value/ Premium as on expiry by using Probability
Step 4: Calculate Premium as on Today
By Using normal Compounding =

( )
By Using Continuous Compounding =
QUESTION NO. 8A
Reliance shares are currently selling at ₹ 100. The price in the next six months may jump to ₹ 115 or fall
to ₹ 90. What is the value of a six month call option with an exercise price of ₹ 100 and rate of return of
10% p.a. Use Risk Neutral Approach?
7.11
QUESTION NO. 8B
The current market price of an equity share of Penchant Ltd is ₹ 420. Within a period of 3 months, the
maximum and minimum price of it is expected to be ₹ 500 and ₹ 400 respectively. If the risk free rate of
interest be 8% p.a., what should be the value of a 3 months Call option under the “Risk Neutral” method
at the strike rate of ₹ 450?
QUESTION NO. 8C
A call option on gold with exercise price ₹ 26,000 per ten gram and three months to expire is being
traded at a premium of ₹ 1,010 per ten gram. It is expected that in three months’ time the spot price
might change to ₹ 27,300 or 24,700 per ten gram. At present this option is at- the-money and the rate
of interest with simple compounding is 12% per annum. Is the current premium for the option justified?
Evaluate the option and comments.
QUESTION NO. 8D
Sumana wanted to buy shares of EIL which has a range of ₹ 411 to ₹ 592 a month later. The present
price per share is ₹ 421. Her broker informs her that the price of this share can sore up to ₹ 522 within
a month or so, so that she should buy a one month CALL of EIL. In order to be prudent in buying the
call, the share price should be more than or at least ₹ 522 the assurance of which could not be given
by her broker.
Though she understands the uncertainty of the market, she wants to know the probability of attaining
the share price ₹ 592 so that buying of a one month CALL of EIL at the execution price of ₹ 522 is justified.
Advise her, Take the risk free interest to be 3.60% and e0.036 = 1.037.
QUESTION NO. 8E
Spot Price is ₹ 60. A One year European Call Option is being quoted in the market at option premium
of ₹ 15 with Exercise Price of ₹ 55. Risk Free Rate of return is 12% p.a.c.c. The stock can either rise or fall
after a year. If it can fall by 30% by what percentage (%) can it rise?
LOS 14 : Two Period Binomial Model

We divide the option period into two equal parts and we are provided with binomial projections for
each path. We then calculate value of the option on maturity. We then apply backward induction
technique to compute the value of option at each nodes.
QUESTION NO. 9A
On 01/04/05, price of E Ltd. share is ₹ 600. In three months, this price can go up by 10% or can come
down by 10%.In next 3 months, the price can again go up by 5% or can come down by 5%. The risk-free
rate of interest is 8% p.a. continuously compounded. Determine value of 6 month call and put at strike
price ₹ 588.
7.12
QUESTION NO. 9B
Consider a two year American call option with-a strike-price of ₹ 50 on a stock the current price of which
is also ₹ 50. Assume that there are two time periods of one year and in each year the stock price can
move up or down by equal percentage of 20%. The risk free interest rate is 6%. Using binomial option
model, calculate the probability of price moving up and down. Also draw a two-step binomial tree
indicating prices and pay offs (option premium) at each node.
LOS 15 : Put Call Parity Theory (PCPT)

Put Call Parity is based on Pay-offs of two portfolio combination, a fiduciary call and a protective put.
Fiduciary Call
A Fiduciary Call is a combination of a pure-discount, riskless bond that pays X at maturity and a Call.
Protective Put
A Protective Put is a share of stock together with a put option on the stock.
𝐗
PCPT  Value of Call + = Value of Put + S
(𝟏 𝐑𝐅𝐑)𝐓
Protective Put
If on Maturity S > X If on Maturity S < X
Put option is lapse i.e. pay off = NIL Put option is exercise i.e. pay off = X–S
Stock is sold in the Market = S Stock is sold in the Market = S
S X
Fiduciary Call
If on Maturity S > X If on Maturity S < X
Call option is exercise i.e. pay off = S– Call option is lapse i.e. pay off = NIL
X
Bond is sold in the Market = X Bond is sold in the Market = X
S X
Through this theory, we can calculate either Value of Call or Value of Put provided other Three
information is given.
Assumptions:
 Exercise Price of both Call & Put Option are same.
 Maturity Period of both Call & Put are Same.
QUESTION NO. 10
A put and a call option each have an expiration date 6 months and an exercise price of ₹ 10. The interest
rate for the period is 3% p.a.
a) If put has a market price of ₹ 2 and share is worth ₹ 9 per share, what is the value of the call?
b) If the put has a market price of Re. 1 and the call ₹ 4, what is the value of the stock per share?
c) If the call has a market value of ₹ 5 and market price of the share e is ₹ 12 per share, what is the
value of the put?
7.13
LOS 16 : Put - Call Parity Theory  ARBITRAGE

As per PCPT,
Value of Call + Value of Put + S

( )
LHS RHS
Case I : If LHS = RHS, arbitrage is not possible.
Case II : If LHS ≠ RHS, arbitrage is possible.
A. If LHS > RHS, Call is Over-Valued & Put is Under-Valued
Option Market Cash Market Net Amount

Short Call Long Put Buy Borrow
i.e. Obligation to sell i.e. Right to sell & Option i.e. Buy one share S+P-C
& Option Premium Premium Paid
Received
B. If LHS < RHS, Call is Under-Valued & Put is Over-Valued
Option Market Cash Market Net Amount

Long Call Short Put Sell Invest
i.e. Right to Buy & i.e. Obligation to buy & i.e. Sell one share S+P-C
Option Premium Paid Option Premium Received
QUESTION NO. 11A

Value of Call: 5 Value of Put: 10 Strike Price: 150
Current Market Price: 125 r = 10% t= 6 months.
Show if any arbitrage opportunity exists. Using PCPT.
QUESTION NO. 11B
The following table provides the prices of options on equity shares of X Ltd. and Y Ltd.
The risk free interest is 9%. You as a financial planner are required to spot any mispricing in the
quotations of option premium and stock prices. Suppose, if you find any such mispricing then how you
can take advantage of this pricing position.
Share Time to Exercise price (₹) Share price (₹) Call Price (₹) Put price (₹)
exercise
X Ltd. 6 Months 100 160 56 4
Y Ltd. 3 Months 80 100 26 2
LOS 17 : Option Strategies

Combination of Call & Put is known as OPTION STRATEGIES.
Types of Option Strategies:
Some important Option Strategies are as follows:
1. Straddle Position
2. Strangle Strategy
7.14
3. Strip Strategy
4. Strap Strategy
5. Butterfly Spread
1. Straddle Position :
Straddle may be of 2 types :
Long Straddle Short Straddle
Buy a Call and Buy a Put on the same stock with Sell a Call and Sell a Put with same exercise price
both the options having the same exercise price. and same exercise date.
Option: Buy One Call and Buy One Put Option: Sell One Call and Sell One Put
Exercise Date: Same of Both Exercise Date: Same of Both
Strike Price / Exercise Price: Same of Both Strike Price / Exercise Price: Same of Both
Note: Note:
A Long Straddle investor pays premium on both A Short Straddle investor receive premium on
Call & Put. both Call and Put.
Note:
 When an investor is not sure whether the price will go up or go down, then in such case we should
create a straddle position.
 If Question is Silent, always assume Long Straddle.
2. Strangle Strategy :
 An option strategy, where the investor holds a position in both a call and a put with different
strike prices but with the same maturity and underlying asset is called Strangles Strategy.
 Selling a call option and a put option is called seller of strangle (i.e. Short Strangle).
 Buying a call and a put is called Buyer of Strangle (i.e. Long Strangle).
 If there is a large price movement in the near future but unsure of which way the price
movement will be, this is a Good Strategy.
3. Strip Strategy (Bear Strategy) 4. Strap Strategy (Bull Strategy)
 Buy Two Put and Buy One Call Option of the  Buy Two Calls and Buy One Put when the
same stock at the same exercise price and for buyer feels that the stock is more likely to rise
the same period. Steeply than to fall.
 Strip Position is applicable when decrease in  Strap Position is applicable when increase in
price is more likely than increase. price is more likely than decrease.
Option: Buy Two Put and Buy One Call Option: Buy Two Calls and Buy One Put
Exercise Date: Same of Both Exercise Date: Same of Both
Strike Price/ Exercise Price: Same of Both Strike Price/ Exercise Price: Same of Both
5. Butterfly Spread :
In Butterfly spread position, an investor will undertake 4 call option with respect to 3 different strike
price or exercise price.
It can be constructed in following manner:
 Buy One Call Option at High exercise Price (S1)
 Buy One Call Option at Low exercise Price (S2)
 Sell two Call Option
QUESTION NO. 12A

Equity shares of A Ltd. are being currently sold for ₹ 90 per share. Both the call option and the put option
for a 3 month period are available for a strike price of ₹ 97 at a premium of ₹ 3 per share and ₹ 2 per
share respectively. An investor wants to create a straddle position in this share. Find out his net pay off
at the expiration of the option period, if the share price on that day happens to be ₹ 90 or ₹ 105.
7.15
QUESTION NO. 12B

You are given three call options on a stock at exercise price of ₹ 30, ₹ 35 and ₹ 40 with expiration date in
three months and the premium of ₹ 4, ₹ 2 and Re. 1 respectively. State how the option can be used to create
a butterfly spread. Construct a table with different market prices and state how profit changes with stock prices
ranging from ₹ 20 to 50 for the butterfly spread. Students can take price difference of 2.
LOS 18 : Binomial Model (Delta Hedging / Perfectly Hedged technique) for Call
Writer
Under this concept, we will calculate option premium for call option.
It is assumed that expected price on expiry may be greater than Current Market Price or less than
Current Market Price.
Steps involved:
Step 1: Compute the Option Value on Expiry Date at high price and at low price
Value of Call as on expiry = Max [(S – X),0]
Step 2: Buy ‘Delta’ No. of shares ‘Δ’ at Current Market Price as on Today. Delta ‘Δ ’ also
known as Hedge Ratio.
Hedge Ratio or ‘Δ’ =

OR
–
=
Step 3: Construct a Delta Hedge Portfolio i.e. Risk-less portfolio / Perfectly Hedge Portfolio
Sell one call option i.e. Short Call ,Buy Delta no. of shares and borrow net amount.
Step 4: Borrow the net Amount required for the above steps
B= [Δ × HP − 𝑉𝐶 ]
Or
B= [Δ × LP − 𝑉𝐶 ]
Where r = rate of interest adjusted for period

Step 5: Calculate Value of call as on today
Borrowed Amount = Amount required to purchase of share – Option Premium Received
B = Δ × CMP – OP
Or
7.16
(Option Premium = Δ × CMP – Borrowed Amount)

Note: Calculation of Cash flow Position/ Value of holding after 1 year
 If on Maturity Actual Market Price is HP
Cash Flow = ∆ × HP – VC
 If on Maturity Actual Market Price is S2
Cash Flow = ∆ × LP – VC
Cash Flow at HP and LP will always be same.
Meaning of perfectly hedge position under binomial model
Perfectly hedge position means Profit or Loss will be Zero or NIL. It can be achieved by buying
Δ shares, sell one call option and borrowing the required amount.
Delta is the number of shares which makes the portfolio perfectly hedged i.e. whether the stock price
on maturity goes up or decline, the value of portfolio doesn’t vary i.e. our profit and loss position will
be Zero.
QUESTION NO. 13A
Current Price ₹ 100; Strike price of 3 months call option ₹ 95. After 3 months, price may be ₹ 150 or ₹
70. Risk free rate: 12% p.a. Find Option Premium by Binomial Model?
QUESTION NO. 13B
The current market price of the equity shares of Sati Ltd. is ₹ 70 per share. It may either be ₹ 90 or ₹ 50
after a year. A call option with a strike price of ₹ 66 (time 1 year) is available. The rate of interest
applicable to the investor is 10%. An investor wants to create a replicating portfolio in order to maintain
his pay off on the call option for 100 shares. Find out Hedge Ratio, Amount of borrowing, fair value of
call and his cash flow position after a year.
QUESTION NO. 13C
Mr. Dayal is interested in purchasing equity shares of ABC Ltd. which are currently selling at ₹ 600 each.
He expects that price of share may go upto ₹ 780 or may go down to ₹ 480 in three months. The chances
of occurring such variations are 60% and 40% respectively. A call option on the shares of ABC ltd. can
be exercised at the end of three months with a strike price of ₹ 630.
a) What combination of share and option should Mr. Dayal select if he wants a perfect hedge ?
b) What should be the value of option today (the risk free rate is 10% p.a.) ?
c) What is expected return on options ?
QUESTION NO. 13D
AB Ltd.'s equity shares are presently selling at a price of ₹ 500 each. An investor is interested in purchasing AB
Ltd.'s shares. The investor expects that there is a 70% chance that the price will go up to ₹ 650 or a 30% chance
that it will go down to ₹ 450, three months from now. There is a call option on the shares of the firm that can
be exercised only at the end of three months at an exercise price of ₹ 550.
Calculate the following:
(i) If the investor wants a perfect hedge, what combination of the share and option should he select ?
(ii) Explain how the investor will be able to maintain identical position regardless of the share price.
(iii) If the risk-free rate of return is 5% for the three months period, what is the value of the option at the
beginning of the period ?
(iv) What is the expected return on the option?
LOS 19 : Black & Scholes Model

The BSM Model uses five variables to value a call option:
1. The price of the Underlying Stock (S)
7.17
2. The exercise price of the option (X)

3. The time remaining to the expiration of the option (t)
4. The riskless rate of return (r)
5. The volatility of the underlying stock price (σ)
Assumptions of BSM Model :
 The price of underlying asset follows a log normal distribution
 Markets are frictionless. There is no taxes, no transaction cost, no restriction on short sale.
 The option valued are European options.
 Risk Free continuous compounding interest rate is known and constant.
 Annualized volatility of the stock is known and constant.
 The underlying asset has no cash flow as dividend, coupons etc.
For Call:
𝐗
Value of a Call Option/ Premium on Call = 𝐒 × 𝐍(𝐝𝟏 ) − × 𝐍(𝐝𝟐 )
𝐞𝐫𝐭
Calculation of d1 and d2
𝐒
𝐥𝐧 𝐫 𝟎.𝟓𝟎𝛔𝟐 ×𝐭
𝐗
d1 =
𝛔× √𝐭
d2 = d1 – σ √𝐭
Or
𝐒
𝐥𝐧 𝐫 𝟎.𝟓𝟎𝛔𝟐 ×𝐭
𝐗
d2 =
𝛔× √𝐭
where
S = Current Market Price
X = Exercise Price
r = risk-free interest rate
t = time until option expiration
σ = Standard Deviation of Continuously Compounded annual return
For Put:
𝐗
Value of a Put Option/ Premium on Put = × [ 𝟏 − 𝐍(𝐝𝟐 )] − 𝐒 × [𝟏 − 𝐍(𝐝𝟏 )]
𝐞𝐫𝐭
Calculation of N(d1) & N(d2)

N(d1) and N(d2) can be calculated by using 2 steps:
1. Calculate the value of d1 and d2
2. Calculate N(d1) and N(d2) by using
Method 1: N(d1) and N(d2) table
Method 2: Z- table or Normal Distribution Curve
Method 1:
Example 1: Example 2:
d1 = 0.70 , d2 = 0.50 d1 = - 1.31 , d2 = - 1.49
N(d1) = N(0.70) = 0.758036 N(d1) = N(- 1.31) = 0.095098
N(d2) = N(0.50) = 0.691462 N(d2) = N(- 1.49) = 0.068112
Example 3:
d1 = 0.4539
0.45 = 0.673645
0.46 = 0.677242
7.18
When d1 increases by 0.01, the value increases by 0.003597

.
When d1 increases by 1, the value increases by
.
.
When d1 increases by 0.0039, the value increases by × 0.0039 = 0.00140283
.
N (d1) = N(0.4539)
= 0.673645 + 0.00140283
= 0.675047
Method 2: Using Normal Distribution Table or Z-Table
Example1: Example2:
d1 = 0.70 , d2 = 0.50 d1 = - 1.31 , d2 = - 1.49
d1 = 0.70 d1 = - 1.31
Z-value of 0.70 (Through table) = 0.258036 Z-value of 1.31 (Through table) = 0.404902
N(d1) = N(0.70) = 0.50 + 0.258036 N(d1) = N(- 1.31) = 0.50 - 0.404902
= 0.758036 = 0.095098
Z-value of 0.50 = 0.191462 d2 = - 1.49

N(d2) = N(0.50) = 0.50 + 0.191462 Z-value of 1.49 (Through table) = 0.431888
= 0.691462 N(d2) = N(- 1.49) = 0.50 - 0.431888
= 0.068112
Calculation of Natural log (ln)
Example1: Example2:
0.75 1.24
Natural log (0.75) ln (1.24) = 0.21511
ln (0.75) = -0.28768
QUESTION NO. 14A
We have been given the following information about X YZ company's shares and call options:
Current Share price = ₹ 185
Option Exercise Price = ₹ 170
Risk Free Interest Rate = 7% (continuous compounded)
Time to Option Expiry = 3 years
Volatility in Share Price (Standard Deviation) = 0.18
Calculate Value of the Option.
QUESTION NO. 14B
From the following data for certain stock, find the value of a call option:
Price of stock now = ₹ 80
Exercise price = ₹ 75
Standard deviation of continuously compounded annual return = 0.40
Maturity period = 6 months
Annual interest rate = 12%
Given
Number of S.D. from Mean, (z) Area of the left or right (one tail)
0.25 0.4013
0.30 0.3821
0.55 0.2912
7.19
0.60 0.2743
e 0.12x0.5 = 1.062
In 1.0667 = 0.0646
LOS 20 : BSM  when dividend amount is given in the question

Adjust Spot Price (S) or CMP as [Spot Price – PV of Dividend Income]
𝐗
Value of a Call Option = [𝐒 − 𝐏𝐕 𝐨𝐟 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐈𝐧𝐜𝐨𝐦𝐞] × 𝐍(𝐝𝟏 ) − 𝐫𝐭 × 𝐍(𝐝𝟐 )
𝐞
𝐒 𝐏𝐕 𝐨𝐟 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐈𝐧𝐜𝐨𝐦𝐞
𝐥𝐧 𝐫 𝟎.𝟓𝟎𝛔𝟐 ×𝐭
𝐗
d1 =
𝛔× √𝐭
d2 = d 1 – σ √𝐭
QUESTION NO. 15
a) The shares of TIC Ltd. are currently priced at ₹ 415 and call option exercisable in three months’ time
has an exercise rate of ₹ 400. Risk free interest rate is 5% p.a. (continuous compounded) and
Standard Deviation (Volatility) of share, price is 22%. Based on the assumption that TIC Ltd. is not
going to declare any dividend over the next three months, is the option worth buying for ₹ 25?
b) Calculate value of a foresaid call option based on Black Scholes valuation model if the current price
is considered as ₹ 380.
c) What would be the worth of put option if current price is considered ₹ 380?
d) If TIC Ltd. share price at present is taken as ₹ 408 and a dividend of ₹ 10 is expected to be paid in
the two months’ time, then, calculate value of the call option.
LOS 21 : Put-Call Ratio
Put- Call Ratio =
The ratio of the volume of put options traded to the volume of Call options traded, which is used as an
indicator of investor’s sentiment (bullish or bearish)
The put-call Ratio to determine the market sentiments, with high ratio indicating a bearish sentiment
and a low ratio indicating a bullish sentiment.
LOS 22 : Option Greek Parameters

Option price depends on 5 factors:
Option Price = f [S, X, t, r, σ], out of these factors X is constant and other causing a change in the
price of option.
We will find out a rate of change of option price with respect to each factor at a time, keeping others
constant.
1. Delta: It is the degree to which an option price will move given a small change in the underlying
stock price. For example, an option with a delta of 0.5 will move half a rupee for every full rupee
movement in the underlying stock.
The delta is often called the hedge ratio i.e. if you have a portfolio short ‘n’ options (e.g. you have
written n calls) then n multiplied by the delta gives you the number of shares (i.e. units of the
underlying) you would need to create a riskless position - i.e. a portfolio which would be worth
the same whether the stock price rose by a very small amount or fell by a very small amount.
7.20
2. Gamma: It measures how fast the delta changes for small changes in the underlying stock price
i.e. the delta of the delta. If you are hedging a portfolio using the delta-hedge technique described
under "Delta", then you will want to keep gamma as small as possible, the smaller it is the less
often you will have to adjust the hedge to maintain a delta neutral position. If gamma is too large,
a small change in stock price could wreck your hedge. Adjusting gamma, however, can be tricky
and is generally done using options.
3. Vega: Sensitivity of option value to change in volatility. Vega indicates an absolute change in
option value for a one percentage change in volatility.
4. Rho: The change in option price given a one percentage point change in the risk-free interest
rate. It is sensitivity of option value to change in interest rate. Rho indicates the absolute change
in option value for a one percent change in the interest rate.
5. Theta: It is a rate change of option value with respect to the passage of time, other things
remaining constant. It is generally negative.
7.21
PRACTICE QUESTIONS
QUESTION NO. 16
A two year tree for a share of stock in ABC Ltd., is as follows:
Consider a two years American call option on the stock of ABC Ltd., with a strike price of ₹ 98. The
current price of the stock is ₹ 100. Risk free return is 5 per cent per annum with a continuous
compounding and e0.05 = 1.05127.
Assume two time periods of one year each.
Using the Binomial Model, calculate:
(i) The probability of price moving up and down;
(ii) Expected pay offs at each nodes i.e. N1, N2 and N3 (round off upto 2 decimal points).
7.22
8.1
Foreign Exchange Exposure & Risk Management

Study Session 8
Globalization of Business
 Raising of Capital from International Capital Markets or easy excess to External Commercial
Borrowings for companies.
 Open Economy to Foreign Investments, Exports, Imports and making investments in Indian
Economy like Infrastructure sector, medical science, etc.
 Participations of FII’s in Indian capital markets.
 Trade tie-ups between countries.
 Different countries have different currencies and the different currencies have different values, so
there is a need of the rule for currency conversions for Global Business and Investments.
Three types of transactions associated with foreign exchange risk:
1. Loans(ECB)
2. Investments (Bonds & Equity)
3. Export & Import
Foreign Exchange Risk
Foreign Exchange Market (3 Tier Market)
Note :
In India, Foreign Exchange Market is regulated by RBI.
8.2
What is Exchange Rate?

 The rate of conversion is the Exchange Rate.
 An exchange rate is the price of one country’s currency expressed in terms of the currency of
another country. E.g. A rate of ₹ 50 per US $ implies that one US $ costs ₹ 50.
Rule 1 : in an exchange rate two currencies are involved.
Rule 2 : in any transaction involving Foreign Currency, you are selling one currency and buying
another.
LOS 2 : Home Currency & Foreign Currency

Home Currency: Country’s own currency.
Example:
For India ‘₹’/INR is home currency
For USA ‘US $’ or ‘Dollar’ is a home currency
For UK ‘£’ or ‘Pound’ or ‘GBP’ is home currency
Foreign Currency: Any currency other than home currency will be a Foreign Currency
Example:
For India, $, £, etc. will be a foreign currency.
For US ‘₹’, £ will be foreign currency.
LOS 3 : Bid & Ask Rate

Bid Rate: Rate at which bank BUYS left hand side currency.
Ask Rate: Rate at which bank SELLS left hand side currency.
One-way Quote: [when Bid and Ask Rate are same]
Example: 1$ = ₹ 65
Explanation:
Bank buys 1$ at ₹ 65.
Bank sells 1$ at ₹ 65.
Two-way Quote: [when Bid and Ask Rate are separately given]
Example:
1$ = ₹ 62 ---------------------------------------- ₹ 65
Left Hand Side Bid Rate / Bank Buying Ask Rate/ Bank Selling
Currency rate of left hand currency rate of left hand currency
Note:
 Difference between Bid & Ask rate represents Profit Margin for the bank.
 Quotation/ Bid & Ask rate or Exchange Rate is always quoted from the point of view of bank.
 Bid Rate must always be less than Ask Rate.
Or
Ask Rate must always be greater than Bid Rate.
 Always solve question from the point of view of investor/ Customer unless otherwise stated.
 The difference between the Ask & Bid rates is called Spread, representing the profit margin of
dealer.
Spread = Ask Rate – Bid Rate
8.3
LOS 4 : Direct Quote & Indirect Quote

Direct Quote: Home Currency Price for 1 unit of foreign currency.
Example: 1$ = ₹ 50 is DQ for Rupee.
Indirect Quote: Foreign Currency Price for 1 unit of Home Currency.
Example: 1Re = 0.0200$ is IDQ for Rupee.
Note:
 If a given quotation is direct for one country, then the same quotation will be indirect for another
country and vice-versa.
 The concept of DQ and IDQ is only theoretical and don’t have any practical relevance.
LOS 5 : Conversion of Direct Quote into Indirect Quote and vice-versa

Case 1: One-way Quote [When bid & ask rates are same]
 Direct Quote can be converted into indirect quote by taking the reciprocal of direct quote.
𝟏
IDQ =
𝐃𝐐
Case 2: Two-way Quote [When bid & ask rates are separately given]
 Direct Quote (DQ) can be converted into Indirect Quote (IDQ) by taking the reciprocal of direct
quote and switching the position.
Example: $1 = ₹ 47.25 --- ₹ 47.85 (1st Quote)

Convert DQ into the IDQ.
Solution:
DQ => $1 = ₹ 47.25 --- ₹ 47.85
IDQ => 1 Re. = −
. .
1 Re. = −
. .
OR 1 Re. = 0.02090 --- 0.02116 (2nd Quote)
Conversion Rules :
 Which currency is given in the question, we need that currency in the LHS
of the quote.
 Decide whether to Buy that currency or Sell.
 If you Buy Bank Sells Use Ask Rate
If you Sell Bank Buys Use Bid Rate
 Always Solve question from the point of view of Customer.
QUESTION NO. 1A
Consider the following ₹/SGD direct quote of ICICI Mumbai: 26.50 – 26. 75
(i) What is the cost of buying ₹ 55,000?
8.4
(ii) How much would you receive by selling ₹ 92,000?

(iii) What is the cost of buying SGD 7,450?
(iv) What is your receipt if you sell SGD 18,340?
QUESTION NO. 1B
The following two way quotes appear in the Foreign Exchange Market:
Spot 2-Months Forward
₹ / US$ ₹ 46.00/ ₹ 46.25 ₹ 47.00/ ₹ 47.50
Required:
(i) How many US dollars should a firm sell to get ₹25 lacs after 2 months?
(ii) How many Rupees is the firm required to pay to obtain US$ 2,00,000 in the Spot Market?
(iii) Assume the firm has US $ 69,000 in current Account earning no interest. ROI on Rupee Investment is
10% p.a. should the firm encash the US $ now or two months later?
LOS 6 : Spot Rate & Forward Rate

Spot Rate: Rate used for buying & selling of foreign currency at ‘As on Today or Immediately’
Forward rate: Rate used for buying & selling of foreign currency at some future Date i.e. Forward
rate is the rate contracted today for exchange of currencies at a specified future date.
LOS 7 : Premium or Discount

Premium: If the currency is costly or Expensive in future as compared to spot it is said to be at a
premium.
SR => 1$ = ₹ 45
FR => 1$ = ₹ 50
In the above quote $ is at Premium.
Discount: If the currency is Cheaper in future as compared to spot it is said to be at a discount.
SR => 1Re. = $ = 0.0222

FR => 1Re. = $ = 0.02
We can say that rupee is at discount.
Calculation of Premium or Discount
𝑭𝑹 𝑺𝑹 𝟏𝟐
× × 100
𝑺𝑹 𝐅𝐨𝐫𝐰𝐚𝐫𝐝 𝐏𝐞𝐫𝐢𝐨𝐝
Note: This formula is applicable only for left hand currency

Conclusion:
 If one currency is at a premium, then another currency must be at a discount. However, the rate
of premium may not be equal to the rate of discount.
 On account of base effect, premium is slightly higher than the discount.
QUESTION NO. 2A
The spot rate for ₹/AUD is 29.36 and the three-month forward rate is 29.45. Which currency is
appreciating and which is depreciating or which currency is trading at a discount and which at a
premium? Which currency is more expensive? Compute the annual AUD premium or discount?
8.5
QUESTION NO. 2B
The spot rate of £ is $ 1.4710 - 1.4810 and swap points for 1 month. 3 months and 6 months forwards
are 65/44, 145/123 and 290/222 respectively. Find out the outright rates for all three forward periods.
Is the £ selling at premium or discount for these periods? How many $ would be required to buy £
1,00,000 spot and after 3 months?
LOS 8 : Calculation of Forward Rate when Spot Rate & Premium or Discount is given
Example 1:
SR  1$ = ₹ 48.50
$ is at premium = 5%
Calculate FR?
Solution:
FR  1$ = ₹ 48.50 (1 + 0.05)
1$ = ₹ 50.925
Example 2:
3 months FR ₹67.20/€
Based on this rate, annualized forward discount on euro is 6%. Cal SR?
Example 3:
6 months FR € 1.3750/£
Based on this rate, annualized forward premium on euro is 5%. Cal SR?
Example 4:
3 months FR ₹92.10/£
a) Based on this rate, annualized forward premium on rupee is 8%. Cal SR?
b) Also calculate 6 months FR, if based on 6 months FR annualized forward discount on pound is
10%?
QUESTION NO. 3
Fleur du lac, a French co. has shipped goods to an American importer under a letter of credit
arrangement, which calls for payment at the end of 90 days; the invoice is for $ 124,000. Presently the
exchange rate is 5.70 French francs to the $. If the French franc were to strengthen by 5% at the end of
90 days what would be the transactions gain or loss in French francs? If it were to weaken by 5% what
would happen?
LOS 9 : SWAP POINTS/ Forward Margin/ Forward-Spot Differential

Difference between Forward Rate and Spot Rate is known as Swap Points.
Example:
SR  1£ = $ 0.02594 --- $ 0.02599
FR  1£ = $ 0.02598 --- $ 0.02608
Calculate Swap points?
Solution:
FR  1£ = $ 0.02598 --- $ 0.02608
SR  1£ = $ 0.02594 --- $ 0.02599
0.00004 0.00009
8.6
So, Swap Point = 4/9

How to ADD or DEDUCT Swap Points
 Swap Point should be Added or Deducted from the last decimal point in the Reverse Order.
 Premium  Add Swap Points
 Discount  Less Swap Points
If Premium / Discount is not mentioned, we observe the following rules:
Case 1: When Swap Points are in increasing order:
 It indicates premium on left hand currency.
 In this case, we will add swap points with spot rates to calculate forward rates.
Case 2: When Swap Points are in decreasing order:
 It indicates discount on left hand currency.
 In this case, we will deduct swap points from Spot Rate to calculate forward rates.
Note : Don’t apply the rule if Premium or Discount is used in the question.
Example: Example:
SR  1$ = 45.4500 ---- 45.4580 SR  1£ = $ 1.4510 ---- 1.4620
2 months Swap Point = 30/42 1 months Swap Point = 55/44
Calculate Forward Rate? Calculate Forward Rate?
Solution: Solution:
1$ = 45.4500 ---- 45.4580 1£ = $ 1.4510 ---- 1.4620
+ 00.0030 ---- 00.0042 (-) 0.0055 ---- 0.0044
FR 1$ = 45.4530 ---- 45.4622 FR 1£ = $ 1.4455 ---- 1.4576
QUESTION NO. 4
Spot rate for FF is $ 0.02493/97 in New York. For 1 month, 3 months & 6 months, the swap points are
3/5, 8/5 & 16/13 respectively. Convert swap points into outright forward rates.
LOS 10 : Cross Rate

Cross Rate between ant two currencies is derived with the help of quotations between these
currencies & third currency.
 Cross Rate is normally used in finding out any missing exchange rate.
 The calculation of cross rate simply requires you to focus on cancellation of common currencies,
to do so you have to multiply with DQ & IDQ.
 Always check ASK Rate > BID Rate.
QUESTION NO. 5A
1 USD= ₹ 45 1 USD = Yen 1.20 Find 1 Yen = ₹?
QUESTION NO. 5B
₹/ $ = 48/49 DM/$ = 4/5 Find ₹/DM= ?/?
QUESTION NO. 5C
₹/$ = 48/49 DM/S = 4/5 DM/FF = 1.15/1.16 ₹/FF= ?/?
LOS 11 : Squaring-up the position or Covering the Position or Closing-out the

Position under FOREX
Covering the Position means taking an opposite or reverse position to calculate profit and loss i.e. we
cover our position to book Profit or Loss.
8.7
Long Position To Cover Short Position

Short Position Long Position
QUESTION NO. 6A
You sold Hong Kong Dollar 1,00,00,000 value spot to your customer at ₹ 5.70 & covered yourself in
London market on the same day, when the exchange rate were as under :
US$ 1 = H.K.$ 7.5880 -7.5920
Local interbank market rates for USS were Spot US$1 = ₹ 42.70 - 42.85
Calculate cover rate & ascertain the profit or loss in the transaction ignore brokerage.
QUESTION NO. 6B
Your forex dealer had entered into a cross currency deal and had sold US $ 10,00,000 against EURO at
US $ 1 = EUR 1.4400 for spot delivery. However, during the day, the market became volatile and the
dealer in compliance with his management's guidelines had to square-up the position when the
quotations were:
Spot US 1 INR 31.4300/4500
1 month swap point 25/20
2 months swap point 45/35
Spot US$1 Euro 1.4400/4450
1 month forward 1.4425/4490
2 months forward 1.4460/4530
What will be the gain or loss in the transaction in terms of ₹ ?
QUESTION NO. 6C
You, a foreign exchange dealer of your bank, are informed that your bank has sold a T.T. on Corporation
for Danish Kroner 10,00,000 at the rate of Danish Kroner 1 = ₹ 6.5150, You are required to cover the
transaction either in London or New York market.
The rates on that date are as under:
Mumbai- London ₹ 74.3000 — ₹ 74.3200
Mumbai – New York ₹ 49.2500 — ₹ 49.2625
London- Copenhagen DKK 11.4200 — DKK 11.4350
New York- Copenhagen DKK 07.5670 — DKK 07.5840
In which market will you cover the transaction, London or New York, and what will be the exchange
profit or loss on the transaction? Ignore brokerages.
LOS 12 : Exchange Margin

Exchange Margin is the extra amount or percentage charged by the bank over and above the rate
quoted by it. Eg. Commission, transaction charges, etc.
Actual Selling Rate of Bank: (Add Exchange Margin)
= Ask Rate (1+ Exchange Margin)
Actual Buying Rate of Bank: (Deduct Exchange Margin)
= Bid Rate (1 – Exchange Margin)
QUESTION NO. 7A
In the inter-bank market, the DM is quoting ₹ 21.50. If the bank charges 0.125% commission for TT
selling and 0.15% for TT buying, what rate would it quote?
8.8
QUESTION NO. 7B
On Jan 28, 2005 an importer customer requested a bank to remit Singapore Dollar SGD 25,00,000
under an irrevocable LC. However due to bank strikes, the bank could affect the remittance only on
February 4,2005. The interbank market rates were as follows:
28th January 4th February
Bombay US 1 INR 45.85/45.90 45.91/45.97
London Pound 1 USD 1.7840/1.7850 1.7765/1.7775
London Pound 1 SGD 3.1575/3.1590 3.1380/3.1390
The bank wishes to retain an exchange margin of 0.125%. How much does the customer stand to gain
or lose due to the delay?(Calculate rate in multiples of 0.0001)
LOS 13 : Triangular Arbitrage

It involves 3 currencies represented by 3 corner points of triangle. We will be starting with one
currency, pass through the other two currencies and come back to the original currency. There are
two paths  clockwise and Anticlockwise.
One path will result in profit while the other path will result in Loss.
QUESTION NO. 8A
Consider the following exchange rate quotations:-
₹/$ 62.50
₹/£ 93.20
$/£ 1.5290
Show the process of arbitrage if you have ₹ 40 Lacs.
QUESTION NO. 8B
Consider the following quotations :
1 Can $ = Aus $ 0.7250 — 0.7290
1 Aus $ = SF 3.6450 — 3.6520
1 Can $ = SF 1.8650 — 1.8720
Check for triangular arbitrage starting with SF 40,000.
QUESTION NO. 8C
The following quotes are available from your dealer:
1 AUD USD 0.6000 — 0.6015
1 MXN USD 0.0933 — 0.0935
8.9
Compute the implied 1 AUD = ___ MXN cross rate?

If your dealer also quotes 1 AUD = MXN 6.3000 – 6.3025, is an arbitrage profit possible? If so,
compute the arbitrage profit in USD if you start with USD 1 Million.
LOS 14 : Purchasing Power Parity Theory (PPPT)

Calculation of Spot Rate
 PPPT is based on the concept of ‘Law of One Price’.
 PPPT is based on the fact that price of a commodity in two different market will always be same.
 If Price of a commodity in two different market are not same, there will be an arbitrage opportunity
exists in the market.
 Suppose Price of a Commodity in India is ₹ X & In USA is $Y. Spot Rate is 1$ = ₹ SR
Then X = Y × SR
SR =
𝐂𝐮𝐫𝐫𝐞𝐧𝐭 𝐏𝐫𝐢𝐜𝐞 (𝐑𝐬.)

Spot Rate (₹ / $) =
𝐂𝐮𝐫𝐫𝐞𝐧𝐭 𝐏𝐫𝐢𝐜𝐞 ($)
 Exchange Rate = Price Ratio
Calculation of Forward Rate
PPPT is also applicable in case of inflation. Suppose Inflation Rate of India is IRs and in US is I$ Forward
Rate 1$ = ₹ F. Now as per PPPT, we have after 1 year:
X (1+ I₹) = y (1+ I$ ) × FR
( )
FR =
( $)
FR = SR ×
$
𝐅𝐑 (𝐑𝐬./$) 𝟏 𝐑𝐮𝐩𝐞𝐞 𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧

=
𝐒𝐑 (𝐑𝐬./$) 𝟏 𝐃𝐨𝐥𝐥𝐚𝐫 ($)𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧
Note:
 The above equation is applicable for any two given currency.
 Determination of Premium or Discount with the help of Inflation Rate: If Inflation Rate of a country
is higher, then the currency of that Country will be at a discount in future and Vice- Versa.
Inflation rate in above equation must be adjusted according to forward period.
Case1: When Period is less than 1 Year. Case2: When Period is more than 1 Year.
𝐅𝐑 (𝐑𝐬./$) 𝟏 𝐏𝐞𝐫𝐢𝐨𝐝𝐢𝐜 𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧 𝐑𝐚𝐭𝐞 ( 𝐑𝐬.) 𝐧
= 𝐅𝐑 (𝐑𝐬./$) 𝟏 𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧 𝐑𝐚𝐭𝐞 (𝐑𝐬.)
𝐒𝐑 (𝐑𝐬./$) 𝟏 𝐏𝐞𝐫𝐢𝐨𝐝𝐢𝐜 𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧 𝐑𝐚𝐭𝐞 ( $ ) = 𝐧
𝐒𝐑 (𝐑𝐬./$) 𝟏 𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧 𝐑𝐚𝐭𝐞 ($)
QUESTION NO. 9A
The rate of inflation in USA is likely to be 3% per annum and in India it is likely to be 6.5%. The current
spot rate of US $ in India is ₹ 43.40. Find the expected rate of US $ in India after one year and 3 years
from now using purchasing power parity theory.
QUESTION NO. 9B
You are told that spot rate is $ 1.65/£. The expected inflation rate in UK and the USA for the next
three years are given below:
8.10
Year UK Inflation (%) US Inflation (%)

1 3.0 2.0
2 3.5 2.5
3 3.0 2.0
Calculate the expected $/£ spot rate after three years
QUESTION NO. 9C
The rate of inflation in India is 8% p.a. and in the USA it is 4%. The current spot rate for USD in India is
₹ 46. What will be the expected rate after 1 year and after 4 years applying purchasing power parity
theory?
LOS 15 : Interest Rate Parity Theory (IRPT)

 IRPT states that exchange rate between currencies are directly affected by their Interest Rate.
 Assumption: Investment opportunity in any two different market will always be same.
𝐅𝐑 (𝐑𝐬./$) 𝟏 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐑𝐚𝐭𝐞 (𝐑𝐬.)
=
𝐒𝐑 (𝐑𝐬./$) 𝟏 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐑𝐚𝐭𝐞 ($)
Note:
 The above equation is applicable for any two given currency.
 Interest Rate should be adjusted according to forward period.
Case1: When Period is less than 1 Year. Case2: When Period is more than 1 Year.
𝐅𝐑 (𝐑𝐬./$) 𝟏 𝐏𝐞𝐫𝐢𝐨𝐝𝐢𝐜 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐑𝐚𝐭𝐞 ( 𝐑𝐬.) 𝐧
= 𝐅𝐑 (𝐑𝐬./$) 𝟏 𝐈𝐧𝐭𝐞𝐫𝐫𝐞𝐬𝐭 𝐑𝐚𝐭𝐞 (𝐑𝐬.)
𝐒𝐑 (𝐑𝐬./$) 𝟏 𝐏𝐞𝐫𝐢𝐨𝐝𝐢𝐜 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐑𝐚𝐭𝐞 ( $ ) = 𝐧
𝐒𝐑 (𝐑𝐬./$) 𝟏 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐑𝐚𝐭𝐞 ($)
Note:
 Determination of Premium or Discount with the help of Interest Rate: If Interest rate of a country
is higher, than the currency of that country will be at a discount in future and vice-versa.
 If IRPT holds, arbitrage is not possible. In that case, it doesn’t matter whether you invest in domestic
country or foreign country, your rate of return will be same.
QUESTION NO. 10A
On 1st April, 3 months interest rate in the US and Germany are 6.5%and 4.5% per annum respectively.
The $/DM spot rate is 0.6560. What would be the forward rate for DM for delivery on 30th June?
QUESTION NO. 10B
The US dollar is selling in India at ₹ 45.50. If the interest rate for a 6 months borrowing in India is 8%
p.a. and the corresponding rate in USA is 2%.p.a.
a) Do you expect US Dollar to be at a premium or at discount in the Indian forward market?
b) What is the expected 6-months forward rate for United States Dollar in India; and
c) What is the rate of forward premium or discount?
QUESTION NO. 10C
The US Dollar is selling in India at ₹ 72.50. If the interest rate for a 3 months borrowing in India is 6%
per annum and the corresponding rate in USA is 2.75%.
(i) Do you expect that US dollar will be at a premium or at discount in the Indian Forex Market?
(ii) What will be the expected 3-months forward rate for US dollar in India?
(iii) What will be the rate of forward premium or discount?
8.11
LOS 16 : Covered Interest Arbitrage (CIA)

Type 1 Type 2
When Bid and Ask rates are same. If Bid & Ask rates are given separately.
When Investment & Borrowing rates are same Investment & Borrowing rate of a given currency
in one country. is separately given.
# (Short – cut is available) # (Hit & Trial method is used)
 When Investment opportunity in any two given countries are different, covered Interest Arbitrage
is possible.
 When IRPT is not applicable, then covered interest arbitrage will be applicable.
 The rule is to “ Borrow from one country & Invest in another Country ”.
 Suppose Interest Rate of India is INT₹ And USA is INT$. Spot Rate is 1$ = ₹ SR, Forward Rate =>
1$ = ₹ FR
Let assume Investor is having ₹ A for investment
Option 1: When investor invest ₹ A in India:
Amount of ₹ Received after one year
A1 = A (1 + INT₹)
Option 2: When investor invest ₹ A in USA:
Amount of Equivalent ₹ Received after one year
𝐀
A2 = [ $ (1 + INT$)] × FR
𝐒𝐑
IF A1 = A2 IF A1 > A2 IF A1 < A2
No arbitrage opportunity. Arbitrage Opportunity is Possible. Arbitrage opportunity is possible.
Arbitrager should invest in India Arbitrager should invest in USA
(Home Country) & borrow from (Foreign Country) & borrow from
USA (Foreign Country) India (Home Country)
Note:
If in 1st try we have arbitrage profit, then no need to solve 2nd case.
If in 1st try we have arbitrage loss, then 2nd case must be solved.
QUESTION NO. 11A
Given the following information:
Exchange Rates — Canadian Dollar 0.665 per DM (spot);
Canadian Dollar 0.670 per DM (3 months)
Interest rates — DM 7% p.a.;
Canadian Dollar 9% p.a.
What operations would be carried out to take the possible arbitrage gains?
QUESTION NO. 11B
The risk free rate of interest rate in USA is 8% p.a. and in UK is 5% p.a. The spot exchange rate between
US $ and UK £ is 1$ = £ 0.75.
Assuming that is interest is compounded on daily basis then at which forward rate of 2 year there will be
no opportunity for arbitrage.
Further, show how an investor could make risk-less profit, if two year forward price is 1 $
= 0.85 £.
Given e-0. 06 = 0.9418 & e-0.16 = 0.8521, e0.16 = 1.1735, e-0.1 = 0.9048
QUESTION NO. 11C
Spot Rate 1 US $ = ₹ 48.0123
180 days Forward Rate for 1 US $ = ₹ 48.8190
8.12
Annualized Interest Rate for 6 months ₹ = 12%

Annualized Interest Rate for 6 months US $ = 8%
Is there any arbitrage possibility? If yes how an arbitrageur can take advantage of the situation, if he is
willing to borrow ₹ 40,00,000 or US $ 83,312. Assume no transaction cost or taxes.
QUESTION NO. 11D
Following are the rates quoted at Bombay for British pound:
₹/BP 52.60/70 Interest Rates India London
3 m Forward 20/70 3 months 8% 5%
6 m Forward 50/75 6 months 10% 8%
Verify whether there is any scope for covered interest arbitrage if you borrow rupees.
QUESTION NO. 11E
Merry is a Forex Dealer with XYZ Bank. She notices following information relating to Canadian
Dollar (CAD) and German Deutschmark (DEM):
Exchange rate – CAD 0.775 per DEM (spot)
CAD 0.780 per DEM (3 months)
Interest rates – DEM 7% p.a.
CAD 9% p.a.
(i) Assuming that there is no transaction cost, determine does the Interest Rate Parity holds in above
quotations.
(ii) If yes, then explain the steps that would be required to make an arbitrage profit if Merry is
authorized to work with CAD 1 Million for the same purpose. Also determine the profit that
would be made in CAD.
Note: Ignore the decimal points in the amounts.
LOS 17 : Forward Contract

 Transaction exposure arises when a firm has a known amount of foreign currency payable or
receivable but home currency equivalent of which is unknown.
 Hedging is defined as an activity converted uncertainty into certainty. The simplest hedging
strategy is hedging through forward contract.
 In case of foreign currency is to be received in future
 In case of foreign currency is to be Paid in future

8.13
QUESTION NO. 12A

ABC Co. have taken a 6 month loan from their foreign collaborators for US dollars 2 million. Interest
payable on maturity is at LIBOR plus 1.0%. Current 6-monthLIBOR is 2%. Enquiries regarding exchange
rates with their bank elicit the following data:
Spot USD 1 ₹ 48.5275
6 months forward ₹ 48.4578
a) What would be their total commitment in Rupees, if they enter into a forward contract?
b) Will you advise them to enter into a forward contract? Explain giving reasons.
QUESTION NO. 12B
ABC Exporters Company, a UK company, is due to receive 500000 Northland dollars in 6 months’ time
for goods supplied. The company decides to hedge its currency exposure by using forward market. The
short-time interest rate in the UK is 12% per annum and the equivalent rate in Northland is 15%. Spot
rate of exchange is 2.5 Northland dollars to the UKP.
You are required: To calculate how much Exporters Company actually gains or losses as a result of the
hedging transaction if, at the end of six months, the UKP in relation to Northland dollar, had
a) gained 4%,
b) lost 2% or
c) Remained stable.
You may assume that forward rate of exchange simply reflects interest differential in the two countries
(i.e. it reflects the interest rate parity analysis of forward rates).
QUESTION NO. 12C
ABC Ltd. of UK has exported goods worth Can $ 5,00,000 receivable in 6 months. The exporter wants to
hedge the receipt in the forward market. The following information is available:
Spot Exchange Rate Can $ 2.5/£
Interest Rate in UK 12%
Interest Rate In Canada 15%
The forward rates truly reflect the interest rates differential. Find out the gain/loss to UK exporter if Can $
spot rates (i) declines 2%, (ii) gains 4% or (iii) remains unchanged over next 6 months.
QUESTION NO. 12D
Excel Exporters are holding an Export bill in United States Dollar (USD) 1,00,000 due 60 days hence.
They are worried about the falling USD value which is currently at ₹ 45.60 per USD. The concerned
Export Consignment has been priced on an Exchange rate of ₹ 45.50 per USD. The Firm’s Bankers have
quoted a 60-day forward rate of ₹ 45.20.
Calculate:
(i) Rate of discount quoted by the Bank
(ii) The probable loss of operating profit if the forward sale is agreed to.
LOS 18 : Money Market Operations

Case 1 : If Foreign Currency is to be received in future:
8.14
Step 1: Borrow in Foreign Currency: Amount of borrowing should be such that Amount Borrowed
+Interest on it becomes equal to the amount to be received.
Step 2: Convert the borrowed foreign currency into home currency by using spot Rate.
Step 3: Invest this home currency amount for the required period.
Step 4: Pay the borrowed amount of foreign currency with interest using the amount to be received
in foreign currency. [May be Ignored]
Case 2: When foreign currency is to be paid in future
Step 1: Invest in Foreign currency. Amount of investment should be such that, “Amount Invested +
Interest on it” becomes equal to amount to be paid
Step 2: Borrow in Home Currency, equivalent amount which is to be invested in foreign currency
using Spot rate.
Step 3: Pay the borrowed amount with interest in Home Currency on Maturity.
Step 4: Pay the outstanding amount with the amount received from investment. [May be ignored]
QUESTION NO. 13A
An Exporter is a UK based company. Invoice amount $ 3,50,000/- . Credit period-three months.
Exchange rates in London Money Market rates
$/£ Spot: 1.5865 – 1.5905 Deposit Loan
3 months Forward 1.6100 – 1.6140 $ 7% 9%
£ 5% 8%
a) Compute and show how a money market hedge can be put in place.
b) Identify whether it would have been advantageous to take forward cover instead?
QUESTION NO. 13B
Importer is a UK based company. Invoice amount $ 3,50,000 to be paid. Credit period six months.
Exchange rates in London Money Market rates
$/£ Spot: 1.5865 – 1.5905 Deposit Loan
6 months Forward 1.5505 – 1.5545 $ 5% 7%
£ 7% 9%
Compute and show how a money market hedge can be put in place.
Identify whether it would have been advantageous to take forward cover instead?
QUESTION NO. 13C
An Indian exporting firm, Rohit and Bros., would be cover itself against a likely depreciation of pound
sterling. The following data is given:
Receivables of Rohit and Bros £ 500,000
Spot rate ₹ 56.00/£
Payment date 3-months
3 months interest rate India: 12 % p.a
UK: 5% p.a
What should the exporter do?
8.15
QUESTION NO. 13D

H Ltd. is an Indian firm exporting handicrafts to North America. All the exports are invoiced in US$. The
firm is considering the use of money market or forward market to cover the receivable of $50,000
expected to be realized in 3 months time and has the following information from its banker:
Exchange Rates
Spot ₹ /$ 72.65/73
3-m forward ₹ l$ 72.95/73.40
The borrowing rates in US and India are 6 % and 12% p.a. and the deposit rates are 4% and 9% p.a.
respectively.
(i) Which option is better for H Ltd. ?
(ii) Assume that H Ltd. anticipates the spot exchange rate in 3-months time to be equal to the current
3-months forward rate. After 3-months the spot exchange rate turned out to be ₹/$: 73/73.42.
What is the foreign exchange exposure and risk of H Ltd.?
LOS 19 : Adjusting Exchange rate quotation when exchange margin is

attached to it
Example:
1 Euro = £ 1.7846 ± 0.0004
Solution:
1 Euro = £ 1.7842 ---- 1.7850
QUESTION NO. 14
Wenden Co is a Dutch-based company which has the following expected transactions.
One month Expected receipt of £ 2,40,000
One month Expected payment of £ 1,40,000
Three months Expected receipts of £ 3,00,000
The finance manager has collected the following information:
Spot rate (£ per €) 1.7820 ± 0.0002
One month forward rate (£ per €) 1.7829 ±0.0003
Three months forward rate (£ per €) 1.7846 ± 0.0004
Money market rates for Wenden Co Borrowing Deposit

One year Euro interest rate 4.9% 4.6%
One year Sterling interest rate 5.4% 5.1%
Required:
a) Calculate the expected Euro receipts in one month and in three months using the forward market.
b) Calculate the expected Euro receipts in three months using a money-market hedge and recommend
whether a forward market hedge should be used.
LOS 20 : Foreign Capital Budgeting

Two approaches are followed in case investment is undertaken in foreign country:
 Home Currency Approach
 Foreign Currency Approach
Home Currency Approach:
Step 1: Compute all cash inflows & outflows arising in foreign currency.
Step 2: Convert these cash Inflows & outflows into home currency by using appropriate exchange
rates (i.e. Forward Rate) (Calculate through Swap Point or IRPT)
8.16
Step 3: Compute a suitable discount rate.

Step 4: Compute Home Currency (NPV)
Foreign Currency Approach:
Step 1: Compute all cash inflows & outflows arising in foreign currency.
Step 2: Compute a suitable discount rate ( RADR).
Step 3: Compute Foreign Currency (NPV)
Step 4: Convert foreign currency NPV into Home currency by using Spot Rate
Note:
 Answer by both approach will be same.
 Discount Rate to be used should be risk-adjusted discount rate (RADR), Since foreign project
involves risk.
(1 + RADR) = (1 + Risk-free rate) (1 + Risk Premium)
 Discount Rate or RADR of both the country are different.

 Risk Premium of both home country and foreign country are assumed to be same.
QUESTION NO. 15A
Ram Pharma Ltd. an Indian based MNC, is evaluating an overseas investment proposal. Ram Pharma's
exports of automobiles products have increased to such an extent that it is considering a project to build
a plant in the U.S. The project will entail an initial outlay of $100 million and is expected to generate the
following cash flows over its four year life.
Year 1 2 3 4
Cash Flows (in $ in millions) 30 40 50 60
The current exchange rate is ₹ 45 per US S, the risk free rate in India 11% and the risk free rate in US is
6%. Ram Pharma's rupee return on a project of this kind is 15%. Should Ram Pharma undertake this
project?
QUESTION NO. 15B
ABC Ltd. is considering a project in US, which will involve an initial investment of US$ 1,10,00,000.
The project will have 5 years of life. Current spot exchange rate is ₹ 48 per US $. The risk free rate in
US is 8% and the same in India is 12 %. Cash inflow from the project is as follows:
Year Cash Inflow
1 US $ 20,00,000
2 US $ 25,00,000
3 US $ 30,00,000
4 US $ 40,00,000
5 US $ 50,00,000
Calculate the NPV of the project using foreign currency approach. Required rupee rate of return on this
project is 14%.
LOS 21 : Cancellation/Modification under Forward Contract

Forward Contract are legal binding contracts, which must be fulfilled by each and every party.
In case of cancellation of Forward Contracts, following rules must be followed:
How to cancel Forward Contract
Forward Contracts must be cancelled by entering into a reverse contract.
8.17
Rate at which contract needs to be Cancelled
Case 1 Cancelled before expiry Forward Rate prevailing as on today for expiry
Case 2 Cancelled on expiry Spot Rate of expiry
Case 3 Cancelled after expiry Spot Rate of the date when customer contracted with the bank.
Case 4 Automatic Cancellation Spot Rate prevailing on 15th day i.e. when grace period ends.
Settlement of Profit/Loss:
Case 1 Cancelled on or before expiry Customer will be eligible for both profit/Loss.
Case 2 Cancelled after expiry or automatic Customer will be eligible only for Loss
cancellation
QUESTION NO. 16
A customer with whom the Bank had entered into 3 months forward purchase contract for Swiss Francs
1,00,000 at the rate of ₹ 36.25 comes to the bank after two months and requests cancellation of the
contract. On this date, the rates are:
Spot CHF 1 ₹ 36.30 ---- 36.35
One month forward CHF 1 ₹ 36.45 ---- 36.52
Determine the amount of Profit or Loss to the customer due to cancellation of the contract.
8.18
LOS 22 : Extension of Forward Contract

Step 1: Cancellation of original Contract
Step 2: Entering into a new forward contract for the extended period.
QUESTION NO. 17A
ICICI booked a forward sale contact for USD 2,50,000 due August 30 @ ₹ 48.35. On 10th
August the customer request the bank to extend the forward contract on 30th September.
Foreign Exchange rates on 10th August are-
Spot 48.1325 — 48.1675
Forward 30 August 47.6625 — 47.7175
Forward 30 September 47.4425 — 47.5375
At what rate contract will be extended? What amount of loss/gain will be receivable payable from
customer?
QUESTION NO. 17B
An importer requests his bank to extend the forward contract of US$ 20,000 which is due for maturity
on 30th October, 2010, for a further period of 3 months. He agrees to pay the required margin money
for such extension of the contract.
Contracted Rate-US$ 1 ₹ 42.32
The US Dollar quoted on 30-10-2010
Spot 41.5000 / 41.5200
3 month’s Premium 0.87% / 0.93%
Margin money for buying and selling rate is 0.075% and 0.20% respectively.
Compute:
a) The cost to the importer in respect of the extension of the forward contract, and
b) The rate of new forward contract.
QUESTION NO. 17C
A bank enters into a forward purchase TT covering an export bill for Swiss Francs 1,00,000 at ₹ 32.4000
due 25th April and covered itself for same delivery in the local interbank market at ₹ 32.4200. However,
on 25th March, exporter sought for cancellation of the contract as the tenor of the bill is changed.
In Singapore market, Swiss Francs were quoted against dollars as under:
USD 1 = Sw. Fcs.
Spot 1.5076 / 1.5120
One month forward 1.5150 / 1.5160
Two months forward 1.5250 / 1.5270
Three months forward 1.5415 / 1.5445
and in the interbank market US dollars were quoted as under:
Spot USD 1 = ₹ 49.4302 / .4455
Spot / April .4100 / .4200
Spot / May .4300 / .4400
Spot / June .4500 / .4600
Calculate the cancellation charges, payable by the customer if exchange margin required by the bank is
0.10% on buying and selling.
QUESTION NO. 17D
An importer customer of your bank wishes to book a forward contract with your bank on 3rd September
for sale to him of SGD 5,00,000 to be delivered on 30th October.
8.19
The spot rates on 3rd September are USD/INR 49.3700/3800 and USD/SGD 1.7058/68. The swap
points are:
USD / INR USD/SGD
Spot/September 0300/0400 1st month forward 48/49
Spot/October 1100/1300 2nd month forward 96/97
Spot/November 1900/2200 3rd month forward 138/140
Spot/December 2700/3100
Spot/January 3500/4000
Calculate the rate to be quoted to the importer by assuming an exchange margin of 5 paisa.
LOS 23 : Early Delivery

The bank may accept the request of customer of delivery at the before due date of forward contract
provided the customer is ready to bear the loss if any that may accrue to the bank as a result of this.
In addition to some prescribed fixed charges bank may also charge additional charges comprising of:
a) Swap Difference: This difference can be loss/ gain to the bank. This arises on account of
offsetting its position earlier created by early delivery as bank normally covers itself against the
position taken in the original forward contract.
b) Interest on Outlay of Funds: It might be possible early delivery request of a customer may result
in outlay of funds. In such bank shall charge from the customer at a rate not less than prime
lending rate for the period of early delivery to the original due date. However, if there is an inflow
of funds the bank at its discretion may pass on interest to the customer at the rate applicable to
term deposits for the same period.
QUESTION NO. 18A

On 1 October 2015 Mr. X an exporter enters into a forward contract with a BNP Bank to sell US$
1,00,000 on 31 December 2015 at ₹ 65.40/$. However, due to the request of the importer, Mr. X
received amount on 28 November 2015. Mr. X requested the bank the take delivery of the
remittance on 30 November 2015 i.e. before due date. The inter-banking rates on 30 November
2015 was as follows:
Spot ₹ 65.22/65.27
One Month Premium 10/15
8.20
If bank agrees to take early delivery then what will be net inflow to Mr. X assuming that the prevailing
prime lending rate is 18%.
QUESTION NO. 18B
On 19th January, Bank A entered into forward contract with a customer for a forward sale of US $ 7,000,
delivery 20th March at ₹ 46.67. On the same day, it covered its position by buying forward from the
market due 19th March, at the rate of ₹ 46.655. On 19th February, the customer approaches the bank
and requests for early delivery of US $. Rates prevailing in the interbank markets on that date are as
under:
Spot (₹/$) 46.5725/5800
March 46.3550/3650
Interest on outflow of funds is 16% and on inflow of funds is 12%. Flat charges for early delivery are
₹ 100.
What is the amount that would be recovered from the customer on the transaction?
Note: Calculation should be made on months basis than on days basis.
QUESTION NO. 18C
On 1st January 2019 Global Ltd., an exporter entered into a forward contract with BBC Bank to sell
US$ 2,00,000 on 31st March 2019 at ₹ 71.50/$. However, due to the request of the importer, Global
Ltd. received the amount on 28 February 2019. Global Ltd. requested the Bank to take delivery of the
remittance on 2nd March 2019. The Inter- banking rates on 28th February were as follows:
Spot Rate ₹ 71.20/71.25
One month premium 5/10
If Bank agrees to take early delivery then what will be the net inflow to Global Ltd. assuming that the
prevailing prime lending rate is 15%. Assume 365 days in a year.
LOS 24 : Cancellation after Due Date/ Automatic Cancellation Late Delivery /

Extension after due date
In these cases the following cancellation charges may be payable:
1. Exchange Difference
2. Swap Loss
3. Interest on outlay of funds

8.21
QUESTION NO. 19A

An importer booked a forward contract with his bank on 10th April for USD 2,00,000 due on 10th June
@ ₹ 64.4000. The bank covered its position in the market at ₹ 64.2800.
The exchange rates for dollar in the interbank market on 10th June and 20th June were:
10th June 20th June

Spot USD 1= ₹ 63.8000/8200 ₹ 63.6800/7200
Sport/June ₹ 63.9200/9500 ₹ 63.8000/8500
July ₹ 64.0500/0900 ₹ 63.9300/9900
August ₹ 64.3000/3500 ₹ 64.1800/2500
September ₹ 64.6000/6600 ₹ 64.4800/5600
Exchange Margin 0.10% and interest on outlay of funds @ 12%. The importer requested
on 20th June for extension of contract with due date on 10th August.
Rates rounded to 4 decimal in multiples of 0.0025.
On 10th June, Bank Swaps by selling spot and buying one month forward.
Calculate:
(i) Cancellation rate
(ii) Amount payable on $ 2,00,000
(iii) Swap loss
(iv) Interest on outlay of funds, if any
(v) New contract rate
(vi) Total Cost
QUESTION NO. 19B
On 10th July, an importer entered into a forward contract with bank for US $ 50,000 due on 10th
September at an exchange rate of ₹ 66.8400. The bank covered its position in the interbank market at
₹ 66.6800.
How the bank would react if the customer requests on 20th September:
(i) to cancel the contract?
(ii) to execute the contract?
(iii) to extend the contract with due date to fall on 10th November?
The exchange rates for US$ in the interbank market were as below:
10th September 20th September
Spot US$1 = 66.1500/1700 65.9600/9900
Spot/September 66.2800/3200 66.1200/1800
Spot/October 66.4100/4300 66.2500/3300
Spot/November 66.5600/6100 66.4000/4900
Exchange margin was 0.1% on buying and selling.
Interest on outlay of funds was 12% p.a.
You are required to show the calculations to:
a) cancel the Contract,
b) execute the Contract, and
c) extend the Contract as above.
8.22
LOS 25 : Centralized Cash Management & Decentralized Cash Management

System
 Under Decentralized Cash Management, every branch is viewed as separate undertaking. Cash
Surplus and Cash Deficit of each branch should not be adjusted.
 Under Centralized Cash Management, every branch cash position is managed by single
centralized authority. Hence, Cash Surplus and Cash Deficit of each branch with each other is
accordingly adjusted
QUESTION NO. 20A
AMK Ltd. an Indian based company has subsidiaries in U.S. and U.K. Forecasts of surplus funds from
two subsidiaries are as below:
U.S. $ 12.5 million
U.K. £ 6 million
Following exchange rate information are obtained: $/₹ £/₹
Spot 0.0215 0.0149
30 days forward 0.0217 0.0150
Annual borrowing/deposits rates (Simple) are available.
₹ 6.4%/6.21%
$ 1.6%/1.5%
£ 3.9%/3.7%
The Indian operations are forecasting a cash deficit of ₹ 500 million. It is assumed that rates
are based on a year of 360 days.
a) Calculate the cash balance at the end of 30 days period in ₹ for each company under each of the
following scenarios ignoring transaction costs and taxes:
(i) Each company invests / finances its own cash balances / deficits in local currency independently.
(ii) Cash balances are pooled immediately in India and the net balances are invested/ borrowed
for the 30 days period.
b) Which method do you think is preferable from the parent company's point of view?
QUESTION NO. 20B
Suppose you are a treasurer of XYZ plc in the UK. XYZ have two overseas subsidiaries, one
based in Amsterdam and one in Switzerland. The Dutch subsidiary has surplus Euros in the
amount of 725,000 which it does not need for the next three months but which will be needed
at the end of that period (91 days). The Swiss subsidiary has a surplus of Swiss Francs in the amount of
998,077 that, again, it will need on day 91. The XYZ plc in UK has a net balance of £75,000 that is not
needed for the foreseeable future.
Given the rates below, what is the advantage of swapping Euros and Swiss Francs into Sterling?
Spot Rate (€) £0.6858- 0.6869
91 day Pts 0.0037/ 0.0040
Spot Rate (£) CHF 2.3295- 2.3326
91 day Pts 0.0242/ 0.0228
Interest rates for the Deposits
Amount of Currency 91 day Interest Rate % pa
£ € CHF
0 - 100,000 1 ¼ 0
100,001 - 500,000 2 1½ ¼
500,001 - 1,000,000 4 2 ½
Over 1,000,000 5.375 3 1
8.23
LOS 26 : Contribution to Sales Ratio based decision under FOREX

𝐂𝐨𝐧𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 ( 𝐒𝐚𝐥𝐞𝐬 𝐕𝐂)
Contribution to Sales Ratio = × 100
𝐒𝐚𝐥𝐞𝐬
Decision:
Higher the C/S Ratio, Better the position.
QUESTION NO. 21
Following information relates to AKC Ltd. which manufactures some parts of an electronics
device which are exported to USA, Japan and Europe on 90 days credit terms.
Cost and Sales information: Japan USA Europe
Variable cost per unit ₹ 225 ₹ 395 ₹ 510
Export sale price per unit Yen 650 US$10.23 Euro 11.99
Receipts from sale due in 90 days Yen 78,00,000 US$1,02,300 Euro 95,920
Foreign Exchange Rate Yen/₹ USS/₹ Euro/₹
Information:
Spot market 2.417-2.437 0.0214-0.021 0.0177-0.0180
3 months forward 2.397-2.427 0.0213-0.0216 0.0176-0.0178
3 months spot 2.423-2.459 0.02144-0.02156 0.0177-0.0179
Advice AKC Ltd. by calculating average contribution to sales ratio whether it should hedge it's foreign
currency risk or not.
LOS 27 : Leading & Lagging

 Leading means advancing the timing of payments and receipts.
 Lagging means postponing or delaying the timing of payments and receipts.
QUESTION NO. 22A

A firm is contemplating import of a consignment from the USA for a value of US $ 10,000. The firm
requires 90 days to make payment. The supplier has offered 60 days interest free credit and is willing to
offer additional 30 days credit at an interest rate of 6% p.a. the bankers of the firm offer a short loan for
30 days at 9% p.a. The banker’s quotations for exchange rate is:
Spot 1 USD ₹ 46
60 day Forward 1 USD ₹ 46.20
90 day Forward 1 USD ₹ 46.35
You are required to advise the firm as to whether it should:
a) Pay the supplier in 60 days, or
b) Avail the supplier’s offer of 90 days credit. Show your calculations.
8.24
QUESTION NO. 22B

Gibralater Limited has imported 5000 bottles of shampoo at landed cost in Mumbai, of US $ 20 each.
The company has the choice for paying for the goods immediately or in 3 months’ time. It has a clean
overdraft limited where 14% p.a. rate of interest is charged.
Calculate which of the following method would be cheaper to Gibralater Limited.
a) Pay in 3 months’ time with interest @ 10% p.a. and cover risk forward for 3 months.
b) Settle now at a current spot rate and pay interest of the overdraft for 3 months.
The rates are as follow :
Mumbai ₹ / $ spot 60.25-60.55
3 months swap 35/25
QUESTION NO. 22C
An Indian importer has to settle an import bill for $ 1,30,000. The exporter has given the Indian importer
two options:
a) Pay immediately without any interest charges.
b) Pay after three months with interest at 5 percent per annum.
The importer's bank charges 15 percent per annum on overdrafts. The exchange rates in the market are
as follows:
Spot rate (₹ /$) 48.35 /48.36
3-Months forward rate (₹ /$) 48.81 /48.83
The importer seeks your advice. Give your advice.
LOS 28 : Exposure Netting

Netting means adjusting receivable and payables (or inflows & Outflows)
Two conditions must be fulfilled:

1. Netting can be done for same currency.
2. Netting can be done for same period.
Note: In case of Netting, No. of forward contracts can be reduced.
QUESTION NO. 23A
A British firm will have following major cash transactions during next six months.
(1) Cash payment, due in the three months £ 1,20,000
(2) Cash receipts, due in three months $ 1,96,000
(3) Purchase of machinery, cash payment due in six months $ 5,00,000
(4) Dividend income, cash receipt due in six months $ 1,00,000
Exchange rates ($/£)
Spot 1.7106 - 1.7140
Three months forward 82/77
Six months forward 139/134
8.25
Calculate the net sterling pounds receipts & payments that the firm might expect in the case of both its
three & six months transactions if the company hedges foreign exchange risk on forward foreign
exchange market. How many Forward Contract should be taken by the company?
QUESTION NO. 23B
NP and Co. has imported goods for US $ 7,00,000. The amount is payable after three months. The
company has also exported goods for US $ 4,50,000 and this amount is receivable in two months. For
receivables amount a forward contract is already taken at ₹ 48.90.
The market rates for ₹ and Dollar are as under:
Spot ₹ 48.50/70
Two months 25/30 points
Three months 40/45 points
The company wants to cover the risk and it has two options as under:
a) To cover payables in the forward market and
b) To lag the receivables by one month and cover the risk only for the net amount. No interest for
delaying the receivables is earned. Evaluate both the options if the cost of Rupee Funds is 12%. Which
option is preferable?
LOS 29 : Forward Premium Paid or Additional cost while taking Forward

Contracts
QUESTION NO. 24A
A company is considering hedging its foreign exchange risk. It has made a purchase on 1st January, 2008
for which it has to make a payment of US $50,000 on September 30,2008. The present exchange rate
is 1 US $ = ₹40. It can purchase forward 1 US $ at ₹ 39. The company will have to make a upfront
premium of 2% of the forward amount purchased.
The cost of funds to the company is 10% p.a and the rate of corporate tax is 50%. Ignore taxation.
Consider the following situations and compute the Profit/Loss the company will make if it hedges its
foreign exchange risk:
a) If the exchange rate on September 30, 2008 is ₹ 42 per US $.
b) If the exchange rate on September 30, 2008 is ₹ 38 per US $.
QUESTION NO. 24B
A company is considering hedging its foreign exchange risk. It has made a purchase on 1st July, 2016
for which it has to make a payment of US$ 60,000 on December 31, 2016. The present exchange rate
is 1 US $ = ₹ 65. It can purchase forward 1 $ at ₹ 64. The company will have to make an upfront
premium @ 2% of the forward amount purchased. The cost of funds to the company is 12% per annum.
In the following situations, compute the profit/loss the company will make if it hedges its foreign
exchange risk with the exchange rate on 31st December, 2016 as :
a) ₹ 68 per US $.
b) ₹ 62 per US $.
c) ₹ 70 per US $.
d) ₹ 65 per US $.
LOS 30 : Letter of Credit

QUESTION NO. 25
Alert Ltd. is planning to import a multi-purpose machine from Japan at a cost 3,400 lacs yen. The
company can avail loans at 18% interest per annum with quarterly rests with which it can import the
machine. However, there is an offer from Tokyo branch of an India based bank extending credit of 180
days at 2% p.a. against opening of an irrevocable letter of credit. Other Information:
8.26
Present exchange rate ₹ 100 = 340 yen.

180 day's forward rate ₹ 100 = 345 yen.
A commission charge for letter of credit is 2% per 12 months. Advise whether the offer from the foreign
branch should be accepted?
LOS 31 : Currency Pairs

Currency Pairs are written by ISO Currency codes of the base currency and the counter currency,
separating them with a slash character.
Example:
A price quote of EUR/USD at 1.30851 means
1 Euro = 1.30851 $
QUESTION NO. 26A
Following are the spot exchange rates quoted at three different forex markets:
USD / INR 48.30 in Mumbai
GBP / INR 77.52 in London
GBP / USD 1.6231 in New York
The arbitrageur has USD 1,00,00,000. Assuming that there are no transaction costs, explain whether
there is any arbitrage gain possible from the quoted spot exchange rates.
QUESTION NO. 26B
Bharat Silk Limited, an established exporter of silk materials, has a surplus of US$ 20 million as on 31st
May 2015. The banker of the company informs the following exchange rates that are quoted at three
different forex markets:
GBP/ INR 99.10 at London
INR/ GBP 0.01 at London
USD/ INR 64.10 at Mumbai
INR/ US$ 0.02 at Mumbai
USD/ GBP 0.65 at New York
GBP/ USD 1.5530 at New York
Assuming that there are no transaction costs, advice the company how to avail the arbitrage gain from
the above quoted spot exchange rates.
LOS 32 : Gain/Loss under FOREX

8.27
QUESTION NO. 27A

X Ltd. an Indian company has an export exposure of 10 million (100 lacs) yen, value September end.
Yen is not directly quoted against Rupee. The current spot rates are USD/INR 41.79 and USD/JPY
129.75. It is estimated that Yen will depreciate to 144 level and Rupee to depreciate against dollar to
43. Forward rate of September 1998: USD/JPY 137.35 and USD/INR 42.89. You are required:
a) To calculate the expected loss if hedging is not done. How the position will change with company
taking forward cover?
b) If the spot rate on 30th September 1998 was eventually USD/JPY 137.85 and USD/INR 42.78, is the
decision to take forward cover justified?
QUESTION NO. 27B
JKL Ltd., an Indian company has an export exposure of JPY 10,000,000 payable August 31, 2014.
Japanese Yen (JPY) is not directly quoted against Indian Rupee.
The current spot rates are:
INR/US $ ₹ 62.22
JPY/US$ JPY 102.34
It is estimated that Japanese Yen will depreciate to 124 level and Indian Rupee to depreciate against US
$ to ₹ 65.
Forward rates for August 2014 are
INR/US $ ₹ 66.50
JPY/US$ JPY 110.35
Required:
Calculate the expected loss, if the hedging is not done. How the position will change, if the firm takes
forward cover?
If the spot rates on August 31, 2014 are:
INR/US $ ₹ 66.25
JPY/US$ JPY 110.85
Is the decision to take forward cover justified?
QUESTION NO. 27C
A Ltd. Operating a garment store in US has imported garments from Indian exporter of invoice amount
of ₹ 1,38,00,000 (equivalent to US$ 3,00,000). The amount is payable in 3 months. It is expected that
the exchange rate will decline by 5% over 3 months period. A Ltd. is interested to take appropriate action
in foreign exchange market. The three month forward rate is quoted at ₹ 44.50. You are required to
calculate expected loss which A Ltd. would suffer due to this decline if risk is not hedged. If there is loss,
then how he can hedge this risk?
QUESTION NO. 27D
A company operating in Japan has today affected sales to an Indian company, the payment being due
3 months from the date of invoice. The invoice amount is 108 lakhs yen. At today's spot rate, it is
equivalent to ₹ 30 lakhs. It is anticipated that the exchange rate will decline by 10% over the 3 months
period and in order to protect the yen payments, the importer proposes to take appropriate action in the
foreign exchange market. The 3 months forward rate is presently quoted as 3.3 yen per rupee. You are
required to calculate the expected loss and to show how it can be hedged by a forward contract.
LOS 33 : Evaluation of Quotation from two Banks

When quotations are received from two banks, customer should select that quotation which is more
beneficial to him.
8.28
Example:
QUESTION NO. 28
You have following quotes from Bank A and Bank B :
Bank A Bank B
SPOT USD/CHF 1.4650/55 USD/CHF 1.4653/60
3 months 5/10
6 months 10/15
SPOT GBP/USD 1.7645/60 GBP/ USD 1.7640/50
3 months 25/20
6 months 35/25
Calculate:
a) How much minimum CHF amount you have to pay for 1 Million GBP spot ?
b) Considering the quotes from Bank A only, for GBP/CHF what are the Implied Swap points for Spot
over 3 months?
LOS 34 : Borrowing and Investment Strategy

QUESTION NO. 29A
An Indian company requires ₹ 40 lacs for 3 months. It can borrow either in ₹ or $ or Yen. If it borrows a
foreign currency it has to hedge himself in the foreign exchange market. Which currency it should borrow
given:
₹/ $ ₹/ Yen
SR 45.65/ 85 0.4065/ 0.4115
3 Months FR 46.90/ 15 0.4218/ 0.4268
Interest rate p.a:
₹ 8%/ 9%
$ 6%/ 6.5%
Yen 0.4%/ 0.5%
QUESTION NO. 29B
Your bank’s London office has surplus funds to the extent of US$ 500000 for a period of 3 months. The
cost of funds to the bank is 4 % p.a. It proposes to invest these funds in London, New York or Frankfurt
and obtain the best yield, without any exchange risk to the bank. The following rates of interest are
available at the three centres of domestic funds there at for a period of 3 months.
London 5 % p.a.
New York 8 % p.a.
Frankfurt 3% p.a.
The market rates in London for US dollars and EURO are as under:
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London on New York

Spot 1.5350/90
1 month 15/18
2 months 30/35
3 months 80/85
London on Frankfurt
Spot 1.8260/90
1 month 60/55
2 months 95/90
3 months 145/140
At which centre, will the investment be made & what will be the net gain (to the nearest pound) to the
bank on the invested funds?
LOS 35 : Expected Spot Rate
Expected Spot Rate = ∑ Spot Rates × Probability
QUESTION NO. 30
In March, 2003 the Multinational Industries makes the following assessment of dollar rates per British
Pound to prevail as on 1.9.2003:
$/Pound 1.60 1.70 1.80 1.90 2.00
Probability 0.15 0.20 0.25 0.20 0.20
a) What is the expected spot rate for 1.9.2003?
b) If as of March, 2003, the 6-month forward rate is $1 .80, should the firm sell forward its pound
receivables due in September, 2003?
LOS 36 : Currency Futures

Steps Involved:
Step1: Decide Position
 Long Position
 Short Position
Note: First we will decide which currency will buy or which currency we will sell then check the
currency on the LHS of the quotation & then accordingly decide Long Position & Short Position
Step 2 : Calculation of Number of contracts/Lots

𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐏𝐨𝐬𝐢𝐭𝐢𝐨𝐧 £ $
No. of Lots = = =
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐨𝐧𝐞 𝐂𝐨𝐧𝐭𝐫𝐚𝐜𝐭 £ £
Note: Convert exposure amount in the same currency as of Lot Size/Contract Size & it will be
converted at CONTRACT RATE.
Step 3: Calculate Settlement Amount/ Total Outflow/Inflow under Future Contract
8.30
1. Calculate Profit and Loss under Future Contract
Change in Future Price × No. of Lots × Value of One Contract
2. Calculate Total Receipt/Total Payment using SR on Expiry
3. Calculation of opportunity cost of initial margin if Given
Total Outflow / Inflow under Future Hedging
QUESTION NO. 31A

XYZ Ltd. is an export oriented business house based in Mumbai.The Company invoices in customer's
currency. Its receipt of US $ 1,00,000 is due on September 1,2005.Market
information as at June, 1,2005.
Exchange Rates Currency Futures
US$/ ₹ Contract Size ₹ 4,72,000
Spot 0.02140 US $/₹
1 month forward 0.02136 June 0.02126
3 month forward 0.02127 September 0.02118
Initial Margin Interest Rates in India
June ₹10,000 7.50%
September ₹15,000 8.00%
st
On September 1 , 2005. The spot rate US $/₹ is 0.02133 and currency future rate for
September contract is 0.02134. Comment which of the following methods would be most advantageous
for XYZ Ltd.
a) Using Forward Contract
b) Using Currency Futures
c) Not Hedging Currency Risks.
It may be assumed that variation in margin would be settled on the maturity of the futures contract.
QUESTION NO. 31B
Nitrogen Ltd, a UK company is in the process of negotiating an order amounting to € 4 million with a
large German retailer on 6 months credit. If successful, this will be the first time that Nitrogen Ltd has
8.31
exported goods into the highly competitive German market. The following three alternatives are being
considered for managing the transaction risk before the order is finalized.
a) Invoice the German firm in Sterling using the current exchange rate to calculate the invoice amount.
b) Alternative of invoicing the German firm in € and using a forward foreign exchange contract to hedge
the transaction risk.
c) Invoice the German first in € and use sufficient 6 months sterling future contracts (to the nearly whole
number) to hedge the transaction risk.
Following data is available:
Spot Rate € 1.1750 - € 1.1770/£
6 months forward premium 0.60-0.55 Euro Cents
6 months future contract is currently trading at € 1.1760/£
6 months future contract size is £ 62500
Spot rate and 6 months future rate € 1.1785/£
Required:
a) Calculate to the nearest £ the receipt for Nitrogen Ltd, under each of the three proposals.
b) In your opinion, which alternative would you consider to be the most appropriate and the reason
thereof.
QUESTION NO. 31C
DSE Ltd. is an export oriented business in Kolkata. DSE Ltd. invoices in customers currency. Its receipts
of US $ 3,00,000 is due on July 1st, 2019.
Market information as at April 1st 2019
Exchange Rates Currency Futures
US $/₹ US $/₹
Spot 0.0154 April 0.0155 Contract Size = ₹ 6,40,000/-
1 Month Forward 0.0150 July 0.0151
3 Months Forward 0.0147
Initial Margin Interest Rates in India

April ₹ 13,000 9%
July ₹ 24,000 8.50%
On July, the spot rate US $/₹ is 0.0146 and currency future rate is 0.0147 Comment which of the
following methods would be most advantageous for DSE Ltd.
(i) Using forward contract.
(ii) Using currency futures
(iii) Not hedging currency risks.
It may be assumed that variation in margin would be settled on the maturity of the futures contract.
LOS 37 : Currency Options

Steps Involved:
Step1: Decide Position
Long Call Short Call
Long Put Short Put
Note: First we will decide which currency will buy or which currency we will sell then check the
currency on the LHS of the quotation & then accordingly decide Long Call & Long Put
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Step2 : Calculation of Number of contracts/Lots

𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐏𝐨𝐬𝐢𝐭𝐢𝐨𝐧 $
No. of Lots = = =17.35 or 17 lots
𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐨𝐧𝐞 𝐂𝐨𝐧𝐭𝐫𝐚𝐜𝐭 $
Note: Convert exposure amount in the same currency as of Lot Size/Contract Size & it will be
converted at CONTRACT RATE.
Step 3: Now the UNHEDGE POSITION should be hedge through forward market as there is no lot
size requirement under forward market.
Step 4: Calculation of Option Premium paid as on today with opportunity cost on it.
Step 5: Calculate / Total Outflow/Inflow under Option Contract

(i) Option Premium paid as on today with opportunity cost on it.
(ii) Unhedged Position under forward contract
(iii) Under Option Contract using Exercise Price
Total Outflow / Inflow under Option Hedging
QUESTION NO. 32A

Best of Luck Ltd. London will have to make a payment of $ 3,64,897 in six months’ time. The company
is considering the various choices it has in order to hedge its transaction exposure.
Exchange rates:
Spot rate $1.5617-1.5673
Six month forward rate $1.5455-1.5609
Money Market rates:
Borrow (%) Invest (%)

US 6 4.5
UK 7 5.5
Foreign currency option prices (1 unit is £12,500):
Exercise price Call option (March) Put option (March)

$ 1.70 $ 0.037 $ 0.096
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By making the appropriate calculations decide which of the following hedging alternatives is the most
attractive to Best of Luck Ltd:
a) Forward market
b) Money market Cover
c) Currency options
QUESTION NO. 32B
An American firm is under obligation to pay interests of Can$ 1010000 and Can$ 705000 on 31st July
and 30th September respectively. The firm is risk averse and its policy is to hedge the risks involved in
all foreign currency transactions. The Finance Manager of the Firm is thinking of hedging the risk
considering two methods i.e. fixed forward or option contracts.
It is now June 30th. Following quotations regarding rates of exchange, US$ per Can$, from the firm’s
bank were obtained:
Spot 1 Month Forward 3 Month Forward
0.9284-0.9288 0.9301 0.9356
Price for a US$ / Can$ option on a U.S stock exchange (cents per Can$, payable on purchase of the
option, contract size Can$ 50,000) are as follows:
Strike Price Calls Puts
(US$/Can$) July Sept July Sept
0.93 1.56 2.56 0.88 1.75
0.94 1.02 NA NA NA
0.95 0.65 1.64 1.92 2.34
According to the suggestion of finance manager if options are to be used, one month option should be
bought at a strike price of 94 cents and 3 months option at a strike price of 95 cents and for the remainder
uncovered by the options the firm would bear the risk. For this, it would use Forward rate as the best
estimate of spot, Transaction costs are ignored.
Recommend, which of the above two methods would be appropriate for the American firm to hedge its
foreign exchange risk on the two interest payments.
QUESTION NO. 32C
XYZ Ltd. a US firm will need £ 3,00,000 in 180 days. In this connection, the following information is
available:
Spot Rate 1 £ = $2.00
180 days forward rate of £ as of today 1 £ = $ 1.96
Interest Rate are as follows UK US
180 days deposit rate 4.5% 5%
180 days borrowing rate 5% 5.5%
A call option on £ that expires in 180 days has an exercise price of $ 1.97 and a premium of $ 0.04.
XYZ Ltd. has forecasted the spot rates 180 days hence as below:
Future Rates Probability
$1.91 25%
$1.95 60%
$2.05 15%
Which of the following strategies would be most preferable for XYZ Ltd.?
a) Forward Contract.
b) A Money Market Hedge
c) An Option Contract
d) No Hedging
Show calculation in each case
8.34
QUESTION NO. 32D

On 19th April following are the spot rate
Spot EUR/USD 1.20000 USD/INR 44.8000
Following are the quotes of European Options:
Currency Pair Call/Put Strike price Premium Expiry date
EUR/USD Call 1 .2000 $ 0.035 July 19
EUR/USD Put 1.2000 $ 0.04 July 19
USD/INR Call 44.8000 ₹ 0.12 Sep. 19
USD/INR Put 44.8000 ₹0.04 Sep. 19
a) A trader sells an at - the -money spot straddle expiring at three months (July 19). Calculate gain or
loss if three months later the spot rate is EUR/USD 1.2900.
b) Which strategy gives a profit to the dealer if five months later (Sept19) expected spot rate is USD/INR
45.00. Also calculate profit for a transaction USD 1.5 million.
QUESTION NO. 32E
th
XYZ, an Indian firm, will need to pay JAPANESE YEN (JY) 5,00,000 on 30 June. In order to hedge the
risk involved in foreign currency transaction, the firm is considering two alternative methods i.e. forward
market cover and currency option contract.
st
On 1 April, following quotations (JY/INR) are made available:
Spot 3 months forward
1.9516/1.9711 1.9726./1.9923
The prices for forex currency option on purchase are as follows:
Strike Price JY 2.125
Call option (June) JY 0.047
Put option (June) JY 0.098
For excess or balance of JY covered, the firm would use forward rate as future spot rate.
You are required to recommend cheaper hedging alternative for XYZ.
QUESTION NO. 32F
Sun Limited, an Indian company will need $ 5,00,000 in 90 days. In this connection, following
information is given below:
Spot Rate - $1 = ₹ 71
90 days forward rate of $1 as of today = ₹ 73
Interest Rates are as follows:
Particulars US India
90 days Deposit Rate 2.50% 4.00%
90 days Borrowing Rate 4.00% 6.00%
A call option on $ that expires in 90 days has an exercise price of ₹ 74 and a premium of Re. 0.10. Sun
Limited has forecasted the spot rates for 90 days as below:
Future Rate Probability
₹ 72.50 25%
₹ 73.00 50%
₹ 74.50 25%
Which of the following strategies would be the most preferable to Sun Limited:
(i) A Forward Contract;
(ii) A Money Market hedge;
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(iii) An Option Contract;

(iv) No Hedging.
Show your calculations in each case.
LOS 38 : Calculation of Return under FOREX

𝐏 𝟏 𝐏𝟎 𝐈
Return (In terms of Home Currency) = 𝟏+ (1+ C) – 1
𝐏𝟎
P0 = Price at the beginning I = Income from Interest/Dividend

P1 = Price at the End C = Change in exchange rate.
QUESTION NO. 33A
An Indian investor invests in a bond in America If the price of the bond in the beginning of the period is
$ 100 and it is $ 105 at the end of the period. The coupon interest during the period is $7. The US dollar
appreciates during this period by 3%. Find the return on investment in terms of home country currency.
QUESTION NO. 33B
The price of a bond just before a year of maturity is $ 5,000. Its redemption value is $ 5,250 at the end
of the said period. Interest is $ 350 p.a. The Dollar appreciates by 2% during the said period. Calculate
the rate of return from US Investor’s and Non-US Investor’s view point.
QUESTION NO. 33C
An American investor is considering to invest in an Indian security with a beta of 1.20. The holding period
of investment will be one year. The current rupee dollar exchange rate is ₹ 46/$. The expected
depreciation of rupee against dollar is 6%. The expected return from the market portfolio in India is 15%.
The risk free rate of return in India is 8%.
You are required to calculate the Expected Return for the US investor.
QUESTION NO. 33D
With the relaxation of investment norms in India in international market upto $ 2,50,000 Mr. X to
hedge himself against the risk of declining Indian economy and weakening of Indian Rupee during last
few year decided to diversify into International Market.
Accordingly, Mr. X invested a sum of ₹ 1.58 crore on 1.1.20x1 in Standard & Poor Index. On 1.1.20x2
Mr. X sold his investment. The other relevant data is given below:
1.1.20x1 1.1.20x2
Index of Stock Market in India 7395 ?
Standard & Poor Index 2028 1919
Exchange Rate 62.00/62.25 67.25/67.50
(i) Determine the return for a US investor.
(ii) Determine return of Mr. X of holding period.
(iii) Determine the value of Index of Stock Market in India as on 1.1.20x2 at which Mr. X would be
indifferent between investment in Standard & Poor Index and Indian Stock Market.
LOS 39 : Broken Date Contracts

A Broken Date Contract is a forward contract for which quotation is not readily available.
Example: If quotes are available for 1 month and 3 months but a customer wants a quote for 2 months,
it will be a Broken Date Contract. It can be calculated by interpolating between the available quotes for
the preceding and succeeding maturities.
8.36
QUESTION NO. 34
On April 3, 2016, a Bank quotes the following:
Spot exchange Rate (US $ 1) INR 66.2525 INR 67.5945
2 months’ swap points 70 90
3 months’ swap points 160 186
In a spot transaction, delivery is made after two days. Assume spot date as April 5, 2016.
Assume 1 swap point = 0.0001,
(i) ascertain swap points for 2 months and 15 days. (For June 20, 2016),
(ii) determine foreign exchange rate for June 20, 2016, and
(iii) compute the annual rate of premium/discount of US$ on INR, on an average rate.
LOS 40 : Treatment of withholding Tax

QUESTION NO. 35
A USA based company is planning to set up a software development unit in India. Software developed
in the Indian unit will be bought back by the US parent at a transfer price of USD $ 10 million. The unit
will remain in existence in India for one year; the software is expected to get developed within this time
frame. The US based company will be subject to corporate tax of 30 percent and a withholding tax of 10
per cent in India and will not be eligible for tax credit in the US. The software developed will be sold in
the US market for US $ 12.0 million. Other estimates are as follows
Rent for fully furnished unit with necessary- hardware in India ₹ 15,00,000
Man power cost (80 software professional will be working for 10 hours ₹ 400 per man hour
each day)
Administrative and other costs ₹ 12,00,000
Advise the US Company on financial viability of the project. The rupee-dollar rate is ₹ 48 / $.
LOS 41 : Implied Differential in Interest Rate

Interest rate is just another name of premium or discount of one country currency in relation to
another country currency (As per IRPT).
Premium or Discount = Difference in Interest Rate
Equation:
𝐅𝐑 (𝐑𝐬./$)–𝐒𝐑(𝐑𝐬./$) 𝟏𝟐
× × 100 = Interest Rate (₹) – Interest Rate($)
𝐒𝐑 𝐅𝐨𝐫𝐰𝐚𝐫𝐝 𝐏𝐞𝐫𝐢𝐨𝐝
QUESTION NO. 36A

Shoe Company sells to a wholesaler in Germany. The purchase price of a shipment is 50,000 deutsche
marks with term of 90 days. Upon payment, Shoe Company will convert the DM to dollars. The present
spot rate for DM per dollar is 1.71, whereas the 90-day forward rate is 1.70.
You are required to calculate and explain:
(i) If Shoe Company were to hedge its foreign-exchange risk, what would it do? What transactions
are necessary?
(ii) Is the deutsche mark at a forward premium or at a forward discount?
What is the implied differential in interest rates between the two countries?
(Use interest-rate parity assumption).
8.37
QUESTION NO. 36B

A German subsidiary of an US based MNC has to mobilize 100000 Euro's working capital for the next
12 months. It has the following options:
Loan from German Bank : @ 5% p.a.
Loan from US Parent Bank : @ 4% p.a.
Loan from Swiss Bank : @ 3% p.a.
Banks in Germany charge an additional 0.25% p.a. towards loan servicing. Loans from outside Germany
attract withholding tax of 8% on interest payments. If the interest rates given above are market
determined, examine which loan is the most attractive using interest rate differential.
LOS 42 : Savings due to Time Value (Discount) & Currency Fluctuation

If the firm decides to pay today rather than in future he may get two types of benefits:
 Benefit on account of discount for pre-payment.
 Benefit on account of currency fluctuation.
QUESTION NO. 37
U.S. Imports Co., purchased 1 Lacs Mark's worth of machines from a firm in Dortmund, Germany. The
value of the dollar in terms of the mark has been decreasing. The firm in Dortmund offers 2/10, net 90
terms.
The spot rate for the mark is dollar 0.55
The 90 days forward rate is dollar 0.56
a) Compute the $ cost of paying the account within 10 days.
b) Compute the $ cost of buying a forward contract to liquidate the account in 90 days.
c) The differential between part 1 and part 2 is the result of the time value of money (the discount for
prepayment) and protection from currency value fluctuation. Determine the magnitude of each of
these components.
LOS 43 : Nostro Account, Vostro Account and LORO Account

Nostro Account [Ours account with you]
This is a current account maintained by a domestic bank/dealer with a foreign bank in foreign
currency.
Example: Current account of SBI bank (an Indian Bank) with swizz bank in Swizz Franc. (CHF) is a
Nostro account.
Vostro Account [Yours account with us]

This is a current account maintained by a foreign bank with a domestic bank/dealer in Rupee currency.
Example: Current account of Swizz bank in India with SBI bank in Rupee (₹) currency
Loro Account [Our account of their Money with you]

This is a current account maintained by one domestic bank on behalf of other domestic bank in foreign
bank in a foreign currency.
8.38
In other words, Loro account is a Nostro account for one bank who opened the bank and Loro account
for other bank who refers first one account.
Example: SBI opened Current account with swizz bank. If PNB refers that account of SBI for its
correspondence, then it is called Loro account for PNB and it is Nostro account for SBI.
Note:
 SPOT purchase/sale of CHF affects both exchange position as well as Nostro account.
 However, forward purchase/sale affects only the exchange position.
1. Nostro A/c (Cash A/c) in Foreign Currency
Particulars Dr. [Debit] outflow Cr. [Credit] Inflow

of Dollars (FC) of Dollars (FC)
2. Exchange Position A/c/
Particulars Long Short

Dollar Buy (FC) Dollar Sell (FC)
8.39
8.40
QUESTION NO. 38A

You as a dealer in foreign exchange have the following position in Swiss Francs on 31st October, 2009:
Swiss Francs (SF)
Balance in the Nostro A/c Credit 1,00,000
Opening Position Overbought 50,000
Purchased a bill on Zurich 80,000
Sold forward TT 60,000
Forward purchase contract cancelled 30,000
Remitted by TT 75,000
Draft on Zurich cancelled 30,000
What steps would you take, if you are required to maintain a credit Balance of Swiss Francs 30,000 in
the Nostro A/c and keep as overbought position on Swiss Francs 10,000?
QUESTION NO. 38B
ABN-Amro Bank, Amsterdam, wants to purchase ₹ 15 million against US$ for funding their Vostro
account with Canara Bank, New Delhi. Assuming the inter-bank, rates of US$ is ₹ 51.3625/3700, what
would be the rate Canara Bank would quote to ABN-Amro Bank? Further, if the deal is struck, what
would be the equivalent US$ amount.
QUESTION NO. 38C
XYZ Bank, Amsterdam, wants to purchase ₹ 25 million against £ for funding their Nostro account and
they have credited LORO account with Bank of London, London.
Calculate the amount of £’s credited. Ongoing inter-bank rates are per $, ₹ 61.3625/3700 & per £, $
1.5260/70.
8.41
QUESTION NO. 38D

Suppose you are a dealer of ABC Bank and on 20.10.2014 you found that balance in your Nostro
account with XYZ Bank in London is £65000 and you had overbought £35000. During the day following
transaction have taken place:
£
DD purchased 12500
Purchased a Bill on London 40000
Sold forward TT 30000
Forward purchase contract cancelled 15000
Remitted by TT 37500
Draft on London cancelled 15000
What steps would you take, if you are required to maintain a credit Balance of £7,500 in the Nostro A/c
and keep as overbought position on £7,500?
QUESTION NO. 38E
You as a forex dealer have dealing position in your account in London:
Particulars £
Opening Balance (Oversold) 187,500
Purchase of cheques not credited to the account 164,000
Outstanding Forward Contracts
Sales 4,096,500
Purchases 3,651,500
DD issued not yet presented for payment 610,040
Bill purchased in hand not due for 1,442,820
What must you do to square up your position?
8.42
PRACTICE QUESTIONS
QUESTION NO. 39
The following table reflect interest rates for the US dollar and French francs. The spot exchange rate is
7.05 francs per dollars. Complete the missing entries:
3 months 6 months 1Year
Dollar interest rate (Annually compounded) 11.5% 12.25% ?
Franc interest rate (Annually compounded) 19.5% ? 20%
Forward franc per dollar ? ? 7.5200
Forward discount per franc Percent per year ? -6.3% ?
QUESTION NO. 40
ABC Technologic is expecting to receive a sum of US$ 400000 after 3 months. The company decided to
go for future contract to hedge against the risk. The standard size of future contract available in the
market is $1000. As on date spot and futures $ contract are quoting at ₹ 44.00 & ₹45.00 respectively.
Suppose after 3 months the company closes out its position futures are quoting at ₹44.50 and spot rate
is also quoting at ₹ 44.50. You are required to calculate effective realization for the company while
selling the receivable. Also calculate how company has been benefitted by using the future option.
QUESTION NO. 41
Zaz plc, a UK Company is in the process of negotiating an order amounting €2.8 million with a large
German retailer on 6 month’s credit. If successful, this will be first time for Zaz has exported goods into
the highly competitive German Market. The Zaz is considering following 3 alternatives for managing the
transaction risk before the order is finalized.
a) Mr. Peter the Marketing head has suggested that in order to remove transaction risk completely Zaz
should invoice the German firm in Sterling using the current €/£ average spot rate to calculate the
invoice amount.
b) Mr. Wilson, CE is doubtful about Mr. Peter’s proposal and suggested an alternative of invoicing the
German firm in € and using a forward exchange contract to hedge the transaction risk.
c) Ms. Karen, CFO is agreed with the proposal of Mr. Wilson to invoice the German first in €, but she
is of opinion that Zaz should use sufficient 6 month sterling future contracts (to the nearest whole
number) to hedge the transaction risk.
Following data is available
Sport Rate € 1.1960 - €1.1970/£
6 months forward points 0.60 – 0.55 Euro Cents
6 month future contract is currently trading at € 1.1943/£
6 month future contract size is £62,500
After 6 month Spot rate and future rate € 1.1873/£
You are required to
a) Calculate (to the nearest £) the £ receipt for Zaz plc, under each of 3 above proposals.
b) In your opinion which alternative you consider to be most appropriate.
QUESTION NO. 42
Columbus Surgicals Inc. is based in US, has recently imported surgical raw materials from the UK and
has been invoiced for £ 480,000, payable in 3 months. It has also exported surgical goods to India and
France.
The Indian customer has been invoiced for £ 138,000, payable in 3 months, and the French customer
has been invoiced for € 590,000, payable in 4 months.
Current spot and forward rates are as follows:
£ / US$
8.43
Spot: 0.9830 - 0.9850

Three months forward: 0.9520 - 0.9545
US$ / €
Spot: 1.8890 - 1.8920
Four months forward: 1.9510 - 1.9540
Current money market rates are as follows:
UK: 10.0% - 12.0% p.a.
France: 14.0% - 16.0% p.a.
USA: 11.5% - 13.0% p.a.
You as Treasury Manager are required to show how the company can hedge its foreign exchange
exposure using Forward markets and Money markets hedge and suggest which the best hedging
technique is.
QUESTION NO. 43
M/s Omega Electronics Ltd. exports air conditioners to Germany by importing all the components from
Singapore. The company is exporting 2,400 units at a price of Euro 500 per unit. The cost of imported
components is S$ 800 per unit. The fixed cost and other variables cost per unit are ₹ 1,000 and ₹ 1,500
respectively. The cash flows in foreign currencies are due in six months.
The current exchange rates are as follows:
₹ /Euro 51.50/55
₹ /S$ 27.20/25
After six months the exchange rates turn out as follows:
₹ /Euro 52.00/05
₹ /S$ 27.70/75
1) You are required to calculate loss/gain due to transaction exposure.
2) Based on the following additional information calculate the loss/gain due to transaction and
operating exposure if the contracted price of air conditioners is ₹ 25,000:
(i) the current exchange rate changes to
₹ /Euro 51.75/80
₹ /S$ 27.10/15
(ii) Price elasticity of demand is estimated to be 1.5
(iii) Payments and receipts are to be settled at the end of six months.
QUESTION NO. 44
You as a banker has entered into a 3 month’s forward contract with your customer to purchase AUD
1,00,000 at the rate of ₹ 47.2500. However after 2 months your customer comes to you and requests
cancellation of the contract. On this date quotation for AUD in the market is as follows:
Spot ₹ 47.3000/3500 per AUD
1 month forward ₹ 47.4500/5200 per AUD
Determine the cancellation charges payable by the customer.
QUESTION NO. 45
Suppose you are a banker and one of your export customer has booked a US$ 1,00,000 forward sale
contract for 2 months with you at the rate of ₹ 62.5200 and simultaneously you covered yourself in the
interbank market at ₹ 62.5900. However on due date, after 2 months your customer comes to you and
requests for cancellation of the contract and also requests for extension of the contract by one month.
On this date quotation for US$ in the market was as follows:
Spot ₹ 62.6800/62.7200
8.44
1 month forward ₹ 62.6400/62.7400

Determine the extension charges payable by the customer assuming exchange margin of 0.10% on
buying as well as selling.
QUESTION NO. 46
Suppose you as a banker entered into a forward purchase contract for US$ 50,000 on 5th March with
an export customer for 3 months at the rate of ₹ 59.6000. On the same day you also covered yourself
in the market at ₹ 60.6025. However on 5th May your customer comes to you and requests extension
of the contract to 5thJuly. On this date (5th May) quotation for US$ in the market is as follows:
Spot ₹ 59.1300/1400 per US$
Spot/ 5th June ₹ 59.2300/2425 per US$
Spot/ 5thJuly ₹ 59.6300/6425 per US$
Assuming a margin 0.10% on buying and selling, determine the extension charges payable by the
customer and the new rate quoted to the customer.
QUESTION NO. 47
On 15th January 2015 you as a banker booked a forward contract for US$ 250000 for your import
customer deliverable on 15th March 2015 at ₹ 65.3450. On due date customer request you to cancel
the contract. On this date quotation for US$ in the inter-bank market is as follows:
Spot ₹ 65.2900/2975 per US$
Spot/ April 3000/ 3100
Spot/ May 6000/ 6100
Assuming that the flat charges for the cancellation is ₹ 100 and exchange margin is 0.10%, then
determine the cancellation charges payable by the customer.
QUESTION NO. 48
K Ltd. currently operates from 4 different buildings and wants to consolidate its operations into one
building which is expected to cost ₹ 90 crores. The Board of K Ltd. had approved the above plan and
to fund the above cost, agreed to avail an External Commercial Borrowing (ECB) of GBP 10 m from
G Bank Ltd. on the following conditions:
• The Loan will be availed on 1st April, 2019 with interest payable on half yearly rest.
• Average Loan Maturity life will be 3.4 years with an overall tenure of 5 years.
• Upfront Fee of 1.20%.
• Interest Cost is GBP 6 months LIBOR + Margin of 2.50%.
• The 6 month LIBOR is expected to be 1.05%.
K Ltd. also entered into a GBP-INR hedge at 1 GBP = INR 90 to cover the exposure on account of the
above ECB Loan and the cost of the hedge is coming to 4.00% p.a.
As a Finance Manager, given the above information and taking the 1 GBP = INR 90:
(i) Calculate the overall cost both in percentage and rupee terms on an annual basis.
(ii) What is the cost of hedging in rupee terms?
(iii) If K Ltd. wants to pursue an aggressive approach, what would be the net gain/loss for K Ltd.
if the INR depreciates/appreciates against GBP by 10% at the end of the 5 years assuming
that the loan is repaid in GBP at the end of 5 years?
Ignore time value and taxes and calculate to two decimals.
QUESTION NO. 49
KGF Bank's Sydney branch has surplus funds of USD $ 7,00,000 for a period of 2 months. Cost of funds
to the bank is 6% p.a. They propose to invest these funds in Sydney, New York or Tokyo and obtain the
best yield, without any exchange risk to the bank. The Following rates of interest are available at the
three centres for investment of domestic funds there for a period of 2 Months.
Sydney 7.5% p.a.
8.45
New York 8% p.a.

Tokyo 4% p.a.
The market rates in Australia for US Dollars and Yen are as under: Sydney on New York:
Spot 0.7100/0.7300
1 Months 10/20
2 Months 25/30
Sydney on Tokyo:
Spot 79.0900/79.2000
1 Months 40/30
2 Months 55/50
At which centre, will the investment be made & what will be the net gain to the bank on the invested
funds?
QUESTION NO. 50
JKL Ltd. is an export business house. The company prepares invoice in customers' currency.
Its debtors of US $. 20,000,000 is due on April 1, 2017. Market information as at January 1, 2017 is:
Exchange rates US$/INR Currency Futures US $/INR
Spot 0.016667 Contract size: 31,021,218
1- month forward 0.016529 1- month 0.016519
3- month forward 0.016129 3- month 0.016118
Initial Margin Interest rates in India

1- month ₹ 32,500 7%
3- month ₹ 50,000 8%
On April 1, 2017 the spot rate US$/INR is 0.016136 and currency future rate is 0.016134. Which of the
following methods would be most advantageous to JKL Ltd.?
(i) Using forward contract
(ii) Using currency futures
Not hedging the currency risk
QUESTION NO. 51
True Blue Cosmetics Ltd. is an old line producer of cosmetics products made up of herbals. Their
products are popular in India and all over the world but are more popular in Europe.
The company invoice in Indian Rupee when it exports to guard itself against the fluctuation in exchange
rate. As the company is enjoying monopoly position, the buyer normally never objected to such invoices.
However, recently, an order has been received from a whole-saler of France for FFr 80,00,000. The
other conditions of the order are as follows:
(a) The delivery shall be made within 3 months.
(b) The invoice should be FFr.
Since, company is not interested in losing this contract only because of practice of invoicing in Indian
Rupee. The Export Manger Mr. E approached the banker of Company seeking their guidance and further
course of action.
The banker provided following information to Mr. E.
(a) Spot rate 1 FFr = ₹ 6.60
(b) Forward rate (90 days) of 1 FFr = ₹ 6.50
(c) Interest rate in India is 9% p.a. and in France 12% p.a.
Mr. E entered in forward contract with banker for 90 days to sell FFr at above mentioned rate.
When the matter came for consideration before Mr. A, Accounts Manager of company, he approaches
you.
8.46
You as a Forex consultant is required to comment on:

(i) Whether an arbitrage opportunity exists or not.
(ii) Whether the action taken by Mr. E is correct and if bank agrees for negotiation of rate, then at
what forward rate company should sell FFr to bank.
QUESTION NO. 52
A Ltd. of U.K. has imported some chemical worth of USD 3,64,897 from one of the U.S. suppliers. The
amount is payable in six months’ time. The relevant spot and forward rates are:
Spot rate USD 1.5617-1.5673
6 months’ forward rate USD 1.5455 –1.5609
The borrowing rates in U.K. and U.S. are 7% and 6% respectively and the deposit rates are 5.5% and
4.5% respectively.
Currency options are available under which one option contract is for US$ 21250. The option premium
for US$ at a strike price of GBP 0.58825/USD is GBP 0.036 (call option) and GBP 0.056 (put option) for
6 months period.
The company has 3 choices:
(i) Forward cover
(ii) Money market cover, and
(iii) Currency option
Which of the alternatives is preferable by the company?
QUESTION NO. 53
Place the following strategies by different persons in the Exposure Management Strategies Matrix.
Strategy 1: Kuljeet a wholesaler of imported items imports toys from China to sell them in the domestic
market to retailers. Being a sole trader, he is always so much involved in the promotion of his trade in
domestic market and negotiation with foreign supplier that he never pays attention to hedge his payable
in foreign currency and leaves his position unhedged.
Strategy 2: Moni, is in the business of exporting and importing brasswares to USA and European
countries. In order to capture the market he invoices the customers in their home currency. Lavi enters
into forward contracts to sell the foreign exchange only if he expects some profit out of it other-wise he
leaves his position open.
Strategy 3: TSC Ltd. is in the business of software development. The company has both receivables and
payables in foreign currency. The Treasury Manager of TSC Ltd. not only enters into forward contracts to
hedge the exposure but carries out cancellation and extension of forward contracts on regular basis to
earn profit out of the same. As a result management has started looking Treasury Department as Profit
Centre.
Strategy 4: DNB Publishers Ltd. in addition to publishing books are also in the business of importing and
exporting of books. As a matter of policy the movement company invoices the customer or receives
invoice from the supplier immediately covers its position in the Forward or Future markets and hence
never leave the exposure open even for a single day.
QUESTION NO. 54
Shanti exported 200 pieces of designer jewellery to USA at $ 200 each. To manufacture and design
this jewellery she imported raw material from Japan costing JP¥ 6000 for each piece.
The labour cost and variable overhead incurred in producing each piece of jewellery was ₹ 1,300 and
₹ 650 respectively.
On the date of export/import exchange rates are as follows:
₹/ US$ ₹ 65.00 – ₹ 66.00
JP¥/ US$ JP¥ 115 – JP¥ 120
Shanti is expecting that by the time the export remittance is received and payment of import is
made the expected Spot Rates are likely to be as follows:
₹/ US$ ₹ 68.90 – ₹ 69.25
8.47
JP¥/ US$ JP¥ 105 – JP¥ 112

You are required to calculate the result of transaction exposure of above transactions.
QUESTION NO. 55
Digital Exporters are holding an Export bill in United States Dollar (USD) 5,00,000 due after 60 days.
They are worried about the falling USD value, which is currently at ₹ 75.60 per USD. The concerned
Export Consignment has been priced on an Exchange rate of ₹ 75.50 per USD. The Firm's Bankers have
quoted a 60-day forward rate of ₹ 75.20. Calculate:
(i) Rate of discount quoted by the Bank, assuming 365 days in a year.
(ii) The probable loss of operating profit if the forward sale is agreed to.
QUESTION NO. 56
Spot rate 1 US$ = ₹ 68.50
USD premium on a six month forward is 3%. The annualized interest in US is 4% and 9% in India.
Is there any arbitrage possibility? If yes, how a trader can take advantage of the situation if he is
willing to borrow USD 3 million.
QUESTION NO. 57
Citi Bank quotes JPY/ USD 105.00 -106.50 and Honk Kong Bank quotes USD/JPY 0.0090- 0.0093.
(a) Are these quotes identical if not then how they are different?
(b) Is there a possibility of arbitrage?
(c) If there is an arbitrage opportunity, then show how would you make profit from the given
quotation in both cases if you are having JPY 1,00,000 or US$ 1,000.
QUESTION NO. 58
(a) Given:
US$ 1 = ¥ 107.31
£ 1 = US$ 1.26
A$ 1 = US$ 0.70
(i) Calculate the cross rate for Pound in Yen terms
(ii) Calculate the cross rate for Australian Dollar in Yen terms
(iii) Calculate the cross rate for Pounds in Australian Dollar terms
QUESTION NO. 59
The current spot exchange rate is $1.35/£ and the three-month forward rate is
$1.30/£. According to your analysis of the exchange rate, you are quite confident that the spot
exchange rate will be $1.32/£ after 3 months.
(i) Suppose you want to speculate in the forward market then what course of action would be
required and what is the expected dollar Profit (Loss) from this speculation?
(ii) What would be your Profit (Loss) in Dollar terms on the position taken as per your speculation if
the spot exchange rate turns out to be $1.26/£.
Assume that you would like to buy or sell £1,000,000.
QUESTION NO. 60
ZX Ltd. has made purchases worth USD 80,000 on 1st May 2020 for which it has to make a payment
on 1st November 2020. The present exchange rate is INR/USD 75. The company can purchase
forward dollars at INR/USD 74. The company will have to make an upfront premium @ 1 per cent of
the forward amount purchased. The cost of funds to ZX Ltd. is 10 per cent per annum.
The company can hedge its position with the following expected rate of USD in foreign exchange
market on 1st May 2020:
Exchange Rate Probability
(i) INR/USD 77 0.15
8.48
(ii) INR/USD 71 0.25

(iii) INR/USD 79 0.20
(iv) INR/USD 74 0.40
You are required to advise the company for a suitable cover for risk.
QUESTION NO. 61
USD 10,000 is lying idle in your Bank Account. You are able to get the following quotes from the
dealers:
Dealer Quote
A EUR/USD 1.1539
B EUR/GBP 0.9094
C GBP/USD 1.2752
Is there an opportunity of gain from these quotes?
QUESTION NO. 62
ICL an Indian MNC is executing a plant in Sri Lanka. It has raised ₹ 400 billion. Half of the amount
will be required after six months’ time. ICL is looking an opportunity to invest this amount on 1st
April,2020 for a period of six months. It is considering two underlying proposals:
Market Japan US
Nature of Investment Index Fund (JPY) Treasury Bills (USD)
Dividend (in billions) 25 -
Income from stock lending (in billions) 11.9276 -
Discount on initial investment at the end 2% -
Interest - 5 per cent per annum
Exchange Rate (1st April, 2020) JPY/INR 1.58 USD/INR 0.014
Exchange Rate (30th September, 2020) JPY/INR 1.57 USD/INR 0.013
You, as an Investment Manager, is required to suggest the best course of option.
QUESTION NO. 63
X Ltd., an Indian company, is considering a proposal to make an investment of USD 1,65,00,000 in
Latin America. The project will have a life of 5 years. The current spot exchange rate is INR/USD 72.
All investments and revenues will occur in USD. The USD and INR risk free rates are 8% and 12%
respectively. The following cash flow is expected form the project.
Year Cash inflow (USD)
1 30,00,000
2 37,50,000
3 45,00,000
4 60,00,000
5 75,00,000
Assume required rate of return on the project as 14%. You are required to calculate:
(i) The viability of the project using foreign currency approach.
(ii) What will be the impact if there is a withholding tax of 10% applicable on the project.
QUESTION NO. 64
M/s. Sky products Ltd., of Mumbai, an exporter of sea foods has submitted a 60 days bill for EUR
5,00,000 drawn under an irrevocable Letter of Credit for negotiation. The company has desired to
keep 50% of the bill amount under the Exchange Earners Foreign Currency Account (EEFC). The rates
for ₹/USD and USD/EUR in inter-bank market are quoted as follows:
8.49
₹/ USD USD/EUR
Spot 67.8000 - 67.8100 1.0775 - 1.8000
1 month forward 10/11 Paise 0.20/0.25 Cents
2 months forward 21/22 Paise 0.40/0.45 Cents
Transit Period is 20 days. Interest on post shipment credit is 8 % p.a. Exchange Margin is 0.1%. Assume
365 days in a year.
(i) Exchange rate quoted to the company
(ii) Cash inflow to the company
(iii) Interest amount to be paid to bank by the company.
QUESTION NO. 65
XYZ has taken a six-month loan from its foreign collaborator for USD 2 millions. Interest is payable
on maturity @ LIBOR plus 1%. The following information is available:
Spot Rate INR/USD 68.5275
6 months Forward rate INR/USD 68.4575
6 months LIBOR for USD 2%
6 months LIBOR for INR 6%
(i) Calculate Rupee requirements if forward cover is taken.
(ii) Advise the company on the forward cover.
What will be your opinion if spot rate of INR/USD is 68.4275 ?
QUESTION NO. 66
A US investor chose to invest in Sensex for a period of one year. The relevant information is given
below.
Size of investment ($) 20,00,000
Spot rate 1year ago (₹/$) 42.50/60
Spot rate now (₹/$) 43.85/90
Sensex 1 year ago 3,256
Senex now 3,765
Inflation in US 5%
Inflation in India 9%
(i) Compute the nominal rate of return to the US investor.
(ii) Compute the real depreciation /appreciation of Rupee.
(iii) What should be the exchange rate if relevant purchasing power parity holds good?
(iv) What will be the real return to an Indian investor in Sensex?
QUESTION NO. 67
On 1st February 2020, XYZ Ltd. a laptop manufacturer imported a particular type of Memory Chips
from SKH Semiconductor of South Korea. The payment is due in one month from the date of Invoice,
amounting to 1190 Million South Korean Won (SKW). Following Spot Exchange Rates (1st February)
are quoted in two different markets:
USD/ INR 75.00/ 75.50 in Mumbai
USD/ SKW 1190.00/ 1190.75 in New York
Since hedging of Foreign Exchange Risk was part of company’s strategic policy and no contract for
hedging in SKW was available at any in-shore market, it approached an off-shore Non- Deliverable
Forward (NDF) Market for hedging the same risk.
8.50
In NDF Market a dealer quoted one-month USD/ SKW at 1190.00/1190.50 for notional amount of
USD 100,000 to be settled at reference rate declared by Bank of Korea.
After 1 month (1st March 2020) the dealer agreed for SKW 1185/ USD as rate for settlement and on
the same day the Spot Rates in the above markets were as follows:
USD/ INR 75.50/ 75.75 in Mumbai
USD/ SKW 1188.00/ 1188.50 in New York
Analyze the position of company under each of the following cases, comparing with Spot Position of
1st February:
(i) Do Nothing.
(ii) Opting for NDF Contract.
Note: Both ₹/ SKW Rate and final payment (to be computed in ₹ Lakh) to be rounded off upto 4
decimal points.
9.1
Interest Rate Risk Management

Study Session 9
LOS 1: Forward Rate Agreement (FRA)
 A forward rate Agreement can be viewed as a forward contract to borrow/lend money at a certain
rate at some future date.
 These Contracts settle in cash.
 The long position in an FRA is the party that would borrow the money. If the floating rate at
contract expiration is above the rate specified in the forward agreement, the long position in the
contract can be viewed as the right to borrow at below market rates & the long will receive a
payment.
 If reference rate at the expiration date is below the contract rate, the short will receive a cash from
the long.
 FRA helps borrower to eliminate interest rate risk associated with borrowing or investing funds.
 Adverse movement in the interest rates will not affect liability of the borrower.
9.2
Payment to the long at settlement is:

𝐝𝐚𝐲𝐬
𝐅𝐥𝐨𝐚𝐭𝐢𝐧𝐠 𝐋𝐈𝐁𝐎𝐑 𝐅𝐨𝐫𝐰𝐚𝐫𝐝 𝐑𝐚𝐭𝐞 ×
𝟑𝟔𝟎
Notional Principal × 𝐝𝐚𝐲𝐬
𝟏 𝐅𝐥𝐨𝐚𝐭𝐢𝐧𝐠 𝐫𝐚𝐭𝐞 𝐋𝐈𝐁𝐎𝐑 × 𝟑𝟔𝟎
Example:
Consider an FRA that:
 Expires/Settles in 30 days.
 Is based on notional principal amount of $ 1 million.
 Is based on 90 days LIBOR.
 Specifies a forward Rate of 5%
Assume that actual 90 days LIBOR 30 days from now (at expiration) is 6%. Compute the cash
settlement payment at expiration and identify at which party makes the payment.
Solution:
If the long could borrow at contract rate of 5% rather than the market rate of 6%, the interest saved
on a 90 day $ 1 million loan would be:
(0.06 – 0.05) (90 / 360) × 1 million = 0.0025 × 1 million = $ 2,500
The $ 2,500 in interest savings would not come until the end of the 90 days loan period. The value
at settlement is the present value of these savings. The correct discount rate to use is the actual
rate at settlement, 6%, not the contract rate of 5%.
The payment at settlement date from the short to the long is: = $ 2,463.05.
. ×
QUESTION NO. 1A
M/s. Parker & Co. is contemplating to borrow an amount of ₹ 60 crores for a period of 3 months in the
coming 6 months’ time from now. The current rate of interest is 9% p.a., but it may go up in 6 months’
time. The company wants to hedge itself against the likely increase in interest rate.
The Company's Bankers quoted an FRA (Forward Rate Agreement) at 9.30% p.a.
What will be the effect of FRA and actual rate of interest cost to the company, if the actual rate of interest
after 6 months happens to be (i) 9.60% p.a. and (ii) 8.80% p.a.?
QUESTION NO. 1B
TM Fincorp has bought a 6×9 ₹ 100 crores FRA at 5.25%. on settlement date MIBOR turns out be as
follows:
9.3
Period Rate
3 Months 5.50
6 Months 5.70
9 Months 5.50
a) Profit/Loss to TM Fincorp in terms of basis points.
b) The settlement amount.
(Assume 360 days in a year)
FRA ARBITRAGE
Step 1 : Calculation of Fair Forward Rate
6 Months Forward rate 3 months from now
Step 2 : Decide from where we should borrow and where should we invest
Step 3 : Calculation of Arbitrage Profit
FRA Quotation: Suppose 3 × 9 FRA (Quoted by Bank)
QUESTION NO. 1C
The following market data is available:
Spot USD/JPY 116.00
Deposit rates p.a. USD JPY
3 months 4.50% 0.25%
6 months 5.00% 0.25%
Forward Rate Agreement (FRA) for Yen is Nil.
a) What should be 3 months FRA rate at 3 months forward?
b) The 6 & 12 months LIBORS are 5% & 6.5% respectively.
c) A bank is quoting 6/12 USD FRA at 6.50 - 6.75%. Is any arbitrage opportunity available? Calculate
profit in such case.
9.4
QUESTION NO. 1D
Electraspace is consumer electronics wholesaler. The business of the firm is highly seasonal in nature. In
6 months of a year, firm has a huge cash deposits and especially near Christmas time and other 6
months firm cash crunch, leading to borrowing of money to cover up its exposures for running the
business.
It is expected that firm shall borrow a sum of €50 million for the entire period of slack season in about
3 months.
A Bank has given the following quotations:
Spot 5.50% - 5.75%
3 × 6 FRA 5.59% - 5.82%
3 × 9 FRA 5.64% - 5.94%
3 month €50,000 future contract maturing in a period of 3 months is quoted at 94.15 (5.85%).
a) How a FRA, shall be useful if the actual interest rate after 3 months turnout to be:
(i) 4.5%, (ii) 6.5%.
b) How 3 months Future contract shall be useful for company if interest rate turns out as mentioned in
part (a) above.
QUESTION NO. 1E
Two companies ABC Ltd. and XYZ Ltd. approach the DEF Bank for FRA (Forward Rate Agreement). They
want to borrow a sum of ₹ 100crores after 2 years for a period of 1 year. Bank has calculated Yield
Curve of both companies as follows:
Year XYZ Ltd. ABC ltd.*
1 3.86 4.12
2 4.20 5.48
3 4.48 5.78
* The difference in yield curve is due to the lower credit rating of ABC Ltd. compared to XYZ Ltd.
a) You are required to calculate the rate of interest DEF Bank would quote under 2V3 FRA, using the
company’s yield information as quoted above.
b) Suppose bank offers Interest Rate Guarantee for a premium of 0.1% of the amount of loan, you are
required to calculate the interest payable by XYZ Ltd. if interest rate in 2 years turns out to be (i)
4.50%, (ii) 5.50%
QUESTION NO. 1F
An Indian company obtains the following quotes (₹/$)
Spot: 35.90/36.10
3 - Months forward rate: 36.00/36.25
The company needs $ funds for six months. Determine whether the company should borrow in $ or
₹ Interest rates are :
3 - Months interest rate : ₹ : 12%, $ : 6%
6 - Months interest rate : ₹ : 11.50%, $ : 5.5%
Also determine what should be the rate of interest after 3-months to make the company indifferent
between 3-months borrowing and 6-months borrowing in the case of:
(i) Rupee borrowing
(ii) Dollar borrowing
Note: For the purpose of calculation you can take the units of dollar and rupee as 100 each.
9.5
LOS 2 : Currency SWAP
QUESTION NO. 2A
Mc. Donald’s Hamburger Co. wishes to lend $ 5,00,000 to its Japanese subsidiary. At the same time,
Yasufuku Heavy Industries is interested in making a medium-term loan of approximately the same
amount to its U.S subsidiary. The two parties are brought together by an investment bank for purpose of
making parallel loans. Mc. Donald will lend $ 500.000 to the U.S. subsidiary of Yasufuku for 4 years at
13%.Principal and interest are payable only at the end of the fourth year with interest compounding
annually.
Yasufuku will lend the Japanese subsidiary of Mc. Donald 70 million Yen for 4 years at 10%. Again the
principal and interest (annual compounding) are payable at the end. The current exchange rate is 140
Yen to the $. However, the dollar is expected to decline by 5 Yen to the dollar per year over the next 4
years
a) If these expectations prove to be correct, what will be the dollar equivalent of principal and interest
payments to Yasufuku at the end of 4 years?
b) What total dollars will Mc. Donald receive at the end of4 years from the payment of principal and
interest on its loan by the U.S. subsidiary of Yasufuku?
c) Which party is better off with the parallel loan arrangement? What would happen if the Yen. Did not
change in value?
QUESTION NO. 2B
A Inc. and B Inc. intend to borrow $ 200,000 and $ 200,000 in ¥ respectively for a time horizon of one
year. The prevalent interest rates are as follows:
Company ¥ Loan $ Loan
A Inc 5% 9%
B Inc 8% 10%
The prevalent exchange rate is $1 = ¥120.
They entered in a currency swap under which it is agreed that B Inc will pay A Inc @ 1% over the ¥ Loan
interest rate which the later will have to pay as a result of the agreed currency swap whereas A Inc will
reimburse interest to B Inc only to the extent of 9%. Keeping the exchange rate invariant, quantify the
opportunity gain or loss component of the ultimate outcome, resulting from the designed currency swap.
9.6
LOS 3 : Interest Rate Swap [ Two Party]
 Two parties exchange their interest rate obligation.

 The plain vanilla interest rate swap involves trading fixed interest rate payments for floating rate
payments.
 The party who wants fixed-rate interest payments agrees to pay fixed-rate interest.
 The Counter party, who receives the fixed payments agrees to pay variable-rate interest/floating
rate interest.
 The difference between the fixed rate payment and the floating rate payment is calculated and
paid to the appropriate counterparty.
 Net interest is paid by the one who owes it.
 Swaps are zero-sum game. What one party gains, the other party losses.
The Net formulae for the Fixed-Rate payer, based on a 360-day year and a floating rate of LIBOR is:
𝐍𝐨.𝐨𝐟 𝐃𝐚𝐲𝐬
(Net Fixed Rate Payment)t = [Swap Fixed Rate – LIBOR t-1] [National Principal]
𝟑𝟔𝟎
Note:
 If this number is positive, fixed-rate payer pays a net payment to the floating-rate party.
 If this number is negative, then the fixed-rate payer receives a net flow from the floating rate
payer
Example:
Calculating the payments on an interest rate Swap
Bank A enters into a $ 1,000,000 quarterly-pay plain vanilla interest rate swap as the fixed-rate payer
at a fixed rate of 6% based on a 360-day year.
The floating-rate payer agrees to pay 90-day LIBOR plus a 1% margin; 90-day LIBOR is currently 4%.
90-day LIBOR rates are: 4.5% 60 Days from now
5.0% 180 days from now
Calculate the amount Bank A pays or receives 90, 270, 360 days from now.
Solution:
The payment 90 days from now depends on current LIBOR and the fixed rate(don’t forget the 1%
margin)
Fixed-rate payer pays:
0.06 − 0.04 + 0.01 × 1,000,000 = $2,500
9.7
270 days from now the payment is based on LIBOR 180 days from now, which is 5%. Adding the 1%
margin makes the floating-rate 6%, which is equal to the fixed rate, so there is no net third quarterly
payment.
The Bank’s “payment” 360 days from now is:
0.06 − 0.055 + 0.01 × 1,000,000 = $1,250
Since the floating-rate payment exceeds the fixed-rate payment, Bank A will receive $ 1,250 at the
fourth payment date.
QUESTION NO. 3A
A Dealer quotes “All-in-Cost” for a generic swap at 8% against six months LIBOR flat. If the notional
principal amount of swap is ₹ 6,00,000 :
a) Calculate semi-annual fixed payment.
b) Find the first floating rate payment for (i) above, if the six-month period from the effective date of
swap to the settlement date comprises 181 days and that the corresponding LIBOR was 6% on the
effective date of swap.
c) In (ii) above, if the settlement is on ‘NET’ basis, how much the fixed rate payer would pay to the
floating rate payer? Generic swap is based on 30 / 360 days.
QUESTION NO. 3B
Derivative Bank entered into a plain vanilla swap through on OIS (Overnight Index Swap) on a principal
of ₹ 10 Crores and agreed to receive MIBOR overnight floating rate for a fixed payment on the principal.
The swap was entered into on Monday, 2nd August, 2010 and was to commence on 3rd August, 2010
and run for a period of 7 days.
Respective MIBOR rates for Tuesday to Monday were:
7.75%, 8.15%, 8.12%, 7.95%, 7.98%, 8.15%
If Derivative Bank received ₹ 317 net on settlement, calculate Fixed rate and interest under both legs.
Notes: (i) Sunday is Holiday, (ii) Work in rounded rupees and avoid decimal working.
LOS 4 : Interest Rate Caps, Floor & Collar

CAP Maximum Rate Borrowings Floating Rate
FLOOR Minimum Rate Investments Floating Rate
Interest Rate Cap : ( Maximum Rate For Borrowing @ Floating )
If a firm borrows at floating rate, it is afraid of interest rate rising, to hedge against the same, it will
buy an interest rate cap i.e. Long call at X=Cap rate
 It is a series/portfolio of interest rate Call option on interest rates.
 Each particular call option being called a CAPLET.
 Caps pay when rate rises above the cap rate.
Interest Rate Floor : ( Minimum Rate For Investment @ Floating )

If a firm invest at floating rate, it is afraid of interest rate falling, to hedge against the same, it will
buy an interest rate Floor i.e. Long put at X=Floor rate
9.8
 It is a series/portfolio of Interest rate put Option on interest rate. Such particular put option being
called a FLOORLET
 Floor pays when rate falls below the Floor Rate.
Interest Rate Collar:

 It is a combination of a Cap and a Floor.
 Premium paid on one option would be compensated with the premium received on selling another
option.
 If premium paid on caps is equal to the premium received on floor, then it would be called Zero
Cost Collar.
+ -
A floating rate borrower may buy a cap [C ] & simultaneously sells a floor i.e.[P ].Initial outflow will
+ -
reduce.( C =Long Call & P =Short Put)
+ -
Similarly, a floating rate investor may buy a Floor (P ) & simultaneously sell a Cap (C ). Initial outflow
+
will reduce.(P =Long Put & C-=Short Call)
QUESTION NO. 4A
a) Suppose that a 1-year cap has a cap rate of 8% and a notional amount of 100 crore. The frequency
of settlement is quarterly and the reference rate is 3- month MIBOR. Assume that 3 - month MIBOR
for the next four quarters is as shown below.
Quarters 3 - months MIBOR (%)
1 8.70
2 8.00
3 7.80
4 8.20
You are required to compute payoff for each quarter.
9.9
b) Suppose that a 1-year floor has a floor rate of 4% and a notional amount of ₹ 200 crore. The
frequency of settlement is quarterly and the reference rate is 3 month MIBOR. Assume that 3-month
MIBOR for the next four quarters is as shown below.
Quarters 3 - months MIBOR (%)
1 4.70
2 4.40
3 3.80
4 3.40
You are required to compute payoff for each quarter.
QUESTION NO. 4B
XYZ Limited borrows £ 15 Million of six months LIBOR + 10.00% for a period of 24 months. The company
anticipates a rise in LIBOR, hence it proposes to buy a Cap Option from its Bankers at the strike rate of
8.00%. The lump sum premium is 1.00% for the entire reset periods and the fixed rate of interest is
7.00% per annum. The actual position of LIBOR during the forthcoming reset period is as under:
Reset Period LIBOR (%)
1 9.00
2 9.50
3 10.00
You are required to show how far interest rate risk is hedged through Cap Option.
For calculation, work out figures at each stage up to four decimal points and amount nearest to £. It
should be part of working notes.
QUESTION NO. 4C
XYZ Inc. having a £ 10 million floating rate loan on July 1, 2013 with resetting of coupon rate every 6
months equal to LIBOR + 50 bp. XYZ is interested in a collar strategy by selling a Floor and buying a
Cap. XYZ buys the 3 years Cap and sell 3 years Floor as per the following details on July 1, 2013:
Notional Principal Amount $ 10 million
Reference Rate 6 months LIBOR
Strike Rate 4% for Floor and 7% for Cap
Premium 0*
*Since Premium paid for Cap = Premium received for Floor
Using the following data you are required to determine:
(i) Effective interest paid out at each reset date,
(ii) The average overall effective rate of interest p.a.
Reset Period LIBOR (%)
31-12-2013 6.00
30-06-2014 7.50
31-12-2014 5.00
30-06-2015 4.00
31-12-2015 3.75
30-06-2016 4.25
QUESTION NO. 4D
A textile manufacturer has taken floating interest rate loan of ₹ 40,00,000 on 1st April, 2012. The rate
of interest at the inception of loan is 8.5% p.a. interest is to be paid every year on 31st March, and the
duration of loan is four years. In the month of October 2012, the Central bank of the country releases
following projections about the interest rates likely to prevail in future.
9.10
(i) On 31st March, 2013, at 8.75%; on 31st March, 2014 at 10% on 31st March, 201? at 10.5% and
on 31st March, 2016 at 7.75%. Show how this borrowing can hedge the risk arising out of expected
rise in the rate of interest when he wants to peg his interest cost at 8.50% p.a.
(ii) Assume that the premium negotiated by both the parties is 0.75% to be paid on 1st October, 2012
and the actual rate of interest on the respective due dates happens to be as: on 31st March, 2013
at 10.2%; on 31st March, 2014 at 11.5%; on 31st March, 2015 at 9.25%; on 31st March, 2016 at
9.0% and 8.25%. Show how the settlement will be executed on the perspective interest due dates.
LOS 5 : Equity Swap

An equity swap is an exchange of future cash flows between two parties that allows each party to diversify its
income for a specified period of time while still holding its original assets. An equity swap is similar to an
interest rate swap, but rather than one leg being the "fixed" side, it is based on the return of an equity index.
The two sets of nominally equal cash flows are exchanged as per the terms of the swap, which may involve
an equity-based cash flow (such as from a stock asset, called the reference equity) that is traded for fixed-
income cash flow (such as a benchmark interest rate).
QUESTION NO. 5
TMC Holding Ltd. has a portfolio of shares of diversified companies valued at ₹ 400 crore enters into a
swap arrangement with None Bank on the terms that it will get 1.15% quarterly on notional principal of
₹ 400 crore in exchange of return on portfolio which is exactly tracking the Sensex which is presently
21600.
You are required to determine the net payment to be received/ paid at the end of each quarter if Sensex
turns out to be 21860, 21780, 22080 and 21960.
9.11
PRACTICE QUESTION
QUESTION NO. 6
IM is an American firm having its subsidiary in Japan and JI is a Japanese firm having its subsidiary in
USA: They face the following interest rates:
IM JI
USD Floating rate LIBOR+0.5% LIBOR+2.5%
JPY Fixed rate 4% 4.25%
IM wishes to borrow USD at floating rate and JI JY at fixed rate. The amount required by both the
companies is same at the current Exchange Rate. A financial institution requires 75 basis points as
commission for arranging Swap. The companies agree to share the benefit/ loss equally.
You are required to find out
(i) Whether a beneficial swap can be arranged ?
(ii) What rate of interest for both IM and JI ?
QUESTION NO. 7
Punjab Bank has entered into a plain vanilla swap through on Overnight Index Swap (OIS) on a principal
of ₹ 2 crore and agreed to receive MIBOR overnight floating rate for a fixed payment on the principal.
The swap was entered into on Monday, 24th July, 2017 and was to commence on 25th July, 2017 and
run for a period of 7 days.
8.70%, 9.10%, 9.12%, 8.95%, 8.98% and 9.10%.
If Punjab Bank received ₹ 507 net on settlement, calculate Fixed rate and interest under both legs.
Notes:
(i) Sunday is a Holiday.
(ii) Workout in rounded rupees and avoid decimal working.
(iii) Consider a year consists of 365 days.
QUESTION NO. 8
The treasurer of a company expects to receive a cash inflow of $15,000,000 in 90 days. The treasurer
expects short-term interest rates to fall during the next 90 days. In order to hedge against this risk, the
treasurer decides to use an FRA that expires in 90 days and is based on 90-day LIBOR. The FRA is
quoted at 1.5%. At expiration, LIBOR is 1.25%. Assume that the notional principal on the contract is
$15,000,000.
(i) Indicate whether the treasurer should take a long or short position to hedge interest rate risk.
(ii) Using the appropriate terminology identify the type of FRA used here.
(iii) Calculate the gain or loss to the company as a consequence of entering the FRA.
QUESTION NO. 9
Drilldip Inc. a US based company has a won a contract in India for drilling oil field. The project will
require an initial investment of ₹ 500 Crores. The oil field along with equipments will be sold to Indian
Government for ₹ 740 Crores in one year time. Since the Indian Government will pay for the amount in
Indian Rupee (₹) the company is worried about exposure due exchange rate volatility.
a) Construct a swap that will help the Drilldip to reduce the exchange rate risk.
b) Assuming that Indian Government offers a swap at spot rate which is 1US$ =₹ 50 in one year, then
should the company should opt for this option or should it just do nothing. The spot rate after one
year is expected to be 1US$ =₹ 54. Further you may also assume that the Drilldip can also take a
US$ loan at 8% p.a.
9.12
QUESTION NO. 10
The Treasury desk of a global bank incorporated in UK wants to invest GBP 200 million on 1st January,
2019 for a period of 6 months and has the following options:
(1) The Equity Trading desk in Japan wants to invest the entire GBP 200 million in high dividend
yielding Japanese securities that would earn a dividend income of JPY 1,182 million. The
dividends are declared and paid on 29th June. Post dividend, the securities are expected to
quote at a 2% discount. The desk also plans to earn JPY 10 million on a stock borrow lending
activity because of this investment. The securities are to be sold on June 29 with a T+1 settlement
and the amount remitted back to the Treasury in London.
(2) The Fixed Income desk of US proposed to invest the amount in 6 month G-Secs that provides a
return of 5% p.a.
The exchange rates are as follows:
Currency Pair 1-Jan-2019 (Spot) 30-Jun-2019 (Forward)
GBP-JPY 148.0002 150.0000
GBP- USD 1.28000 1.30331
QUESTION NO. 11
IB an Indian firm has its subsidiary in Japan and Zaki a Japanese firm has its subsidiary in India and
face the following interest rates:
Company IB Zaki
INR floating rate BPLR + 0.50% BPLR + 2.50%
JPY (Fixed rate) 2% 2.25%
Zaki wishes to borrow Rupee Loan at a floating rate and IB wishes to borrow JPY at a fixed rate. The
amount of loan required by both the firms is same at the current exchange rate. A financial institution
may arrange a swap and requires 25 basis points as its commission. Gain, if any, is to be shared by
the firms equally.
You are required to find out:
(i) Whether a swap can be arranged which may be beneficial to both the firms?
(ii) What rate of interest will the firms end up paying?
10.1
Bond Valuation
Study Session 10
LOS 1 : Introduction (Fixed Income Security)
Bonds are the type of long term obligation which pay periodic interest & repay the principal amount
on maturity.
Three types of Cash Flows
(i) Interest
(ii) Principal Repayment
(iii) Re-Investment Income
Purpose of Bond’s indenture & describe affirmative and negative covenants
 The contract that specifies all the rights and obligations of the issuer and the owners of a fixed
income security is called the Bond indenture.
 These contract provisions are known as covenants and include both negative covenants
(prohibitions on the borrower) and affirmative covenants (actions that the borrower promises to
perform) sections.
1. Negative Covenants : This Includes
a) Restriction on asset sales (the company can’t sell assets that have been pledged as collateral).
b) Negative pledge of collateral (the company can’t claim that the same assets back several debt
issues simultaneously).
c) Restriction on additional borrowings (the company can’t borrow additional money unless
certain financial conditions are met).
2. Affirmative Covenants: This Includes
a) Maintenance of certain financial ratios.
b) Timely payment of principal and interest.
Common Options embedded in a bond Issue, Options benefit the issuer or the Bondholder
 Security owner options:
a) Conversion option
b) Put provision
c) Floors set a minimum on the coupon rate
 Security issuer option:
a) Call provisions
b) Prepayment options
c) Caps set a maximum on the coupon rate
LOS 2 : Terms used in Bond Valuation

(i) Face Value ₹ 1,000
(ii) Maturity Year 10 Years
(iii) Coupon rate 10%
(iv) Coupon Amount ₹ 1,000 × 10% = ₹ 100 p.a.
(v) B0 / Value of the Bond as on Today/ Current Market ₹ 950
Price/Issue Price/ Net Proceeds
(vi) Yield to Maturity/ Kd / Discount Rate / Required return 12%
of investor / Cost of debt / Expected Return/ Opportunity
Cost / Market Rate of Interest
(vii) Redemption Value/ Maturity Value ₹ 1,200
10.2
Note :
(i) Coupon Rate is used to calculate Interest Amount.
(ii) Face Value is always used to calculate Interest Amount.
(iii) If Maturity Value is not given, then it is assumed to be equal to Face Value.
(iv) If Face Value is not given, then it is assumed to be ₹ 100 or ₹ 1000 according to the Question.
(v) If Maturity Year is not given, then it is assumed to be equal to infinity.
LOS 3 : Valuation of Straight Bond / Plain Vanilla Bond

Straight Coupon Bonds are those bonds which pay equal amount of interest and repay principal
amount on Maturity.
Step 1: Estimates the cash flows over the Life of the bond.
Step 2: Determine the appropriate discount rate.
Step 3: Calculate the present value of the estimated cash flow using appropriate discount
rate.
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐯𝐚𝐥𝐮𝐞 𝐨𝐫 𝐏𝐚𝐫 𝐯𝐚𝐥𝐮𝐞
B0 = + +..................+ +
(𝟏 𝐘𝐓𝐌)𝟏 (𝟏 𝐘𝐓𝐌)𝟐 (𝟏 𝐘𝐓𝐌)𝐧 (𝟏 𝐘𝐓𝐌)𝐧
Or
Interest × PVAF (Yield %, n year) + Maturity Value × PVF (Yield %, nth year)
n = No. of years to Maturity
QUESTION NO. 1A
A ₹ 1,000 par value bond bearing a coupon rate of 14 per cent matures after 5 years, the required rate
of return on this bond is 13 per cent. Calculate the value of the bond.
QUESTION NO. 1B
Nominal value of 10% bonds issued by a company is ₹100. The bonds are redeemable at
₹ 110 at the end of year 5. Determine the value of the bond if required yield is (i) 5%, (ii) 5.1%, (iii) 10%
and (iv) 10.1%.
QUESTION NO. 1C
The Nominal value of 10% Bonds issued at par by M/s. SK Ltd. is ₹ 100. The bonds are redeemable at ₹
110 at the end of year 5.
(I) Determine the value of the bond if required yield is :
(i) 8%
(ii) 9%
(iii) 10%
(iv) 11%
(II) When will the value of the bond be highest ? Given below are Present Value Factors :
Year 1 2 3 4 5
PV Factor @ 8% 0.926 0.857 0.794 0.735 0.681
PV Factor @ 9% 0.917 0.842 0.772 0.708 0.650
PV Factor @ 10% 0.909 0.826 0.751 0.683 0.621
PV Factor @ 11% 0.901 0.812 0.731 0.659 0.593
10.3
LOS 4 : Coupon Rate Structures

1. Zero – Coupon Bond (Pure Discount Securities)
a) They do not pay periodic interest.
b) They pay the Par value at maturity and the interest results from the fact that Zero – Coupon Bonds
are initially sold at a price below Par Value. (i.e. They are sold at a significant discount to Par
Value).
2. Step – up Notes
a) They have coupon rates that increase over – time at a specified rate.
b) The increase may take place one or more times during the life cycle of the issue.
3. Deferred – Coupon Bonds
a) They carry coupons, but the initial coupon payments are deferred for some period.
b) The coupon payments accrue, at a compound rate, over the deferral period and are paid as a
lump sum at the end of that period.
c) After the initial deferment period has passed, these bonds pay regular coupon interest for the rest
of the life of the issue (to maturity).
4. Floating – Rate Securities
a) These are bond for which coupon interest payments over the life of security vary based on a
specified reference rate.
b) Reference Rate may be LIBOR [London Interbank Offered Rate] or EURIBOR or any other rate and
then adds or subtracts a stated margin to or from that reference rate.
New coupon rate = Reference rate ± quoted margin
5. Inflation – indexed Bond (TIPS)
They have coupon formulas based on inflation.

E.g.: Coupon rate = 3% + annual change in CPI
LOS 5 : Valuation of Perpetual Bond/ Irredeemable Bond/ Non – Callable Bond

They are infinite bond, never redeemable, non- callable bond.
𝐀𝐧𝐧𝐮𝐚𝐥 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭
Value of Bond =
𝐘𝐓𝐌
QUESTION NO. 2A
A bond pays ₹ 90 interest annually up to perpetuity, (i) What is its value if the current yield is 10 %? (ii)
If the current yield changes to 8% and 12%, then what it its value?
QUESTION NO. 2B
John inherited the following securities on his uncle's death:
Type of Security Nos. Annual Maturity Yield
Coupon Years
Bond A (₹ 1,000) 10 9% 3 12
Bond B (₹ 1,000) 10 10% 5 12
Preference Shares C (₹ 100) 100 11% — 13
Preference Shares D (₹ 100) 100 12% — 13
Compute the current value of his uncle's portfolio.
10.4
LOS 6 : Valuation of Zero-Coupon Bond

 Zero- coupon Bond has only a single payment at maturity.
 Value of Zero- Coupon Bond is simply the PV of the Par or Face Value.
𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐕𝐚𝐥𝐮𝐞
Bond value =
(𝟏 𝐘𝐓𝐌)𝐧
QUESTION NO. 3A
Suppose we are considering investing in a zero-coupon bond that matures in 5 years and has a face
value of ₹ 1000. If these bonds are priced to yield 10%, what is the present value of the bonds?
QUESTION NO. 3B
On 1 June 2003 the financial manager of Gadgets Corporation's Pension Fund Trust is reviewing strategy
regarding the fund. Over 60% of the fund is invested in fixed rate long-term bonds. Interest rates are
expected to be quite volatile for the next few years. Among the pension fund's current investments are
two AAA rated bonds:
(i) Zero coupon June 2018
(ii) 12% Gilt June 2018 (interest is payable semi-annually)
The current annual redemption yield (yield to maturity) on both bonds is 6%. The semi-annual yield may
be assumed to be 3%. Both bonds have a par value and redemption value of $ 100.
Required: Estimate the market price of each of the bonds if interest rates:
a) increase by 1 %;
b) decrease by 1 %.
LOS 7 : Confusion regarding Coupon Rate & YTM

YTM  Required Return / Investor’s Expectation / Mkt. Rate of Interest.
 YTM is always subjected to change according to Market Conditions.
Coupon Rate  Rate of Interest paid by the company.
 Coupon Rate is always constant throughout the life of the bond and it is not affected by change
in market condition.
 Sometimes interest is expressed in terms of Basis Point i.e. 1% = 100 Basis Points
LOS 8 : Valuation of Semi – annual Coupon Bonds

Pay interest every six months
𝐘𝐓𝐌 𝐩.𝐚. 𝐂𝐨𝐮𝐩𝐨𝐧 𝐫𝐚𝐭𝐞 𝐩.𝐚

a) b) c) n × 2
𝟐 𝟐
Note:
If quarterly use 4 instead of 2
If monthly use 12 instead of 2
QUESTION NO. 4A
A 6 years bond of ₹ 1,000 has an annual rate of interest of 14 %. The interest is paid half yearly. If the
required rate of return is 16 % what is the value of bond?
QUESTION NO. 4B
A bond with 7.5% coupon interest, Face Value ₹ 10,000 & term to maturity of 2 years, presently yields
6%. Interest payable half yearly. Calculate Market Price.
10.5
QUESTION NO. 4C
On 31st March, 2013, the following information about Bonds is available:
Name of Security Face Maturity Date Coupon Coupon Date(s)
Value ₹ Rate
Zero coupon 10,000 31st March, 2023 N.A. N.A.
T-Bill 1,00,000 20th June, 2013 N.A. N.A.
10.71% GOI 2023 100 31st March, 2023 10.71 31st March
10 % GOI 2018 100 31st March, 2018 10.00 31st March & 30th
September
Calculate:
(i) If 10 years yield is 7.5% p.a. what price the Zero Coupon Bond would fetch on 31st March, 2013?
(ii) What will be the annualized yield if the T-Bill is traded @ 98500?
(iii) If 10.71% GOI 2023 Bond having yield to maturity is 8%, what price would it fetch on April 1, 2013
(after coupon payment on 31st March)?
(iv) If 10% GOI 2018 Bond having yield to maturity is 8%, what price would it fetch on April 1, 2013
(after coupon payment on 31st March)?
QUESTION NO. 4D
Pet feed plc has outstanding, a high yield Bond with following features:
Face Value £ 10,000
Coupon 10%
Maturity Period 6 Years
Special Feature Company can extend the life of Bond to 12 years.
Presently the interest rate on equivalent Bond is 8%.
(a) If an investor expects that interest will be 8%, six years from now then how much he should pay for
this bond now.
(b) Now suppose, on the basis of that expectation, he invests in the Bond, but interest rate turns out to
be 12%, six years from now, then what will be his potential loss/ gain if the company extents the life
of Bond for another 6 years.
LOS 9 : Valuation of Bond with Changing Coupon Rate

Coupon rate changes from one year to another year as per the terms of bond-indenture.
QUESTION NO. 5A
The Elu Co. is contemplating a debenture issue on the following terms:
Face Value ₹ 100 per debenture
Term to maturity 7 years
Coupon rate of interest:
Years
1-2 8% p.a.
3-4 12% p.a.
5-7 15% p.a.
The current market rate of interest on similar debentures is 15% per annum. The company proposes to
price the issue so as to yield a (compounded) return of 16% per annum to the investor. Determine the
issue price. Assume redemption at a premium of 5% on face value.
Present value interest factor @ 16% p.a.
Period 0 1 2 3 4 5 6 7
Factor 1.000 0.862 0.743 0.641 0.552 0.476 0.410 0.354
10.6
QUESTION NO. 5B
Bright Computers Limited is planning to issue a debenture series with a face value of ₹ 1,000 each for a term
of 10 years with the following coupon rates:
Years Rates
1-4 8%
5-8 9%
9-10 13%
The current market rate on similar debenture is 15% p.a. The company proposes to price the issue in such a
way that a yield of 16% compounded rate of return is received by the investors. The redeemable price of the
debenture will be at 10% premium on maturity. What should be the issue price of debenture?
Pv @ 16% for 1 to 10 years are: .862, .743, .641, .552, .476, .410, .354, .305, .263, .227
respectively.
LOS 10: Over – Valued & Under – Valued Bonds

Case Value Decision
PV of MP of Bond < Actual MP of Bond Over – Valued Sell
PV of MP of Bond > Actual MP of Bond Under – Valued Buy
PV of MP of Bond = Actual MP of Bond Correctly Valued Either Buy/ Sell
LOS 11: Self – Amortization Bond

 They make periodic interest and principal payments over the life of the bond. i.e. at regular
interval.
 Interest is calculated on balance amount.
QUESTION NO. 6
A PSU is proposing to sell 8 years bond of ₹ 1000 at 10% coupon rate per annum Bond amount will be
amortized equally over its life. If an investor has a minimum required rate of return of 8%, what is the
bond's present value?
LOS 12: Holding Period Return (HPR) for Bonds

𝐁 𝟏 𝐁 𝟎 𝐈𝟏
HPR =
𝐁𝟎
𝐁𝟏 𝐁𝟎 𝐈𝟏
= +
𝐁𝟎 𝐁𝟎
(Capital gain Yield/ Return) (Interest Yield /Current Yield)

10.7
LOS 13 : Calculation of Current Yield/ Interest Yield
𝐀𝐧𝐧𝐮𝐚𝐥 𝐂𝐚𝐬𝐡 𝐂𝐨𝐮𝐩𝐨𝐧 𝐏𝐚𝐲𝐦𝐞𝐧𝐭

Current Yield =
𝐁𝐨𝐧𝐝 𝐏𝐫𝐢𝐜𝐞 𝐨𝐫 𝐌𝐚𝐫𝐤𝐞𝐭 𝐏𝐫𝐢𝐜𝐞
Note: Current Yield is always calculated on per annum basis.

1. If existing bond :-
B0 = Current Market Price of Bond (1st preference)
Or
Present value Market Price of Bonds (2nd preference)
2. If new bond issued :-
B0 = Issue Price
Issue Price = Face value – Discount + Premium
3. Company Point of view :-
B0 = Net Proceeds
Net Proceeds = Face value – Discount + Premium (-) Floating Cost
QUESTION NO. 7
What is the current yield of the 6.5 % August 2005 maturity bond, which has a maturity value of ₹ 1000.
The current bond price is ₹ 1075.3125?
LOS 14 : YTM (Yield to Maturity) / Kd / Cost of debt/ Market rate of Interest/

Market rate of return
 YTM is an annualized overall return on the bond if it is held till maturity.
 YTM is the IRR of a Bond
 It is the annualized rate of return on the investment that the investor expect (on the date of
investment) to earn from the date of investment to the date of maturity. It is also referred to as
required rate of return.
Alternative 1: By IRR technique.
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐯𝐚𝐥𝐮𝐞 𝐨𝐫 𝐏𝐚𝐫 𝐯𝐚𝐥𝐮𝐞
B0 = + +..................+ +
(𝟏 𝐘𝐓𝐌)𝟏 (𝟏 𝐘𝐓𝐌)𝟐 (𝟏 𝐘𝐓𝐌)𝐧 (𝟏 𝐘𝐓𝐌)𝐧
10.8
 YTM & price contain the same information

 If YTM given, calculate Price.
 If Price given, calculate YTM.
𝐋𝐨𝐰𝐞𝐫 𝐑𝐚𝐭𝐞 𝐍𝐏𝐕
YTM = Lower Rate + × Difference in Rate
𝐋𝐨𝐰𝐞𝐫 𝐑𝐚𝐭𝐞 𝐍𝐏𝐕 𝐇𝐢𝐠𝐡𝐞𝐫 𝐑𝐚𝐭𝐞 𝐍𝐏𝐕
Alternative 2: By approximation formula
𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐕𝐚𝐥𝐮𝐞 𝐂𝐌𝐏/𝐁𝟎

𝐧
YTM = 𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐕𝐚𝐥𝐮𝐞 𝐂𝐌𝐏/𝐁𝟎
𝟐
QUESTION NO. 8A
Ganesh, wishes to find the YTM on his company's 10-year, 10% bond which is currently selling for ₹ 900.
Face Value is ₹ 1,000.
Calculate the YTM, using (i) Approximation formula (ii) IRR Technique.
QUESTION NO. 8B
If the market price of the bond is ₹ 95; years to maturity = 6 yrs; coupon rate = 13% p.a (paid annually)
and issue price is ₹ 100. What is the yield to maturity?
QUESTION NO. 8C
An investors is considering the purchase of the following Bond:
Face value ₹100
Coupon rate 11%
Maturity 3 years
a) If he wants a yield of 13% what is the maximum price he should be ready to pay for?
b) If the Bond is selling for ₹ 97.60, what would be his yield?
LOS 15 : YTM (Yield to Maturity) of Semi-Annual Bond
𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐕𝐚𝐥𝐮𝐞 𝐂𝐌𝐏/𝐁𝟎

𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐟𝐨𝐫 𝟔 𝐦𝐨𝐧𝐭𝐡𝐬
𝐧×𝟐
YTM per 6 months = 𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐕𝐚𝐥𝐮𝐞 𝐂𝐌𝐏/𝐁𝟎
𝟐
YTM per annum = YTM of 6 month × 2

10.9
QUESTION NO. 9
A Bond with a face value of ₹ 1000, a 12% coupon payable half yearly is refundable at a
premium of 4% 5 years from today. The bond is currently trading at 1050. The yield applicable for such
bonds is T + 2%, where T = 8%.
a) Find the Market Price of the bond?
b) What is the current yield?
c) What is the YTM on the bond?
d) What will be the investment action?
LOS 16 : YTM of a Zero – Coupon Bond
𝑴𝒂𝒕𝒖𝒓𝒊𝒕𝒚 𝑽𝒂𝒍𝒖𝒆
Bond value =
(𝟏 𝒀𝑻𝑴)𝒏
 If YTM is given, calculate B0.

 If B0 is given, Calculate YTM.
LOS 17 : YTM of a Perpetual Bond
𝑨𝒏𝒏𝒖𝒂𝒍 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕
Bond value =
𝒀𝑻𝑴
 If YTM is given, calculate B0.

 If B0 is given, Calculate YTM.
QUESTION NO. 10
Calculate Market Price of: 10% Government of India security currently quoted at ₹ 110, but interest rate
is expected to go up by 1 %.
LOS 18 : Calculation of Kd in case of Floating Cost

 Floating Cost is cost associated with issue of new bonds.
e.g. Brokerage, Commission, etc
 We should take Bond value (B0) Net of Floating Cost.
𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐕𝐚𝐥𝐮𝐞 𝐍𝐞𝐭 𝐏𝐫𝐨𝐜𝐞𝐞𝐝𝐬
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭(𝟏 𝐭𝐚𝐱 𝐫𝐚𝐭𝐞)
𝐧
Kd = 𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐕𝐚𝐥𝐮𝐞 𝐍𝐞𝐭 𝐏𝐫𝐨𝐜𝐞𝐞𝐝𝐬
𝟐
QUESTION NO. 11
A company issues ₹ 10 lacs 12% debentures of ₹ 100 each. The debentures are redeemable after the
expiry of fix period of 7 years. The company is in 35% tax bracket.
Required:
a) Calculate cost of debt. after tax, if debentures are issued at (a) Par (b) 10% Discount
(c) 10% Premium.
b) If brokerage is paid at 2%, what will be the cost of debentures, if issue is at Par?
10.10
LOS 19 : Treatment of Tax

Tax is important part for our analysis, it must be considered if it is given in question.
Two types of Tax rates are given :-
1. Interest Tax rate/ Normal Tax Rate
We should take Interest Net of Tax i.e. Interest Amount (1 – Tax)
2. Capital Gain Tax rate
Take Maturity value after Capital Gain Tax i.e. Maturity Value – Capital Gain Tax Amount
Maturity value – (Maturity value – B0) × Capital gain tax rate
𝐌𝐕 𝐧𝐞𝐭 𝐨𝐟 𝐂𝐆 𝐓𝐚𝐱 𝐁𝟎
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭( 𝟏 𝐓𝐚𝐱 𝐫𝐚𝐭𝐞)
𝐧
YTM = 𝐌𝐕 𝐧𝐞𝐭 𝐨𝐟 𝐂𝐆 𝐓𝐚𝐱 𝐁𝟎
𝟐
QUESTION NO. 12
There is a 9%, 5 year bond issue in the market. The issue price is ₹90 and the redemption price is ₹ 105.
For an investor with marginal Income tax rate of 30% and capital gains tax of 10% (assuming no
indexation), what is the post-tax yield to maturity?
LOS 20 : Yield to call (YTC) & Yield to Put (YTP)
1. Yield to Call
Callable Bond : When company call its bond or Re-purchase its bond prior to the date of Maturity.
Call Price: Price at which Bond will call by the Company.
Call Date: Date on which Bond is called by the Company prior to Maturity.
n: No. of Years upto Call Date.
𝐂𝐚𝐥𝐥 𝐏𝐫𝐢𝐜𝐞 𝐁𝟎
𝐧
YTC = 𝐂𝐚𝐥𝐥 𝐏𝐫𝐢𝐜𝐞 𝐁𝟎
𝟐
2. Yield to Put
Puttable Bond: When investor sell their bonds prior to the date of maturity to the company.
Put Price: Price at which Bond will put/ Sell to the Company.
Put Date: Date on which Bond is sold by the investor prior to Maturity.
n: No. of years upto Put Date.
𝐏𝐮𝐭 𝐏𝐫𝐢𝐜𝐞 𝐁𝟎
𝐧
YTP = 𝐏𝐮𝐭 𝐏𝐫𝐢𝐜𝐞 𝐁𝟎
𝟐
QUESTION NO. 13
a) Nominal value of 10% debentures of a company is ₹ 100. The debentures can be called at call price
of ₹ 110 after 4 years. Interests are paid annually. Determine Yield To Call (YTC) if current market
price of debentures is ₹ 102.
10.11
b) Nominal value of 8% debentures of a company is ₹ 100. The debentures are Puttable at exercise
price ₹ 105 after 5 years. Interests are paid annually. Determine Yield To Put (YTP) if current market
price of debentures is ₹ 103.
LOS 21 : Yield to worst

 It is the lowest yield between YTM, YTC, YTP, Yield to first call.
 Yield to worst is lowest among all.
QUESTION NO. 14
Given the following data calculate Yield To Worst: YTM - 10%, YTC = 7%, YTP=9%
LOS 22 : Return Calculation
 When bonds are purchased and sold within time frame.
QUESTION NO. 15
Vipin purchased at par a bond with a Face Value of ₹ 1,000. The bond had five year to maturity and a
10% coupon rate. The bond was called two years later for a price of ₹ 1,200 after making its second
annual interest payment. Vipin then reinvested the proceeds in a bond selling at its Face Value of ₹ 1,000
with three years to maturity and a 7% coupon rate. What was Vipin's actual YTM over the five-year
period?
LOS 23 : Conversion Value/ Stock Value of Bond

 Converted into equity shares after certain period.
 Conversion Ratio = No. of share Received per Convertible Bond
 When Conversion Value > Bond value, option can be exercised otherwise not.
Conversion Value = No. of equity MPS at the

×
shares issued time of Conversion
QUESTION NO. 16A

There is conversion option on an 8% convertible debenture, if unconverted it is redeemable at par in 10
years' time; conversion will be for 20 ordinary shares, the current share price being 3.70. The current
required return on unconvertible debentures with a 10-year maturity is 12%. Find the straight debt value
i.e. value obtained when securities are not converted and conversion value of this security as on today
.Should the bond be converted as on today.
QUESTION NO. 16B
XYZ Ltd. has issued convertible debentures with interest rate of 12%. Every debenture has an
option to convert to 20 equity shares at any time until the date of maturity. Debentures will be redeemed
at ₹ 100 on maturity which is after 5 years. An investor normally requires a rate of return of 8% p.a. on
a five year security. As an investor when will you exercise conversion if the current market price of equity
shares is
(i) ₹ 4 (ii) ₹ 5 (iii) ₹ 6
QUESTION NO. 16C
Sabanam Ltd. has issued convertible debentures with coupon rate 11%. Each debenture has an option
to convert to 16 equity shares at any time until the date of maturity. Debentures will be redeemed at
₹ 100 on maturity of 5 years. An investor generally requires a rate of return of 8% p.a. on a 5-year
10.12
security. As an advisor, when will you advise the investor to exercise conversion for given market
prices of the equity share of (i) ₹ 5, (ii) ₹ 6 and (iii) ₹ 7.10
Cumulative PV factor for 8% for 5 years : 3.993
PV factor for 8% for year : 0.681
LOS 24 : Credit Rating Requirement

 As per SEBI regulation, no public or right issue of debt/bond instruments shall be made unless
credit rating from credit rating agency has been obtained and disclosed in the offer document.
 Rating is based on the track record, financial statement, profitability ratios, debt – servicing
capacity ratios, credit worthiness & risk associated with the company.
 Higher rated Bonds means low risk and a lower rated bond means high risk.
 Higher the risk higher will be the expectation and higher will be the discount rate.
QUESTION NO. 17
Based on the credit rating of bonds Mr. Mohan has decided to apply the following discount rates for
valuing bonds:
Credit rating Discount rates
AAA 364-day T-bill rate + 3% spread
AA AAA + 2% spread
A AAA + 3% spread
He is considering to invest in a AA rated, ₹ 1000 face value bond currently selling at ₹ 1025.86. The
bond has five years to maturity and the coupon rate on the bond is 15% p.a. payable annually. The next
interest payment is due one year from today and the bond is redeemable at par. (Assume the 364-day
T-bill rate to be 9%).
a) You are required to calculate the intrinsic value of the bond for Mr. Mohan. Should he invest in the
bond?
b) Calculate the current yield and yield to maturity of the bond.
LOS 25 : Strips (Separate Trading of Registered Interest & Principal Securities)

Program
Under this, Strip the coupons from the principal, repackage the cash flows and sell them separately
as Zero – Coupon Bonds, at discount.
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐌𝐚𝐭𝐮𝐫𝐢𝐭𝐲 𝐯𝐚𝐥𝐮𝐞

Value of Bond = + +..................+ +
(𝟏 𝐤 𝐝 )𝟏 (𝟏 𝐤 𝐝 )𝟐 (𝟏 𝐤 𝐝 )𝐧 (𝟏 𝐤 𝐝 )𝐧
Coupon Strips Principal Strips

QUESTION NO. 18
Nominal Value of 12% bonds issued by a company is ₹ 100.The bonds are redeemable at
₹ 125 at the end of year 5.Coupons are paid annually. Determine value of interest strip & principal strip.
Annual Yield rate is 10%.
10.13
LOS 26 : Relationship between Coupon Rate & YTM

Bonding Selling At
Par Coupon Rate = Yield to Maturity
Discount Coupon Rate < Yield to Maturity
Premium Coupon Rate > Yield to Maturity
QUESTION NO. 19
Calculate value of bond if rate of return is (i) 12 % (ii) 10%, (iii) 14%.
Coupon rate = 12%, Bond face value = ₹ 1,000 Redeemable at Par, Maturity 10 years. What conclusion
can you draw?
LOS 27 : Cum Interest & Ex-interest Bond Value

 When Bond value include amount of interest it is known as Cum-Interest Bond Value, other -wise
not.
 If question is Silent, we will always assume ex-interest.
 Assume value of Bond (B0) as ex – interest.
 If it is given Cum-Interest then deduct Interest and proceeds your calculations.
Full Price = Clean Price + Interest accrued

Or
Cum - Interest Price = Ex – Interest Price + Interest Accrued
Valuation of a Bond between two coupon dates
QUESTION NO. 20A

C Ltd. has ₹ 500,000 of 7 % debentures outstanding which are redeemable in 8 years’ time at par. The
current price is ₹ 81 cum interest and the company pays corporation tax at 35%.
Calculate the after-tax cost of this debt finance.
QUESTION NO. 20B
Face Value = ₹ 1,00,000; Coupon Rate = 12% payable at the end of each year i.e. Dec.;
YTM = 15%; Valuation Date = 1st April 2009; Redemption Date = 31st Dec 2015; CMP = ₹92550
Redemption at par on maturity.
Find out the intrinsic value of the bond. Find Full price and split into clean price and interest accrued
amount.
QUESTION NO. 20C
MP Ltd. issued a new series of bonds on January 1,2000. The bonds were sold at par (₹ 1,000), having
a coupon rate 10% p.a. and mature on 31st December, 2015. Coupon payments are made semi-
10.14
annually on June 30th and December 31st each year. Assume that you purchased an outstanding MP
Ltd. Bond on 1st March, 2008 when the going interest rate was 12%.
Required:
a) What was the YTM of MP Ltd. Bonds as on January 1, 2000?
b) What amount you should pay to complete the transaction for purchasing the bond on 1st March
2008 ? Of that amount how much should be accrued interest and how much would represent bonds
basic value.
LOS 28 : Relationship between Bond Value & YTM

 When the coupon rate on a bond is equal to its market yield, the bond will trade at its par value.
 If yield required in the market subsequently rises, the price of the bond will fall & it will trade at a
discount.
 If required yield falls, the bond price will increase and bond will trade at a premium.
Crux:
 If YTM increases, bond value decreases & vice-versa, other things remaining same.
 YTM & Bond value have inverse relationship.
Convexity of a Bond
 However, this relationship is not a straight line relationship but it is convex to the origin.
 So, we find that price rise is greater than price fall, we call it positive convexity (i.e. % rise is greater
than % fall)
QUESTION NO. 21
Given a five-year, 8% coupon bond with a face value of ₹ 1,000 and coupon payments made annually,
determine its values given it is trading at the following yields: 8%, 6%, and 10%. Comment on the price
and yield relation you observe. What are the percentage changes in value when the yield goes from 8%
to 6% and when it goes from 8% to 10%?
LOS 29 : Value of the Bond at the end of each Year

𝐁𝟏 𝐈𝟏
B0 =
(𝟏 𝐘𝐓𝐌)𝟏
𝐁𝟐 𝐈𝟐
B1 =
(𝟏 𝐘𝐓𝐌)𝟏
.
.
.
So on
10.15
QUESTION NO. 22
A 7% Bond was issued several years ago when the market interest rate was also 7%.Now the bond has
a remaining life of 3 years when it would be redeemed at par value of ₹ 1,000. The market rate of
interest has increased to 8%. Find out the current market price, price after 1 year and price after 2 years
from today.
LOS 30 : Relationship between Bond Value & Maturity

 Prior to Maturity, a bond can be selling at significant discount or premium to Par value.
 Regardless of its required yield, the price will converge to par value as Maturity approaches.
 Value of premium bond decrease to par value , value of Discount bond increases to Par value.
 Premium and discount vanishes.
QUESTION NO. 23
Coupon rate on three bonds A,B & C are 10%, 12% and 8%.Face Value is ₹ 100.On Maturity all three
bonds are repayable at par value. Yield Rate is 10%.Life-5 years. Demonstrate the following:
a) A Premium bond decreases as the maturity decreases and becomes equal to par value on maturity.
b) A Discount bond increases as the maturity decreases and becomes equal to par value on maturity.
c) A Par value bond always remains a par value bond till maturity Others things remaining constant.
LOS 31 : Floating Rate Bonds

 Floating Rate Bonds are those bonds where coupon rate is decided according to the Reference
rate (Market Interest Rate).
 Coupon Rate should be changed with the change in Reference rate (Market Interest Rate).
 In this case
Coupon Rate = YTM

10.16
QUESTION NO. 24
ABC Ltd. has the following outstanding bonds.
Bond Coupon Maturity
Series X 8% 10 Years
Series Y Variable (Changes annually comparable to prevailing Rate.) 10 Years
Initially these bonds were issued at face value of ₹ 10,000 with yield to maturity of 8%.
Assuming that:
(i) After 2 years from the date of issue, YTM is 10%, then what should be the price of each bond for the
remaining 8 years?
(ii) If after 2 years YTM is 7%, then what should be the price of each bond for the remaining 8 years?
(iii) What conclusion you can draw from the prices of bonds computed above.
LOS 32 : Duration of a Bond (Macaulay Duration)

 Duration of the bond is a weighted average of the time (in years) until each cash flow will be
received i.e. our initial investment is fully recovered.
 Duration is a measurement of how long in years it takes for the price of a bond to be repaid by
its internal cash flows.
 Duration of bond will always be less than or equal to maturity years.
Duration =
𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝑴𝒂𝒕𝒖𝒓𝒊𝒕𝒚 𝒗𝒂𝒍𝒖𝒆

𝟏× +𝟐× + .......+𝒏 × + 𝒏×
(𝟏 𝒀𝑻𝑴)𝟏 (𝟏 𝒀𝑻𝑴)𝟐 (𝟏 𝒀𝑻𝑴)𝒏 (𝟏 𝒀𝑻𝑴)𝒏
𝑪𝑴𝑷/𝑩𝟎
QUESTION NO. 25A

Consider a bond which has the following features:
Face Value ₹ 100 Coupon (interest rate) 15% payable annually
Years the maturity 6 years Redemption Value 100
Current Market Price ₹ 89.50 Yield to Maturity 18%
What is the duration of bond?
QUESTION NO. 25B
Mr. A is planning for making investment in bonds of one of the two companies X Ltd. and Y Ltd. The
detail of these bonds is as follows:
Company Face Value Coupon Rate Maturity Period
X Ltd. ₹ 10,000 6% 5 Years
Y Ltd. ₹ 0,000 4% 5 Years
The current market price of X Ltd.’s bond is ₹ 10,796.80 and both bonds have same Yield To Maturity
(YTM). Since Mr. A considers duration of bonds as the basis of decision making, you are required to
calculate the duration of each bond and your decision.
QUESTION NO. 25C
Find the current market price of bond having face value ₹ 1,00,000 redeemable after 6 year maturity
with YTM at 16% payable annually and duration 4.3202 years
10.17
LOS 33 : Duration of a Zero - Coupon Bond

Duration of a Zero Coupon Bond will always be equal to its Maturity Years
QUESTION NO. 26
Suppose we are considering investing in a zero-coupon bond that matures in 5 years and has a face
value of ₹ 1000. If these bonds are priced to yield 10%, what is the present value of the bonds? What is
its Duration?
LOS 34 : Relationship between Duration of Bond & YTM

 If YTM increases, Bond Value decreases so duration of the bond decreases (recovery is less) & vice
versa.
 Higher the YTM, lower will be duration of a bond. Lower the YTM, higher will be duration of a
bond, other things remaining constant.
QUESTION NO. 27
a) Consider two bonds one with 5 years to maturity and the other with 20 years to maturity. Both the
bonds have a face value of ₹ 1,000 and coupon rate of 8% (with annual interest payments) and both
are selling at par. Assume that the yields of both the bonds fall to 6%, whether the price of bond will
increase or decrease? What percentage of this increase/ decrease comes from a change in the
present value of bond's principal amount and what percentage of this increase/ decrease comes from
a change in the present value of bond's interest payments?
b) Consider a bond selling at par value of ₹ 1,000 with 6 years to maturity and a 7% coupon rate (with
annual interest payment), what is bond's duration?
c) If the YTM of the bond in (b) above increases to 10%, how it affects the bond's duration? And why?
d) Why should the duration of a coupon carrying bond always be less than the time to its maturity?
LOS 35 : Calculation of yield when Coupon Payment is not available for Re-
Investment
QUESTION NO. 28A

XL Ltd. has made an issue of 14 per cent non-convertible debentures on January 1, 2007.
These debentures have a face value of ₹ 100 and is currently traded in the market at a price of ₹ 90.The
bond is redeemable at par on December 31,2011 at the end of 5 years
Required:
a) Estimate the current yield and the YTM of the bond.
b) Calculate the duration of the NCD.
c) Assuming that intermediate coupon payments are not available for reinvestment calculate the
realized yield on the NCD.
10.18
QUESTION NO. 28B

XL Ispat Ltd. has made an issue of 14 per cent non-convertible debentures on January 1, 2007. These
debentures have a face value of ₹ 100 and is currently traded in the market at a price of ₹ 90.
Interest on these NCDs will be paid through post-dated cheques dated June 30 and December
31. Interest payments for the first 3 years will be paid in advance through post-dated cheques while for
the last 2 years post-dated cheques will be issued at the third year. The bond is redeemable at par on
December 31, 2011 at the end of 5 years.
Required :
(i) Estimate the current yield and YTM of the bond.
(ii) Calculate the duration of the NCD.
(iv) Assuming that intermediate coupon payments are, not available for reinvestment calculate the
realised yield on the NCD.
QUESTION NO. 28C
Mr. X purchases a 5 year 8.5% Coupon Bond for a price of ₹907.60 (Face Value ₹1000) that has a YTM
of 11%. You are required to compute reinvested interest amount on this bond.
LOS 36 : Modified Duration/ Sensitivity/ Volatility/ Effective Duration

 Volatility measures the sensitivity of interest rate to bond prices.
 Duration of a bond can be used to estimate the price sensitivity. It can be calculated through
below formula.
 Modified duration will always be lower than Macaulay’s Duration.
 Volatility measures the % change in the bond value with 1% change in YTM.
Example:
If Volatility is 5%, it means if YTM increases by 1% bond value will decrease by 5% or vice versa.
Method 1:
𝐌𝐚𝐜𝐚𝐮𝐥𝐚𝐲 𝐃𝐮𝐫𝐚𝐭𝐢𝐨𝐧
Modified Duration =
𝟏 𝐘𝐓𝐌
Method 2:
𝐁𝐕 ∆𝒀 𝐁𝐕 ∆𝒀
Effective Duration =
𝟐 × 𝐁𝐕𝟎 × ∆𝒀
Convexity Adjustment
As mentioned above duration is a good approximation of the percentage of price change for a small
change in interest rate. However, the change cannot be estimated so accurately of convexity effect as
duration base estimation assumes a linear relationship.
This estimation can be improved by adjustment on account of ‘convexity’. The formula for convexity
is as follows:
C* x (∆y)2 x100
∆y = Change in Yield
C* =
Δ
V0 = Initial Price
V+ = price of Bond if yield increases by ∆y
V- = price of Bond if yield decreases by ∆y
10.19
QUESTION NO. 29A

The following data are available for a bond
Years the maturity 6 years Redemption Value ₹ 1,000
Yield to Maturity 17%
What are the current market price, duration and volatility of this bond? Calculate the expected market
price, if increase in required yield is by 75 basis points.
QUESTION NO. 29B
The following data is available for a bond :
Years the maturity 6 years Redemption Value ₹ 1,000
Yield to Maturity 15%
(Round-off your answers to 3 decimals)
Calculate the following in respect of the bond :
(i) Current Market Price
(ii) Duration of the Bond
(iii) Volatility of the Bond
(iv) Expected market price if increase in required yield is by 100 basis points.
(v) Expected market price if decrease in required yield is by 75 basis points.
LOS 37 : Ratios related to Convertible Bond
1. Conversion Premium/ Premium over Conversion Value
= Market value of Convertible bond

(-)
CV (No. of Shares × MPS)
𝐂𝐨𝐧𝐯𝐞𝐫𝐬𝐢𝐨𝐧 𝐏𝐫𝐞𝐦𝐢𝐮𝐦
% Conversion Premium =
𝐂𝐨𝐧𝐯𝐞𝐫𝐬𝐢𝐨𝐧 𝐕𝐚𝐥𝐮𝐞
𝑪𝒐𝒏𝒗𝒆𝒓𝒔𝒊𝒐𝒏 𝑷𝒓𝒆𝒎𝒊𝒖𝒎
2. Conversion Premium per share =
𝑪𝒐𝒏𝒗𝒆𝒓𝒔𝒊𝒐𝒏 𝑹𝒂𝒕𝒊𝒐
3. Conversion Parity Price/ No Gain No Loss / Market Conversion Price
When the market value of convertible bond = Conversion Value.
𝐌𝐚𝐫𝐤𝐞𝐭 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝐂𝐨𝐧𝐯𝐞𝐫𝐭𝐢𝐛𝐥𝐞 𝐛𝐨𝐧𝐝

=
𝐍𝐨.𝐨𝐟 𝐞𝐪𝐮𝐢𝐭𝐲 𝐬𝐡𝐚𝐫𝐞 𝐢𝐬𝐬𝐮𝐞𝐝 𝐨𝐧 𝐂𝐨𝐧𝐯𝐞𝐫𝐬𝐢𝐨𝐧
OR
= Current MPS + Conversion Premium per share
10.20
4. Premium Pay Back Period or Break Even Period of Convertible Bond
It is a time period, when bond would be converted into equity share so that the loss on conversion
would be set-off by income from interest.
𝐂𝐨𝐧𝐯𝐞𝐫𝐬𝐢𝐨𝐧 𝐏𝐫𝐞𝐦𝐢𝐮𝐦
Break Even Period =
𝐅𝐚𝐯𝐨𝐮𝐫𝐚𝐛𝐥𝐞 𝐈𝐧𝐜𝐨𝐦𝐞 𝐃𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐢𝐚𝐥
OR
𝐌𝐚𝐫𝐤𝐞𝐭 𝐏𝐫𝐢𝐜𝐞 𝐨𝐟 𝐁𝐨𝐧𝐝 𝐂𝐨𝐧𝐯𝐞𝐫𝐬𝐢𝐨𝐧 𝐕𝐚𝐥𝐮𝐞
=
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐨𝐧 𝐁𝐨𝐧𝐝 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐨𝐧 𝐒𝐡𝐚𝐫𝐞
5. Downside Risk or Premium over Non-Convertible Bond
Downside Risk reflects the extent of decline in market value of convertible bonds at which
conversion option become worthless.
= Market value of Convertible bond
(-)
Market value of Non- Convertible bond
𝐃𝐨𝐰𝐧𝐬𝐢𝐝𝐞 𝐑𝐢𝐬𝐤
% Downside Risk/ % Price Decline =
𝐌𝐚𝐫𝐤𝐞𝐭 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝐍𝐨𝐧 𝐜𝐨𝐧𝐯𝐞𝐫𝐭𝐢𝐛𝐥𝐞 𝐛𝐨𝐧𝐝
6. Premium Over Investment Value of Non-Convertible bond / MV of NCB :
𝐌𝐚𝐫𝐤𝐞𝐭 𝐏𝐫𝐢𝐜𝐞 𝐨𝐟 𝐂𝐁 𝐈𝐧𝐯𝐞𝐬𝐭𝐦𝐞𝐧𝐭 𝐕𝐚𝐥𝐮𝐞 / 𝐌𝐕 𝐨𝐟 𝐍𝐨𝐧 𝐂𝐨𝐧𝐯𝐞𝐫𝐭𝐢𝐛𝐥𝐞 𝐁𝐨𝐧𝐝

=
𝐈𝐧𝐯𝐞𝐬𝐭𝐦𝐞𝐧𝐭 𝐕𝐚𝐥𝐮𝐞 / 𝐌𝐕 𝐨𝐟 𝐍𝐨𝐧 𝐂𝐨𝐧𝐯𝐞𝐫𝐭𝐢𝐛𝐥𝐞 𝐁𝐨𝐧𝐝
7. Floor Value : Floor Value is the maximum of :
a) Conversion Value
b) Market Value of Non-Convertible Bond.
Note: Market Value of Convertible Bond (Assume 5 Years)
𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐂𝐨𝐧𝐯𝐞𝐫𝐬𝐢𝐨𝐧 𝐕𝐚𝐥𝐮𝐞 (𝐂𝐕𝟓 )

= + +..................+ +
(𝟏 𝐘𝐓𝐌)𝟏 (𝟏 𝐘𝐓𝐌)𝟐 (𝟏 𝐘𝐓𝐌)𝟓 (𝟏 𝐘𝐓𝐌)𝟓
CV5 = MPS at the end of Year 5 × No. of Shares.

QUESTION NO. 30A
The data given below relates to a convertible bond :
Face Value ₹ 250 Coupon (interest rate) 12%
No. of shares per bond 20 Market price of share ₹ 12
Straight value of bond ₹ 235 Market price of convertible bond ₹ 265
10.21
Calculate:
(i) Stock value of bond. or Conversion Value Of Bond
(ii) The percentage of downside risk
(iii) The conversion premium
(iv) The conversion parity price of the stock
QUESTION NO. 30B
A convertible bond with a face value of ₹ 1,000 is issued at ₹ 1,350 with a coupon rate of 10.5%. The
conversion rate is 14 shares per bond. The current market price of bond and share is ₹ 1,475 and ₹ 80
respectively. What is the premium over conversion value?
QUESTION NO. 30C
Pineapple Ltd has issued fully convertible 12 percent debentures of ₹ 5,000 face value, convertible into
10 equity shares. The current market price of the debentures is ₹ 5,400. The present market price of
equity shares is ₹ 430.
Calculate:
(i) the conversion percentage premium, and
(ii) the conversion value
QUESTION NO. 30D
A Ltd. has in issue 9% bonds which are redeemable at their par value of £100 in five years' time.
Alternatively, each bond may be converted on that date into 20 ordinary shares of the company. The
current ordinary share price of A Ltd. is £4.45 and this is expected to grow at a rate of 6.5% per year for
the foreseeable future. A Ltd. has a cost of debt of 7% per year. Required:
Calculate the following current values for each £ 100 convertible bond:
a) market value;
b) floor value;
c) Conversion premium.
QUESTION NO. 30E
XYZ company has current earnings of ₹ 3 per share with 5,00,000 shares outstanding. The company
plans to issue 40,000, 7% convertible preference shares of ₹ 50 each at par. The preference shares are
convertible into 2 shares for each preference shares held. The equity share has a current market price
of ₹ 21 per share.
(i) What is preference share’s conversion value?
(ii) What is conversion premium?
(iii) Assuming that total earnings remain the same, calculate the effect of the issue on the earning per
share
a) Before conversion
b) After conversion.
(iv) If profits after tax increases by ₹ 1 million what will be the basic EPS
a) Before conversion and
b) After conversion (On a fully diluted basis).
QUESTION NO. 30F
Tata Ltd. have issued earlier a 11.5% convertible bond of face value ₹ 1000 maturing in 2007. After a
period of 3 years, on the option of the investors each of these bonds can be converted into 50 equity
shares of face value of ₹ 10 each. The investment value of similar non-convertible bond is ₹ 870.The
current market prices of the bond and the share are ₹ 970 and ₹ 18.50 respectively. The dividend per
share for 2000-2001 is ₹ 2.12.
You are required to Calculate:
a) Premium Over Conversion Value
10.22
b) Premium Over Investment value of NCB

c) Conversion parity Price Of Share
d) Break Even Period
QUESTION NO. 30G
The following data is related to 8.5% Fully Convertible (into Equity shares) Debentures issued by JAC Ltd.
at ₹ 1000.
Market Price of Debenture ₹ 900
Conversion Ratio 30
Straight Value of Debenture ₹ 700
Market Price of Equity share on the date of Conversion ₹ 25
Expected Dividend Per Share ₹1
a) Conversion Value of Debenture
b) Market Conversion Price
c) Conversion Premium per share
d) Ratio of Conversion Premium
e) Premium over Straight Value of Debenture
f) Favourable income differential per share
g) Premium pay back period
QUESTION NO. 30H
GHI Ltd., AAA rated company has issued, fully convertible bonds on the following terms, a year ago:
Face value of bond ₹ 1000
Coupon (interest rate) 8.5%
Time to Maturity (remaining) 3 years
Interest Payment Annual, at the end of year
Principal Repayment At the end of bond maturity
Conversion ratio (Number of shares per bond) 25
Current market price per share ₹ 45
Market price of convertible bond ₹ 1175
AAA rated company can issue plain vanilla bonds without conversion option at an interest rate of 9.5%.
Required: Calculate as of today:
a) Straight Value of bond.
b) Conversion Value of the bond.
c) Conversion Premium.
d) Percentage of downside risk.
e) Conversion Parity Price.
t 1 2 3
PVIF0.095, t 0.9132 0.8340 0.7617
QUESTION NO. 30I
A Ltd. has issued convertible bonds, which carries a coupon rate of 14%. Each bond is convertible into
20 equity shares of the company A Ltd. The prevailing interest rate for similar credit rating bond is 8%.
The convertible bond has 5 years maturity. It is redeemable at par at ₹ 100.
The relevant present value table is as follows.
Present values t1 t2 t3 t4 t5
PVIF0.14, t 0.877 0.769 0.675 0.592 0.519
PVIF0.08, t 0.926 0.857 0.794 0.735 0.681
10.23
You are required to estimate:

(Calculations be made upto 3 decimal places)
a) Current market price of the bond, assuming it being equal to its fundamental value
b) Minimum market price of equity share at which bond holder should exercise conversion option
c) Duration of the bond.
QUESTION NO. 30J
Suppose Mr. A is offered a 10% Convertible Bond (par value ₹1,000) which either can be redeemed after
4 years at a premium of 5% or get converted into 25 equity shares currently trading at ₹33.50 and
expected to grow by 5% each year. You are required to determine the minimum price Mr. A shall be
ready to pay for bond if his expected rate of return is 11%.
QUESTION NO. 30K
A hypothetical company ABC Ltd. issued a 10% Debenture (Face Value of ₹ 1000) of the duration of 10
years is currently trading at ₹ 850 per debenture. The bond is convertible into 50 equity shares being
currently quoted at ₹ 17 per share.
If yield on equivalent comparable bond is 11.80%, then calculate the spread of yield of the above bond
from this comparable bond.
The relevant present value table is as follows:
Present t1 t2 t3 t4 t5 t6 t7 t8 t9 t10
Values
PVIF0.11, t 0.901 0.812 0.731 0.659 0.593 0.535 0.482 0.434 0.391 0.352
PVIF0.13 t 0.885 0.783 0.693 0.613 0.543 0.480 0.425 0.376 0.333 0.295
LOS 38: Callable Bond

Those bonds which can be called before the date of Maturity.
Step 1 : Calculate Net Initial Outflow.
Step 2 : Calculate Tax Saving on Call Premium & Unamortized Issue Cost.
Step 3 : Calculate Annual Saving on Cash Outflow.
Step 4 : Calculation of Overlapping Interest
Step 5 : Calculate Present Value of Total Net Savings by replacing Outstanding Bonds with New
Bonds.
QUESTION NO. 31A
A firm has a bond outstanding of ₹300,00,000. The bond has 12 years remaining until maturity, has a
12.5 % coupon and is callable at ₹ 1,050 per bond; it had flotation costs of ₹ 4,20,000, which are being
amortized at ₹ 30,000 annually. The flotation costs for a new issue will be ₹ 9,00,000& the current
interest rate will be 10 %. After tax cost of the debt (Kd) is 6%, Should the firm refund the outstanding
debt (and issue new bond)? Consider Corporate Income-tax rate at 50%.
QUESTION NO. 31B
T is contemplating calling ₹ 3 crores of 30 years, ₹ 1,000 bond issued 5 years ago with a coupon interest
rate of 14%. The bonds have a call price of ₹1,140 and had initially collected proceeds of ₹ 2.91 crores
due to a discount of ₹ 30 per bond. The initial floating cost was ₹ 3,60,000. The company intends to sell
₹ 3 crores of 12% coupon rates, 25 years bonds to raise funds for retiring the old bonds. It proposes to
sell the new bonds at their par value of ₹ 1,000. The estimated floatation cost is ₹ 4,00,000. The company
is paying 40% tax and its after cost of debt is 8%. As the new bonds must first be sold and their proceeds,
then used to retire old bonds, the company expects a two months period of overlapping interest during
which interest must be paid on both the old and new bonds. What is the feasibility of refunding bonds?
10.24
QUESTION NO. 31C

M/s. Earth Limited has 11% bond worth of ₹ 2 Crores outstanding with 10 years remaining to maturity.
The company is contemplating the issue of a ₹ 2 Crores 10 year bond carrying the coupon rate of 9%
and use the proceeds to liquidate the old bonds.
The unamortized portion of issue cost on the old bonds is ₹ 3 lakhs which can be written off no sooner
the old bonds are called. The company is paying 30% tax and it's after tax cost of debt is 7%. Should
Earth Limited liquidate the old bonds?
You may assume that the issue cost of the new bonds will be ₹ 2.5 lakhs and the call premium is 5%.
QUESTION NO. 31D
ABC Ltd. has ₹300 million, 12 per cent bonds outstanding with six years remaining to maturity. Since
interest rates are falling, ABC Ltd. is contemplating of refunding these bonds with a ₹300 million issue
of 6 year bonds carrying a coupon rate of 10 per cent. Issue cost of the new bond will be₹6 million and
the call premium is 4 per cent. ₹9 million being the unamortized portion of issue cost of old bonds can
be written off no sooner the old bonds are called off. Marginal tax rate of ABC Ltd. is 30 per cent. You
are required to analyse the bond refunding decision.
LOS 39: Spot Rate

 Yield to maturity is a single discount rate that makes the present value of the bond’s promised
cash flow equal to its Market Price.
 The appropriate discount rates for individual future payments are called Spot Rate.
 Discount each cash flow using a discount rate i.e. specific to the maturity of each cash flow.
Example
Consider an annual-pay bond with a 10% coupon rate and three years of maturity. This bond will
make three payments. For a ₹ 1000 bond these payments will be ₹ 100 in one year, ₹ 100 at the end
of two years, and ₹100 three years from now. Suppose we are given the following spot rates:
1 year = 8%
2 year = 9%
3 year = 10%
Solution:
Discounting each promised payment by its corresponding spot rate, we can value the bond as:
= + +
( . )
= 1003.21
( . ) ( . )
LOS 40: Relationship between Forward Rate and Spot Rate

Forward Rate is a borrowing/ landing rate for a loan to be made at some future date.
1f0 = Spot Rate or Current YTM (rate of 1 year loan)
1f1 = Rate for a 1 year loan, one year from now
1f2 = Rate for a 1 year loan to be made two years from now
Relationship:
(1+S1)1 = (1 + 1f0 )
(1+S2)2 = (1 + 1f0 ) (1 + 1f1)
Or S2 = {(1 + 1f0 ) (1 + 1f1)}1/ 2 – 1
3
(1 + S3) = (1+1f0 ) (1+ 1f1 ) (1 + 1f2 )
Or S3 = {(1 + 1f0 ) (1 + 1f1) (1 + 1f2 )}1/ 3 - 1
Example:
Using forward rates:
The current 1-year rate (1f0) is 4%
The 1-year forward rate for lending from time =1 to time=2 is 1f1 =5%, and
10.25
The 1-year forward rate for lending from time =2 to time =3 is 1f2 =6%.
Calculate value of a 3-year annual-pay bond with 5% coupon and a par value of ₹ 1000.
Solution:
Bond value = + +
( ) ( )( ) ( )( )( )
= + + = ₹ 1000.98
( . ) ( . )( . ) ( . )( . )( . )
QUESTION NO. 32A
ABC Ltd issued 9%, 5yr Bond of ₹ 1000/- each having a maturity of 3 Years. The present rate of interest
is 12% for one year tenure. It is expected that Forward rate of interest for one year tenure is going to fall
by 75 basis points and further by 50 basis points for every next year in future for the same tenure. This
bond has a Beta value of 1.02 and is more popular in the market due to less credit risk.
Calculate:
a) Intrinsic Value of the Bond.
b) Expected price of Bond in the market.
QUESTION NO. 32B
From the following data for Government Securities, calculate the forward rates:
Face Value (₹) Interest Rate Maturity (Year) Current Price (₹)
1,00,000 0% 1 91,500
1,00,000 10% 2 98,500
1,00,000 10.5% 3 99,000
QUESTION NO. 32C
The following is the Yield structure of AAA rated debenture:
Period (or Maturity) Yield (%)
3 months 8.5%
6 months 9.25
1 year 10.50
2 years 11.25
3 years and above 12.00
a) Based on the expectation theory calculate the implicit one-year forward rates in year 2 and year 3.
b) If the interest rate increases by 50 basis points, what will be the percentage change in the price of
the bond having a maturity of 5 years? Assume that the bond is fairly priced at the moment at ₹
1,000.
QUESTION NO. 32D
Consider the following data for Government securities:
Face Value (₹) Interest Rate Maturity (Year) Current Price (₹)
1,00,000 0% 1 91,000
1,00,000 10.5% 2 99,000
1,00,000 11.0% 3 99,500
1,00,000 11.5% 4 99,900
Calculate the forward interest rates.
10.26
LOS 41 : Duration of a Portfolio

It is simply the weighted average of the durations of the individual securities in the Portfolio.
Portfolio Duration = W1D1 + W2D2 + W3D3 + ------------------ + WnDn
Wi=
Di = Duration of bond (i)

N = No. Of bonds in the Portfolio
Note :
 Other factors are constant, Long term bonds are more volatile than Short term bonds.
 Other factors are constant, Lower coupon bonds are more volatile than Higher coupon bonds.
 Other factors are constant, Lower Yield bonds are more volatile than Higher Yield bonds.
LOS 42 : Passive Portfolio Management (Bond Immunization)

 Bond immunization is an investment strategy used to minimize the interest rate risk of bond
investments by adjusting the portfolio duration to match the investor's investment time horizon.
 To immunize a bond portfolio, you need to know the duration of the bonds in the portfolio and
adjust the portfolio so that the portfolio's duration equals the investment time horizon.
 Changes to interest rates actually affect two parts of a bond's value. One of them is a change in
the bond's price, or price effect. When interest rates change before the bond matures, the bond's
final value changes, too. An increase in interest rates means new bond issues offer higher
earnings, so the prices of older bonds decline on the secondary market.
 Interest rate fluctuations also affect a bond's reinvestment risk. When interest rates rise, a bond's
coupon may be reinvested at a higher rate. When they decrease, bond coupons can only be
reinvested at the new, lower rates.
 Interest rate changes have opposite effects on a bond's price and reinvestment opportunities.
While an increase in rates hurts a bond's price, it helps the bond's reinvestment rate. The goal of
immunization is to offset these two changes to an investor's bond value, leaving its worth
unchanged.
 A portfolio is immunized when its duration equals the investor's time horizon. At this
point, any changes to interest rates will affect both price and reinvestment at the same rate,
keeping the portfolio's rate of return the same. Maintaining an immunized portfolio means
rebalancing the portfolio's average duration every time interest rates change, so that the average
duration continues to equal the investor's time horizon.
QUESTION NO. 33A
Mr. A will need ₹ 1,00,000 after two years for which he wants to make one time necessary investment
now. He has a choice of two types of bonds. Their details are as below :
Bond X Bond Y
Face value ₹ 1,000 ₹ 1,000
Coupon 7% payable annually 8% payable annually
Years to maturity 1 4
Current price ₹ 972.73 ₹ 936.52
Current yield 10% 10%
Advice Mr. A whether he should invest all his money in one type of bond or he should buy both the
bonds and, if so in which quantity?
Assume that there will not be any call risk or default risk.
10.27
QUESTION NO. 33B

The following data are available for three bonds A, B and C. These bonds are used by a bond portfolio
manager to fund an outflow scheduled in 6 years. Current yield is 9%. All bonds have face value of ₹100
each and will be redeemed at par. Interest is payable annually.
Bond Maturity (Years) Coupon rate
A 10 10%
B 8 11%
C 5 9%
(i) Calculate the duration of each bond.
(ii) The bond portfolio manager has been asked to keep 45% of the portfolio money in Bond A.
Calculate the percentage amount to be invested in bonds B and C that need to be purchased to
immunise the portfolio.
(iii) After the portfolio has been formulated, an interest rate change occurs, increasing the yield to 11%.
The new duration of these bonds are: Bond A = 7.15 Years, Bond B = 6.03 Years and Bond C =
4.27 years.
Is the portfolio still immunized? Why or why not?
(iv) Determine the new percentage of B and C bonds that are needed to immunize the portfolio. Bond
A remaining at 45% of the portfolio.
Present values be used as follows :
PVIF0.09, t 0.917 0.842 0.772 0.708 0.650
t6 t7 t8 t9 t10
PVIF0.09, t 0.596 0.547 0.502 0.460 0.4224
LOS 43: Hedging Interest Rate Risk using Bond Futures
Profit of seller of futures

= (Futures Settlement Price x Conversion factor) – Quoted Spot Price of Deliverable Bond
Loss of Seller of futures
= Quoted Spot Price of deliverable bond – (Futures Settlement Price x Conversion factor)
An interest rate future is a contract between the buyer and seller agreeing to the future delivery of
any interest-bearing asset. The interest rate future allows the buyer and seller to lock in the price of
the interest-bearing asset for a future date.
Interest rate futures are used to hedge against the risk that interest rates will move in an adverse
direction, causing a cost to the company.
10.28
For example, borrowers face the risk of interest rates rising. Futures use the inverse relationship
between interest rates and bond prices to hedge against the risk of rising interest rates.
A borrower will enter to sell a future today. Then if interest rates rise in the future, the value of the
future will fall (as it is linked to the underlying asset, bond prices), and hence a profit can be made
when closing out of the future (i.e. buying the future).
Bonds form the underlying instruments, not the interest rate. Further, IRF, settlement is
done at two levels:
 Mark-to-Market settlement done on a daily basis and
 physical delivery which happens on any day in the expiry month.
Final settlement can happen only on the expiry date. In IRF following are two important terms:
a) Conversion factor: All the deliverable bonds have different maturities and coupon rates. To make
them comparable to each other, RBI introduced Conversion Factor.
(Conversion Factor) x (futures price) = actual delivery price for a given deliverable bond.
b) Cheapest to Deliver (CTD : It is called CTD bond because it is the least expensive bond in the
basket of deliverable bonds.
Profit & Loss = the difference between cost of acquiring the bonds for delivery and the price received
by delivering the acquired bond.
10.29
PRACTICE QUESTION
QUESTION NO. 34
Today being 1st January 2019, Ram is considering to purchase an outstanding Corporate Bond having
a face value of ₹ 1,000 that was issued on 1st January 2017 which has 9.5% Annual Coupon and 20
years of original maturity (i.e. maturing on 31st December 2027). Since the bond was issued, the
interest rates have been on downside and it is now selling at a premium of ₹ 125.75 per bond.
Determine the prevailing interest on the similar type of Bonds if it is held till the maturity which shall
be at Par.
PV Factors:
1 2 3 4 5 6 7 8 9
6% 0.943 0.890 0.840 0.792 0.747 0.705 0.665 0.627 0.592
8% 0.926 0.857 0.794 0.735 0.681 0.630 0.583 0.540 0.500
QUESTION NO. 35
The following data are available for a bond:
Face Value ₹ 10,000 to be redeemed at par on maturity
Coupon rate 8.5 per cent per annum
Years to Maturity 5 years
Yield to Maturity (YTM) 10 per cent You are required to calculate:
(i) Current market price of the Bond,
(ii) Macaulay’s Duration,
(iii) Volatility of the Bond,
(iv) Convexity of the Bond,
(v) Expected market price, if there is a decrease in the YTM by 200 basis points
(a) By Macaulay’s Duration based estimate
(b) By Intrinsic Value Method.
Given
Years 1 2 3 4 5
PVIF (10%, n) 0.909 0.826 0.751 0.683 0.621
PVIF (8%, n) 0.926 0.857 0.794 0.735 0.681
QUESTION NO. 36
Following are the yields on Zero Coupon Bonds (ZCB) having a face value of ₹ 1,000
Maturity (Years) Yield to Maturity (YTM)
1 10%
2 11%
3 12%
Assume that the term structure of interest rate will remain the same.
You are required to
(i) Calculate the implied one year forward rates
(ii) Expected Yield to Maturity and prices of one year and two year Zero Coupon Bonds at the end
of the first year.
QUESTION NO. 37
In March 2020, XYZ Bank sold some 7% Interest Rate Futures underlying Notional 7.50% Coupon
Bonds. The exchange provides following details of eligible securities that can be delivered:
Security Quoted Price of Bonds Conversion Factor
7.96 GOI 2023 1037.40 1.0370
10.30
6.55 GOI 2025 926.40 0.9060

6.80 GOI 2029 877.50 0.9195
6.85 GOI 2026 972.30 0.9643
8.44 GOI 2027 1146.30 1.1734
8.85 GOI 2028 1201.70 1.2428
Recommend the Security that should be delivered by the XYZ Bank if Future Settlement Price is 1000.
QUESTION NO. 38
ABC Ltd. wants to issue 9% Bonds redeemable in 5 years at its face value of ₹ 1,000 each. The annual
spot yield curve for similar risk class of Bond is as follows:
Year Interest Rate
1 12%
2 11.62%
3 11.33%
4 11.06%
5 10.80%
(i) Evaluate the expected market price of the Bond if it has a Beta value of 1.10 due to its popularity
because of lesser risk.
(ii) Interpret the nature of the above yield curve and reasons for the same.
Note: Use PV Factors upto 4 decimal points and value in ₹ upto 2 decimal points.
11.1
Portfolio Management
Study Session 11
 Portfolio means combination of various underlying assets like bonds, shares, commodities, etc.
 Portfolio Management refers to the process of selection of a bundle of securities with an

objective of maximization of return & minimization of risk.
Steps in Portfolio Management Process
 Planning: Determine Client needs and circumstances, including the client’s return objectives, risk
tolerance, constraints and preferences. Create, and then periodically review and Update, an
investment policy statement (IPS) that spells out these needs and Circumstances.
 Execution: Construct the client portfolio by determining suitable allocations to various asset
classes and on expectations about macroeconomic variables such as inflation, interest rates and
GDP Growth (top-down analysis). Identify attractive price securities within an asset class for client
portfolios based on valuation estimates from security analysis (bottom-up analysis).
 Feedback: Monitor and rebalance the portfolio to adjust asset class allocations and securities
holdings in response to market performance. Measure & report performance relative to the
performance benchmark specified in the IPS.
LOS 2 : Major return Measures
(i) Holding Period Return (HPR) :
HPR is simply the percentage increase in the value of an investment over a given time period.
𝐏𝐫𝐢𝐜𝐞 𝐚𝐭 𝐭𝐡𝐞 𝐞𝐧𝐝 𝐩𝐫𝐢𝐜𝐞 𝐚𝐭 𝐭𝐡𝐞 𝐛𝐞𝐠𝐠𝐢𝐧𝐢𝐧𝐠 𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝

HPR =
𝐩𝐫𝐢𝐜𝐞 𝐚𝐭 𝐭𝐡𝐞 𝐛𝐞𝐠𝐠𝐢𝐧𝐢𝐧𝐠
QUESTION NO. 1
The dividend per share and market price per share of AB Corp during the last few years are listed
below. Compute the annual return and the average return.
Per Share (`) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Dividend 1.50 1.75 2.50 3.20 3.80 4.501
Market Price 30.00 20.00 28.00 42.00 50.00 80.00
(ii) Arithmetic Mean Return (AMR) :
It is the simple average of a series of periodic returns.
𝐑𝟏 𝐑𝟐 𝐑𝟑 𝐑𝟒 ⋯ 𝐑𝐧
Average Return =
𝐧
11.2
(iii) Geometric Mean Return (GMR) :
𝒏
GMR = (𝟏 + 𝑹𝟏 ) (𝟏 + 𝑹𝟐 ) (𝟏 + 𝑹𝟑 )(𝟏 + 𝑹𝟒 ) … … … (𝟏 + 𝑹𝒏 ) − 𝟏
Example:
An investor purchased $1,000 of a mutual fund’s shares. The fund had the following total returns
over a 3-year period: +5%, -8%, +12%. Calculate the value at the end of the 3 year period, the
holding period return, the mean annual return
Solution:
Ending value = (1,000) (1.05)(0.92)(1.12) = $ 1,081.92
𝟏𝟎𝟖𝟏.𝟗𝟐 𝟏𝟎𝟎𝟎
Holding period return = ×100 = 8.192/ 3 = 2.73%
𝟏𝟎𝟎𝟎
Arithmetic mean return = (5% - 8% + 12%) / 3 = 3%
11.3
LOS 3 : Calculation of Return of an individual security
∑𝐗 E(x) = 𝐗 = ∑ 𝐏𝐗𝐢 𝐗 𝐢
𝐗=
𝐧
LOS 4 : Calculation of Risk of an individual security
Risk of an individual security will cover under following heads:
Risk of Individual Security
Variance Standard Co-efficient

(σ2) Deviation (σ) Of variation
1. Standard Deviation of Security (S.D) :- (S.D) or σ (sigma) is a measure of total risk / investment
risk.
Standard Deviation (σ)
Past Data Probability Based Data

(σ ) =
∑(𝐗 𝐗 )𝟐
(σ) = ∑ 𝐩𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲(𝐗 − 𝐗 )𝟐
𝐧
Note:
 For sample data, we may use (n-1) instead of n in some cases.
x = Given Data, x = Average Return , n = No. of events/year
 ∑(X − X ) will always be Zero (for Past Data)
 ∑(X − X ) may or may not be Zero in this case. (for Probability Based Data)
 S.D can never be negative. It can be zero or greater than zero.
 S.D of risk-free securities or government securities or U.S treasury securities is always assumed
to be zero unless, otherwise specified in question.
Decision: Higher the S.D, Higher the risk and vice versa.
11.4
2. Variance
Variance (σ2)
Past Data Probability Based Data

𝟐
∑(𝐗 − 𝐗 )
(𝛔𝟐) = 𝐩𝐫𝐨𝐛𝐚𝐛𝐢𝐥𝐢𝐭𝐲(𝐗 − 𝐗 )𝟐
𝐧
Decision:
Higher the Variance, Higher the risk and vice versa.
3. Co-efficient of Variation (CV) :
CV is used to measure the risk (variable) per unit of expected return (mean)
𝐒𝐭𝐚𝐧𝐝𝐚𝐫𝐝 𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐗
CV =
𝐀𝐯𝐞𝐫𝐚𝐠𝐞/𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝐗
Decision:
Higher the C.V, Higher the risk and vice versa.
LOS 5 : Rules of Dominance in case of an individual Security or when two

securities are given
Rule No. 1: For a given 2 securities, given same S.D or Risk, select that security which gives
higher return
X Ltd. Y ltd.
σ 5 5
Return 10 15
Decision: Select Y. Ltd.
Rule No. 2: For a given 2 securities, given same return, select which is having lower risk
in comparison to other.
X Ltd. Y ltd.
σ 5 10
Return 15 15
Decision Select X. Ltd.
Rule No. 3:
X Ltd. Y ltd.
σ 5 10
Return 10 25
Decision: Based on CV (Co-efficient of Variation).
When Risk and return are different, decision is based on CV.
CV x = 5/10 = 0.50 CV y = 10/25 = 0.40
Decision:- Select Y. Ltd.
11.5
LOS 6 : Calculation of Return of a Portfolio of assets

It is the weighted average return of the individual assets/securities.
Where, W i =
Sum of the weights must always =1 i.e. W A + W B= 1
LOS 7 : Risk of a Portfolio of Assets
1. Standard Deviation of a Two-Asset Portfolio
σ1,2 = 𝛔𝟐𝟏 𝐰𝟏𝟐 + 𝛔𝟐𝟐 𝐰𝟐𝟐 + 𝟐𝛔𝟏 𝐰𝟏 𝛔𝟐 𝐰𝟐 𝐫𝟏,𝟐

where
r1,2 = Co-efficient of Co-relation σ 1 = S.D of Security 1 σ 2 = S.D of Security 2
w1 = Weight of Security 1 w2 = Weight of Security 2
2. Variance of a Two-Asset Portfolio = (SD)2
3. Co-Variance
∑( 𝐗 𝐗 ) ( 𝐘 𝐘) Cov X,Y = ∑ 𝐏𝐫𝐨𝐛. (𝐗 − 𝐗)(𝐘 − 𝐘)

Cov X,Y =
𝐧
X = Return on Asset 1 Y = Return on Asset 2

X = mean return on Asset 1Y = mean return on Asset 2
n = No. of Period
Co-variance measures the extent to which two variables move together over time.
 A positive co-variance’s means variables (e.g. Rates of return on two stocks) are trend to move
together.
 Negative co-variance means that the two variables trend to move in opposite directions.
 A co-variance of Zero means there is no linear relationship between the two variables.
11.6
 Co-Variance or Co-efficient of Co-relation between risk-free security & risky security will
always be zero.
4. Co-efficient of Correlation
𝐂𝐨𝐯𝟏,𝟐
r 1,2 =
𝛔𝟏 𝛔𝟐
Or
Cov1,2 = r1,2 σ1 σ2
Or
S.D of two-asset Portfolio (σ 1,2 )= 𝛔𝟐𝟏 𝐰𝟏𝟐 + 𝛔𝟐𝟐 𝐰𝟐𝟐 + 𝟐𝐰𝟏 𝐰𝟐 𝐂𝐎𝐕𝟏,𝟐
 The correlation co-efficient has no units. It is a pure measure of co-movement of the two
stock’s return and is bounded by -1 and +1.
 +1 means that deviations from the mean or expected return are always proportional in the
same direction, They are perfectly Positively Correlated. It is a case of maximum Portfolio risk.
 -1 means that deviation from the mean or expected values are always proportional in opposite
directions. They are perfectly negatively correlated. It is a case of minimum portfolio risk.
 A correlation coefficient of ZERO means no linear relationship between the two stock’s return.
QUESTION NO. 2A
The historical rates of return of two securities over the past ten years are given. Calculate the Covariance
and the correlation coefficient of the two securities:
Years 1 2 3 4 5 6 4 8 9 10
Security 1 12 8 7 14 16 15 18 20 16 22
(Return %)
Security 2 20 22 24 18 15 20 24 25 22 20
(Return %)
QUESTION NO. 2B
Consider the following information on two stocks, A and B:
Years Return on A (%) Return on B (%)
2006 10 12
2007 16 18
a) The expected return on a portfolio containing A and B in the proportion of 40% and 60%respectively.
b) The Standard deviation of return from each of the two stocks.
c) The covariance of returns from the two stocks.
d) Correlation coefficient between the returns of the two stocks.
e) The risk of a portfolio containing A and B in the proportion of 40% and 60%.
QUESTION NO. 2C
A S is presently concerned with the investment of `1,00,000. She has two securities S1 and S2 for this
purpose. The relevant information in respect of these two securities is as follows:
S1 S2
Expected Return 12% 20%
σ of Return 10% 18%
11.7
Coefficient of Correlation (r) between S1 and S2 =.15

She has decided to consider only five portfolios of S1 and S2 as follows:
(i) All funds invested in S1
(ii) 50% of funds in each of S1 and S2
(iii) 75% of funds in S1and 25% in S2
(iv) 25% of funds in S1 and 75% in S2
(v) All funds invested in S2
Find out:
a) Expected return under different portfolios.
b) Risk factors associated with these portfolios.
c) Which portfolio is best from the point of view of risk
d) Which portfolio is best from the point of view of return?
QUESTION NO. 2D
Following information is available on Return (%) of shares of two companies A and B :
Probabilities Return of A Return of B
0.05 6 8
0.20 12 18
0.50 20 28
0.20 24 34
0.05 30 44
Compute expected return from the portfolio, If the investment in A & B is in the ratio of 70:30, what is
the risk of the portfolio
QUESTION NO. 2E
A stock costing `120 pays no dividends. The possible prices that the stock might sell for at the end of the
year with the respective probabilities are:
Price Probability
115 0.10
120 0.10
125 0.20
130 0.30
135 0.20
140 0.10
Required:
a) Calculate the expected return.
b) Calculate the Standard deviation of returns.
QUESTION NO. 2F
Following information is available in respect of dividend, market price and market condition after one
year.
Market condition Probability Market Price (`) Dividend Per Share
Good 0.25 115 9
Normal 0.50 107 5
Bad 0.25 97 3
The existing Market Price of an equity share is ` 106 (F.V Re. 1), which is cum debenture of ` 6 each per
share with 10% rate of interest. X Finance Company Ltd. has offered the buy-back of debentures at F.V.
a) Find out the expected return and variability of returns of the equity shares.
11.8
b) Advice whether buy-back offer is to be accepted or not.

QUESTION NO. 2G
The return of security ‘L’ and security ‘K’ for the past five years are given below:
Year Security-L Return % Security-K Return %
2012 10 11
2013 04 - 06
2014 05 13
2015 11 08
2016 15 14
Calculate the risk and return of portfolio consisting above information.
LOS 8 : Portfolio risk as Correlation varies

Example:
Consider 2 risky assets that have return variance of 0.0625 and 0.0324, respectively. The assets
standard deviation of returns are then 25% and 18%, respectively. Calculate standard deviations of
portfolio returns for an equal weighted portfolio of the two assets when their correlation of return is
1, 0.5, 0, -0.5, -1.
Solution:
σ portfolio= σ w + σ w + 2σ w σ w r , = (σ w + σ w )
r = correlation = +1
σ portfolio = w1σ1 + w2σ2
σ = portfolio standard deviation = 0.5(25%) + 0.5(18%) = 21.5%
r = correlation = 0.5
σ = (0.5) 0.0625 + (0.5) 0.0324 + 2(0.5)(0.5)(0.5)(0.25)(0.18) = 18.70%
r = correlation = 0
σ = (0.5) 0.0625 + (0.5) 0.0324 = 15.40%
r = correlation = (-) 0.5
σ = (0.5) 0.0625 + (0.5) 0.324 + 2(0.5)(0.5)(˗0.5)(0.25)(0.18) = 11.17%
r = correlation = -1
σ portfolio = w1σ1 - w2σ2
σ = portfolio standard deviation = 0.5(25%) - 0.5(18%) = 3.5%
Note:
 The portfolio risk falls as the correlation between the asset’s return decreases.
 The lower the correlation of assets return, the greater the risk reduction (diversification) benefit of
combining assets in a portfolio.
 If assets return when perfectly negatively correlated, portfolio risk could be minimum.
 If assets return when perfectly positively correlated, portfolio risk could be maximum.
Portfolio Diversification refers to the strategy of reducing risk by combining many different types of
assets into a portfolio. Portfolio risk falls as more assets are added to the portfolio because not all
assets prices move in the same direction at the same time. Therefore, portfolio diversification is
affected by the:
a) Correlation between assets: Lower correlation means greater diversification benefits.
b) Number of assets included in the portfolio: More assets means greater diversification benefits.
11.9
QUESTION NO. 3
Following information is available in respect of A Ltd. and B Ltd.
Average Return Standard
Deviation
A Ltd. 26.3 % 37.3 %
B Ltd. 11.6 % 23.3 %
An investor has intended to invest 50 % of his funds in each of these. Find out the risk of the portfolio
if the correlation coefficient between the returns of these securities is: 0,-.5 , + .5 , -1 or + 1 .State
the conclusion.
LOS 9 : Standard-deviation of a 3-asset Portfolio

𝛔𝟏,𝟐,𝟑 =
𝛔𝟐𝟏 𝐖𝟏𝟐 + 𝛔𝟐𝟐 𝐖𝟐𝟐 + 𝛔𝟐𝟑 𝐖𝟑𝟐 + 𝟐 𝛔𝟏 𝛔𝟐 𝐖𝟏 𝐖𝟐 𝐫𝟏,𝟐 + 𝟐 𝛔𝟏 𝛔𝟑 𝐖𝟏 𝐖𝟑 𝐫𝟏,𝟑 + 𝟐 𝛔𝟐 𝛔𝟑 𝐖𝟐 𝐖𝟑 𝐫𝟐,𝟑
Or
𝛔𝟏,𝟐,𝟑 = 𝛔𝟐𝟏 𝐖𝟏𝟐 + 𝛔𝟐𝟐 𝐖𝟐𝟐 + 𝛔𝟐𝟑 𝐖𝟑𝟐 + 𝟐 𝐖𝟏 𝐖𝟐 𝐂𝐨𝐯𝟏,𝟐 + 𝟐 𝐖𝟏 𝐖𝟑 𝐂𝐨𝐯𝟏,𝟑 + 𝟐 𝐖𝟐 𝐖𝟑 𝐂𝐨𝐯𝟐,𝟑
Portfolio consisting of 4 securities
𝛔𝟐𝟏 𝐖𝟏𝟐 + 𝛔𝟐𝟐 𝐖𝟐𝟐 + 𝛔𝟐𝟑 𝐖𝟑𝟐 + 𝛔𝟐𝟒 𝐖𝟒𝟐 + 𝟐 𝛔𝟏 𝛔𝟐 𝐖𝟏 𝐖𝟐 𝐫𝟏,𝟐 + 𝟐 𝛔𝟐 𝛔𝟑 𝐖𝟐 𝐖𝟑 𝐫𝟐,𝟑 +
𝛔𝟏,𝟐,𝟑,𝟒 =
𝟐 𝛔𝟑 𝛔𝟒 𝐖𝟑 𝐖𝟒 𝐫𝟑,𝟒 + 𝟐 𝛔𝟒 𝛔𝟏 𝐖𝟒 𝐖𝟏 𝐫𝟒,𝟏 + 𝟐 𝛔𝟐 𝛔𝟒 𝐖𝟐 𝐖𝟒 𝐫𝟐,𝟒 + 𝟐 𝛔𝟏 𝛔𝟑 𝐖𝟏 𝐖𝟑 𝐫𝟏,𝟑
QUESTION NO. 4
Following information is available in respect of a portfolio:
Security A B C
Weight 25% 50% 25%
S.D. 0.1689 0.0716 0.0345
Correlation with A — 0.45 0.35
Correlation with B — — 0.20
Find out the S.D. of the portfolio.
LOS 10 : Standard Deviation of Portfolio consisting of Risk-free security &

Risky Security
A = Risky Security
B = Risk-free Security
We know that S.D of Risk-free security is ZERO.
σ A,B = 𝛔𝟐𝐀 𝐰𝐀𝟐 + 𝛔𝟐𝐁 𝐰𝐁𝟐 + 𝟐𝛔𝐀 𝐰𝐀 𝛔𝐁 𝐰𝐁 𝐫𝐀,𝐁 = 𝛔𝟐𝐀 𝐰𝐀𝟐 + 𝟎 + 𝟎
σ A,B = σA WA
11.10
LOS 11 : Calculation of Portfolio risk and return using Risk-free securities and
Market Securities
 Under this we will construct a portfolio using risk-free securities and market securities.
Case 1: Investment 100% in risk-free (RF) & 0% in Market
[S.D of risk free security is always 0(Zero).]
Risk = 0%
Return = risk-free return
Case 2: Investment 0% in risk-free (RF) & 100% in Market
Risk = σm
Return = Rm
Case 3: Invest part of the money in Market & part of the money in Risk-free (σ of RF = 0)
Return = Rm Wm + RF WRF
Risk of the portfolio = σm × Wm
Case 4: Invest more than 100% in market portfolio. Addition amount should be borrowed
at risk-free rate.
Let the additional amount borrowed weight = x

Return of Portfolio = Rm× (1+ x) – RF × x
Risk of Portfolio = σm × (1+ x)
Example:
Assume that the risk-free rate, R f is 5%; the expected rate of return on the market, E(RM), is 11%; and
that the standard deviation of returns on the market portfolio, σ M, is 20%. Calculate the expected
return and standard deviation of returns for portfolios that are 25%, 75% and 125% invested in the
market portfolio. We will use RM to represent these portfolio weights.
Solution:
Expected portfolio returns are calculated as E(RP) = (1- WM) ×Rf + WM E(RM), So we have following:
E (RP) = 0.75 × 5% + 0.25 ×11% = 6.5%
E (RP) = 0.25 × 5% + 0.75 ×11% = 9.5%
E (RP) = -0.25 × 5% + 1.25 ×11% = 12.5%
Portfolio standard deviation is calculated as σ P =W M × σ M and σ of risk-free= 0, so we have the
following:
σ P = 0.25×20% = 5%
σ P = 0.75×20% = 15%
σ P = 1.25×20% = 25%
Note:
 With a weight of 125% in the market portfolio, the investor borrows an amount equal to 25% of
his portfolio assets at 5%.
 An investor with ` 10,000 would then borrow ` 2,500 and invest a total of ` 12,500 in the market
portfolio. This leveraged portfolio will have an expected return of 12.5% and standard deviation
of 25%.
11.11
QUESTION NO. 5
You are able to both borrow and lend at the risk-free rate of 9%. The market portfolio security has an
expected return of 15% and a S.D. of 21%. Determine the expected return and S.D. of the following
portfolios:
a) All wealth is invested in the risk-free asset.
b) All wealth is invested in the market portfolio.
c) 1/3 third is invested in the risk-free assets and 2/3 in the market portfolio.
d) All wealth is invested in the market portfolio. Furthermore, you borrow an additional 1/3 of your
wealth to invest in the market portfolio.
LOS 12 : Optimum Weights

For Risk minimization, we will calculate optimum weights.
𝛔𝟐
𝐁 𝐂𝐨𝐯𝐚𝐫𝐢𝐚𝐧𝐜𝐞 (𝐀,𝐁)
WA =
𝛔𝟐
𝐀 𝛔𝟐
𝐁 – 𝟐× 𝐂𝐨𝐯𝐚𝐫𝐢𝐚𝐧𝐜𝐞 (𝐀,𝐁)
WB = 1- WA (Since WA + WB = 1)
We know that
Covariance (A,B) = r A,B ×σ A ×σ B
QUESTION NO. 6A
A Ltd. and B Ltd. have low positive correlation coefficient of + 0.5. Their respective return and risk profile
is as follow: R A = 10%, R B = 15%, σ A = 20%, σ B = 25% .Compute the proportion of A & B to minimize
risk.
QUESTION NO. 6B
An investor has decided to invest `1,00,000 in the shares of two companies, namely, ABC and XYZ. The
projections of returns from the shares of the two companies along with their
probabilities are as follows:
Probability ABC(%) XYZ(%)
0.20 12 16
0.25 14 10
0.25 -7 28
0.30 28 -2
You are required to
(i) Comment on return and risk of investment in individual shares.
(ii) Compare the risk and return of these two shares with a Portfolio of these shares in equal proportions.
(iii) Find out the proportion of each of the above shares to formulate a minimum risk portfolio.
LOS 13 : CAPM (Capital Asset Pricing Model)

For Individual Security:
The relationship between Beta (Systematic Risk) and expected return is known as CAPM.
Required return/ Expected Return
𝐁𝐞𝐭𝐚 𝐬𝐞𝐜𝐮𝐫𝐢𝐭𝐲
= Risk-free Return + (Return Market – Risk free return)
𝐁𝐞𝐭𝐚 𝐌𝐚𝐫𝐤𝐞𝐭
OR
E (R) = Rf + βs (Rm – Rf)
11.12
Note:
 Market Beta is always assumed to be 1.
 Market Beta is a benchmark against which we can compare beta for different securities and
portfolio.
 Standard Deviation & Beta of risk free security is assumed to be Zero (0) unless
otherwise stated.
 Rm – Rf = Market Risk Premium.
 If Return Market (Rm) is missing in equation, it can be calculated through HPR (Holding Period
Return)
 R m is always calculated on the total basis taking all the securities available in the market.
 Security Risk Premium = β (Rm – Rf)
For Portfolio of Securities:
Required return/ Expected Return = Rf + βPortfolio (Rm – Rf)
QUESTION NO. 7A
As a manager you are given the following information:
Investment in equity shares of Initial Dividends Market price Beta risk
Price (end of year) factor
Cement Ltd. 25 2 50 0.8
Steel Ltd. 35 2 60 0.7
Liquor Ltd. 45 2 135 0.5
Govt. of India Bonds 1,000 140 1005 0.01

a) Expected rate of returns of portfolio in each using CAPM.
b) Average return of portfolio.
(Risk Free return is 14%)
QUESTION NO. 7B
Your client is holding the following securities:
Particulars of Securities Cost ` Dividends ` Market Price ` Beta
Equity Shares: X Company 8,000 800 8,200 0.8
Y Company 10,000 800 10,500 0.7
Z Company 16,000 800 22,000 0.5
PSU Bonds 34,000 3,400 32,300 0.2
Assuming a Risk-free Rate of 15%, Calculate
a) Expected rate of return in each using the CAPM.
b) Average return of the portfolio.
QUESTION NO. 7C
Mr. FedUp wants to invest an amount of ` 520 lacs and had approached his Portfolio Manager. The
Portfolio Manager had advised Mr. FedUp to invest in the following manner:
Security Moderate Better Good Very Good Best
Amount (in ` Lacs) 60 80 100 120 160
Beta 0.50 1.00 0.80 1.20 1.50
You are required to advise Mr. FedUp in regard to the following, using Capital Asset
11.13
Pricing Methodology:
a) Expected return on the portfolio, if the Government Securities are at 8% and the NIFTY is yielding 10%.
b) Advisability of replacing Security 'Better' with NIFTY.
QUESTION NO. 7D
Mr. Tempest has the following portfolio of four shares:
Name Beta Investment ` Lac.
Oxy Rin Ltd. 0.45 0.80
Boxed Ltd. 0.35 1.50
Square Ltd. 1.15 2.25
Ellipse Ltd 1.85 4.50
The risk free rate of return is 7% and the market rate of return is 14%.
Required.
a) Determine the portfolio return.
b) Calculate the portfolio Beta.
QUESTION NO. 7E
Mr. Shyam is holding the following securities:
Particulars of Securities Cost ` Dividend Interest ` Market Price ` Beta
Gold Ltd. 10,000 1,725 9,800 0.60
Silver Ltd. 15,000 1,000 16,200 0.80
Bronze Ltd. 14,000 700 20,000 0.60
GOI Bonds 36,000 3,600 34,500 0.01
Average return of the portfolio is 15.7%. Using Average Beta, Calculate:
a) Expected rate of return in each case, using the Capital Asset Pricing Model (CAPM)
b) Risk free rate of return.
LOS 14 : Decision Based on CAPM

Case Decision Strategy
CAPM Return > Estimated Return/ HPR Over-Valued Sell
CAPM Return < Estimated Return/ HPR Under-Valued Buy
CAPM Return = Estimated Return/ HPR Correctly Valued Buy, Sell or Ignore
 CAPM return need to be calculated by formula, Rf + β (Rm – Rf)
 Actual return / Estimated return can be calculated through HPR (Through data given)
QUESTION NO. 8
The expected returns and beta of three stocks are as follows.
Stock A B C
Expected Return(%) 18 11 15
Beta Factor 1.7 0.6 1.2
If the risk-free rate is 9% and the expected rate of return of the market portfolio is 14%, which of the
above stocks are over, under or correctly valued in the market? What is your strategy?
LOS 15 : Interpret Beta/ Beta co-efficient / Market sensitivity Index

The sensitivity of an asset’s return to the return on the market index in the context of market return is
referred to as its Beta.
Note:
 Beta is a measure of Systematic Risk.
11.14
 However, Beta is not equal to Systematic Risk.

Example:
If Beta = 2, it means when market increases by 1%, security will increase by 2% and if market decrease
by 1%, security will decrease by 2%.
𝐂𝐡𝐚𝐧𝐠𝐞 𝐢𝐧 𝐒𝐞𝐜𝐮𝐫𝐢𝐭𝐲 𝐑𝐞𝐭𝐮𝐫𝐧 𝐂𝐎𝐕𝐢.𝐦 𝛔𝐢

β= = = rim β=
∑𝒙 𝒚 𝒏𝒙𝒚
𝐂𝐡𝐚𝐧𝐠𝐞 𝐢𝐧 𝐌𝐚𝐫𝐤𝐞𝐭 𝐑𝐞𝐭𝐮𝐫𝐧 𝝈𝟐𝒎 𝛔𝐦 ∑ 𝒚𝟐 𝒏 𝒚𝟐
Calculation of Beta
1. Beta Calculation with % change Formulae
𝐂𝐡𝐚𝐧𝐠𝐞 𝐢𝐧 𝐒𝐞𝐜𝐮𝐫𝐢𝐭𝐲 𝐑𝐞𝐭𝐮𝐫𝐧
Beta =
𝐂𝐡𝐚𝐧𝐠𝐞 𝐢𝐧 𝐌𝐚𝐫𝐤𝐞𝐭 𝐑𝐞𝐭𝐮𝐫𝐧
Note:
 This equation is normally applicable when two return data is given.
 In case more than two returns figure are given, we apply other formulas.
QUESTION NO. 9A
Expected return from A Ltd. share is 16% when market return is 12%. Expected return from A Ltd.
share is 18% when market return is 13%. Calculate Beta.
2. Beta of a security with Co-variance Formulae
𝐂𝐨 𝐯𝐚𝐫𝐢𝐚𝐧𝐜𝐞 𝐨𝐟 𝐀𝐬𝐬𝐞𝐭 𝐢’𝐬 𝐫𝐞𝐭𝐮𝐫𝐧 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐦𝐚𝐫𝐤𝐞𝐭 𝐫𝐞𝐭𝐮𝐫𝐧 𝐂𝐎𝐕𝐢.𝐦

β= =
𝐕𝐚𝐫𝐢𝐚𝐧𝐜𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐌𝐚𝐫𝐤𝐞𝐭 𝐑𝐞𝐭𝐮𝐫𝐧 𝛔𝟐
𝐦
QUESTION NO. 9B
Annual rates of return of ABC Ltd., and the market rates of return are given below.
a) Determine the beta coefficient value of the stocks of ABC.
b) What conclusion do you draw?
Year 1 Year 2 Year 3 Year 4 Year 5
ABC (S) (8) 15 12 13 18
Market (M) (10) 18 14 16 22
QUESTION NO. 9C
Given below is information of market rates of Returns and Data from two Companies A and B:
Year 2007 Year 2008 Year 2009
Market (%) 12.0 11.0 9.0
Company A (%) 13.0 11.5 9.8
Company B (%) 11.0 10.5 9.5
You are required to determine the beta coefficients of the Shares of Co. A and Co. B.
11.15
QUESTION NO. 9D
You have been given the following information, about Pink and Zinc Ltd.
Pink and Zinc Market
Years Avg. Share DPS(`) Avg. Index Dividend Return on Govt.
Price (`) Yield % bonds %
2000 242 20 1812 4 6
2001 279 25 1950 5 5
2002 305 30 2258 6 4
2003 322 35 2220 7 5
a) Compute Beta value of company as at the end of 2003.
b) What is your observation?
QUESTION NO. 9E
The distribution of return of security 'F' and the market portfolio 'P' is given below
Probability Return
F P
0.30 30 -10
0.40 20 20
0.30 0 30
You are required to calculate the expected return of security 'F' and the market portfolio 'P', the
covariance between the market portfolio and security and beta for the security.
QUESTION NO. 9F
Mr. Gupta is considering investment in the shares of R. Ltd. He has the following expectations of
return on the stock and the market:
Return (%)
Probability R. Ltd. Market
0.35 30 25
0.30 25 20
0.15 40 30
0.20 20 10
(i) Calculate the expected return, variance and standard deviation for R. Ltd.
(ii) Calculate the expected return variance and standard deviation for the market.
(iii) Find out the beta co-efficient for R. Ltd. shares.
3. Beta of a security with Correlation Formulae
.
We know that Correlation Co-efficient (rim) =
to get Cov im = rim σ σ

Substitute Cov im in β equation, We get β i =
𝛔𝐢
β= rim
𝛔𝐦
11.16
QUESTION NO. 9G
The following information is available in respect of Security A:
Equilibrium Return 12%
Market Return 12%
6% Treasury Bond trading at ` 120
Co-variance of Market Return and Security 196%
Return
Coefficient of Correlation 0.80
You are required to determine the Standard Deviation of:
a) Market Return and
b) Security Return
4. Beta of a security with Regression Formulae
∑𝐱 𝐲 𝐧𝐱𝐲
β=
∑ 𝐲𝟐 𝐧 𝐲𝟐
x = Security Return
y = Market Return
Note: Advisable to use Co-Variance formula to calculate Beta.
(Solve Question NO. 9B by using Regression Formulae)
LOS 16 : Beta of a portfolio

It is the weighted average beta of individual security.
Beta of Portfolio = Beta X Ltd. ×W X Ltd. + Beta Y Ltd. ×W Y Ltd.
Where, W i =
QUESTION NO. 10A

A company has a choice of investments between several different equity oriented mutual funds. The
company has an amount of `1 crore to invest. The details of the mutual funds are as follows:
Mutual Fund Beta
A 1.6
B 1.0
C 0.9
D 2.0
E 0.6
Required:
(i) If the company invests 20% of its investment in each of the first two mutual funds and an equal
amount in the mutual funds C, D and E, what is the beta of the portfolio?
(ii) If the company invests 15% of its investment in C, 15% in A, 10% in E and the balance in equal
amount in the other two mutual funds, what is the beta of the portfolio?
(iii) If the expected return of market portfolio is 12% at a beta factor of 1.0, what will be the portfolios
expected return in both the situations given above?
11.17
QUESTION NO. 10B

A Ltd. has an expected return of 22% and S.D. of 40%.
B Ltd. has an expected return of 24% and S.D. of 38%.
A Ltd. has a beta of 0.86 and
B Ltd. has a beta of 1.24.
The correlation coefficient between the return of A Ltd. & B Ltd. is 0.72.
The S.D. of the market return is 20%.
Suggest:
a) Is investing in B Ltd. better than investing in A Ltd.?
b) If you invest 30% in B Ltd. & 70% in A Ltd., what is your expected rate of return & portfolio Standard
Deviation?
c) What is the market portfolios expected rate of return and how much is the risk-free rate?
d) What is the beta of Portfolio if A Ltd.’s weight is 70% and B Ltd.’s weight is 30%?
QUESTION NO. 10C
B Ltd. has been enjoying a substantial net cash inflow and until the surplus funds are needed to meet
tax and dividend payments, and to finance further capital expenditure in several months’ time, they have
been invested in a small portfolio of short - term equity investments. Details of the portfolio, which
consists of shares in four companies, are as follows:
Company No. of Shares Equity Beta M.P.S. (`) Dividend Yield
Held
D Ltd. 60,000 1.16 4.29 19.5%
E Ltd. 80,000 2.28 2.92 24.0%
F Ltd. 1,00,000 0.90 2.17 17.5%
G Ltd. 1,25,000 1.50 3.14 26.0%
The current market return is 19% per year and the risk free rate is 11% per year.
a) On the basis of the data given, calculate the risk of short-term investment portfolio relative to that of
the market.
b) Recommend with reasons whether B Ltd. should change the composition of its portfolio.
LOS 17 : Evaluation of the performance of a portfolio (Also used in Mutual

Fund)
𝐑𝐏 − 𝐑𝐅 𝐑𝐏 − 𝐑𝐅 P = RP – (RF + (R m – RF))
Or
𝛔𝐏 𝛃𝐏 Alpha = Actual Return –
11.18
1. Sharpe’s Ratio (Reward to Variability Ratio):
 It is excess return over risk-free return per unit of total portfolio risk.
 Higher Sharpe Ratio indicates better risk-adjusted portfolio performance.
𝐑𝐏 𝐑𝐅
Sharpe’s Ratio =
𝛔𝐏
Where RP = Return Portfolio

σP = S.D of Portfolio
Note:
 Sharpe Ratio is useful when Standard Deviation is an appropriate measure of Risk.
 The value of the Sharpe Ratio is only useful for comparison with the Sharpe Ratio of another
Portfolio.
2. Treynor’s Ratio (Reward to Volatility Ratio):

Excess return over risk-free return per unit of Systematic Risk (β )
𝐑𝐏 𝐑𝐅
Treynor’s Ratio =
𝛃𝐏
Decision: Higher the ratio, Better the performance.
3. Jenson’s Measure/Alpha:
This is the difference between a fund’s actual return & CAPM return
α P = RP – (RF + β (R m – RF))
Or
Alpha = Actual Return – CAPM Return
It is excess return over CAPM return.

 If Alpha is +ve, performance is better.
 If Alpha is -ve , performance is not better.
4. Market Risk - return trade – off:

Excess return of market over risk-free return per unit of total market risk.
𝐑𝐌 − 𝐑𝐅
𝛔𝐌
QUESTION NO. 11A

The following are the data on five mutual funds:
Fund Return Standard Deviation Beta
A 15 7 1.25
B 18 10 0.75
C 14 5 1.40
D 12 6 0.98
11.19
E 16 9 1.50
You are required to compute Reward to Variability & Volatility Ratio and rank these portfolio using:
 Sharpe method and
 Treynor's method
assuming the risk free rate is 6%.
QUESTION NO. 11B
The five portfolios of a Mutual Fund experienced following results during last 10 years periods :
Portfolio Average Annual Standard Deviation Correlation with the
Return % Market Return
A 20.0 2.3 0.8869
B 17.0 1.8 0.6667
C 18.0 1.6 0.6000
D 16.0 1.8 0.8670
E 13.5 1.9 0.5437
Market Risk : 1.2
Market Rate of Return : 14.3%
Risk Free Rate : 10.1%
Beta may be calculated only upto two decimal. Rank the portfolio using JENSEN’s ALPHA method.
QUESTION NO. 11C
An investor holds two stocks A and B. A manager prepared ex-ante probability distribution for the
possible Economic situation and the conditional returns for two stocks and the market index as given:
Economic Scenario Probability Conditional Returns %
A B Market
Growth 0.40 25 20 18
Stagnation 0.30 10 15 13
Recession 0.30 -5 -8 -3
The risk free rate during the next year is expected to be around 11%. Determine whether the Investor
should liquidate his holdings in stocks A and B or on the contrary make fresh investments in them. CAPM
assumptions are holding true. Use Jenson's Measure
QUESTION NO. 11D
Five portfolios experienced the following results during a 7- year period:
Portfolio Average Annual Standard Deviation Correlation with
Return (Rp) (%) (Sp) the market returns
(r)
A 19.0 2.5 0.840
B 15.0 2.0 0.540
C 15.0 0.8 0.975
D 17.5 2.0 0.750
E 17.1 1.8 0.600
Market Risk (σm) 1.2
Market rate of Return (Rm) 14.0
Risk-free Rate (Rf) 9.0
Rank the portfolios using (a) Sharpe’s method, (b) Treynor’s method and (c) Jensen’s Alpha
QUESTION NO. 11E
11.20
There are two Mutual Funds viz. D Mutual Fund Ltd. and K Mutual Fund Ltd. Each having close ended
equity schemes.
NAV as on 31-12-2014 of equity schemes of D Mutual Fund Ltd. is `70.71 (consisting 99% equity and
remaining cash balance) and that of K Mutual Fund Ltd. is 62.50 (consisting 96% equity and balance in
cash).
Following is the other information:
Particular Equity Schemes
D Mutual Fund Ltd. K Mutual Fund Ltd.
Sharpe Ratio 2 3.3
Treynor Ratio 15 15
Standard deviation 11.25 5
There is no change in portfolios during the next month and annual average cost is ` 3 per unit for the
schemes of both the Mutual Funds.
If Share Market goes down by 5% within a month, calculate expected NAV after a month for the schemes
of both the Mutual Funds.
For calculation, consider 12 months in a year and ignore number of days for particular month.
LOS 18 : Characteristic Line (CL)

Characteristic Line represents the relationship between Asset excess return and Market Excess return.
Equation of Characteristic Line:
Y= + X
Where Y= Average return of Security

X= Average Return of Market
α= Intercept i.e. expected return of an security when the return from the market portfolio
is ZERO, which can be calculated as Y – β × X = α
β= Beta of Security
Note:
,
The slope of a Characteristic Line is i.e. Beta
QUESTION NO. 12
The rates of return on security of Company X and market portfolio for 10 periods are given below:
Period 1 2 3 4 5 6 4 8 9 10
11.21
Return of Security 20 22 25 21 18 -5 17 19 -7 20
X(%)
Return of Market 22 20 18 16 20 8 -6 5 6 11
Portfolio (%)
a) What is the beta of Security X?
b) What is the characteristic line (equation) for Security X?
LOS 19 : New Formula for Co-Variance using Beta
(Cov A,B) = β A × β B × σ 2 m
LOS 20 : New Formula for Correlation between 2 stocks

Correlation between A & B
rAB = rA, Mkt. × rB, Mkt.
LOS 21 : Co-variance of an Asset with itself is its Variance
Cov (m,m) = Variance m

Co-variance Matrix
COV A B C
A 𝜎 COVAB COVAC
B COVBA 𝜎 COVBC
C COVCA COVCB 𝜎
LOS 22 : Correlation of an Asset with itself is = 1
r (A,A) = 1
Correlation Matrix
or A B C
A 1 rAB rAC
B rBA 1 rBC
C rCA rCB 1
QUESTION NO. 13
A study by a mutual fund has revealed the following data in respect of 3 securities:
Security Standard Deviation Correlation with Index
A 20 0.60
11.22
B 18 0.95
C 12 0.75
The standard deviation of market portfolio (BSE Sensex) is observed to be 15%.
a) What is the Sensitivity of returns of each stock with respect to market?
b) What are the co-variances among the various stocks? Present your answer in a Co-variance matrix.
c) What would be the risk of portfolio consisting of all three stocks equally?
d) What is the beta of the portfolio consisting of equal investment in each stock?
e) What is the total, systematic and unsystematic risk of the portfolio in (d)?
Unsystematic Risk (Controllable Risk):-

 The risk that is eliminated by diversification is called Unsystematic Risk (also called unique, firm-
specific risk or diversified risk). They can be controlled by the management of entity. E.g. Strikes,
Change in management, etc.
Systematic Risk (Uncontrollable Risk):-

 The risk that remains can’t be diversified away is called systematic risk (also called market risk or
non-diversifiable risk). This risk affects all companies operating in the market.
 They are beyond the control of management. E.g. Interest rate, Inflation, Taxation, Credit Policy
11.23
LOS 23 : Sharpe Index Model or Calculation of Systematic Risk (SR) &

Unsystematic Risk (USR)
Risk is expressed in terms of variance.
Total Risk (TR) = Systematic Risk (SR) + Unsystematic Risk (USR)
For an Individual Security:
Total Risk (%2) = 𝛔𝟐𝒔
Unsystematic Risk
Systematic Risk (%2)
(%2) (𝛔𝟐𝒆𝒊 )
USR = TR – SR
SR = 𝛃𝟐𝒔 × 𝛔𝟐𝒎
𝛔𝟐𝒔 - 𝛃𝟐𝒔 × 𝛔𝟐𝒎
𝛔𝟐𝒆𝒊 = USR/ Standard Error/ Random Error/ Error Term/ Residual Variance.
For A Portfolio of Securities:
Total Risk = 𝛔𝟐𝒑
or
= ( ∑ W i β i ) x 𝛔𝟐𝒎 + ∑ W
2
i
2
x USR i
Systematic Risk (%2) Unsystematic Risk (%2)
USR = TR - SR
SRp = 𝛃𝟐𝒑 × 𝛔𝟐𝒎 = 𝛔𝟐𝒑 - 𝛃𝟐𝒑 × 𝛔𝟐𝒎
2
(∑W i i )2 x 𝛔𝟐𝒎 ∑W i x USR i
QUESTION NO. 14A

The returns on stock A and market portfolio for a period of 6 years are as follows:
Year Return on A (%) Return on market portfolio (%)
1 12 8
2 15 12
3 11 11
4 2 -4
5 10 9.5
6 -12 -2
11.24

a) Characteristic line for stock A
b) The systematic and unsystematic risk of stock A
QUESTION NO. 14B
A portfolio having following features:
Security β Random Error σei Weight
L 1.60 7 0.25
M 1.15 11 0.30
N 1.40 3 0.25
K 1.00 9 0.20
You are required to find out the risk of the portfolio if the standard deviation of the market index
(σ m) is 18%.
QUESTION NO. 14C
Following information is available regarding expected return, standard deviation and beta of 6 share
are available in the stock market.
Security Expected Return Beta S.D ( %)
1 5 0.70 9
2 10 1.05 14
3 11 0.95 12
4 12.5 1.10 20
5 15 1.40 17.5
6 16 1.70 25
Suppose risk free rate of return is 4% and Market return is 6% and standard deviation is 10%.You are
required to Compute.
a) Which security is undervalued and which is overvalued.
b) Assuming that funds are equally invested these six stocks, then compute.
(i) Return of portfolio
(ii) Risk of Portfolio
c) Suppose if above portfolio is invested in with margin of 40% and cost of borrowing is 4% then
what will be the position.
QUESTION NO. 14D
Following are the details of a portfolio consisting of three shares:
Share Portfolio Weight Beta Expected return in % Total variance
A 0.20 0.40 14 0.015
B 0.50 0.50 15 0.025
C 0.30 1.10 21 0.100
Standard Deviation of Market Portfolio Returns = 10%
You are given the following additional data:
Covariance (A, B) = 0.030
Covariance (A, C) = 0.020
Covariance (B, C) = 0.040
a) The Portfolio Beta
b) Residual variance of each of the three shares
c) Portfolio variance using Sharpe Index Model
d) Portfolio variance (on the basis of modern portfolio theory given by Markowitz)
11.25
QUESTION NO. 14E

Mr. Abhishek is interested in investing ` 2,00,000 for which he is considering following three alternatives:
(i) Invest ` 2,00,000 in Mutual Fund X (MFX)
(ii) Invest ` 2,00,000 in Mutual Fund Y (MFY)
(iii) Invest ` 1,20,000 in Mutual Fund X (MFX) and ` 80,000 in Mutual Fund Y (MFY)
Average annual return earned by MFX and MFY is 15% and 14% respectively. Risk free rate of return is
10% and market rate of return is 12%.
Covariance of returns of MFX, MFY and market portfolio Mix are as follow:
MFX MFY Mix
MFX 4.800 4.300 3.370
MFY 4.300 4.250 2.800
Mix 3.370 2.800 3.100
a) Variance of return from MFX, MFY and market return,
b) Portfolio return, beta, portfolio variance and portfolio standard deviation,
c) Expected return, systematic risk and unsystematic risk; and
d) Sharpe ratio, Treynor ratio and Alpha of MFX, MFY and Portfolio Mix
QUESTION NO. 14F
Following are the details of a portfolio consisting of 3 shares:
Shares Portfolio Weight Beta Expected Return Total Variance
(%)
X Ltd. 0.3 0.50 15 0.020
Y Ltd. 0.5 0.60 16 0.010
Z Ltd. 0.2 1.20 20 0.120
Standard Deviation of Market Portfolio Return = 12% You are required to calculate the following:
(i) The Portfolio Beta.
(ii) Residual Variance of each of the three shares.
(iii) Portfolio Variance using Sharpe Index Model.
QUESTION NO. 14G
The returns and market portfolio for a period of four years are as under:
Year % Return of Stock B % Return on Market Portfolio
1 10 8
2 12 10
3 9 9
4 3 -1
For stock B, you are required to determine:
(i) Characteristic line; and
(ii) The Systematic and Unsystematic risk.
LOS 24 : Co-efficient of Determination

 Co-efficient of Determination = (Co-efficient of co-relation)2 = r2
 Co-efficient of determination (r2) gives the percentage of variation in the security’s return i.e.
explained by the variation of the market index return.
Example:
If r2 = 18%, In the X Company’s stock return, 18% of the variation is explained by the variation of the
index and 82% is not explained by the index.
11.26
 According to Sharpe, the variance explained by the index is the systematic risk. The unexplained
variance or the residual variance is the Unsystematic Risk.
Use of Co-efficient of Determination in Calculating Systematic Risk & Unsystematic Risk:
 Explained by Index [Systematic Risk]

𝑺𝑹
= = 𝒓𝟐 𝐨𝐫 𝐒𝐑 = 𝐓𝐑 × 𝒓𝟐 𝐢. 𝐞. 𝛔𝟐𝒊 × r2
𝑻𝑹
 Not Explained by Index [Unsystematic Risk]

𝑼𝑺𝑹
= = 𝒓𝟐 𝐨𝐫 𝐔𝐒𝐑 = 𝐓𝐑 × 𝟏 − 𝒓𝟐 𝐢. 𝐞. 𝛔𝟐𝒊 × (1 - r2)
𝑻𝑹
QUESTION NO. 15
The following details are given for X and Y companies’ stocks and the Bombay Sensex for a period of
one year. Calculate the systematic and unsystematic risk for the companies’ stocks. If equal amount of
money is allocated for the stocks what would be the portfolio risk.
X Stock Y Stock Sensex
Average return 0.15 0.25 0.06
Variance of return 6.30 5.86 2.25
β 0.71 0.27 —
Correlation Co-efficient 0.424 (With Sensex) — —
Co-efficient of determination (r2) 0.18 — —
LOS 25 : Portfolio Rebalancing

 Portfolio re-balancing means balancing the value of portfolio according to the market condition.
 Three policy of portfolio rebalancing:
a) Buy & Hold Policy : [“Do Nothing” Policy]
b) Constant Mix Policy: [“Do Something” Policy]
c) Constant Proportion Portfolio Insurance Policy (CPPI): [“Do Something” Policy]
Value of Equity (Stock) = m × [Portfolio Value – Floor Value]
Where m = multiplier
 The performance feature of the three policies may be summed up as follows:
a) Buy and Hold Policy
(i) Gives rise to a straight line pay off.
(ii) Provides a definite downside protection.
(iii) Performance between Constant mix policy and CPPI policy.
b) Constant Mix Policy
(i) Gives rise to concave pay off drive.
(ii) Doesn’t provide much downward protection and tends to do relatively poor in the up market.
(iii) Tends to do very well in flat but fluctuating market.
c) CPPI Policy
(i) Gives rise to a convex pay off drive.
(ii) Provides good downside protection and performance well in up market.
(iii) Tends to do very poorly in flat but in fluctuating market.
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Note:
 If Stock market moves only in one direction, then the best policy is CPPI policy and worst policy is
Constant Mix Policy and between lies buy & hold policy.
 If Stock market is fluctuating, constant mix policy sums to be superior to other policies.
Example:
Consider a payoff from initial investment of 100000 when the market moves from 100 to 80 and
back to 100 under three policies:
a) Buy and hold policy under which the initial stock bond mix is 50:50.
b) Constant mix policy under which the stock bond mix is 50:50
c) A CPPI policy which takes to form investment in stock = 2 (Portfolio value – 75000 i.e. floor value)
Compute the value of equity and bond at each state
Solution:
1. Buy and Hold Policy
(i) When Market is at 100

Stock 50,000
Bond 50,000
1,00,000
(ii) When Market Falls from 100 to 80 i.e. 20% decrease
Before Re-balancing After Re-balancing
Stock 40,000 Stock 40,000
Bond 50,000 Bond 50,000
90,000 90,000
Action: No Action
(iii) When Market Rises from 80 to 100 i.e. 25% increase
Bond 50,000 Bond 50,000
1,00,000 1,00,000
Action: No Action
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2. Constant Mix Policy

Stock 50,000
Bond 50,000
1,00,000
Bond 50,000 Bond 45,000
90,000 90,000
Action: Sell Bond & Buy Stock of ` 5000
Bond 45,000 Bond 50,625
1,01,250 1,01,250
Action: Sell Stock & Buy Bond of ` 5625
3. CPPI Policy

Stock = 2 × [1,00,000 – 75,000] 50,000
Bond 50,000
1,00,000
Stock 40,000 Stock 2 × [90,000 – 75,000] 30,000
Bond 50,000 Bond (Balance Figure) 60,000
90,000 90,000
Action: Sell Stock & Buy Bond of ` 10,000
Stock 37,500 Stock 2 × [97,500 – 75,000] 45,000
Bond 60,000 Bond (Balance Figure) 52,500
97,500 97,500
Action: Buy Equity & sell Bond of ` 7500
QUESTION NO. 16A
Indira has a fund of ` 3 lacs which she wants to invest in share market with rebalancing target after every
10 days to start with for a period of one month from now. The present NIFTY is 5326. The minimum
NIFTY within a month can at most be 4793.4. She wants to know as to how she would rebalance her
portfolio under the following situations, according to the theory of Constant Proportion Portfolio
Insurance Policy, using “2” as the multiplier:
1. Immediately to start with.
2. 10 days later-being the 1st day of rebalancing if NIFTY falls to 5122.96.
3. 10 days further from the above date if the NIFTY touches 5539.04.
For the sake of simplicity, assume that the value of her equity component will change in tandem with
that of the NIFTY and the risk free securities in which she is going to invest will have no Beta.
11.29
QUESTION NO. 16B

Ms. Sunidhi is working with an MNC at Mumbai. She is well versant with the portfolio management
techniques and wants to test one of the techniques on an equity fund she has constructed and compare
the gains and losses from the technique with those from a passive buy and hold strategy. The fund
consists of equities only and the ending NAVs of the fund he constructed for the last 10 months are given
below:
Month Ending NAV (`/unit) Month Ending NAV (`/unit)
Dec-08 40 May-09 37
Jan-09 25 Jun-09 42
Feb-09 36 Jul-09 43
Mar-09 32 Aug-09 50
Apr-09 38 Sep-09 52
Assume Sunidhi had invested a notional amount of `2 lakhs equally in the equity fund and a conservative
portfolio (of bonds) in the beginning of December 2008 and the total portfolio was being rebalanced
each time the NAV of the fund increased or decreased by 15%.
You are required to determine the value of the portfolio for each level of NAV following the Constant
Ratio Plan.
LOS 26 : Arbitrage Pricing Theory/ Stephen Ross’s Apt Model

Overall Return
= Risk free Return

+
{Beta Inflation × Inflation differential or factor risk Premium}
+
{Beta GNP × GNP differential or Factor Risk Premium}
+ ……. & So on.
Where, Differential or Factor risk Premium = [Actual Values – Expected Values]

QUESTION NO. 17A
An investor is considering to make an investment in the stock of Reliance Company. Following are
attributes of five economic forces that influence the return of Reliance’s share
Factor Beta Expected Value Actual Value
GNP 1.95 6.00% 6.50%
Inflation 0.85 5.00% 5.75%
Interest rate 1.20 7.00% 8.00%
Stock market index 2.50 9.50% 11.50%
Industrial production 2.20 9.00% 10.00%
The risk-free (anticipated) rate of return on Reliance share is 9%. How much is total return on the share
under Arbitrage Pricing Theory?
QUESTION NO. 17B
Consider a 2- factor APT Model (Risk Free rate 5%)
Stock Factor Sensitivity
F1 F2
A 0.8 1.2
B 1.5 0.6
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C 2.5 1.5
Factor Risk Premium 5% 3%
a) Find out the Expected Return on each stock?
b) Find out the weights combining A, B, C in such a manner that the β1 of the portfolio is 2 (take WA =
40%). Also Compute β2 of the portfolio and Expected Return.
c) An investor has own fund of ` 200 lacs. He short sells 100 lacs of stock A. He invest the proceeds in
a stock B & C in the ratio of 3:2. Find out the factor sensitivity of this portfolio.
QUESTION NO. 17C
Mr. X owns a portfolio with the following characteristics:
Risk Free
Security A Security B
Security
Factor 1 sensitivity 0.80 1.50 0
Expected Return 15% 20% 10%
It is assumed that security returns are generated by a two factor model.
a) If Mr. X has ` 1,00,000 to invest and sells short ` 50,000 of security B and purchases ` 1,50,000 of
security A what is the sensitivity of Mr. X’s portfolio to the two factors?
b) If Mr. X borrows ` 1,00,000 at the risk free rate and invests the amount he borrows along with the
original amount of ` 1,00,000 in security A and B in the same proportion as described in part (i),
what is the sensitivity of the portfolio to the two factors?
c) What is the expected return premium of factor 2?
QUESTION NO. 17D
Mr. Nirmal Kumar has categorized all the available stock in the market into the following types:
(i) Small cap growth stocks
(ii) Small cap value stocks
(iii) Large cap growth stocks
(iv) Large cap value stocks
Mr. Nirmal Kumar also estimated the weights of the above categories of stocks in the market index.
Furthermore, the sensitivity of returns on these categories of stocks to the three important factor are
estimated to be:
Category of Stocks Weight in the Factor I Factor II Factor III
Market Index (Beta) (Price Book) (Inflation)
Small cap growth 25% 0.8 1.39 1.35
Small cap value 10% 0.9 0.75 1.25
Large cap growth 50% 1.165 2.75 8.65
Large cap value 15% 0.85 2.05 6.75
Risk Premium 6.85% -3.50% 0.65%
The rate of return on treasury bonds is 4.5% Required:
a) Using Arbitrage Pricing Theory, determine the expected return on the market index.
b) Using Capital Asset Pricing Model (CAPM), determine the expected return on the market index.
c) Mr. Nirmal Kumar wants to construct a portfolio constituting only the ‘small cap value’ and ‘large
cap growth’ stocks. If the target beta for the desired portfolio is 1, determine the composition of his
portfolio.
11.31
LOS 27 : Adjustment in CAPM

When two or more Risk Free Rates are given, we are taking the Simple Average of given Rates.
Effect of Increase & Decrease in Inflation Rates
 Increase in Inflation Rates:
Revised RF = RF + RF × Inflation Rate
 Decrease in Inflation Rates:
Revised RF = RF − RF × Deflation Rate

QUESTION NO. 18A
The risk free rate of return Rf is 9 percent. The expected rate of return on the market portfolio Rm is 13
percent. The expected rate of growth for the dividend of Platinum Ltd. is 7 percent. The last dividend paid
on the equity stock of firm A was ` 2.00. The beta of Platinum Ltd. equity stock is 1.2.
a) What is the equilibrium price of the equity stock of Platinum Ltd.?
b) How would the equilibrium price change when
 The inflation premium increases by 2 percent?
 The expected growth rate increases by 3 percent?
 The beta of Platinum Ltd. equity rises to 1.3?
QUESTION NO. 18B
The risk free rate of return is 5%. The expected rate of return on the market portfolio is 11%. The
expected rate of growth in dividend of X Ltd. is 8%. The last dividend paid was
` 2.00 per share. The beta of X Ltd. equity stock is 1.5.
(i) What is the present price of the equity stock of X Ltd.?
(ii) How would the price change when:
• The inflation premium increases by 3%
• The expected growth rate decreases by 3% and
• The beta decreases to 1.3.
QUESTION NO. 18C
XYZ Ltd. paid a dividend of ` 2 for the current year. The dividend is expected to grow at 40% for the next
5 years and at 15% per annum thereafter. The return on 182 days T-bills is 11% per annum and the
market return is expected to be around 18% with a variance of 24%. The co-variance of XYZ's return with
that of the market is 30%. You are required to calculate the required rate of return and intrinsic value of
the stock.
11.32
LOS 28 : Modern Portfolio Theory/ Markowitz Portfolio Theory/ Rule of

Dominance in case of selection of more than two securities
Under this theory, we will select the best portfolio with the help of efficient frontier.
Efficient Frontier:
 Those portfolios that have the greatest expected return for each level of risk make up the efficient
frontier.
 All portfolios which lie on efficient frontier are efficient portfolios.
Efficient Portfolios:
Rule 1: Those Portfolios having same risk but given higher return.
Rule 2: Those Portfolios having same return but having lower risk.
Rule 3: Those Portfolios having lower risk and also given higher returns.
Rule 4: Those Portfolios undertaking higher risk and also given higher return
In-efficient Portfolios:
Which don’t lie on efficient frontier.
Solution Criteria:
For selection of best portfolio out of the efficient portfolios, we must consider the risk-return
preference of an individual investor.
 If investors want to take risk, invest in the Upper End of efficient frontier portfolios.
 If investors don’t want to take risk, invest in the Lower End of efficient frontier portfolios.
Note:
CV is not used in this case, CV is only used for selection of one security between many securities &
major drawback is that it always select securities with lower risk.
QUESTION NO. 19
Following is the data regarding six portfolios:
A B C D E F
Return (%) 8 8 12 4 9 8
Risk (S.D.) 4 5 12 4 5 6
a) Assuming three will have to be selected, state which ones will be picked
b) Assuming perfect correlation, whether it is preferable to invest 75% in A and 25% in C or to invest
100% in E.
11.33
LOS 29 : Capital Market Line (CML)
The line of possible portfolio risk and Return combinations given the risk-free rate and the risk and
return of a portfolio of risky assets is referred to as the Capital Allocation Line.
 Under the assumption of homogenous expectations (Maximum Return & Minimum Risk), the
optimal CAL for investors is termed the Capital Market Line (CML).
 CML reflect the relationship between the expected return & total risk (σ).
Equation of this line:
𝛔𝐩
E(R p) = RF + [E (RM) – RF]
𝛔𝐦
LOS 30 : SML (Security Market Line)

SML reflects the relationship between expected return and systematic risk (β)
Equation:
𝐂𝐎𝐕𝐢,𝐌𝐚𝐫𝐤𝐞𝐭
E (R i) = RFR + [E (R Market) – RFR]
𝛔𝟐
𝐦𝐚𝐫𝐤𝐞𝐭
Beta
 If Beta = 0 E(R) = R f
 If Beta = 1 E(R) = R m
11.34
Graphical representation of CAPM is SML.

According to CAPM, all securities and portfolios, diversified or not, will plot on the SML in equilibrium.
QUESTION NO. 20
Probability Market Return A Ltd. Return B Ltd. Return
0.5 7% 4% 9%
0.5 25% 40% 18%
You are required to Calculate:
a) The Beta of the two stocks
b) Expected Return of each stock
c) Security Market Line (SML) equation , if risk-free rate is 7.5%.
d) The Jenson’s Alpha of the two stocks.
LOS 31 : Cut-Off Point or Sharpe’s Optimal Portfolio

Calculate Cut-Off point for determining the optimum portfolio
Steps Involved
Step 1: Calculate Excess Return over Risk Free per unit of Beta i.e.
Step 2: Rank them from highest to lowest.
Step 3: Calculate Optimal Cut-off Rate for each security.
Cut-off Point of each Security
𝐑𝐢 𝐑𝐟× 𝛃
∑𝐍
𝐢 𝟏
𝛔𝟐
𝐞𝐢
Ci=
𝛃𝟐
∑𝐍
𝐢 𝟏𝛔𝟐
𝐢
𝐞𝐢
Step 4: The Highest Cut-Off Rate is known as “Cut-off Point”. Select the securities which lies on or
above cut-off point.
11.35
Step 5: Calculate weights of selected securities in optimum portfolio.
a) Calculate Z i of Selected Security
( )
ZI= − Cut off Point
b) Calculate weight percentage
Wi =
∑
Example:
Ramesh wants to invest in stock market. He has got the following information about individual
securities:
Security Expected Return Beta 𝛔𝟐𝐞𝐢
A 15 1.5 40
B 12 2 20
C 10 2.5 30
D 09 1 10
E 08 1.2 20
F 14 1.5 30
Market index variance is 10 percent and the risk free rate of return is 7%. What should be the optimum
portfolio assuming no short sales?
Solution:
Securities need to be ranked on the basis of excess return to beta ratio from highest to the lowest.
Security Ri Βi Ri-Rf 𝑹𝒊 − 𝑹𝒇
𝜷𝒊
A 15 1.5 8 5.33
B 12 2 5 2.5
C 10 2.5 3 1.2
D 09 1 2 2
E 08 1.2 1 0.83
F 14 1.5 7 4.67
Ranked Table:
𝑵 𝑵
2
𝑹𝒊 − 𝑹𝒇 × 𝜷 𝑹𝒊 − 𝑹𝒇 × 𝜷 𝜷𝟐𝒊 𝜷𝟐𝒊
Security Ri-Rf Βi σ ei Ci
𝝈𝟐𝒆𝒊 𝝈𝟐𝒆𝒊 𝝈𝟐𝒆𝒊 𝝈𝟐𝒆𝒊
𝒆 𝒊 𝒆 𝒊
A 8 1.5 40 0.30 0.30 0.056 0.056 1.923

F 7 1.5 30 0.35 0.65 0.075 0.131 2.814
B 5 2 20 0.50 1.15 0.20 0.331 2.668
D 2 1 10 0.20 1.35 0.10 0.431 2.542
C 3 2.5 30 0.25 1.60 0.208 0.639 2.165
E 1 1.2 20 0.06 1.66 0.072 0.711 2.047
CA = 10 x 0.30 / [1 + ( 10 x 0.056)] = 1.923
CF = 10 x 0.65 / [1 + ( 10 x 0.131)] = 2.814
CB = 10 x 1.15 / [1 + ( 10 x 0.331)] = 2.668
CD = 10 x 1.35 / [1 + ( 10 x 0.431)] = 2.542
11.36
CC = 10 x 1.60 / [1 + ( 10 x 0.639)] = 2.165

CE = 10 x 1.66 / [1 + ( 10 x 0.7111)] = 2.047
Cut off point is 2.814
( )
Z i= − C
.
Z A= 5.33 − 2.814 = 0.09435
.
Z F= 4.67 − 2.814 = 0.0928
X A = 0.09435 / [0.09435 +0.0928] = 50.41%
X F = 0.0928 / [0.09435 + 0.0928] = 49.59%
Funds to be invested in security A & F are 50.41% and 49.59% respectively.
LOS 32 : Tracking Error

 Tracking error can be defined as the divergence or deviation of a fund’s return from the
benchmarks return it is following.
 The passive fund managers closely follow or track the benchmark index. Although they design
their
 investment strategy on the same index but often it may not exactly replicate the index return. In
such situation, there is possibility of deviation between the returns.
 The tracking error can be calculated on the basis of corresponding benchmark return vis a vis
 quarterly or monthly average NAVs.
 Higher the tracking error higher is the risk profile of the fund. Whether the funds outperform or
 underperform their benchmark indices; it clearly indicates that of fund managers are not following
the benchmark indices properly. In addition to the same other reason for tracking error are as
follows:
 Transaction cost
 Fees charged by AMCs
 Fund expenses
 Cash holdings
 Sampling biasness
Thus from above it can be said that to replicate the return to any benchmark index the tracking
error should be near to zero.
The Tracking Error is calculated as follows:
∑ ̅
TE =
d = Differential return
𝑑̅ = Average differential return
n = No. of observation
11.37
PRACTICE QUESTIONS
QUESTION NO. 21
Consider the following data on 3 securities
Correlation Matrix
Stock E (R) S.D. A B C
A 20% 10% 1 0.2 0.6
B 30% 12% 0.2 1 0.4
C 40% 15% 0.6 0.4 1
Find the E (RP) and S.D of the portfolio comprising the following two portfolios:
Portfolio 1 : Weight 60%
Portfolio 2 : Weight 40%
Portfolio 1 : comprises of 50% Stock A; 30% of Stock B; 20% of Stock C
Portfolio 2 : comprises of 20% Stock A; 40% of Stock B; 40% of Stock C
QUESTION NO. 22
X Co., Ltd., invested on 1.4.2009 in certain equity shares as below:
Name of Co. No. of Shares Cost (`)
M Ltd. 1,000 (` 100 each) 2,00,000
N Ltd. 500 (` 10 each) 1,50,000
In September, 2009, 10% dividend was paid out by M Ltd. and in October, 2009, 30% dividend paid out
by N Ltd. On 31.3.2010 market quotations showed a value of ` 220 and ` 290 per share for M Ltd. and
N Ltd. respectively.
On 1.4.2010, investment advisors indicate (a) that the dividends from M Ltd. and N Ltd. for the year
ending 31.3.2011 are likely to be 20% and 35%, respectively and (b) that the probabilities of market
quotations on 31.3.2011 are as below:
Probability Factor Price/ Share of M Ltd. Price/ Share of N Ltd.
0.2 220 290
0.5 250 310
0.3 280 330
a) Calculate the average return from the portfolio for the year ended 31.3.2010;
b) Calculate the expected average return from the portfolio for the year 2010-11; and
c) Advise X Co. Ltd., of the comparative risk in the two investments by calculating the standard deviation
in each case.
QUESTION NO. 23
Assuming that shares of ABC Ltd. and XYZ Ltd. are correctly priced according to Capital Asset Pricing
Model. The expected return from and Beta of these shares are as follows:
Share Beta Expected return
ABC 1.2 19.8%
XYZ 0.9 17.1%
You are required to derive Security Market Line.
QUESTION NO. 24
Suppose that economy A is growing rapidly and you are managing a global equity fund that has so far
invested only in developed-country stocks. Now you have decided to add stocks of economy A to your
portfolio. The table below shows the expected rates of return, standard deviations, and correlation
11.38
coefficients (all estimated for the aggregate stock market of developed countries and stock market of
Economy A).
Developed country Stocks of Economy A
Stocks
Expected rate of return (annualized percent) 10 15
Risk [Annualized Standard Deviation (%)] 16 30
Correlation Coefficient (r) 0.30
Assuming the risk-free interest rate to be 3%, you are required to determine:
a) What percentage of your portfolio should you allocate to stocks of Economy A if you want to increase
the expected rate of return on your portfolio by 0.5%?
b) What will be the standard deviation of your portfolio assuming that stocks of Economy A are included
in the portfolio as calculated above?
c) Also show how well the Fund will be compensated for the risk undertaken due to inclusion of stocks
of Economy A in the portfolio?
QUESTION NO. 25
The following information is available for the share of X Ltd. and stock exchange for the last 4 years
Index of Return from Return from
X LTD. Stock Market Funds Govt.
Exchange Securities Securities
Share Price Divided
Yield
Present Year 197 10% 2182 16% 15%
1 Years ago 164.2 12% 1983 15% 15%
2 Years ago 155 8% 1665 16% 16%
3 Years ago 121 10% 1789 10% 14%
4 Years ago 95 10% 1490 18% 15%
With above information available please calculate:
a) Expected Return on X Ltd.’s share.
b) Expected Return on Market Index.
c) Risk Free Rate of Return
d) Beta of X Ltd.
QUESTION NO. 26
Assuming that two securities X and Y are correctly priced on Security Market Line (SML) and expected
return from these securities are 9.40% (Rx) and 13.40% (Ry) respectively. The Beta of these securities are
0.80 and 1.30 respectively.
Mr. A, an investment manager states that the return on market index is 9%. You are required to
determine,
(a) Whether the claim of Mr. A is right. If not then what is the correct return on market index.
(b) Risk Free Rate of Return
QUESTION NO. 27
Suppose if Treasury Bills give a return of 5% and Market Return is 13%, then determine
(i) The market risk premium
(ii) β Values and required returns for the following combination of investments.
Treasury Bill 100 70 30 0
Market 0 30 70 100
11.39
QUESTION NO. 28
If the rate of return and Standard Deviation of Market Portfolio (Index) is 8% and 6% respectively and
the risk free rate of return is 5%, you are required to:
(i) Construct an efficient portfolio which produces expected return of 7.5%.
(ii) Calculate the risk of above portfolio.
(iii) Suppose if Mr. X has `1,00,000 of his personal funds, then how he would construct his portfolio
giving expected return of 10% and what will be risk of this portfolio.
QUESTION NO. 29
Ms. Kiran had a surplus fund of ` 2,00,000 on 31.03.2016. She is interested in constructing a portfolio
of shares of the core sectors to be weighted equally in rupee value terms. Her friend Shaila based on
her research advised her to purchase following shares:
Company No. of Shares Price Per Share
O Ltd. 100 400
H Ltd. 1000 40
A Ltd. 320 125
R Ltd. 400 100
T Ltd. 200 200
On April 1, 2016, the prices of these stocks were as follows:
Company Price Per Share
O Ltd. 300
H Ltd. 60
A Ltd. 120
R Ltd. 150
T Ltd. 125
You are required to exhibit how Kiran can rebalance her portfolio on 1.4.2016 so that her exposure
to individual stock is maintained at original level in terms of rupee value.
QUESTION NO. 30
The returns of a portfolio A and market portfolio for the last 12 months are indicated as follows:
Month Portfolio A Market Portfolio
January - 0.52 0.82
February 2.20 0.04
March 2.17 2.80
April 4.17 1.72
May 2.04 0.27
June 3.00 0.39
July 1.99 1.95
August 4.00 0.64
September -1.38 1.53
October 2.67 2.70
November 3.99 2.52
December 1.86 2.09
Standard Deviation (σ) 1.6223 0.9498
(i) You are required to find out the monthly returns attributable to the sheer skill of the Portfolio
Manager.
(ii) What part of the monthly return is attributable to the higher risk assumed by the Portfolio Manager?
11.40
Assume that the risk-free rate of return is 12% per annum and the portfolio is fully diversified.
QUESTION NO. 31
Following are risk and return estimates for two stocks
Stock Expected returns (%) Beta Specific SD of expected return (%)
A 14 0.8 35
B 18 1.2 45
The market index has a Standard Deviation (SD) of 25% and risk free rate on Treasury Bills is 6%.
(i) The standard deviation of expected returns on A and B.
(ii) Suppose a portfolio is to be constructed with the proportions of 25%, 40% and 35% in stock A, B
and Treasury Bills respectively, what would be the expected return, standard deviation of expected
return of the portfolio?
QUESTION NO. 32
The following are the details of three mutual funds of MFL:
Growth Balanced Regular Market
Fund Fund Fund
Average Return (%) 7 6 5 9
Variance 92.16 54.76 40.96 57.76
Coefficient of Determination 0.3025 0.6561 0.9604
The yield on 182 days Treasury Bill is 9 per cent per annum.
(i) Rank the funds as per Sharpe's measure.
(ii) Rank the funds as per Treynor's measure.
(iii) Compare the performance with the market.
QUESTION NO. 33
Ramesh has identified stocks of two companies A and B having good investment potential:
Following data is available for these stocks:
Year A (Market Price per Share in ₹) B (Market Price per Share in ₹)
2013 19.60 8.70
2014 18.75 12.80
2015 33.42 16.20
2016 42.64 18.25
2017 43.25 15.60
2018 44.60 13.25
2019 34.75 18.60
(i) The Risk and Return by investing in Stock A and B
(ii) The Risk and Return by investing in a portfolio of these Stocks if he invests in Stock A and B in
proportion of 6 : 4.
(iii) The better opportunity for investment
12.1
International Financial Management

Study Session 12
LOS 1 : International Capital Budgeting
 Capital Budgeting is the process of Identifying & Evaluating capital projects i.e. projects where the
cash flows to the firm will be received over a period longer than a year.
 Any corporate decisions with an IMPACT ON FUTURE EARNINGS can be examined using capital
budgeting framework.
 Categories of Capital Budgeting Projects:
a) Replacement projects to maintain the business
b) Replacement projects for cost reduction
c) Expansion projects
d) New product or market development
e) Mandatory projects
Types of Capital Budgeting Proposals:
a) Mutually Exclusive Proposals: when acceptance of one proposal implies the automatic rejection of
the other proposal.
b) Complementary Proposals: when the acceptance of one proposal implies the acceptance of other
proposal complementary to it, rejection of one implies rejection of all complementary proposals.
c) Independent Proposals: when the acceptance/rejection of one proposal doesn’t affect the
acceptance/rejection of other proposal.
LOS 2 : Net Present Value (NPV)

NPV=PV of Cash Inflows – PV of Cash Outflows
Decision: If NPV is
+ve Accept the project- increase shareholder’s wealth
-ve Reject the project-decrease shareholder’s wealth
Zero Indifferent-No effect on shareholder’s wealth
𝐂𝐅𝟏 𝐂𝐅𝟐 𝐂𝐅𝐧
NPV= - CF0 + + + −−−−−−−−−−−−−−−+
(𝟏 𝒌𝟎 )𝟏 (𝟏 𝒌𝟎 )𝟐 (𝟏 𝒌𝟎 )𝐧
Where,
CF0 = the initial investment outlay.
CF t = after- tax cash flow at time t
Ko = required rate of return for project.
LOS 3 : Profitability Index (PI)/ Benefit cost Ratio/ Desirability Factor/Present

Value Index
𝐏𝐕 𝐨𝐟 𝐂𝐚𝐬𝐡 𝐈𝐧𝐅𝐥𝐨𝐰𝐬
PI =
𝐂𝐅𝟎 𝐨𝐫 𝐏𝐫𝐞𝐬𝐞𝐧𝐭 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝐎𝐮𝐭𝐟𝐥𝐨𝐰𝐬
CF0 = Initial Cash Out Flows

Note:
 NPV = - CF0 + PV of future Cash In Flows
12.2
 CF0 + NPV = PV of Future Cash In Flows

 If NPV is given, then Add Initial outlay in NPV to get, PV of Cash inflows.
Decision:
 If NPV is Positive, the PI will be greater than one.
 If NPV is Negative, the PI will be Less than one.
Rule:
If PI > 1, Accept the project
PI < 1, Reject the project
PI = 1, Indifferent
LOS 4 : Pay-Back Period Method (PBP)

The pay- back period (PBP) is the number of years it takes to recover the initial cost of an investment.
Case I: When Cash inflows are Constant/ equal
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐈𝐧𝐯𝐞𝐬𝐭𝐦𝐞𝐧𝐭/ 𝐨𝐮𝐭𝐟𝐥𝐨𝐰
Pay-back Period =
𝐀𝐧𝐧𝐮𝐚𝐥 𝐂𝐚𝐬𝐡 𝐈𝐧𝐟𝐥𝐨𝐰
Case II: When Cash inflows are unequal
𝐔𝐧𝐫𝐞𝐜𝐨𝐯𝐞𝐫𝐞𝐝 𝐂𝐨𝐬𝐭
Pay-back Period = Full years until recovery +
𝐂𝐚𝐬𝐡 𝐅𝐥𝐨𝐰 𝐝𝐮𝐫𝐢𝐧𝐠 𝐧𝐞𝐱𝐭 𝐘𝐞𝐚𝐫
Decision:
 Shorter the PBP, better the project.
Drawback:
 PBP does not take into account the time value of money and cash flows beyond the payback
period.
Benefit:
 The main benefit of the pay-back period is that it is a good measure of project liquidity.
LOS 5 : Discount pay-back period

 The discounted payback period uses the present value (PV) of project’s estimated Cash flows.
 It is the number of years it takes a project to recover its initial investment in present value terms.
 Discounted pay-back period must be greater than simple pay-back period.
LOS 6 : IRR Techniques (Internal Rate of Return)

 IRR is the discount rate that makes the PV of a project’s estimated cash inflows equal to the PV of
the project’s estimated cash outflows.
 i.e. IRR is the discount rate that makes the following relationship:
PV (Inflows) = PV (Outflows)
 IRR is also the discount rate for which the NPV of a project is equal to ZERO.
𝐋𝐨𝐰𝐞𝐫 𝐑𝐚𝐭𝐞 𝐍𝐏𝐕
IRR= Lower Rate + × Difference in Rate (HR-LR)
𝐋𝐨𝐰𝐞𝐫 𝐑𝐚𝐭𝐞 𝐍𝐏𝐕 𝐇𝐢𝐠𝐡𝐞𝐫 𝐑𝐚𝐭𝐞 𝐍𝐏𝐕
How to find the starting rate for calculation of IRR:
Step 1: Calculate Fake Pay-back period:
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐈𝐧𝐯𝐞𝐬𝐭𝐦𝐞𝐧𝐭
Fake Pay-back Period =
𝐀𝐯𝐞𝐫𝐚𝐠𝐞 𝐀𝐧𝐧𝐮𝐚𝐥 𝐂𝐚𝐬𝐡 𝐅𝐥𝐨𝐰
Step 2: Locate the above figure in Present Value Annuity Factor Table and take this discount rate to
start the calculation of IRR.
12.3
Accept/Reject Criteria:
IRR > Cost of Capital Accept the Proposal
IRR = Cost of Capital Indifferent
IRR< Cost of Capital Reject the Proposal
LOS 7 : Net Profitability Index or Net PI

𝐍𝐏𝐕
Net PI =
𝐈𝐧𝐢𝐭𝐢𝐚𝐥 𝐈𝐧𝐯𝐞𝐬𝐭𝐦𝐞𝐧𝐭 / 𝐏𝐫𝐞𝐬𝐞𝐧𝐭 𝐕𝐚𝐥𝐮𝐞 𝐨𝐟 𝐎𝐮𝐭𝐟𝐥𝐨𝐰𝐬
Decision: Higher the Better.
LOS 8 : Calculation of NPV

Total Fund Approach / Overall Project Approach
Discount Rate K0
Initial Outflow Equity – Share Capital (Fund) + Debenture + Long-term Loan +
Preference Share Capital
Or
Total Cost of Project
Operating Cash
Cash Inflow available for overall project
Inflows
SV adjusted for Tax
Terminal Cash flows
Release of Working Capital
NPV NPV that a project earns for the company as a whole.
Calculation of Project Cash Flows
Sale Price Per Unit xxx
Less : Variable Cost Per Unit xxx
Contribution Per Unit xxx
× No. of Unit xxx
Total Contribution xxx
Less : Fixed Cost xxx
EBDIT xxx
Less : Depreciation xxx
EBIT xxx
Less : Tax xxx
NOPAT xxx
Add : Depreciation xxx
CFAT xxx
Note 1 : Treatment of Depreciation
[EBDIT – Depreciation] [1 – Tax Rate] + Depreciation
Or
EBDIT (1 – Tax Rate) + Tax saving on Depreciation
Note 2 : Treatment of Interest Cost / Finance Cost
 Finance Cost are already reflected in the Projects required rate of return / WACC / Ko
 This shows that Interest on Long Term Loans as well as its Tax Saving is already considered by Ko
Note 3 : Net Investment in Working Capital
NWC investment = Change in non-cash current assets
(-)
Change in non-cash current liabilities
12.4
(Other than cash and cash equivalents, notes payable, short-term liabilities and current portion of
long-term loans.)
Time
Introduction of Working Capital Outflow Year 0
Release of Working Capital Inflow End of project Life
 Working Capital should never be adjusted for tax as it is a balance sheet item. Working capital is
also not subject to depreciation.
Note 4 : Treatment of Tax
If we have loss in a particular year, there are two adjustments :-
 Set-off : assumed the firm as other profitable business, Loss in a year generate tax savings in that
year.
 Carry Forward : The company has an individual business or a new business having no other
operations, loss in a year will be carried forward to future years for the purpose of Set-off.
Note 5 : Key Points to Remember
1. Decisions are based on cash flows, not accounting income:
2. Consider INCREMENTAL CASH FLOWS, the change in cash flows that will occur if the project is
undertaken.
3. Sunk costs should not be included in the analysis : These costs are not effected by the
accept/reject decisions. e.g. Consulting fees paid to a marketing research firm to estimate demand
for a new product prior to a decision on the project.
4. Externities / Cannibalization : When considering the full implication of a new project, loss in
sales of existing products should be taken into account & also consider positive effects on sale of
a firm’s other product line.
5. Cash flows are based on Opportunity Costs : Opportunity costs should be included in projects
costs.
6. The timing of cash flows is important : Cash flows received earlier are worth more than cash
flows to be received later.
7. Cash flows are analyzed on an after-tax basis.
LOS 9 : Modified NPV/ IRR

When Cost of Capital & Re-investment rate are separately given, then we calculate Modified NPV.
Modified IRR: It is the discount rate at which Modified NPV is Zero.
𝑻𝒆𝒓𝒎𝒊𝒏𝒂𝒍 𝑽𝒂𝒍𝒖𝒆
i.e. Modified NPV = - PV of Cash Outflow
(𝟏 𝑲𝟎 )𝒏
‘or’
𝑻𝒆𝒓𝒎𝒊𝒏𝒂𝒍 𝑽𝒂𝒍𝒖𝒆
PV of cash outflow =
(𝟏 𝑲𝟎 )𝒏
12.5
LOS 10 : Inflation under Capital Budgeting
Cash Flow:
Conversion of Real Cash Flow into Money Cash Flow & Vice-versa
Money Cash Flow = Real Cash Flow (1 + Inflation Rate)n

Or
𝐌𝐨𝐧𝐞𝐲 𝐂𝐚𝐬𝐡 𝐅𝐥𝐨𝐰
Real Cash Flow =
(𝟏 𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧 𝐑𝐚𝐭𝐞)𝐧
Discount Rate:
Conversion of Real Discount Rate into Money Discount Rate & Vice-versa
(1 + Money Discount Rate) = (1+ Real Discount Rate) ( 1+Inflation Rate)
NPV:
12.6
Note:
 Answer in both the case will be same.
 Depreciation is not affected by inflation rate as depreciation is changed on the book value of the
asset & not market value.
QUESTION NO. 1A
A multinational company is planning to set up a subsidiary company in India (where hitherto it was
exporting) in view of growing demand for its product and competition from other MNCs. The initial
project cost (consisting of Plant and Machinery including installation) is estimated to be US$ 500 million.
The net working capital requirements are estimated at US$ 50 million. The company follows straight line
method of depreciation.
Presently, the company is exporting two million units every year at a unit price of US$ 80, its variable
cost per unit being US$ 40.
The Chief Financial Officer has estimated the following operating cost and other data in respect of
proposed project:
(i) Variable operating cost will be US $ 20 per unit of production;
(ii) Additional cash fixed cost will be US $ 30 million p.a. and project's share of allocated fixed cost will
be US $ 3 million p.a. based on principle of ability to share;
(iii) Production capacity of the proposed project in India will be 5 million units;
(iv) Expected useful life of the proposed plant is five years with no salvage value;
(v) Existing working capital investment for production & sale of two million units through exports was
US $ 15 million;
(vi) Export of the product in the coming year will decrease to 1.5 million units in case the company
does not open subsidiary company in India, in view of the presence of competing MNCs that are
in the process of setting up their subsidiaries in India;
(vii) Applicable Corporate Income Tax rate is 35%, and
(viii) Required rate of return for such project is 12%.
Assuming that there will be no variation in the exchange rate of two currencies and all profits will be
repatriated, as there will be no withholding tax, estimate Net Present Value (NPV) of the proposed project
in India.
Present Value Interest Factors (PVIF) @ 12% for five years are as below:
Year 1 2 3 4 5
PVIF 0.8929 0.7972 0.7118 0.6355 0.5674
QUESTION NO. 1B
XY Limited is engaged in large retail business in India. It is contemplating for expansion into a country
of Africa by acquiring a group of stores having the same line of operation as that of India. The exchange
rate for the currency of the proposed African country is extremely volatile. Rate of inflation is presently
40% a year. Inflation in India is currently 10% a year. Management of XY Limited expects these rates
likely to continue for the foreseeable future.
Estimated projected cash flows, in real terms, in India as well as African country for the first three years
of the project are as follows:
Year-0 Year-1 Year-2 Year-3
Cash flows in Indian ₹ (000) -50,000 -1,500 -2,000 -2,500
Cash flows in African Rands (000) - 2,00,000 50,000 70,000 90,000
XY Ltd. assumes the year 3 nominal cash flows will continue to be earned each year indefinitely. It
evaluates all investments using nominal cash flows and a nominal discounting rate. The present
exchange rate is African Rand 6 to ₹ 1.
You are required to calculate the net present value of the proposed investment considering the following:
(i) African Rand cash flows are converted into rupees and discounted at a risk adjusted rate.
(ii) All cash flows for these projects will be discounted at a rate of 20% to reflect it’s high risk.
12.7
Ignore taxation.
Year - 1 Year - 2 Year - 3
PVIF @ 20% 0.833 0.694 0.579
QUESTION NO. 1C
XYZ Ltd. a company based in India, manufactures very high quality modern furniture and sells to a small
number of retail outlets in India and Nepal. It is facing tough competition. Recent studies on marketability
of products have clearly indicated that the customer is now more interested in variety and choice rather
than exclusivity and exceptional quality. Since the cost of quality wood in India is very high, the company
is reviewing the proposal for import of woods in bulk from Nepalese supplier.
The estimate of net Indian (₹) and Nepalese Currency (NC) cash flows for this proposal is shown below:
Net Cash Flows (in millions)
NC 25.000 2.600 3.800 4.100
Indian (₹) 0 2.869 4.200 4.600
The following information is relevant :
(i) XYZ Ltd. evaluates all investments by using a discount rate of 9% p.a. All Nepalese customers are
invoiced in NC. NC cash flows are converted to Indian (₹) at the forward rate and discounted at
the Indian rate.
(ii) Inflation rates in Nepal and India are expected to be 9% and 8% p.a. respectively. The current
exchange rate is ₹ 1 = NC 1.6
Assuming that you are the finance manager of XYZ Ltd., calculate the net present value (NPV) and
modified internal rate of return (MIRR) of the proposal.
You may use following values with respect to discount factor for ₹ 1 @ 9%.
Year 1 0.917 1.188
Year 2 0.842 1.090
Year 3 0.772 1
QUESTION NO. 1D
Opus Technologies Ltd., an Indian IT company is planning to make an investment through a wholly
owned subsidiary in a software project in China with a shelf life of two years. The inflation in China is
estimated as 8 percent. Operating cash flows are received at the year end.
For the project an initial investment of Chinese Yuan (CN¥) 30,00,000 will be in a piece of
land. The land will be sold after the completion of project at estimated value of CN¥ 35,00,000. The
project also requires an office complex at cost of CN¥ 15,00,000 payable at the beginning of project.
The complex will be depreciated on straight-line basis over two years to a zero salvage value. This
complex is expected to fetch CN¥ 5,00,000 at the end of project.
The company is planning to raise the required funds through GDR issue in Mauritius. Each GDR will have
5 common equity shares of the company as underlying security which are currently trading at ₹ 200 per
share (Face Value = ₹ 10) in the domestic market. The company has currently paid a dividend of 25%
which is expected to grow at 10% p.a. The total issue cost is estimated to be 1 percent of issue size.
The annual sales is expected to be 10,000 units at the rate of CN¥ 500 per unit. The price of
unit is expected to rise at the rate of inflation. Variable operating costs are 40 percent of
sales. Current Fixed Operating costs is CN¥ 22,00,000 per year which is expected to rise at
the rate of inflation.
The tax rate applicable in China for business income and capital gain is 25 percent and as per GOI Policy
no further tax shall be payable in India. The current spot rate of CN¥ 1 is ₹ 9.50. The nominal interest
rate in India and China is 12% and 10% respectively and the international parity conditions hold.
a) Identify expected future cash flows in China and determine NPV of the project in CN¥.
12.8
b) Determine whether Opus Technologies should go for the project or not, assuming that there neither
there is any restriction nor any charges/taxes payable on the transfer of funds from China to India.
QUESTION NO. 1E
Perfect Inc., a U.S. based Pharmaceutical Company has received an offer from Aidscure Ltd., a company
engaged in manufacturing of drugs to cure Dengue, to set up a manufacturing unit in Baddi (H.P.), India
in a joint venture.
As per the Joint Venture agreement, Perfect Inc. will receive 55% share of revenues plus a royalty @ US
$0.01 per bottle. The initial investment will be ₹200 crores for machinery and factory. The scrap value
of machinery and factory is estimated at the end of five (5) year to be ₹5 crores. The machinery is
depreciable @ 20% on the value net of salvage value using Straight Line Method. An initial working
capital to the tune of ₹50 crores shall be required and thereafter ₹5 crores each year.
As per GOI directions, it is estimated that the price per bottle will be ₹7.50 and production will be 24
crores bottles per year. The price in addition to inflation of respective years shall be increased by ₹1 each
year. The production cost shall be 40% of the revenues.
The applicable tax rate in India is 30% and 35% in US and there is Double Taxation Avoidance Agreement
between India and US. According to the agreement tax credit shall be given in US for the tax paid in
India. In both the countries, taxes shall be paid in the following year in which profit have arisen.
The Spot rate of $ is ₹57. The inflation in India is 6% (expected to decrease by 0.50% every year) and 5%
in US.
As per the policy of GOI, only 50% of the share can be remitted in the year in which they are earned
and remaining in the following year.
Though WACC of Perfect Inc. is 13% but due to risky nature of the project it expects a return of 15%.
Determine whether Perfect Inc. should invest in the project or not (from subsidiary point of view).
QUESTION NO. 1F
Its Entertainment Ltd., an Indian Amusement Company is happy with the success of its Water Park in
India. The company wants to repeat its success in Nepal also where it is planning to establish a Grand
Water Park with world class amenities. The company is also encouraged by a marketing research report
on which it has just spent ₹ 20,00,000 lacs.
The estimated cost of construction would be Nepali Rupee (NPR) 450 crores and it would be completed
in one years’ time. Half of the construction cost will be paid in the beginning and rest at the end of year.
In addition, working capital requirement would be NPR 65 crores from the year end one. The after tax
realizable value of fixed assets after four years of operation is expected to be NPR 250 crores. Under the
Foreign Capital Encouragement Policy of Nepal, company is allowed to claim 20% depreciation
allowance per year on reducing balance basis subject to maximum capital limit of NPR 200 crore. The
company can raise loan for theme park in Nepal @ 9%.
The water park will have a maximum capacity of 20,000 visitors per day. On an average, it is expected
to achieve 70% capacity for first operational four years. The entry ticket is expected to be NPR 220 per
person. In addition to entry tickets revenue, the company could earn revenue from sale of food and
beverages and fancy gift items. The average sales expected to be NPR 150 per visitor for food and
beverages and NPR 50 per visitor for fancy gift items. The sales margin on food and beverages and fancy
gift items is 20% and 50% respectively. The park would open for 360 days a year.
The annual staffing cost would be NPR 65 crores per annum. The annual insurance cost would be NPR
5 crores. The other running and maintenance costs are expected to be NPR 25 crores in the first year of
operation which is expected to increase NPR 4 crores every year. The company would apportion existing
overheads to the tune of NPR 5 crores to the park.
All costs and receipts (excluding construction costs, assets realizable value and other running and
maintenance costs) mentioned above are at current prices (i.e. 0 point of time) which are expected to
increase by 5% per year.
The current spot rate is NPR 1.60 per ₹. The tax rate in India is 30% and in Nepal it is 20%.
12.9
The current WACC of the company is 12%. The average market return is 11% and interest rate on
treasury bond is 8%. The company’s current equity beta is 0.45. The company’s funding ratio for the
Water Park would be 55% equity and 45% debt.
Being a tourist Place, the amusement industry in Nepal is competitive and very different from its Indian
counterpart. The company has gathered the relevant information about its nearest competitor in Nepal.
The competitor’s market value of the equity is NPR 1850 crores and the debt is NPR 510 crores and the
equity beta is 1.35.
State whether Its Entertainment Ltd. should undertake Water Park project in Nepal or not.
LOS 11 : Overall Beta/ Asset Beta/ Project Beta/ Firm Beta

Situation 1 :
100 % Equity Firm  Unlevered Firm
Equity = Assets = Overall

Situation 2 :
Debt + Equity Firm  Levered Firm
Levered = Unlevered = Overall = Assets
 Overall Beta of the companies belonging to the same industry/sector, always remain same.
 Equity Beta and debt Beta may change with the change in Capital structure.
 Overall Beta of a project can’t be changed with the change in capital structure of a particular
company.
 According to MM, the change in capital structure doesn’t change the overall beta.
 Debt is always assume to be risk free, so. Debt Beta = 0.
𝑬𝒒𝒖𝒊𝒕𝒚 𝑫𝒆𝒃𝒕 (𝟏 𝒕𝒂𝒙)
Overall Beta = equity Beta × + 𝐃𝐞𝐛𝐭 𝐁𝐞𝐭𝐚 ×
𝑬𝒒𝒖𝒊𝒕𝒚 𝑫𝒆𝒃𝒕 (𝟏 𝒕𝒂𝒙) 𝑬𝒒𝒖𝒊𝒕𝒚 𝑫𝒆𝒃𝒕 (𝟏 𝒕𝒂𝒙)
Overall Cost of Capital/ Discount Rate

Cost of Capital (K o) = K e We + K d W d
K o = R f + β Overall (R m – R f)
K e = R f + β equity (R m – R f) OR
(Only applicable when tax rate is missing)
K d = Interest (1 – tax rate)
Note:
 If interest rate is not given, it is assumed to be equal to risk-free rate.
 If Beta Debt is not given, it is assumed to be equal to Zero
 If debt = 0 Overall Beta = Equity Beta
i.e. for 100% equity firm overall beta & equity beta is same
Estimating the project Discount Rate
CAPM can be used to arrive at the project discount rate by taking the following steps:
1. Estimate the project beta.
2. Putting the value of Beta computed above into the Capital Asset Pricing Model (CAPM) to arrive
at the cost of equity.
3. Estimate the cost of debt.
4. Calculate the WACC for the project.
QUESTION NO. 2A
Acme Inc. is considering a project in the food distribution business. It has a D/E ratio of 2, Marginal tax
rate of 40%, and its debt currently has a interest of 14%. Balfor, a publicly traded firm that operates only
in the food distribution business has a D/E ratio of 1.5, a marginal tax rate of 30% and an equity beta
12.10
of 0.9. the risk free rate is 5% and expected market return = 12%. Calculate Balfor’s asset beta, the
projects equity beta and the appropriate WACC to use in evaluating the project.
QUESTION NO. 2B
XYZ, a large business house is planning to acquire ABC another business entity in similar line of business.
XYZ has expressed its interest in making a bid for ABC. XYZ expects that after acquisition the annual
earning of ABC will increase by 10%.
Following information, ignoring any potential synergistic benefits arising out of possible acquisitions, are
available:
XYZ ABC Proxy entity for XYZ & ABC in the
same line of business
Paid up Capital (₹ Crore) 1025 106 --
Face Value of Share is ₹10
Current share price ₹ 129.60 ₹ 55 --
Debt : Equity (at market values) 1:2 1:3 1:4
Equity Beta -- -- 1.1
Assume Beta of debt to be zero and corporate tax rate as 30%, determine the Beta of combined entity.
QUESTION NO. 2C
B Ltd. is planning for a diversification project in hospitality sector. Its current equity beta is 1.20, whereas
equity beta in hospitality sector is 1.625. Gearing of hospitality sector is 30% debts and 70% equity.
Expected market return is 15% and risk free rate is 10%. Corporate debt is assumed to be risk free.
Compute suitable discount rate assuming 30% tax if the project is financed by:
(1) 20% debt and 80% equity;
(2) 30% debt and 70% equity;
(3) Equity only;
Calculate cost of overall capital.
QUESTION NO. 2D
The total market value of the equity share of O.R.E. Company is ₹ 60,00,000 & total value of the debt is
₹ 40,00,000. The treasurer estimate that the beta of the stock is currently 1.5 & that the expected risk
premium on the market is 10%. The industry bill rate is 8%.
Required:
(i) What is the beta of the Company’s existing portfolio of assets?
(ii) Estimate the Company’s Cost of capital and the discount rate for an expansion of the company’s
present business.
QUESTION NO. 2E
X Limited pays no taxes and is entirely financed by equity shares. The company’s equity has a beta of
0.6 and is expected to earn 20%. The company has now decided to buy back half of the equity shares
by borrowing an equal amount. If the debt yields a risk-free return of 10%.Calculate:
(i) The beta of the equity shares after the buyback.
(ii) The risk premium on the equity shares before the buyback.
(iii) The required return and risk premium on equity shares after the buyback
(iv) The required return on debt.
(v) The percentage increase in expected earnings per share.
(vi) The new price-earning multiple.
12.11
QUESTION NO. 2F
Equity of KGF Ltd. (KGFL) is ₹ 410 Crores, its debt, is worth ₹ 170 Crores. Printer Division segments value
is attributable to 74%, which has an Asset Beta (βp) of 1.45, balance value is applied on Spares and
Consumables Division, which has an Asset Beta (βsc) of 1.20 KGFL Debt beta (βD) is 0.24.
(i) Equity Beta (βE),
(ii) Ascertain Equity Beta (βE), if KGF Ltd. decides to change its Debt Equity position by raising further
debt and buying back of equity to have its Debt Equity Ratio at 1.90. Assume that the present Debt
Beta (βD1) is 0.35 and any further funds raised by way of Debt will have a Beta (βD2) of 0.40.
(iii) Whether the new Equity Beta (βE) justifies increase in the value of equity on account of leverage?
LOS 12 : Proxy Beta (If more than one comparable co. data is given)
 Sometimes overall beta of similar companies belonging to same sector may be
 slightly different.
 In such case we use proxy beta concept by taking average of all the given companies.
QUESTION NO. 3A
The XYZ Ltd. in the manufacturing business is planning to set up a software development company. The
project will have a D/E ratio of 0.27. The company has identified following four pure play firms in the
line of software business.
Pure play firm β L / β equity D/E
ABC 1.1 0.3
DEF 0.9 0.25
GHI 0.95 0.35
JKL 1.0 0.3
Assuming tax rate applicable to XYZ Ltd. as 35 per cent, R f as 12%, K d as 14% and RM as 18%, you are
required to compute the WACC to be used to compute NPV of the project.
QUESTION NO. 3B
ABC, a large business house is planning to sell its wholly owned subsidiary B Ltd.
Another large business entity A Ltd. has expressed its interest in making a bid for B Ltd. A Ltd expects
that after acquisition the annual earning of B Ltd. will increase by 10%.
Following information, ignoring any potential synergistic benefits arising out of possible acquisitions, are
available:
(i) Profit after tax for B Ltd. for the financial year which has just ended is estimated to be ₹ 10 Cr.
(ii) B Ltd's after tax profit has an increasing trend of 7% each year and the same is expected to continue.
(iii) Estimated post tax market return is 10% and risk free rate is 4%. These rates are expected to continue.
(iv) Corporate tax rate is 30%.
A Ltd. ABC Ltd. Proxy entity for B Ltd. in the
same line of business
No. of Shares 100 Lakhs 80 Lakhs —
Current share price ₹ 287 ₹ 375 —
Dividend payout ratio 40% 50% 50%
Debt : Equity (at market values) 1:2 1:3 1:4
Equity Beta 1 1.1 1.1
P/E ratio 10 13 12
Assume gearing level of B Ltd. to be the same as for ABC and a debt beta of zero. You are required to
calculate:
12.12
a) Appropriate cost of equity for B Ltd. based on the data available for the proxy entity.
b) A range of values for B Ltd. both before and after any potential synergistic benefits to A Ltd of the
acquisition.
LOS 13 : ADR & GDR

QUESTION NO. 4A
Odessa Limited has proposed to expand its operations for which it requires funds of $ 15 million, net of
issue expenses which amount to 2% of the issue size. It proposed to raise the funds though a GDR issue.
It considers the following factors in pricing the issue:
(i) The expected domestic market price of the share is ₹ 300 (Face Value ₹100)
(ii) 3 shares underlying each GDR
(iii) Underlying shares are priced at 10% discount to the market price
(iv) Expected exchange rate is ₹ 60/$
You are required to compute the number of GDR's to be issued and cost of GDR to Odessa Limited, if
20% dividend is expected to be paid with a growth rate of 20%.
QUESTION NO. 4B
X Ltd. is interested in expanding its operation and planning to install manufacturing plant at US. For
the proposed project it requires a fund of $ 10 million (net of issue expenses/ floatation cost). The
estimated floatation cost is 2%. To finance this project it proposes to issue GD₹
You as financial consultant is required to compute the number of GDRs to be issued and cost of the
GD R with the help of following additional information.
1. Expected market price of share at the time of issue of GDR is ₹ 250 (Face Value ₹ 100)
2 Shares shall underly each GDR and shall be priced at 10% discount to market price.
3 Expected exchange rate ₹ 60/$.
4 Dividend expected to be paid is 20% with growth rate 12%.
12.13
PRACTICE QUESTIONS
QUESTION NO. 5
ABC Ltd. manufactures Car Air Conditioners (ACs), Window ACs and Split ACs constituting 60%, 25%
and 15% of total market value. The stand-alone Standard Deviation and Coefficient of Correlation with
market return of Car AC and Window AC is as follows:
S.D. Coefficient of Correlation
Car AC 0.30 0.6
Window AC 0.35 0.7
No data for stand-alone SD and Coefficient of Correlation of Split AC is not available. However, a
company who derives its half value from Split AC and half from Window AC has a SD of 0.50 and
Coefficient of correlation with market return is 0.85. Index has a return of 10% and has SD of 0.20.
Further, the risk-free rate of return is 4%.
(i) Beta of ABC Ltd.
(ii) Cost of Equity of ABC Ltd.
Assuming that ABC Ltd. wants to raise debt of an amount equal to half of its Market Value then
determine equity beta, if yield of debt is 5%.
QUESTION NO. 6
A proposed foreign investment involves creation of a plant with an annual output of 1 million units.
The entire production will be exported at a selling price of USD 10 per unit.
At the current rate of exchange dollar cost of local production equals to USD 6 per unit. Dollar is
expected to decline by 10% or 15%. The change in local cost of production and probability from the
expected current level will be as follows:
Decline in value of USD (%) Reduction in local cost of production Probability
(USD/unit)
0 - 0.4
10 0.30 0.4
15 0.15 Additional reduction 0.2
The plant at the current rate of exchange will have a depreciation of USD 1 million annually. Assume
local Tax rate as 30%.
(i) Annual Cash Flow After Tax (CFAT) under all the different scenarios of exchange rate.
(ii) Expected value of CFAT assuming no repatriation of profits.
(iii) Viability of the investment proposal assuming an initial investment of USD 25 million on plant
and working capital with a required rate of return of 11% on investment and on the basis of
CFAT arrived under option (ii). The CFAT will grow @ 3% per annum in perpetuity.
12.14
13.1
Miscellaneous
Study Session 13
LOS 1 : Buy Back of shares/Repurchase
 Buyback is reverse of issue of shares of a company where the company offers to take back its
share owned by the investors at a specified price.
QUESTION NO. 1A
Abhishek Ltd. has a surplus cash of ₹ 90 lakhs and wants to distribute 30% of it to the shareholders. The
Company decides to buyback shares. The Finance Manager of the Company estimates that its share
price after repurchase is likely to be 10% above the buyback price; if the buyback route is taken. The
number of shares outstanding at present is 10 lacs and the current EPS is ₹ 3. Calculate
a) The price at which the shares can be repurchased, if the market capitalization of the company should
be ₹ 200 lacs after buyback.
b) The number of shares that can be re-purchased.
c) The impact of share re-purchase on the EPS, assuming the net income is same.
QUESTION NO. 1B
Eager Ltd. has a market capitalization of ₹ 1,500 crores and the current market price of its share is ₹
1,500. It made a PAT of 200 crores and the Board is considering a proposal to buy back 20% of the
shares at a premium of 10% to the current market price. It plans to fund this through a 16% bank loan.
You are required to calculate the post buy back Earnings Per Share (EPS). The company's corporate tax
rate is 30%.
QUESTION NO. 1C
ABB Ltd. has a surplus cash balance of ₹ 180 lakhs and wants to distribute 50% of it to the equity
shareholders. The company decides to buyback equity shares. The company estimates that its equity
share price after re-purchase is likely to be 15% above the buyback price. if the buyback route is taken.
Other information is as under:
1. Number of equity shares outstanding at present (Face value ₹ 10 each) is ₹ 20 lakhs.
2. The current EPS is ₹ 5.
I. The price at which the equity shares can be re-purchased, if market capitalization of the company
should be ₹ 400 lakhs after buy back.
II. Number of equity shares that can be re-purchased.
III. The impact of equity shares re-purchase on the EPS, assuming that the net income remains
unchanged.
LOS 2 : Right Shares

Right Shares are those shares which are issued to existing shareholders at a price which is normally
less than Current Market Price.
Choice before Shareholder in respect of Right Issue Effect on Shareholder’s wealth
1. Exercise his rights and subscribe for Right shares. No change in wealth
2. Do not exercise Decrease in Wealth
3. Sell the rights in the market. No change in wealth
4. Exercise his right for few shares and sell the balance No change in wealth
rights in the market.
13.2
Theoretical Post Right (Ex-Right) Price per share =
𝐌𝐏𝐒 𝐂𝐮𝐦 𝐑𝐢𝐠𝐡𝐭×𝐄𝐱𝐢𝐬𝐭𝐢𝐧𝐠 𝐍𝐨.𝐨𝐟 𝐒𝐡𝐚𝐫𝐞𝐬 𝐑𝐢𝐠𝐡𝐭 𝐒𝐡𝐚𝐫𝐞 𝐏𝐫𝐢𝐜𝐞/𝐎𝐟𝐟𝐞𝐫 𝐏𝐫𝐢𝐜𝐞×𝐍𝐨.𝐨𝐟 𝐑𝐢𝐠𝐡𝐭 𝐒𝐡𝐚𝐫𝐞 𝐢𝐬𝐬𝐮𝐞𝐝
𝐄𝐱𝐢𝐬𝐭𝐢𝐧𝐠 𝐍𝐨.𝐨𝐟 𝐄𝐪𝐮𝐢𝐭𝐲 𝐒𝐡𝐚𝐫𝐞𝐬 𝐍𝐞𝐰 𝐍𝐨.𝐨𝐟 𝐒𝐡𝐚𝐫𝐞𝐬
QUESTION NO. 2A
Pragya Limited has issued 75,000 equity shares of ₹ 10 each. The current market price per share is ₹ 24.
The company has a plan to make a right issue of one new equity share at a price of ₹ 16 for every four
share held.
a) Calculate the theoretical post right price per share;
b) Calculate the theoretical value of the right alone;
c) Discuss the effect of the rights issue on the wealth of a shareholder, who has 1,000 shares assuming
he sells the entire rights;
d) State the effect, if the same shareholder does not take any action and ignores the issue.
e) State the effect, if the same shareholder subscribe for the entire issue.
f) State the effect, if the same shareholder exercise 60% of the right and sell 40% of his rights.
QUESTION NO. 2B
ABC Limited's shares are currently selling at ₹ 13 per share. There are 10,00,000 shares outstanding.
The firm is planning to raise ₹ 20 lakhs to finance a new project.
Required: What is the ex-right price of shares and the value of a right, if
a) The firm offers one right share for every two shares held.
b) The firm offers one right share for every four shares held.
c) How does the shareholders' wealth change from (a) to (b)? How does right issue increases
shareholders' wealth?
QUESTION NO. 2C
AMKO Limited has issued 75,000 equity shares of ₹10 each. The current market price per share is ₹36.
The company has a plan to make a rights issue of one new equity share at a price of ₹24 for every four
shares held.
(i) Calculate the theoretical post-rights price per share.
(ii) Calculate the theoretical value of the right alone.
QUESTION NO. 2D
Telbel Ltd. is considering undertaking a major expansion an immediate cash outlay of ₹ 150 crore. The
Board of Director of company are expecting to generate an additional profit of ₹ 15.30 crore after a
period of one year. Further, it is expected that this additional profit shall grow at the rate of 4% for
indefinite period in future.
Presently, Telbel Ltd. is completely equity financed and has 50 crore shares of ₹10 each. The current
market price of each share is ₹ 22.60 (cum dividend). The company has paid a dividend of ₹ 1.40 per
share in last year. For the last few years dividend is increasing at a compound rate of 6% p.a. and it is
expected to be continued in future also. This growth rate shall not be affected by expansion project in
any way.
Board of Directors are considering following ways of financing the possible expansion:
(1) A right issue on ratio of 1:5 at price of ₹15 per share.
(2) A public issue of shares.
In both cases the dividend shall become payable after one year. You as a Financial Consultant
required to:
(a) Determine whether it is worthwhile to undertake the project or not.
13.3
(b) Calculate ex-dividend market price of share if complete expansion is financed from the right issue.
(c) Calculate the number of new equity shares to be issued and at what price assuming that new
shareholders do not suffer any loss after subscribing new shares.
(d) Calculate the total benefit from expansion to existing shareholders under each of two financing
option.
LOS 3 : Money Market Instruments (MMI)

Similar to Bonds, the money market instruments are important source of finance to industry, trade,
commerce and the government sector for meeting their short-term requirement for both national and
international trade. They are those instruments which are available for a period of less than one year.
Example: Certificate of deposit, Commercial Paper, T-Bills, etc.
Example 1:
M Ltd. has to make a payment on 30th March 04 of ₹ 80 lacs. It has surplus cash today, i.e.31st Dec
03 & has decided to invest sufficient cash in a bank's Certificate of Deposit scheme offering a yield of
8% p.a. on simple interest basis. What is the amount to be invested now? Take 91 days of investment.
Solutions:
Calculation of Investment Amount
Let the amount to be invested now be ₹ X
Then we have X + X × × = ₹ 80,00,000 => X = ₹ 7843558.61187
Example 2:
RBI Sold a 91 day T Bill of face value of ₹ 100 at a yield of 6%. What was the issue price?
Solutions:
Let the issue price be X. Now we have, X + X × × = ₹ 100 => X = ₹ 98.526
Note:
(i) The maturity value of treasury bill is always equal to face value.
(ii) Treasury bills are always issued at a discount.
Example 3:
X Ltd. issued commercial paper as per following detail: Date of issue: 17thJanuary, 1998; Date of
Maturity: 17th April, 1998; No. of days 90; Interest Rate: 11.25% p.a. What was the net amount
received by the company on issue of commercial paper? Assume Maturity Value or Face Value to be
500 lacs.
Solutions:
Let the net amount received by the company be X.
.
Then we have, X + X × × = ₹ 500,00,000 => x = ₹ 48650449.85
QUESTION NO. 3
A money market instrument with face value of ₹ 100 and discount yield of 6% will mature in 45 days.
1. Current Price of the Instrument.
2. Rate of Interest.
3. Effective Annual Return.
(1 Year=360 Days )
LOS 4: Effective Yield under Money Market Instruments

𝐅𝐕 𝐈𝐬𝐬𝐮𝐞 𝐏𝐫𝐢𝐜𝐞 𝟏𝟐
Effective Rate of Interest = × × 100
𝐈𝐬𝐬𝐮𝐞 𝐏𝐫𝐢𝐜𝐞 𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐏𝐞𝐫𝐢𝐨𝐝
13.4
Cost of Funds:
Effective rate of Interest p.a
+ Brokerage p.a
+ Rating Charges p.a
+ Stamp Duty p.a
= Total cost of Funds p.a
Example 1:
Amount of Issue – ₹ 100
Period - 6 months
Rate of discount – 20%
Discount = =100× × × 100 =₹ 10.00
Hence CD will be issued for ₹ 100 – 10 = ₹ 90.00. The effective rate to the bank will, however, be
calculated on the basis of the following formula:
𝐅𝐕 𝐈𝐬𝐬𝐮𝐞 𝐏𝐫𝐢𝐜𝐞
Effective Rate of Interest/Effective Yield = × × 100
𝐈𝐬𝐬𝐮𝐞 𝐏𝐫𝐢𝐜𝐞 𝐑𝐞𝐪𝐮𝐢𝐫𝐞𝐝 𝐏𝐞𝐫𝐢𝐨𝐝
Accordingly, the Yield as per the data given in the example will be:
= × × 100 = 22.22% p.a
Example 2:
From the following particulars, calculate the effective interest p.a. as well as the total cost of funds of
ABC Ltd., which is planning a CP issue:
Issue price of CP -► ₹ 97,350;
Face Value -► ₹ 1,00,000;
Maturity period -► 3 months
Issue Expenses :
Brokerage : 0.125% for 3 months;
Rating Charges: 0.5% p.a.;
Stamp Duty: 0.125% for 3 months.
Solution:
Effective Rate of Interest = × × 100
, , ,
= × × 100 = 10.89 p.a
,
Cost of fund to the Company:
Effective Interest 10.89
Brokerage (.125 × 12/3) 0.5
Rating Charges 0.5
Stamp Duty(.125 × 12/3) 0.5
12.39%
Question 4A
From the following particulars, calculate the effective rate of interest p.a. as well as the total cost of funds
to Bhaskar Ltd., which is planning a CP issue:
Issue Price of CP ₹ 97,550
Face Value ₹ 1,00,000
Maturity Period 3 Months Issue Expenses:
Brokerage 0.15% for 3 months
Rating Charges 0.50% p.a
Stamp Duty 0.175% for 3 months
13.5
Question 4B
1. Z Co. Ltd. issued commercial paper worth ₹10 crores as per following details:
Date of issue : 16th January, 2019
Date of maturity: 17th April, 2019
No. of days : 91
Interest rate 12.04% p.a
What was the net amount received by the company on issue of CP? (Charges of intermediary may be
ignored)
QUESTION NO. 4C
AXY Ltd. is able to issue commercial paper of ₹ 50,00,000 every 4 months at a rate of 12.5% p.a. The
cost of placement of commercial paper issue is ₹ 2,500 per issue. AXY Ltd. is required to maintain line
of credit ₹ 1,50,000 in bank balance. The applicable income tax rate for AXY Ltd. is 30%. What is the
cost of funds (after taxes) to AXY Ltd. for commercial paper issue? The maturity of commercial paper is
four months.
QUESTION NO. 4D
Wonderland Limited has excess cash of ₹ 20 lakhs, which it wants to invest in short term
marketable securities. Expenses relating to investment will be ₹ 50,000.
The securities invested will have an annual yield of 9%.
The company seeks your advice
(i) as to the period of investment so as to earn a pre-tax income of 5%.
(ii) the minimum period for the company to break even its investment expenditure over time value of
money.
Los 5: Repurchase Options (Repo.) and Reverse Repurchase Agreement

(Reverse Repo):
 The term Repurchase Agreement (Repo) and Reverse Repurchase Agreement (Reverse Repo) refer
to a type of transaction in which money market participant raises funds by selling securities and
simultaneously agreeing to repurchase the same after a specified time generally at a specified
price, which typically includes interest at an agreed upon rate. Sometimes it is also called Ready
Forward Contract as it involves funding by selling securities (held on Spot i.e. Ready Basis) and
repurchasing them on a forward basis.
QUESTION NO. 5
Bank A enter into a Repo for 14 days with Bank B in 10% Government of India Bonds 2028 @ 5.65%
for ₹ 8 crore. Assuming that clean price (the price that does not have accrued interest) be ₹ 99.42 and
initial Margin be 2% and days of accrued interest be 262 days. You are required to determine
(i) Dirty Price
(ii) Repayment at maturity. (consider 360 days in a year)
LOS 6 : Venture Capital Investing

Venture Capital Investments are private, non-exchange-traded equity investments in a Business
Venture.
Investments are usually made through limited partnerships, with investors anticipating relatively high
returns in exchange for the illiquidity and high-risk profile of a venture capital investments.
Stages of Venture Capital Investing:
Seed Stage:
Investors are providing Capital in the early stage of the business and may help fund research and
development of product ideas.
13.6
Early Stage:
Start-up Financing refers to Capital use to complete Product Development and fund initial marketing
Efforts.
First-Stage : Financing refers to funding to commercial production and sales of the product.
Later Stage : Major Expansion of the Company.
Note:
 Conditional probability of failure i.e. 22% in 3rd Year refers to the probability of failing in the 3rd
year provided success in the 1st and 2nd Year.
 Joint probability of failure cannot be calculated as joint probability of success because if failure in
1st Year cannot go in 2nd Year.
QUESTION NO. 6
TMC is a venture capital financier. It received a proposal for financing requiring an investment of ₹ 45
crore which returns ₹ 600 crore after 6 years if succeeds. However, it may be possible that the project
may fail at any time during the six years
The following table provide the estimates of probabilities of the failure of the projects.
Year 1 2 3 4 5 6
Probability of Failure 0.28 0.25 0.22 0.18 0.18 0.10
In the above table the probability that the project fails in the second year is given that it has survived
throughout year 1. Similarly for year 2 and so forth.
TMC is considering an equity investment in the project. The beta of this type of project is 7. The market
return and risk free rate of return are 8% and 6% respectively. You are required to compute the expected
NPV of the venture capital project and advice the TMC.
LOS 7 : Moving Averages

Two types of moving Average are:
1. AMA (Arithmetic Moving Average)
2. EMA (Exponential Moving Average)
AMA - Example:
Day 1 2 3 4 5 6 7 8 9 10
Closing Price 40 45 39 42 48 43 52 47 45 38
Calculate 5 day’s AMA?
Solution:
Day Closing Price 5 Days AMA
1 40 —
2 45 —
3 39 —
4 42 —
5 48 42.80
6 43 43.40
7 52 44.80
8 47 46.40
9 45 47.00
10 38 45.00
EMA
EMA today = EMA Yesterday + a × [Price today - EMA Yesterday ]

13.7
Note:
a = Exponent/ Multiplier/ Smoothing Constant.
‘a’ will always be given in question, however ‘a’ can also be calculated by using following relation:
𝟐
a=
𝟏 𝐏𝐞𝐫𝐢𝐨𝐝
QUESTION NO. 7A
Closing values of BSE Sensex from 6th to 17th day of the month of January of the year 200X were as
follows:
Day Date Day Sensex
1 6 Thu 14522
2 7 Fri 14925
3 8 Sat No Trading
4 9 Sun No Trading
5 10 Mon 15222
6 11 Tue 16000
7 12 Wed 16400
8 13 Thu 17000
9 14 Fri No Trading
10 15 Sat No Trading
11 16 Sun No Trading
12 17 Mon 18000
Calculate Exponential moving Average (EMA) of Sensex during the above period. The previous day
exponential moving average of Sensex can be assumed as 15,000. The value of exponent for 31 days
EMA is 0.062. Give detailed analysis on the basis of your calculations.
Solution:
EMA of each day can be calculated by using following equation
EMA Today = EMA of previous day + Exponent x [ Sensex Price Today - EMA of previous day]
Date 1 2 3 4 5
Sensex EMA For (1 – 2) 3 × 0.062 2±4
Previous Day
6 14522 15000 (478) (29.636) 14970.364
7 14925 14970.364 (45.364) (2.812) 14967.55
10 15222 14967.55 254.45 15.776 14983.32
11 16000 14983.32 1016.68 63.034 15046.354
12 16400 15046.354 1353.646 83.926 15130.28
13 17000 15130.28 1869.72 115.922 15246.203
17 18000 15246.203 2753.797 170.735 15416.938
Conclusion - The market is bullish. The market is likely to remain bullish for short term to medium
term if other factors remain the same. On the basis of this indicator (EMA) the investors/brokers can
take long position.
QUESTION NO. 7B
Closing values of BSE Sensex from 6th to 17th day of the month of January of the year 200 X were as
follows:
Days Date Day Sense x
1 6 THU 29522
2 7 FRI 29925
13.8
3 8 SAT No Trading
4 9 SUN No Trading
5 10 MON 30222
6 11 TUE 31000
7 12 WED 31400
8 13 THU 32000
9 14 FRI No Trading
10 15 SAT No Trading
11 16 SUN No Trading
12 17 MON 33000
Compute Exponential Moving Average (EMA) of Sensex during the above period. The 30 days simple
moving average of Sensex can be assumed as 30,000. The value of exponent for 30 days EMA is 0.062.
Provide detailed analysis on the basis of your calculations.
Solution:
EMA of each day can be calculated by using following equation
EMA Today = EMA of previous day + Exponent x [ Sensex Price Today - EMA of previous day]
Date 1 2 3 4 5
Sensex EMA for Previous 1-2 3×0.062 EMA 2 + 4
day
6 29522 30000 (478) (29.636) 29970.364
7 29925 29970.364 (45.364) (2.812) 29967.55
10 30222 29967.55 254.45 15.776 29983.32
11 31000 29983.32 1016.68 63.034 30046.354
12 31400 30046.354 1353.646 83.926 30130.28
13 32000 30130.28 1869.72 115.922 30246.202
17 33000 30246.202 2753.798 170.735 30416.937
Conclusion – The market is bullish. The market is likely to remain bullish for short term to medium term
if other factors remain the same. On the basis of this indicator (EMA) the investors/brokers can take long
position.
QUESTION NO. 7C
Closing values of BSE Sensex from 6th to 17th day of the month of January of the year 20xx were as
follows:
Days Date Day Sensex
1 6 THU 34522
2 7 FRI 34925
3 8 SAT No Trading
4 9 SUN No Trading
5 10 MON 35222
6 11 TUE 36000
7 12 WED 36400
8 13 THU 37000
9 14 FRI No Trading
12 17 MON 38,000
13.9
Calculate Exponential Moving Average (EMA) of Sensex during the above period. The 30 days simple
moving average of Sensex can be assumed as 35,000. The value of exponent for 30 days EMA is 0.064.
Provide analyzed conclusion on the basis of your calculations.
(Calculations should be up to three decimal points.)
QUESTION NO. 8
The closing value of Sensex for the month of October, 2007 is given below:
Date Closing Sensex Value
1.10.07 2800
3.10.07 2780
4.10.07 2795
5.10.07 2830
8.10.07 2760
9.10.07 2790
10.10.07 2880
11.10.07 2960
12.10.07 2990
15.10.07 3200
16.10.07 3300
17.10.07 3450
19.10.07 3360
22.10.07 3290
23.10.07 3360
24.10.07 3340
25.10.07 3290
29.10.07 3240
30.10.07 3140
31.10.07 3260
You are required to test the weak form of efficient market hypothesis by applying the run test at 5% and
10% level of significance.
Following value can be used :
Value of t at 5% is 2.101 at 18 degrees of freedom
Value of t at 10% is 1.734 at 18 degrees of freedom
Solution :
Date Closing Sign of Price
Sensex Charge
1.10.07 2800
3.10.07 2780 -
4.10.07 2795 +
5.10.07 2830 +
8.10.07 2760 -
9.10.07 2790 +
10.10.07 2880 +
11.10.07 2960 +
12.10.07 2990 +
15.10.07 3200 +
16.10.07 3300 +
17.10.07 3450 +
13.10
19.10.07 3360 -
22.10.07 3290 -
23.10.07 3360 +
24.10.07 3340 -
25.10.07 3290 -
29.10.07 3240 -
30.10.07 3140 -
31.10.07 3260 +
Total of sign of price changes (r) = 8
No of Positive changes = n1 = 11
No. of Negative changes = n2 = 8
2𝑛 𝑛
𝜇 = +1
𝑛 + 𝑛
2 × 11 × 8 176
𝜇= +1= + 1 = 10.26
11 + 8 19
2𝑛 𝑛 2𝑛 𝑛 − 𝑛 − 𝑛
𝜎^ =
𝑛 + 𝑛 𝑛 + 𝑛 −1
2 × 11 × 8 2 × 11 × 8 − 11 − 8 176 × 157
𝜎^ = = = √4.252 = 2.06
11 + 8 11 + 8 − 1 19 18
Since too few runs in the case would indicate that the movement of prices is not random. We employ
a two- tailed test the randomness of prices.
Test at 5% level of significance at 18 degrees of freedom using t- table
The lower limit
= 𝜇 − 𝑡 × 𝜎 ^ = 10.26 – 2.101 × 2.06 = 5.932
Upper limit
= 𝜇 + 𝑡 × 𝜎 ^ = 10.26 + 2.101 × 2.06 = 14.588
At 10% level of significance at 18 degrees of freedom
Lower limit
= 10.26 – 1.734 × 2.06 = 6.688
Upper limit
= 10.26 + 1.734 × 2.06 = 13.832
As seen r lies between these limits. Hence, the market exhibits weak form of efficiency.
*For a sample of size n, the t distribution will have n-1 degrees of freedom.
QUESTION NO. 9
ANP plan, a hedge fund currently has assets of ₹ 20 Crores. Mr. X, the manager of fund charges fixed
fee of 0.10% of portfolio asset. In addition to it he charges incentive/ bonus fee of 2%. The bonus will
be linked to gross return each year in excess of the portfolio maximum value since the start of fund. The
maximum value the fund achieved so far since start of fund was ₹ 21 Crores.
You are required to compute the fee payable to CA, X, if return on the fund this year turns out to be (i)
29%, (ii) 4.5%, (iii) -1.8%
Solution:
a) If return is 29%
Fixed fee (A) 0.10% of ₹ 20 Cr. ₹ 2,00,000
New Fund Value (1.29 × ₹ 20 Cr.) ₹ 25.80 Cr.
13.11
Excess Value of best achieved (25.8 Cr. – 21.0 Cr.) ₹ 4.80 Cr.
Incentive Fee (2% of 4.80 Cr.) (B) ₹ 9,60,000
Total Fee (A) + (B) ₹
11,60,000
b) If return is 4.5%
Fixed fee (A) 0.10% of ₹ 20 Cr. ₹ 2,00,000
New Fund Value (1.045 × ₹ 20 Cr.) ₹ 20.90 Cr.
Excess Value of best achieved (20.90 Cr. – 21.0 Crores) (₹ 0.10 Cr.)
Incentive Fee (as does not exceed best achieved) (B) Nil
Total Fee (A) + (B) ₹ 2,00,000
c) If return is ( - 1.8%)
No incentive only fixed fee of ₹ 2,00,000 will be paid
QUESTION NO. 10
Mr. A is contemplating purchase of 1,000 equity shares of a Company. His expectation of return is 10%
before tax by way of dividend with an annual growth of 5%. The Company’s last dividend was ₹ 2 per
share. Even as he is contemplating, Mr. A suddenly finds, due to a Budget announcement Dividends
have been exempted from Tax in the hands of the recipients. But the imposition of Dividend Distribution
Tax on the Company is likely to lead to a fall in dividend of 20 paise per share. A’s marginal tax rate is
30%.
Required:
Calculate what should be Mr. A’s estimates of the price per share before and after the Budget
announcement?
QUESTION NO. 11
Following information is available of M/s. TS Ltd.
(₹ in crores)
PBIT 5.00
Less : Interest on Debt (10%) 1.00
PBT 4.00
Less: Tax @ 25% 1.00
PAT 3.00
No. of outstanding shares of ₹ 10 each 40 lakh
EPS (₹) 7.5
Market price of share (₹) 75
P/E ratio 10 Times
TS Ltd. has an undistributed reserves of ₹ 8 crores. The company requires ₹ 3 crores for the purpose of
expansion which is expected to earn the same rate of return on capital employed as present. However,
if the debt to capital employed ratio is higher than 35%, then P/E ratio is expected to decline to 8 Times
and rise in the cost of additional debt to 14%. Given this data which of the following options the company
would prefer, and why?
Option (i) : If the required amount is raised through debt, and
Option (ii) : If the required amount is raised through equity and the new shares will be issued at a
price of ₹ 25 each.
13.12
Los 8: Enterprise Value (EV)

Calculate Enterprise Value (EV) in two ways:
a) Take Entity Value as the base, and then adjust for debt values for arriving the ‘EV’;
or
b) Take a balance sheet based approach and arrive at EV.
Let’s apply the above concepts into a relative valuation illustration:
Illustration 1
A Ltd. made a Gross Profit of ₹ 10,00,000 and incurred Indirect Expenses of ₹ 4,00,000. The number of
issued Equity Shares is 1,00,000. The company has a Debt of ₹ 3,00,000 and Reserves & Surplus to the
tune of ₹ 5,00,000. The market related details are as follows:
Risk Free Rate of Return 4.5%
Market Rate of Return 12%
β of the Company 0.9
Determine:
1) Per Share Earning Value of the Company.
2) Equity Value of the company if applicable EBITDA multiple is 5.
Solution
a) Capitalization Rate using CAPM 4.5% + 0.9(12% - 4.5%) = 11.25%
Calculation of Earning Value Per Share
(₹ 000)
Gross Profit 1000
Less: Indirect Expenses (400)
EBITDA 600
Earning Value of Company (600/ 0.1125) 5333.33
Number of Shares 1,00,000
Earning Value Per Share ₹ 53.33
(b) Equity Value of Company
(₹ 000)
EBITDA 600
EBITDA Multiple 5
Capitalized Value 3000
Less: Debt (300)
Add: Surplus Funds 500
Equity Value (Enterprise Value) 3200
Now let us see how EV can be arrived at using Balance Sheet approach in the following illustration.
Illustration 2
The balance sheet of H K Ltd. is as follows:
₹ 000
Non-Current Assets 1000
Current Assets
Trade Receivables 500
Cash and cash equivalents 500
2000
Shareholders' funds 800
Long Term Debt 200
Current Liabilities and Provisions 1000
2000
13.13
The shares are actively traded and the Current Market Price (CMP) is ₹ 12 per share. Shareholder funds
represent 70,000 shares of ₹ 10 each and rest is retained earnings. Calculate the Enterprise Value of HK Ltd.
Solution
Shares outstanding 70,000
CMP ₹ 12
Market Capitalization ₹ 8,40,000
Add: Debt ₹ 2,00,000
Less: Cash & Cash equivalents (₹ 5,00,000)
Enterprise Value (EV) ₹ 5 40 000
Los 9: Chop-Shop Method

 This approach attempts to identify multi-industry companies that are undervalued and would have
more value if separated from each other. In other words as per this approach an attempt is made
to buy assets below their replacement value.
This approach involves following three steps:
Step 1: Identify the firm’s various business segments and calculate the average capitalization ratios for
firms in those industries.
Step 2: Calculate a “theoretical” market value based upon each of the average capitalization
ratios.
Step 3: Average the “theoretical” market values to determine the “chop-shop” value of the
firm.
Example:
Capital/ Sales Ratio = 0.75
Sales = 15,00,000
Calculate Capitalized Value?
Solution:
= 0.75
Capitalized Value = Sales × 0.75
= 15,00,000 × 0.75 => 11,25,000
QUESTION NO. 12
Using the chop-shop approach (or Break-up value approach), assign a value for Cornett GMBH. Whose
stock is currently trading at a total market price of €4 million. For Cornett, the accounting data set forth
three business segments: consumer wholesaling, specialty services, and assorted centers Data for the
firm’s three segments are as follows:
BUSINESS SEGMENT Segment Sales Segment Assets Segment Income
Consumer Wholesaling € 1,500,000 € 750,000 € 100,000
Specialty services € 800,000 € 700,000 € 150,000
Assorted centers € 2,000,000 € 3,000,000 € 600,000
Industry data for “pure-play” firms have been compiled and are summarized as follows:
BUSINESS SEGMENT Capitalization/Sales Capitalization/Assets Capitalization/Op
erating Income
Consumer wholesaling 0.75 0.60 10
Specialty services 1.10 0.90 7
Assorted centers 1.00 0.60 6
13.14
Solution
Cornett, GMBH. – Break-up valuation
Business Segment Capital-to-Sales Segment Sales Theoretical Values
Consumer wholesaling 0.75 €1,500,000 €1,125,000
Specialty services 1.10 €800,000 €880,000
Assorted centers 1.00 €2,000,000 €2,000,000
Total value €4,005,000
Consumer wholesaling 0.60 €750,000 €450,000
Specialty services 0.90 €700,000 €630,000
Assorted centers 0.60 €3,000,000 €1,800,000
Consumer wholesaling 10.00 €100,000 €1,000,000
Specialty services 7.00 €150,000 €1,050,000
Assorted centers 6.00 €600,000 €3,600,000
, , , , , ,
Average theoretical value = = 4,178,333.33 say 4,178,000
Average theoretical value of Cornett GMBH. = €4,178,000
QUESTION NO. 13
Compute EVA of A Ltd. with the following information:
All Figure are in ₹ Lac
Profit and Loss Statement Balance Sheet
Revenue 1000 PPE 1000
Direct Costs -390 Current Assets 300
Selling, General & Admin. Exp. (SGA) -200 1300
EBIT 410 Equity 700
Interest -10 Reserves 100
EBT 400 Non-Current Borrowings 100
Tax Expense -120 Current Liabilities & Provisions 400
EAT 280 1300
Assume Bad Debts provision of ₹ 20 Lac is included in the SGA, and same amount is reduced from the
trade receivables in current assets.
Also assume that the pre-tax Cost of Debt is 12%, Tax Rate is 30% and Cost of Equity (i.e.
shareholder’s expected return) is 8.45%.
Solution
Step I: Computation of NOPAT
NOPAT
EBIT 410
Less: Taxes -123
Add: Non-Cash Expenses 20
NOPAT 307
Step II: Finding out the Invested Capital:
Invested Capital
Total Assets 1300
13.15
Less: Non Interest bearing liabilities -400

900
Add: Non Cash adjustment 20
920
Note: It is assumed that the current liabilities also include the 100 of tax liability.
Step III: Compute the WACC
WACC = Cost of equity + Cost of debt
In this case, WACC = (800/900*8.45%) + [100/900*12% (1 - 0.30)] = 8.44%
Step IV: Find out the Capital Charge
Capital Charge = Invested Capital * WACC = 920 * 8.44% = 77.65
Step V: EVA = Adjusted NOPAT – Capital Charge = 307 – 77.65 = 229.35
13.16
PRACTICE QUESTIONS
QUESTION NO. 14
KLM Limited has issued 90,000 equity shares of ₹ 10 each. KLM Limited’s shares are currently selling
at ₹ 72. The company has a plan to make a rights issue of one new equity share at a price of ₹ 48
for every four shares held.
(a) Calculate the theoretical post-rights price per share and analyse the change
(b) Calculate the theoretical value of the right alone.
(c) Suppose Mr. A who is holding 100 shares in KLM Ltd. is not interested in subscribing to the
right issue, then advice what should he do.
QUESTION NO. 15
Mr. X is of the opinion that market has recently shown the Weak Form of Market Efficiency. In order
to test the validity of his impression he has collected the following data relating to the movement of
the SENSEX for the last 20 days.
Days Open High Low Close
1 33470.94 33513.79 33438.03 33453.99
2 33453.64 33478.11 33427.82 33434.83
3 33414.06 33440.29 33397.65 33431.93
4 33434.94 33446.18 33377.78 33383.41
5 33372.92 33380.27 33352.12 33370.93
6 33375.85 33389.49 33331.42 33340.75
7 33340.89 33340.89 33310.95 33330.98
8 33326.84 33340.91 33306.17 33335.08
9 33307.16 33328.22 33296.43 33301.97
10 33298.64 33318.60 33254.28 33259.03
11 33260.04 33228.85 33241.66 33251.53
12 33255.92 33289.46 33249.46 33285.89
13 33288.86 33535.67 33255.98 33329.28
14 33335.00 33346.21 33276.72 33284.17
15 33293.83 33310.86 33278.54 33298.78
16 33300.02 33337.79 33300.02 33325.38
17 33323.36 33356.34 33322.44 33329.95
18 33322.81 33345.98 33317.44 33319.67
19 33317.51 33321.18 33294.19 33302.32
20 33290.86 33324.96 33279.62 33319.61
You are required:
To test the Weak Form of Market Efficiency using Auto-Correlation test, taking time lag of 10 days.
QUESTION NO. 16
AB Industries has Equity Capital of ₹ 12 Lakhs, total Debt of ₹ 8 Lakhs, and annual sales of ₹ 30
Lakhs. Two mutually exclusive proposals are under consideration for the next year. The details of the
proposals are as under:
Particulars Proposal Proposal
no. 1 no. 2
Target Assets to Sales Ratio 0.65 0.62
Target Net Profit Margin (%) 4 5
13.17
Target Debt Equity Ratio (DER) 2:3 4:1

Target Retention Ratio (of Earnings) (%) 75 -
Annual Dividend (₹ In Lakhs) - 0.30
New Equity Raised (₹ in Lakhs) - 1
You are required to calculate sustainable growth rate for both the proposals.
QUESTION NO. 17
The Management of a multinational company TL Ltd. is engaged in construction of Infrastructure
Project. A proposal to construct a Toll Road in Nepal is under consideration of the Management.
The following information is available:
The initial investment will be in purchase of equipment costing USD 250 lakhs. The economic life of
the equipment is 10 years. The depreciation on the equipment will be charged on straight line
method.
EBIDTA to be collected from the Toll Road is projected to be USD 33 lakhs per annum for a period of
20 years.
To encourage investment Nepalese government is offering a 15 year term loan of USD 150 lakhs at
an interest rate of 6 per cent per annum. The interest is to be paid annually. The loan will be repaid
at the end of 15 year in one tranche.
The required rate of return for the project under all equity financing is 12 per cent per annum.
Post tax cost of debt is 5.6 per cent per annum.
Corporate Tax Rate is 30 per cent.
All cash Flows will be in USD.
Ignore inflation.
You are required to advise the management on the viability of the proposal by using Adjusted Net
Present Value method.
Given
PVIFA (12%, 10) = 5.650, PVIFA (12%, 20) = 7.469, PVIFA (8%,15) = 8.559, PVIF (8%, 15) = 0.315.
QUESTION NO. 18
The Balance Sheet of M/s. Sundry Ltd. as on 31-03-2020 is follows:
(₹ in lakhs)
Share Capital 300 Fixed Assets 600
Reserves 200 Inventory 500
Long Term Loan 400 Receivables 240
Short Term Loan 300 Cash 60
Payables & Provisions 200
Total 1400 Total 1400
Sales for the year was ₹ 600 lakhs. The sales are expected to grow by 20% during the year. The profit
margin and dividend pay-out ratio are expected to be 4% and 50% respectively.
The company further desires that during the current year Sales to Short Term Loan and Payables and
Provision should be in the ratio of 4 : 3. Ratio of fixed assets to Long Term Loans should be 1.5.
Debt Equity Ratio should not exceed 1.5.
(i) The amount of External Fund Requirement (EFR)
(ii) The amount to be raised from Short Term, Long Term and Equity funds.
13.18
QUESTION NO. 19
Bank A enters into a Repo for 21 days with Bank B in 8% Government of India Bonds 2020 @ 6.10%
for ₹ 5 crore. Assuming that clean price is ₹ 97.30 and initial margin is 1.50% and days of accrued
interest are 240 days (assume 360 days in a year).
Compute:
(i) the dirty price.
(ii) The repayment at maturity.
QUESTION NO. 20
Mr. A is holding 1000 shares of face value of ₹ 100 each of M/s. ABC Ltd. He wants to hold these
shares for long term and have no intention to sell.
On 1st January 2020, M/s XYZ Ltd. Has made short sales of M/s. ABC Ltd.’s shares and
approached Mr. A to lend his shares under Stock Lending Scheme with following terms:
(i) Shares to be borrowed for 3 months from 01-01-2020 to 31-03-2020,
(ii) Lending Charges/Fees of 1% to be paid every month on the closing price of the stock quoted in
Stock Exchange and
(iii) Bank Guarantee will be provided as collateral for the value as on 01 -01-2020.
Other Information:
(a) Cost of Bank Guarantee is 8% per annum,
(b) On 29-02-2020 M/s. ABC Ltd.’s share quoted in Stock Exchange on various dates are as follows:
Date Share Price in Scenario -1 Bullish Share Price in Scenario -2 Bullish
01-01-2020 1000 1000
31-01-2020 1020 980
29-02-2020 1040 960
31-03-2020 1050 940
(i) Earning of Mr. A through Stock Lending Scheme in both the scenarios,
(ii) Total Earnings of Mr. A during 01-01-2020 to 31-03-2020 in both the scenarios,
(iii) What is the Profit or loss to M/s. XYZ by shorting the shares using through Stock Lending Scheme
in both the scenarios?
14.1
Risk Management
Study Session 14
Q. No. 1 : What are the types of risk faced by an organization?
A business organization faces many types of risks. Important among them are discussed as below:
1) Strategic Risk
A successful business always needs a comprehensive and detailed business plan. Everyone
knows that a successful business needs a comprehensive, well-thought-out business plan. But
it’s also a fact of life that, if things changes, even the best-laid plans can become outdated if it
cannot keep pace with the latest trends. This is what is called as strategic risk. So, strategic risk
is a risk in which a company’s strategy becomes less effective and it struggles to achieve its goal.
It could be due to technological changes, a new competitor entering the market, shifts in
customer demand, increase in the costs of raw materials, or any number of other large-scale
changes.
We can take the example of Kodak which was able to develop a digital camera by 1975. But, it
considers this innovation as a threat to its core business model, and failed to develop it.
However, it paid the price because when digital camera was ultimately discovered by other
companies, it failed to develop it and left behind. Similar example can be given in case of Nokia
when it failed to upgrade its technology to develop touch screen mobile phones. That delay
enables Samsung to become a market leader in touch screen mobile phones.
However, a positive example can be given in the case of Xerox which invented photocopy
machine. When laser printing was developed, Xerox was quick to lap up this opportunity and
changes its business model to develop laser printing. So, it survived the strategic risk and
escalated its profits further.
2) Compliance Risk
Every business needs to comply with rules and regulations. For example with the advent of
Companies Act, 2013, and continuous updating of SEBI guidelines, each business organization
has to comply with plethora of rules, regulations and guidelines. Non-compliance leads to
penalties in the form of fine and imprisonment.
However, when a company ventures into a new business line or a new geographical area, the
real problem then occur For example, a company pursuing cement business likely to venture
into sugar business in a different state. But laws applicable to the sugar mills in that state are
different.
So, that poses a compliance risk. If the company fails to comply with laws related to a new area
or industry or sector, it will pose a serious threat to its survival.
3) Operational Risk
This type of risk relates to internal risk. It also relates to failure on the part of the company to
cope with day to day operational problems. Operational risk relates to ‘people’ as well as
‘process’. We will take an example to illustrate this. For example, an employee paying out ₹
1,00,000 from the account of the company instead of ₹ 10,000.
This is a people as well as a process risk. An organization can employ another person to check
the work of that person who has mistakenly paid ₹ 1,00,000 or it can install an electronic system
that can flag off an unusual amount.
4) Financial Risk
Financial Risk is referred as the unexpected changes in financial conditions such as prices,
exchange rate, Credit rating, and interest rate etc. Though political risk is not a financial risk in
14.2
direct sense but same can be included as any unexpected political change in any foreign country
may lead to country risk which may ultimately may result in financial loss.
Accordingly, the broadly Financial Risk can be divided into following categories.
a) Counter Party Risk
This risk occurs due to non-honouring of obligations by the counter party which can be
failure to deliver the goods for the payment already made or vice-versa or repayment of
borrowings and interest etc. Thus, this risk also covers the credit risk i.e. default by the
counter party.
b) Political Risk
Generally this type of risk is faced by and overseas investors, as the adverse action by the
government of host country may lead to huge loses. This can be on any of the following
form.
 Confiscation or destruction of overseas properties.
 Rationing of remittance to home country.
 Restriction on conversion of local currency of host country into foreign currency.
 Restriction as borrowings.
 Invalidation of Patents
 Price control of products
c) Interest Rate Risk
This risk occurs due to change in interest rate resulting in change in asset and liabilities.
This risk is more important for banking companies as their balance sheet’s items are more
interest sensitive and their base of earning is spread between borrowing and lending rates.
As we know that the interest rates are two types i.e. fixed and floating. The risk in both of
these types is inherent. If any company has borrowed money at floating rate then with
increase in floating the liability under fixed rate shall remain the same. This fixed rate, with
falling floating rate the liability of company to pay interest under fixed rate shall
comparatively be higher.
d) Currency Risk
This risk mainly affects the organization dealing with foreign exchange as their cash flows
changes with the movement in the currency exchange rates. This risk can be affected by
cash flow adversely or favourably. For example, if rupee depreciates vis-à-vis US$
receivables will stand to gain vis-à-vis to the importer who has the liability to pay bill in
US$. The best case we can quote Infosys (Exporter) and Indian Oil Corporation Ltd.
(Importer).
Q. No. 2 : The Financial Risk can be viewed from different perspective. Explain.
OR Explain Financial Risk from the point of view of Stake Holder,
Company & Government.
The financial risk can be evaluated from different point of views as follows:
(a) From stakeholder’s point of view: Major stakeholders of a business are equity shareholders
and they view financial gearing i.e. ratio of debt in capital structure of company as risk since in
event of winding up of a company they will be least prioritized.
Even for a lender, existing gearing is also a risk since company having high gearing faces more
risk in default of payment of interest and principal repayment.
(b) From Company’s point of view: From company’s point of view if a company borrows
excessively or lend to someone who defaults, then it can be forced to go into liquidation.
(c) From Government’s point of view: From Government’s point of view, the financial risk can
be viewed as failure of any bank or (like Lehman Brothers) down grading of any financial
institution leading to spread of distrust among society at large. Even this risk also includes willful
defaulter This can also be extended to sovereign debt crisis.
14.3
Q. No. 3 : What is VAR & its features? Explain the significance of VAR? OR
Describe Value at Risk & its application.
 VAR is a measure of risk of investment. Given the normal market condition in a set of period, say,
one day it estimates how much an investment might lose. This investment can be a portfolio,
capital investment or foreign exchange etc., VAR answers two basic questions -
(i) What is worst case scenario?
(ii) What will be loss?
It was first applied in 1922 in New York Stock Exchange, entered the financial world in 1990s and
become world’s most widely used measure of financial risk.
Features of VAR
Following are main features of VAR
(i) Components of Calculations: VAR calculation is based on following three components :
(a) Time Period
(b) Confidence Level – Generally 95% and 99%
(c) Loss in percentage or in amount
(ii) Statistical Method: It is a type of statistical tool based on Standard Deviation.
(iii) Time Horizon: VAR can be applied for different time horizons say one day, one week, one
month and so on.
(iv) Probability: Assuming the values are normally attributed, probability of maximum loss can be
predicted.
(v) Control Risk: Risk can be controlled by selling limits for maximum loss.
(vi) Z Score: Z Score indicates how many standard Deviations is away from Mean value of a
population. When it is multiplied with Standard Deviation it provides VAR.
Application of VAR
VAR can be applied
(a) to measure the maximum possible loss on any portfolio or a trading position.
(b) as a benchmark for performance measurement of any operation or trading.
(c) to fix limits for individuals dealing in front office of a treasury department.
(d) to enable the management to decide the trading strategies.
(e) as a tool for Asset and Liability Management especially in banks.
Example:
The concept of VAR can be understood in a better manner with help of following example:
Suppose you hold ₹ 2 crore shares of X Ltd. whose market price standard deviation is 2% per day.
Assuming 252 trading days a year, determine maximum loss level over the period of 1 trading day
and 10 trading days with 99% confidence level.
Answer :
Assuming share prices are normally for level of 99%, the equivalent Z score from Normal table of
Cumulative Area shall be 2.33.
Volatility in terms of rupees shall be: 2% of ₹ 2 Crore = ₹ 4 lakh
The maximum loss for 1 day at 99% Confidence Level shall be: ₹ 4 lakh x 2.33 = ₹ 9.32 lakh,
and expected maximum loss for 10 trading days shall be: √10 x ₹ 9.32 lakh = 29.47 lakhs
14.4
Q. No. 4 : What are the appropriate methods for identification and

management of Financial Risk? OR Explain the various parameters
to identify the currency risk.
1) Counter Party risk:
The various hints that may provide counter party risk are as follows:
(a) Failure to obtain necessary resources to complete the project or transaction undertaken.
(b) Any regulatory restrictions from the Government.
(c) Hostile action of foreign government.
(d) Let down by third party.
(e) Have become insolvent.
The various techniques to manage this type of risk are as follows:
(1) Carrying out Due Diligence before dealing with any third party.
(2) Do not over commit to a single entity or group or connected entities.
(3) Know your exposure limits.
(4) Review the limits and procedure for credit approval regularly.
(5) Rapid action in the event of any likelihood of defaults.
(6) Use of performance guarantee, insurance or other instruments.
2) Political risk:
Since this risk mainly relates to investments in foreign country, company should assess country
(1) By referring political ranking published by different business magazines.
(2) By evaluating country’s macro-economic conditions.
(3) By analyzing the popularity of current government and assess their stability.
(4) By taking advises from the embassies of the home country in the host countries.
(5) Further, following techniques can be used to mitigate this risk.
(i) Local sourcing of raw materials and labour.
(ii) Entering into joint ventures
(iii) Local financing
(iv) Prior negotiations
From the following actions by the Governments of the host country this risk can be identified:
1. Insistence on resident investors or labour.
2. Restriction on conversion of currency.
3. Repatriation of foreign assets of the local govt.
4. Price fixation of the products.
3) Interest Rate Risk:
Generally, interest rate Risk is mainly identified from the following:
1. Monetary Policy of the Government.
2. Any action by Government such as demonetization etc.
3. Economic Growth
4. Release of Industrial Data
5. Investment by foreign investors
6. Stock market changes
4) Currency Risk:
Just like interest rate risk the currency risk is dependent on the Government action and economic
development. Some of the parameters to identity the currency risk are as follows:
(1) Government Action: The Government action of any country has visual impact in its
currency. For example, the UK Govt. decision to divorce from European Union i.e. Brexit
brought the pound to its lowest since 1980’s.
14.5
(2) Nominal Interest Rate: As per interest rate parity (IRP) the currency exchange rate depends
on the nominal interest of that country.
(3) Inflation Rate: Purchasing power parity theory discussed in later chapters impact the value
of currency.
(4) Natural Calamities: Any natural calamity can have negative impact.
(5) War, Coup, Rebellion etc.: All these actions can have far reaching impact on currency’s
exchange rates.
(6) Change of Government: The change of government and its attitude towards foreign
investment also helps to identify the currency risk.
14.6
PRACTICAL QUESTIONS
QUESTION 1 :
Consider a portfolio consisting of a ₹ 200,00,000 investment in share XYZ and a ₹ 200,00,000
investment in share ABC. The daily standard deviation of both shares is 1% and that the coefficient of
correlation between them is 0.3. You are required to determine the 10- day 99% value at risk for the
portfolio?
Solution :
The standard deviation of the daily change in the investment in each asset is ₹ 2,00,000 i.e. 2 lakhs.
The variance of the portfolio’s daily change is V = 22 + 22 + 2 x 0.3 x 2 x 2 = 10.4
σ (Standard Deviation) = √10.4 = ₹ 3.22 lakhs
Accordingly, the standard deviation of the 10-day change is ₹ 3.22 lakhs x √10 = ₹ 10.18 lakh
From the Normal Table we see that z score for 1% is 2.33. This means that 1% of a normal distribution
lies more than 2.33 standard deviations below the mean.
The 10-day 99 percent value at risk is therefore 2.33 × ₹ 10.18 lakh = ₹ 23.72 lakh
QUESTION 2 :
Neel holds ₹ 1 crore shares of XY Ltd. whose market price standard deviation is 2% per day. Assuming
252 trading days in a year, determine maximum loss level over the period of 1 trading day and 10
trading days with 99% confidence level. Assuming share prices are normally for level of 99%, the
equivalent Z score from Normal table of Cumulative Area shall be 2.33.
Solution :
Assuming share prices are normally distributed, for level of 99%, the equivalent Z score from Normal
table of Cumulative Area is 2.33.
Volatility in terms of rupees is:
2% of ₹ 1 Crore = ₹ 2 lakh
The maximum loss for 1 day at 99% Confidence Level is
₹ 2 lakh x 2.33 = ₹ 4.66 lakh,
and expected maximum loss for 10 trading days shall be:
√10 x ₹ 4.66 lakh = 14.73 lakhs or 14.74 lakhs
QUESTION NO. 3 :
Following is the information about Mr. J's portfolio:
Investment in shares of ABC Ltd. ₹ 200 lakh
Investment in shares of XYZ Ltd. ₹ 200 lakh
Daily standard deviation of both shares 1%
Co-efficient of correlation between both shares 0.3
Required:
Determine the 10 days 99% Value At Risk (VAR) for Mr. J' s portfolio. Given : The Z score from the Normal
Table at 99% confidence level is 2.33. (Show your calculations up to four decimal points).
Solution :
Volatility (standard deviation) of the daily change in the investment in each share in terms of rupees-
1% of ₹ 200 lakh = ₹ 2 lakh
The variance of the portfolio’s daily change - V
= 22 + 22 + 2 x 0.3 x 2 x 2 = 10.4 lakh
Standard Deviation of the portfolio’s daily change = √10.4 = ₹ 3.2249 lakhs
The standard deviation of the 10-day change
= ₹ 3.2249 lakhs x √10 = ₹ 10.1981 lakhs
Therefore, the 10-days 99% VAR = 2.33 × ₹ 10.1981 lakhs = ₹ 23.7616 lakhs
14.7
QUESTION NO. 4 :
On Tuesday morning (before opening of the capital market) an investor, while going through his bank
statement, has observed that an amount of ₹ 7 lakhs is lying in his bank account. This amount is
available for use from Tuesday till Friday. The Bank requires a minimum balance of ₹ 1000 all the
time. The investor desires to make a maximum possible investment where Value at Risk (VaR) should
not exceed the balance lying in his bank account. The standard deviation of market price of the
security is 1.5 per cent per day. The required confidence level is 99 per cent.
Given
Standard Normal Probabilities
z 0.00 .01 .02 .03 0.04 .05 .06 .07 .08 .09
2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
2.3 .9893 .9896 .9998 .9901 .9904 .9906 .9909 .9911 .9913 .9916
2.4 .9918 .9920 .9922 .9923 .9925 .9929 .9931 .9932 .9934 .9936
You are required to determine the maximum possible investment.
Solution :
Particulars Amount (`)
Amount available in bank account 7,00,000
Minimum balance to be kept 1,000
Available amount which can be used for potential investment for 4 days 6,99,000
Maximum Loss for 4 days at 99% level 6,99,000
Maximum Loss for 1 day at 99 % level = Maximum Loss for 4 days / 3,49,500
√No. of days = 699000/ √4
Z Score at 99% Level 2.33
Volatility in terms of Rupees (Maximum Loss/ Z Score at 99% level) 1,50,000
= 349500/ 2.33
Maximum Possible Investment (Volatility in Rupees/Std Deviation) 1,00,00,000
= 150000/.015
QUESTION NO. 5 :
ABC Ltd. is considering a project X, which is normally distributed and has mean return of ₹ 2 crore
with Standard Deviation of ₹ 1.60 crore.
In case ABC Ltd. loses on any project more than ₹ 1.00 crore there will be financial difficulties.
Determine the probability the company will be in financial difficulty.
Given: Standard Normal Distribution Table (Z-Score) providing area between Mean and Z score
Z Score Area
1.85 0.4678
1.86 0.4686
1.87 0.4693
1.88 0.4699
1.89 0.4706
Solution :
For calculating probability of financial difficulty, we shall calculate the area under Normal Curve
corresponding to the Z Score obtained from the following equation (how many SD is away from Mean
Value of financial difficulty):
z=
. .
=
.
14.8
= -1.875 say 1.875

Corresponding area from Z Score Table by using interpolation shall be found as follows:
Z Score Area under Normal Curve
1.87 0.4693
1.88 0.4699
0.01 0.0006
.
The corresponding value of 0.005 Z score = 0.005 × = 0.0003
.
Thus the Value of 1.875 shall be = 0.4693 + 0.0003 = 0.4696
Thus the probability the company shall be in financial difficulty is 46.96%.
15.1
Exam Papers
Final (New) Examination : May 2018
Question 1
(a) Tatu Ltd. wants to takeover Mantu Ltd. and has offered a swap ratio of 1:2 (0.5 shares for
everyone share of Mantu Ltd.). Following information is provided
Tatu Ltd. Mantu Ltd.
Profit after tax ` 24,00,000 ` 4,80,000
EPS `3 `2
Market price per share `30 ` 14
(i) The number of equity shares to be issued by Tatu Ltd. for acquisition of Mantu Ltd.
(ii) What is the EPS of Tatu Ltd. after the acquisition?
(iii) Determine the equivalent earnings per share of Mantu Ltd.
(iv) What is the expected market price per share of Tatu Ltd. after the acquisition, assuming its
PE multiple remains unchanged?
(v) Determine the market value of the merged firm.
(8 Marks)
(b) Following information is given:
Exchange rates: Canadian dollar 0.666 per DM (spot)
Canadian dollar 0.671 per DM (3-months)
Interest rates: DM 7.5% p.a.
Canadian Dollar - 9.5% p.a.
To take the possible arbitrage gains, what operations would be carried out?
(8 Marks)
(c) Write a short note on Real Estate Regulatory Authority (RERA).
(4 Marks)
Question 2
(a) Consider the following information on two stocks, X and Y.
Year 2016 2017
Return on X (%) 10 16
Return on Y (%) 12 18
(i) The expected return on a portfolio containing X and Y in the proportion of 40% and 60%
respectively.
(ii) The Standard Deviation of return from each of the two stocks.
(iii) The Covariance of returns from the two stocks.
(iv) The Correlation coefficient between the returns of the two stocks.
15.2
(v) The risk of a portfolio containing X and Y in the proportion of 40% and 60%.
(10 Marks)
(b) Sabanam Ltd. has issued convertible debentures with coupon rate 11%. Each debenture has an
option to convert to 16 equity shares at any time until the date of maturity. Debentures will be
redeemed at ` 100 on maturity of 5 years. An investor generally requires a rate of return of 8%
p.a. on a 5-year security. As an advisor, when will you advise the investor to exercise conversion
for given market prices of the equity share of (i) ` 5, (ii) ` 6 and (iii) ` 7.10.
Cumulative PV factor for 8% for 5 years 3.993
PV factor for 8% for year 5 0.681
(6 Marks)
(c) Explain the interface of financial Policy and Strategic Management.
(4 Marks)
Question 3
(a) Herbal World is a small, but profitable producer of beauty cosmetics using the plant Aloe Vera.
Though it is not a high-tech business, yet Herbal's earnings have averaged around` 18.5 lakh
after tax, mainly on the strength of its patented beauty cream to remove the pimples.
The patent has nine years to run, and Herbal has been offered ` 50 lakhs for the patent rights.
Herbal's assets include ` 50 lakhs of property, plant and equipment and ` 25 lakhs of working
capital. However, the patent is not shown in the books of Herbal World. Assuming Herbal's cost
of capital being 14 percent, calculate its Economic Value Added (EVA).
(5 Marks)
(b) SG Mutual Fund Company has the following assets under it on the close of business as on:
1st August 2017 2nd August 2017
Company No. of Shares Market price per share Market price per
(`) share (`)
Q Ltd. 2,000 200.00 205.00
R Ltd. 30,000 312.40 360.00
S Ltd. 40,000 180.60 191.55
T Ltd. 60,000 505.10 503.90
Total No. of Units issued by the Mutual Fund is 6,00,000.
(i) Calculate Net Assets Value (NAV) of the Fund.
(ii) Following information is also given:
Assuming that Mr. Zubin, an investor, submits a cheque of ` 30,00,000 to the Mutual Fund
and the Fund Manager of this entity purchases 8,000 shares of R Ltd; and the balance
amount is held in Bank. In such a case, what would be the position of the Fund?
(iii) Calculate new NAV of the Fund as on 2nd August 2017.(
10 marks)
(c) Discuss what you understand about Embedded Derivatives.
(5 Marks)
Question 4
(a) An established company is going to be de merged in two separate entities. The valuation of the
company is done by a well-known analyst. He has estimated a value of ` 5,000 lakhs, based on
the expected free cash flow for next year of ` 200 lakhs and an expected growth rate of 5%.
While going through the valuation procedure, it was found that the analyst has made the
15.3
mistake of using the book values of debt and equity in his calculation. While you do not know
the book value weights he used, you have been provided with the following information:
(i) The market value of equity is 4 times the book value of equity, while the market value of
debt is equal to the book value of debt,
(ii) Company has a cost of equity of 12%,
(iii) After tax cost of debt is 6%.
You are required to advise the correct value of the company.
(8 Marks)
(b) Mr. KK purchased a 3-month call option for 100 shares in PQR Ltd. at a premium of ` 40 per
share, with an exercise price of ` 560. He also purchased a 3-month put option for 100 shares
of the same company at a premium of ` 10 per share with an exercise price of ` 460. The market
price of the share on the date of Mr. KK's purchase of options, is ` 500. Compute the profit or
loss that Mr. KK would make assuming that the market price falls to ` 360 at the end of 3
months.
(4 Marks)
(c) Interpret the Capital Asset Pricing Model (CAPM) and its relevant assumptions.
(4 Marks)
(d) Explain the difference between Islamic Finance and Conventional Finance.
(4 Marks)
Question 5
(a) Closing values of BSE Sensex from 6th to 17th day of the month of January of the year 200 X
were as follows:
Days Date Day Sense x
1 6 THU 29522
2 7 FRI 29925
3 8 SAT No Trading
4 9 SUN No Trading
5 10 MON 30222
6 11 TUE 31000
7 12 WED 31400
8 13 THU 32000
9 14 FRI No Trading
12 17 MON 33000
Compute Exponential Moving Average (EMA) of Sensex during the above period. The 30 days
simple moving average of Sensex can be assumed as 30,000. The value of exponent for 30 days
EMA is 0.062.
Provide detailed analysis on the basis of your calculations.
(8 Marks)
(b) Punjab Bank has entered into a plain vanilla swap through on Overnight Index Swap (OIS) on
a principal of ` 2 crore and agreed to receive MIBOR overnight floating rate for a fixed payment
on the principal. The swap was entered into on Monday, 24th July, 2017 and was to commence
on 25th July, 2017 and run for a period of 7 days.
15.4
8.70%, 9.10%, 9.12%, 8.95%, 8.98% and 9.10%.

If Punjab Bank received ` 507 net on settlement, calculate Fixed rate and interest under both
legs.
Notes:
(i) Sunday is a Holiday.
(ii) Workout in rounded rupees and avoid decimal working.
(iii) Consider a year consists of 365 days.
(8 Marks)
(c) Explain the advantages of bringing venture capital in the company.
(4 Marks)
Question 6
(a) Omega Ltd. is interested in expanding its operation and planning to install manufacturing plant
at US. For the proposed project, it requires a fund of $10 million (net of issue expenses or
floatation cost). The estimated floatation cost is 2%. To finance this project, it proposes to issue
GDRs.
As a financial consultant, you are requested to compute the number of GDRs to be issued and
cost of the GDR with the help of following additional information:
(i) Expected market price of share at the time of issue of GDR is ` 250 (Face Value being `
100)
(ii) 2 shares shall underlay each GDR and shall be priced at 4% discount to market price.
(iii) Expected exchange rate ` 64/$
(iv) Dividend expected to be paid is 15% with growth rate 12%.
(8 Marks)
(b) Neel holds ` 1 crore shares of XY Ltd. whose market price standard deviation is 2% per day.
Assuming 252 trading days in a year, determine maximum loss level over the period of 1 trading
day and 10 trading days with 99% confidence level. Assuming share prices are normally for
level of 99%, the equivalent Z score from Normal table of Cumulative Area shall be 2.33.
(4 Marks)
(c) Discuss briefly the steps involved in the Securitization mechanism.
OR
Explain the benefits of Securitization from the perspective of both originator as well as the
investor.
(4 Marks)
(d) The risk free rate of return is 5%. The expected rate of return on the market portfolio is 11%.
The expected rate of growth in dividend of X Ltd. is 8%. The last dividend paid was ` 2.00 per
share. The beta of X Ltd. equity stock is 1.5.
(i) What is the present price of the equity stock of X Ltd.?
(ii) How would the price change when:
• The inflation premium increases by 3%
• The expected growth rate decreases by 3% and
• The beta decreases to 1.3.
(4 Marks)
16.1
Exam Papers
Final (New) Examination : November 2018
Question 1
(a) Tangent Ltd. is considering calling ` 3 crores of 30 years, ` 1,000 bond issued 5 years ago
with a coupon interest rate of 14 per cent. The bonds have a call price of ` 1,150 and had
initially collected proceeds of ` 2.91 crores since a discount of ` 30 per bond was offered.
The initial floating cost was ` 3,90,000. The Company intends to sell ` 3 crores of 12 per cent
coupon rate, 25 years bonds to raise funds for retiring the old bonds. It proposes to sell the
new bonds at their par value of ` 1,000. The estimated floatation cost is ` 4,25,000. The
company is paying 40% tax and its after tax cost of debt is 8 per cent. As the new bonds
must first be sold and then their proceeds to be used to retire the old bonds, the company
expects a two months period of overlapping interest during which interest must be paid on both
the old and the new bonds. You are required to evaluate the bond retiring decision. [PVIFA 8%,
25 = 10.675]
(8 Marks)
(b) A dealer in foreign exchange has the following position in Swiss Francs on 31 st January, 2018:
(Swiss Francs)
Balance in the Nostro A/c Credit 1,00,000
Opening Position Overbought 50,000
Purchased a bill on Zurich 70,000
Sold forward TT 49,000
Forward purchase contract cancelled 41,000
Remitted by TT 75,000
Draft on Zurich cancelled 40,000
Examine what steps would the dealer take, if he is required to maintain a credit balance
of Swiss Francs 30,000 in the Nostro A/c and keep as overbought position on Swiss Francs
10,000?
(8 Marks)
(c) Explain Angel Investors.
(4 Marks)
Question 2
(a) Shares of Volga Ltd. are being quoted at a price-earning ratio of 8 times. The company retains
50% of its Earnings Per Share. The Company's EPS is ` 10.
(1) the cost of equity to the company if the market expects a growth rate of 15% p.a.
(2) the indicative market price with the same cost of capital and if the anticipated growth
rate is 16% p.a.
(3) the market price per share if the company's cost of capital is 20% p.a. and the anticipated
growth rate is 18% p.a.
(8 Marks)
16.2
(b) Mr. Kapoor owns a portfolio with the following characteristics:

Security X Security Y Risk Free Security
Expected Return 15% 20% 10%
It is assumed that security returns are generated by a two factor model.
(i) If Mr. Kapoor has ` 1,00,000 to invest and sells short ` 50,000 of security Y and purchases
` 1,50,000 of security X, what is the sensitivity of Mr. Kapoor's portfolio to the two factors?
(ii) If Mr. Kapoor borrows ` 1,00,000 at the risk free rate and invests the amount he borrows
along with the original amount of ` 1,00,000 in security X and Y in the same proportion
as described in part (i), what is the sensitivity of the portfolio to the two factors?
(iii) What is the expected return premium of factor 2?
(8 Marks)
(c) Discuss about the Primary Participants in the process of Securitization.
(4 Marks)
Question 3
(a) A mutual fund having 300 units has shown its NAV of ` 8.75 and ` 9.45 at the beginning and
at the end of the year respectively. The Mutual fund has given two options to the investors:
(i) Get dividend of ` 0.75 per unit and capital gain of ` 0.60 per unit, or
(ii) These distributions are to be reinvested at an average NAV of ` 8.65 per unit.
What difference would it make in terms of returns available and which option is preferable
by the investors?
(8 Marks)
(b) The equity share of SSC Ltd. is quoted at ` 310. A three month call option is available at a
premium of ` 8 per share and a three month put option is available at a premium of ` 7 per
share.
Ascertain the net payoffs to the option holder of a call option and a put option, considering
that:
(i) the strike price in both cases is ` 320; and
(ii) the share price on the exercise day is ` 300, 310, 320, 330 and 340.
Also indicate the price range at which the call and the put options may be gainfully exercised.
(8 Marks)
(c) How different stakeholders view the financial risk?
(4 Marks)
Question 4
(a) TK Ltd. and SK Ltd. are both in the same industry. The former is in negotiation for acquisition
of the latter. Information about the two companies as per their latest financial statements are
given below:
TK Ltd. SK Ltd.
` 10 Equity shares outstanding 24 Lakhs 12 Lakhs
Debt:
10% Debentures (` Lakhs) 1160 -
12.5% Institutional Loan (` Lakhs) - 480
16.3
Earnings before interest, depreciation and tax 800.00 230.00

(EBIDAT) (` Lakhs)
Market Price/Share (`) 220.00 110.00
TK Ltd. plans to offer a price for SK Ltd. business, as a whole, which will be 7 times of EBIDAT
as reduced by outstanding debt and to be discharged by own shares at market price.
SK Ltd. is planning to seek one share in TK Ltd. for every 2 shares in SK Ltd. based on the
market price. Tax rate for the two companies may be assumed as 30%.
Calculate and show the following under both alternatives -TK Ltd.'s offer and SK Ltd.' s plan:
(i) Net consideration payable.
(ii) No. of shares to be issued by TK Ltd.
(iii) EPS of TK Ltd. after acquisition.
(iv) Expected market price per share of TK Ltd. after acquisition.
(v) State briefly the advantages to TK Ltd. from the acquisition.
Calculations may be rounded off to two decimals points.
(12 Marks)
(b) An Indian company obtains the following quotes (`/$)
Spot: 35.90/36.10
The company needs $ funds for six months. Determine whether the company should borrow in
$ or ` Interest rates are :
3 - Months interest rate : ` : 12%, $ : 6%
6 - Months interest rate : ` : 11.50%, $ : 5.5%
Also determine what should be the rate of interest after 3-months to make the company
indifferent between 3-months borrowing and 6-months borrowing in the case of:
(i) Rupee borrowing
(ii) Dollar borrowing
Note: For the purpose of calculation you can take the units of dollar and rupee as 100 each.
(8 Marks)
Question 5
(a) Following details are available for X Ltd.
Income Statement for the year ended 31st March, 2018
Particulars Amount
Sales 40,000
Gross Profit 12,000
Administrative Expenses 6,000
Profit Before tax 6,000
Tax @ 30% 1,800
Profit After Tax 4,200
Balance sheet as on 31st March, 2018
Particulars Amount
Fixed Assets 10,000
16.4
Total Assets 16,000

Equity Share Capital 15,000
Sundry Creditors 1,000
Total Liabilities 16,000
The Company is contemplating for new sales strategy as follows :
(i) Sales to grow at 30% per year for next four years.
(ii) Assets turnover ratio, net profit ratio and tax rate will remain the same.
(iii) Depreciation will be 15% of value of net fixed assets at the beginning of the year.
(iv) Required rate of return for the company is 15%
Evaluate the viability of new strategy.
(12 Marks)
(b) A dealer quotes 'All-in-cost' for a generic swap at 6% against six month LIBOR flat. If the notional
principal amount of swap is ` 8,00,000:
(i) Calculate semi-annual fixed payment.
(ii) Find the first floating rate payment for (i) above if the six month period from the effective
date of swap to the settlement date comprises 181 days and that the corresponding LIBOR
was 5% on the effective date of swap.
(iii) In (ii) above, if the settlement is on 'Net' basis, how much the fixed rate payer would pay
to the floating rate payer? Generic swap is based on 30/360 days basis.
(4 Marks)
(c) Explain the concept of Riba in Islamic Finance.
(4 Marks)
Question 6
(a) The following data are available for three bonds A, B and C. These bonds are used by a bond
portfolio manager to fund an outflow scheduled in 6 years. Current yield is 9%. All bonds have
face value of `100 each and will be redeemed at par. Interest is payable annually.
Bond Maturity (Years) Coupon rate
A 10 10%
B 8 11%
C 5 9%
(i) Calculate the duration of each bond.
(ii) The bond portfolio manager has been asked to keep 45% of the portfolio money in Bond
A. Calculate the percentage amount to be invested in bonds B and C that need to be
purchased to immunise the portfolio.
(iii) After the portfolio has been formulated, an interest rate change occurs, increasing the
yield to 11%. The new duration of these bonds are: Bond A = 7.15 Years, Bond B =
6.03 Years and Bond C = 4.27 years.
Is the portfolio still immunized? Why or why not?
(iv) Determine the new percentage of B and C bonds that are needed to immunize the
portfolio. Bond A remaining at 45% of the portfolio.
Present values be used as follows :
PVIF0.09,t 0.917 0.842 0.772 0.708 0.650
16.5
Present Values t6 t7 t8 T9 t10

PVIF0.09,t 0.596 0.547 0.502 0.460 0.4224
(12 Marks)
(b) On 19th January, Bank A entered into forward contract with a customer for a forward sale
of US $ 7,000, delivery 20th March at ` 46.67. On the same day, it covered its position by
buying forward from the market due 19th March, at the rate of ` 46.655. On 19th February,
the customer approaches the bank and requests for early delivery of US $. Rates prevailing
in the interbank markets on that date are as under:
Spot (`/$) 46.5725/5800
March 46.3550/3650
Interest on outflow of funds is 16% and on inflow of funds is 12%. Flat charges for early delivery
are ` 100.
What is the amount that would be recovered from the customer on the transaction?
Note: Calculation should be made on months basis than on days basis.
(8 Marks)
16.6
17.1
Exam Papers
Final (New) Examination : May 2019
Question 1
(a) Compute Economic Value Added (EVA) of Good luck Ltd. from the following information:
Profit & Loss Statement
Particulars (` in Lakh)
(a) Income -
Revenue from Operations 2000
(b) Expenses -
Direct Expenses 800
Indirect Expenses 400
(c) Profit before interest & tax(a-b) 800
(d) Interest 30
(e) Profit before tax (c - d) 770
(f) Tax 231
(g) Profit after tax (e - f) 539
Balance Sheet
Particulars (` in Lakh)
Equity and Liabilities :
(a) Shareholder's Fund -
Equity Share Capital 1000
(b) Non- Current Liabilities -
Long Term Borrowings 200
(c) Current Liabilities 800
Total 2600
Assets :
(a) Non - Current Assets 2000
(b) Current Assets 600
Total 2600
(1) Cost of Debts is 15%.
(2) Cost of Equity (i.e. shareholders' expected return) is 12%.
(3) Tax Rate is 30%.
(4) Bad Debts Provision of ` 40 lakhs is included in indirect expenses and ` 40 lakhs reduced
from receivables in current assets.
(8 Marks)
(b) The shares of G Ltd. we currently being traded at ` 46. The company published its results for
the year ended 31st March 2019 and declared a dividend of ` 5. The company made a return
of 15% on its capital and expects that to be the norm in which it operates. G Ltd. Also expects
the dividends to grow at 10% for the first three years and thereafter at 5%.
(8 Marks)
17.2
You are required to advise whether the share of the company is being traded at a premium or
discount.
(c) State the important features of National Pension Scheme (NPS).
(4 Marks)
Question 2
(a) Given is the following information
Day Ltd. Night Ltd.
Net Earnings ` 5 crores ` 3.5 crores
No. of Equity Shares 10,00,000 7,00,000
The shares of Day Ltd. and Night Ltd. trade at 20 and 15 times their respective P/E ratios.
Day Ltd. considers taking over Night Ltd. By paying ` 55 crores considering that the market price
of Night Ltd. reflects its true value. It is considering both the following options:
I. Takeover is funded entirely in cash.
II. Takeover is funded entirely in stock.
You are required to calculate the cost of the takeover and advise Day Ltd. on the best alternative.
(8 Marks)
(b) ABB Ltd. has a surplus cash balance of ` 180 lakhs and wants to distribute 50% of it to the
equity shareholders. The company decides to buyback equity shares. The company estimates
that its equity share price after re-purchase is likely to be 15% above the buyback price. if the
buyback route is taken.
Other information is as under:
1. Number of equity shares outstanding at present (Face value ` 10 each) is ` 20 lakhs.
2. The current EPS is ` 5.
I. The price at which the equity shares can be re-purchased, if market capitalization of the
company should be ` 400 lakhs after buy back.
II. Number of equity shares that can be re-purchased.
III. The impact of equity shares re-purchase on the EPS, assuming that the net income remains
unchanged.
(8 Marks)
(c) List the main applications of Value At Risk (VAR).
(4 Marks)
Question 3
(a) Following are the details of a portfolio consisting of 3 shares:
Shares Portfolio Weight Beta Expected Total
Return (%) Variance
X Ltd. 0.3 0.50 15 0.020
Y Ltd. 0.5 0.60 16 0.010
Z Ltd. 0.2 1.20 20 0.120
Standard Deviation of Market Portfolio Return = 12% You are required to calculate the
following:
(i) The Portfolio Beta.
17.3
(ii) Residual Variance of each of the three shares.

(iii) Portfolio Variance using Sharpe Index Model.
(8 Marks)
(b) Mr. John established the following spread on the TTK Ltd.'s stock:
1. Purchased one 3-month put option with a premium of ` 15 and an exercise price of ` 900.
2. Purchased one 3-month call option with a premium of ` 90 and an exercise price of `
1100.
TTK Ltd.'s stock is currently selling) at ` 1000. Calculate gain or loss, if the price of stock of
TTK Ltd. –
(i) Remains at ` 1000 after 3 months.
(ii) Falls to ` 700 after 3 months.
(iii) Raises to ` 1200 after 3 months.
Assume the size of option is 200 shares of TTK Ltd.
(8 Marks)
(c) Briefly explain the steps involved in Mechanism of Securitization.
(4 Marks)
Question 4
(a) A Mutual Fund Company introduces two schemes - Dividend Plan and Bonus Plan. The face
value of the Unit is `10 on 1-4-2014. Mr. R invested ` 5 lakh in Dividend Plan and ` 10 lakh in
Bonus Plan. The NAV of Dividend Plan is ` 46 and NAV of Bonus Plan is ` 42. Both the plans
matured on 31-03-2019. The particulars of Dividend and Bonus declared over the period are
as follows:
Date Dividend Bonus Ratio NAV of Dividend NAV of Bonus
% Plan Plan
(`) (`)
31-12-2014 12% - 47.0 42.0
30-09-2015 - 1:4 48.0 43.0
31-03-2016 15% - 49.5 41.5
30-09-2017 - 1:6 50.0 44.0
31-03-2018 10% - 48.0 43.5
31-03-2019 - - 49.0 44.0
You are required to calculate the effective yield per annum in respect of the above two plans.
(8 Marks)
(b) Following financial information’s are available of XP Ltd. for the year 2018:
Equity Share Capital (` 10 each) ` 200 Lakh
Reserves and Surplus ` 600 Lakh
10% Debentures (` 100 each) ` 350 Lakh
Total Assets ` 1200 Lakh
Assets Turnover Ratio 2 times
Tax Rate 30%
Current Market Price per Equity Share ` 28
Required Rate of Return of Investors 18%
17.4

(i) Prepare Income Statement for the year 2018.
(ii) Determine its Sustainable Growth Rate.
(iii)Determine the fair price of the company's share using Dividend Discount Model.
(iv) Give your opinion on investment in the company's share at current price.
(8 Marks)
(c) Explain briefly the sources for funding a Start-up.
(4 Marks)
Question 5
(a) A Rice Trader has planned to sell 22000 kg of Rice after 3 months from now. The spot price of
the Rice is ` 60 per kg and 3 months future on the same is trading at ` 59 per kg. Size of the
contract is 1000 kg. The price is expected to fall as low as ` 56 per kg, 3 months hence. What
the trader can do to mitigate its risk of reduced profit? If he decides to make use of future
market, what would be the effective realized price for its sale when after 3 months, spot price is
` 57 per kg and future contract price for 3 months is ` 58 per kg?
(8 Marks)
(b) On 1st January 2019 Global Ltd., an exporter entered into a forward contract with BBC Bank
to sell US$ 2,00,000 on 31st March 2019 at ` 71.50/$. However, due to the request of the
importer, Global Ltd. received the amount on 28 February 2019. Global Ltd. requested the
Bank to take delivery of the remittance on 2nd March 2019. The Inter- banking rates on 28th
February were as follows:
Spot Rate ` 71.20/71.25
One month premium 5/10
If Bank agrees to take early delivery then what will be the net inflow to Global Ltd. assuming
that the prevailing prime lending rate is 15%. Assume 365 days in a year.
(8 Marks)
(c) State the benefits of listing to a Small and Medium Enterprise (SME).
(4 Marks)
Question 6
(a) Sun Limited, an Indian company will need $ 5,00,000 in 90 days. In this connection, following
information is given below:
Spot Rate - $1 = ` 71
90 days forward rate of $1 as of today = ` 73
Interest Rates are as follows:
Particulars US India
90 days Deposit Rate 2.50% 4.00%
90 days Borrowing Rate 4.00% 6.00%
A call option on $ that expires in 90 days has an exercise price of ` 74 and a premium of Re.
0.10. Sun Limited has forecasted the spot rates for 90 days as below:
Future Rate Probability
` 72.50 25%
` 73.00 50%
` 74.50 25%
17.5
Which of the following strategies would be the most preferable to Sun Limited:
(i) A Forward Contract;
(ii) A Money Market hedge;
(iii) An Option Contract;
(iv) No Hedging.
Show your calculations in each case.
(8 Marks)
(b) K Ltd. currently operates from 4 different buildings and wants to consolidate its operations into
one building which is expected to cost ` 90 crores. The Board of K Ltd. had approved the above
plan and to fund the above cost, agreed to avail an External Commercial
Borrowing (ECB) of GBP 10 m from G Bank Ltd. on the following conditions:
• The Loan will be availed on 1st April, 2019 with interest payable on half yearly rest.
• Average Loan Maturity life will be 3.4 years with an overall tenure of 5 years.
• Upfront Fee of 1.20%.
• Interest Cost is GBP 6 months LIBOR + Margin of 2.50%.
• The 6 month LIBOR is expected to be 1.05%.
K Ltd. also entered into a GBP-INR hedge at 1 GBP = INR 90 to cover the exposure on account
of the above ECB Loan and the cost of the hedge is coming to 4.00% p.a.
As a Finance Manager, given the above information and taking the 1 GBP = INR 90:
(i) Calculate the overall cost both in percentage and rupee terms on an annual basis.
(ii) What is the cost of hedging in rupee terms?
(iii) If K Ltd. wants to pursue an aggressive approach, what would be the net gain/loss for K
Ltd. if the INR depreciates/appreciates against GBP by 10% at the end of the 5 years
assuming that the loan is repaid in GBP at the end of 5 years?
Ignore time value and taxes and calculate to two decimals.
(8 Marks)
(c) Discuss briefly the important constituents of International Financial Centre (IFC).
OR
What are the differences between Islamic Finance and Conventional Finance?
(4 Marks)
17.6
18.1
Exam Papers
Question 1
1. (a) A Ltd., a listed company, is considering merger of B Ltd. which is also a listed company,
with itself by means of a stock swap (exchange). B Ltd. has agreed to a plan under which
A Ltd. will offer the current market value of B Ltd.'s shares.
Earnings after tax (`) 10,00,000 2,50,000
Number of shares outstanding 4,00,000 2,00,000
Current market price (`) per share 50 20
On the basis of above information, you are required to calculate the following:
(i) What is the pre-merger Earnings per Share (EPS) and P/E ratio of both the
companies?
(ii) If B Ltd.'s P/E is 10, what is its current market price per share? What is the exchange
ratio? What will A Ltd.'s post-merger EPS be?
(iii) What must the exchange ratio be for A Ltd.'s Pre-merger and Post-merger EPS to be
the same?
(8 Marks)
(b) P Ltd. is contemplating to borrow an amount of ` 50 crores for a period of 3 months in the
coming 6 months time from now. The current rate of interest is 8% per annum but it may
go up in 6 months time. The company wants to hedge itself against the likely increase in
interest rate.
The Company's Bankers quoted an FRA (Forward Rate Agreement) at 8.30% per annum.
Compute the effect of FRA and actual rate of interest cost to the company, if the actual
rate of interest during consideration period happens to be (i) 8.60% p.a., or (ii) 7.80% p.a.
(Show your workings on the basis of months)
(8 Marks)
(c) State briefly the basic characteristics of venture capital financing?
(4 Marks)
Question 2
(a) Cinderella Mutual Fund, an approved mutual fund, sponsored open-ended equity oriented
scheme "Rudolf Opportunity Fund". There are three plans under the scheme viz. 'A' - Dividend
Re-investment plan, 'B' - Bonus plan and 'C' - Growth plan.
At the time of initial public offer on 1-4-2009, Mr. Amit, Mr. Ashish and Mr. Arun, three investors
invested ` 2,00,000 each at face value of ` 10 per unit and chosen plan 'B', 'C' and 'A'
respectively.
The particulars of the fund over the period are as follows:
Date Dividend Bonus Ratio Net Asset Value per unit (`)
%
31.07.2013 10 - 30.70 31.20 35.40
18.2
31.03.2014 35 5:4 58.42 31.05 58.25

30.10.2017 20 - 42.18 26.45 56.45
15.03.2018 12.50 - 46.45 27.72 62.78
31.03.2018 - 1:3 45.20 20.05 67.12
25.03.2019 20 1:4 48.10 19.95 71.42
31.07.2019 - - 53.75 22.98 82.07
On 31st July, 2019, all the three investors redeemed all the balance units.
1. Consider the following:
(a) Long-term capital gain is exempt from Income-tax.
(b) Short-term capital gain is subject to 10% Income-tax.
(c) Security Transaction Tax is 0.2% only on sale/ redemption of units.
(d) Ignore Education Cess.
2. You are required:
(i) To calculate the Effective Yield per annum (annual rate of return) of each of the
investors.
(ii) To suggest the name of investor with the highest Effective Yield per annum with the
difference to his nearest investor.
(Show your calculations up to two decimal points)
(10 Marks)
(b) A future contract is available on R Ltd. that pays an annual dividend of ` 4 and whose stock is
currently priced at ` 125. Each future contract calls for delivery of 1,000 shares to stock in one
year, daily marking to market. The corporate treasury bill rate is 8%.
Required:
(i) Given the above information, what should the price of one future contract be ?
(ii) If the company stock price decreases by 6%, what will be the price of one futures contract?
(iii) As a result of the company stock price decrease, will an investor that has a long position
in one futures contract of R Ltd. realizes a gain or loss ? What will be the amount of his
gain or loss ?
(Ignore margin and taxation, if any)
(6 Marks)
(c) Identify the benefits of Securitization from the angle of Originator.
(4 Marks)
Question 3
(a) AB Ltd.'s equity shares are presently selling at a price of ` 500 each. An investor is interested in
purchasing AB Ltd.'s shares. The investor expects that there is a 70% chance that the price will
go up to ` 650 or a 30% chance that it will go down to ` 450, three months from now. There
is a call option on the shares of the firm that can be exercised only at the end of three months
at an exercise price of ` 550.
(i) If the investor wants a perfect hedge, what combination of the share and option should he
select ?
(ii) Explain how the investor will be able to maintain identical position regardless of the share
price.
18.3
(iii)If the risk-free rate of return is 5% for the three months period, what is the value of the
option at the beginning of the period ?
(iv) What is the expected return on the option?
(8 Marks)
(b) Closing values of BSE Sensex from 6th to 17th day of the month of January of the year 20xx
were as follows:
Days Date Day Sensex
1 6 THU 34522
2 7 FRI 34925
3 8 SAT No Trading
4 9 SUN No Trading
5 10 MON 35222
6 11 TUE 36000
7 12 WED 36400
8 13 THU 37000
9 14 FRI No Trading
12 17 MON 38,000
Calculate Exponential Moving Average (EMA) of Sensex during the above period. The 30 days
simple moving average of Sensex can be assumed as 35,000. The value of exponent for 30 days
EMA is 0.064. Provide analyzed conclusion on the basis of your calculation s.
(Calculations should be up to three decimal points.)
(8 Marks)
(c) What is a startup to avail the benefits of government scheme ?
(4 Marks)
Question 4
(a) Following information is available of M/s. TS Ltd.
(` in crores)
PBIT 5.00
Less : Interest on Debt (10%) 1.00
PBT 4.00
Less: Tax @ 25% 1.00
PAT 3.00
No. of outstanding shares of ` 10 each 40 lakh
EPS (`) 7.5
Market price of share (`) 75
P/E ratio 10 Times
TS Ltd. has an undistributed reserves of ` 8 crores. The company requires ` 3 crores for the
purpose of expansion which is expected to earn the same rate of return on capital employed as
present. However, if the debt to capital employed ratio is higher than 35%, then P/E ratio is
expected to decline to 8 Times and rise in the cost of additional debt to 14%. Given this data
which of the following options the company would prefer, and why?
Option (i) : If the required amount is raised through debt, and
18.4
Option (ii) : If the required amount is raised through equity and the new shares will be issued
at a price of ` 25 each.
(8 Marks)
(b) Following information relates to M/s A Lt d. which is a manufacturing-cum-exporting unit. It
is exporting some electronic components to Japan, USA and Europe on 90 days credit terms:
Cost and Sales Information:
Japan USA Europe
Variable cost per unit ` 225 ` 395 ` 510
Export sale price per unit Yen 650 $ 10.23 Euro 11.99
Receipts from sale due in 90 Yen 78,00,000 $ 1,02,300 Euro 95920
days
Foreign exchange rate
information
Japan USA Europe
Yen/Re $/Re Euro/Re
Spot market 2.417-2.437 0.0214-0.0217 0.0177-0.0180
3 months forward 2.397-2.427 0.0213-0.0216 0.0176-0.0178
3 months spot 2.423-2.459 0.02144-0.02156 0.0177-0.0179
Advice the company by calculating average contribution to sales ratio whether it should hedge
its currency risk or not.
(8 Marks)
(c) Following is the information about Mr. J's portfolio:
Investment in shares of ABC Ltd. ` 200 lakh
Investment in shares of XYZ Ltd. ` 200 lakh
Daily standard deviation of both shares 1%
Co-efficient of correlation between both shares 0.3
Required:
Determine the 10 days 99% Value At Risk (VAR) for Mr. J' s portfolio. Given : The Z score from
the Normal Table at 99% confidence level is 2.33. (Show your calculations up to four decimal
points).
(4 Marks)
Question 5
(a) Mr. X holds the following portfolio:
Securities Cost (`) Dividends Market Beta
(`) Price (`)
Equity shares:
A Ltd. 16,000 1,600 16,400 0.9
B Ltd. 20,000 1,600 21,000 0.8
C Ltd. 32,000 1,600 44,000 0.6
PSU Bonds 68,000 6,800 64,600 0.4
The risk-free rate of return is 12%. Calculate the following:
(i) The expected rate of return on his portfolio using Capital Asset Pricing Model (CAPM).
(ii) The average return on his portfolio. (Calculate up to two decimal points)
(8 Marks)
(b) TG Ltd., a multinational company is planning to set up a subsidiary company in India (where
hitherto it was exporting) in view of growing demand for its product and competition from other
MNCs. The initial project cost (consisting of plant and machinery including installation) is
18.5
estimated to be US $ 500 million. The net working capital requirements are estimated at US $
100 million. The company follows straight line method of depreciation. Presently, the company
is exporting 2 million units every year at a unit price of US $ 100, its variable cost per unit being
US $ 50.
The Chief Financial Officer has estimated the following operating cost and other data in respect
of the proposed project:
(a) Variable operating cost will be US $ 25 per unit of production.
(b) Additional cash fixed cost will be US $ 40 million per annum.
(c) Production and Sales capacity of the proposed project in India will be 5 million units.
(d) Expected useful life of the proposed plant is 5 years with no salvage value.
(e) Existing working capital investment for production and sale of 2 million units through
exports was US $ 20 million.
(f) Export of the product in the coming year will decrease to 1.5 million units in case the
company does not open subsidiary company in India, in view of the presence of competing
MNCs that are in the process of setting up their subsidiaries in India.
(g) Applicable Corporate Income Tax rate is 30%.
(h) Required rate of return for such project is 12%.
Assume that there will be no variation in the exchange rate of two countries, all profits will be
repatriated and there will be no withholding tax.
Estimate the Net Present Value (NPV) of the proposed project in India. Present Value Interest
Factors (PVIF) @ 12% for 5 years are as under:
Year: 1 2 3 4 5
PVIF: 0.8929 0.7972 0.7118 0.6355 0.5674
(Compute your workings to 4 decimals)
(8 Marks)
(c) Discuss briefly the key decisions which fall within the scope of financial strategy.
(4 Marks)
Question 6
(a) Following are risk and return estimates for two stocks
Stock Expected returns (%) Beta Specific SD of expected return (%)
A 14 0.8 35
B 18 1.2 45
The market index has a Standard Deviation (SD) of 25% and risk free rate on Treasury Bills is
6%.
(i) The standard deviation of expected returns on A and B.
(ii) Suppose a portfolio is to be constructed with the proportions of 25%, 40% and 35% in
stock A, B and Treasury Bills respectively, what would be the expected return, standard
deviation of expected return of the portfolio?
(8 Marks)
(b) Mr. X, a financial analyst, intends to value the business of PQR Ltd. in terms of the future cash
generating capacity. He has projected the following after tax cash flows :
Year : 1 2 3 4 5
Cash flows (` in lakh) 1,760 480 640 860 1,170
18.6
It is further estimated that beyond 5th year, cash flows will perpetuate at a constant growth rate
of 8% per annum, mainly on account of inflation. The perpetual cash flow is estimated to be `
10,260 lakh at the end of the 5th year.
Required:
(i) What is the value of the firm in terms of expected future cash flows, if the cost of capital of
the firm is 20%.
(ii) The firm has outstanding debts of ` 3,620 lakh and cash/bank balance of ` 2,710 lakh.
Calculate the shareholder value per share if the number of outstanding shares is 151.50
lakh.
(iii) The firm has received a takeover bid from XYZ ltd. of ` 225 per share. Is it a good offer?
[Given: PVIF at 20% for year 1 to Year 5: 0.833, 0.694, 0.579, 0.482, 0.402]
(8 Marks)
(c) State the main problems faced in Securitization in India?
OR
List the main objectives of International Cash Management.
(4 Marks)
19.1
Exam Papers
Question 1
(a) ZX Ltd. has made purchases worth USD 80,000 on 1st May 2020 for which it has to make a
payment on 1st November 2020. The present exchange rate is INR/USD 75. The company can
purchase forward dollars at INR/USD 74. The company will have to make an upfront premium
@ 1 per cent of the forward amount purchased. The cost of funds to ZX Ltd. is 10 per cent per
annum.
The company can hedge its position with the following expected rate of USD in foreign exchange
market on 1st May 2020:
Exchange Rate Probability
(i) INR/USD 77 0.15
(ii) INR/USD 71 0.25
(iii) INR/USD 79 0.20
(iv) INR/USD 74 0.40
You are required to advise the company for a suitable cover for risk.
(8 Marks)
(b) A two year tree for a share of stock in ABC Ltd., is as follows:
Consider a two years American call option on the stock of ABC Ltd., with a strike price of ₹ 98.
The current price of the stock is ₹ 100. Risk free return is 5 per cent per annum with a continuous
compounding and e0.05 = 1.05127.
Assume two time periods of one year each.
Using the Binomial Model, calculate:
(i) The probability of price moving up and down;
(ii) Expected pay offs at each nodes i.e. N1, N2 and N3 (round off upto 2 decimal points).
(8 Marks)
(c) On Tuesday morning (before opening of the capital market) an investor, while going through
his bank statement, has observed that an amount of ₹ 7 lakhs is lying in his bank account. This
amount is available for use from Tuesday till Friday. The Bank requires a minimum balance of
₹ 1000 all the time. The investor desires to make a maximum possible investment where Value
at Risk (VaR) should not exceed the balance lying in his bank account. The standard deviation
19.2
of market price of the security is 1.5 per cent per day. The required confidence level is 99 per
cent.
Given
Standard Normal Probabilities
z 0.00 .01 .02 .03 0.04 .05 .06 .07 .08 .09
2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890
2.3 .9893 .9896 .9998 .9901 .9904 .9906 .9909 .9911 .9913 .9916
2.4 .9918 .9920 .9922 .9923 .9925 .9929 .9931 .9932 .9934 .9936
You are required to determine the maximum possible investment.
(4 Marks)
Question 2
(a) AB Industries has Equity Capital of ₹ 12 Lakhs, total Debt of ₹ 8 Lakhs, and annual sales of ₹ 30
Lakhs. Two mutually exclusive proposals are under consideration for the next year. The details
of the proposals are as under:
Particulars Proposal Proposal
no. 1 no. 2
Target Assets to Sales Ratio 0.65 0.62
Target Net Profit Margin (%) 4 5
Target Debt Equity Ratio (DER) 2:3 4:1
Target Retention Ratio (of Earnings) (%) 75 -
Annual Dividend (₹ In Lakhs) - 0.30
New Equity Raised (₹ in Lakhs) - 1
You are required to calculate sustainable growth rate for both the proposals.
(8 Marks)
(b) IB an Indian firm has its subsidiary in Japan and Zaki a Japanese firm has its subsidiary in India
and face the following interest rates:
Company IB Zaki
INR floating rate BPLR + 0.50% BPLR + 2.50%
JPY (Fixed rate) 2% 2.25%
Zaki wishes to borrow Rupee Loan at a floating rate and IB wishes to borrow JPY at a fixed rate.
The amount of loan required by both the firms is same at the current exchange rate. A financial
institution may arrange a swap and requires 25 basis points as its commission. Gain, if any, is
to be shared by the firms equally.
(i) Whether a swap can be arranged which may be beneficial to both the firms?
(ii) What rate of interest will the firms end up paying?
(8 Marks)
(c) Peer – to – Peer Lending and Crowd funding are same and traditional methods of funding. Do
you agree? Justify your stand.
(4 Marks)
Question 3
(a) The following data are available for a bond:
Face Value ₹ 10,000 to be redeemed at par on maturity
19.3
Coupon rate 8.5 per cent per annum

Years to Maturity 5 years
Yield to Maturity (YTM) 10 per cent You are required to calculate:
(i) Current market price of the Bond,
(ii) Macaulay’s Duration,
(iii) Volatility of the Bond,
(iv) Convexity of the Bond,
(v) Expected market price, if there is a decrease in the YTM by 200 basis points
(a) By Macaulay’s Duration based estimate
(b) By Intrinsic Value Method.
Given
Years 1 2 3 4 5
PVIF (10%, n) 0.909 0.826 0.751 0.683 0.621
PVIF (8%, n) 0.926 0.857 0.794 0.735 0.681
(7 Marks)
(b) M/S. Corpus an AMC, on 1.04.2015 has floated two schemes viz. Dividend Plan and Bonus
Plan. Mr. X, an investor has invested in both the schemes. The following details (except the issue
price) are available:
Date Dividend Bonus Ratio NAV
(%) Dividend Plan Bonus Plan
1.04.2015 ? ?
31.12.2016 1 :4 (One unit on 4 units 47 40
held)
31.03.2017 12 48 42
31.03.2018 10 50 39
31.12.2018 1 :5 (One unit on 5 units 46 43
held)
31.03.2019 15 45 42
31.03.2020 - - 49 44
Additional details
Investment (₹) ₹ 9,20,000 ₹ 10,00,000
Average Profit (₹) ₹ 27, 748.60
Average Yield (%) 6.40
You are required to calculate the issue price of both the schemes as on 1.04.2015.
(10 Marks)
(c) An individual attempts to found and build a company from personal finances or from the
operating revenues of the new company. What this method is called? Discuss any two methods.
(3 Marks)
Question 4
(a) ICL is proposing to take over SVL with an objective to diversify. ICL’s profit after tax (PAT) has
grown @ 18 per cent per annum and SVL’s PAT is grown @ 15 per cent per annum. Both the
companies pay dividend regularly. The summarised Profit & Loss Account of both the companies
are as follows:
19.4
₹ in Crores
Particulars ICL SVL
Net Sales 4,545 1,500
PBlT 2,980 720
Interest 750 25
Provision for Tax 1,440 445
PAT 790 250
Dividends 235 125
ICL SVL
Fixed Assets
Land & Building (Net) 720 190
Plant & Machinery (Net) 900 350
Furniture & Fixtures (Net) 30 1,650 10 550
Current Assets 775 580
Less: Current Liabilities
Creditors 230 130
Overdrafts 35 10
Provision for Tax 145 50
Provision for dividends 60 470 50 240
Net Assets 1,955 890
Reserves and Surplus 1,050 1,300 660 785
Borrowing 655 105
Capital Employed 1,955 890
Market Price Share (₹) 52 75

ICL’s Land & Buildings are stated at current prices. SVL’s Land & Buildings are revalued three
years ago. There has been an increase of 30 per cent per year in the value of Land & Buildings.
SVL is expected to grow @ 18 per cent each year, after merger.
ICL’s Management wants to determine the premium on the shares over the current market price
which can be paid on the acquisition of SVL. You are required to determine the premium using:
(i) Net Worth adjusted for the current value of Land & Buildings plus the estimated average
profit after tax (PAT) for the next five years.
(ii) The dividend growth formula.
(iii) ICL will push forward which method during the course of negotiations?
Period (t) 1 2 3 4 5
FVIF (30%, t) 1.300 1.690 2.197 2.856 3.713
FVIF (15%, t) 1.15 2.4725 3.9938 5.7424 7.7537
(12 Marks)
(b) USD 10,000 is lying idle in your Bank Account. You are able to get the following quotes from
the dealers:
Dealer Quote
A EUR/USD 1.1539
19.5
B EUR/GBP 0.9094
C GBP/USD 1.2752
Is there an opportunity of gain from these quotes?
(4 Marks)
(c) Side Pocketing enhances the value of the Mutual Fund. Do you agree? Briefly explain the process
of side pocketing.
(4 Marks)
Question 5
(a) ICL an Indian MNC is executing a plant in Sri Lanka. It has raised ₹ 400 billion. Half of the
amount will be required after six months’ time. ICL is looking an opportunity to invest this
amount on 1st April,2020 for a period of six months. It is considering two underlying proposals:
Market Japan US
Nature of Investment Index Fund (JPY) Treasury Bills (USD)
Dividend (in billions) 25 -
Income from stock lending (in billions) 11.9276 -
Discount on initial investment at the end 2% -
Interest - 5 per cent per annum
Exchange Rate (1st April, 2020) JPY/INR 1.58 USD/INR 0.014
Exchange Rate (30th September, 2020) JPY/INR 1.57 USD/INR 0.013
You, as an Investment Manager, is required to suggest the best course of option.
(8 Marks)
(b) The following are the details of three mutual funds of MFL:
Growth Balanced Regular Market
Fund Fund Fund
Average Return (%) 7 6 5 9
Variance 92.16 54.76 40.96 57.76
Coefficient of Determination 0.3025 0.6561 0.9604
The yield on 182 days Treasury Bill is 9 per cent per annum.
(i) Rank the funds as per Sharpe's measure.
(ii) Rank the funds as per Treynor's measure.
(iii) Compare the performance with the market.
(8 Marks)
(c) In an efficient market, technical analysis may not work perfectly. However, with imperfections,
inefficiencies and irrationalities, which characterises the real world, technical analysis may be
helpful.
Critically analyse the statement.
(4 Marks)
Question 6
(a) An investor is considering to purchase the equity shares of LX Ltd., whose current market price
(CMP) is ₹ 112. The company is proposing a dividend of ₹ 4 for the next year. LX Ltd. is expected
to grow @ 20 per cent per annum for the next four years. The growth will decline linearly to 16
19.6
per cent per annum after first four years. Thereafter, it will stabilise at 16 per cent per annum
infinitely. The investor requires a return of 20 per cent per annum.
You are required
(i) To calculate the intrinsic value of the share of LX Ltd.
(ii) Whether it is worth to purchase the share at this price.
Period 1 2 3 4 5 6 7
PVIF (20%, n) 0.833 0.694 0.579 0.482 0.402 0.335 0.279
(8 Marks)
(b) The Management of a multinational company TL Ltd. is engaged in construction of Infrastructure
Project. A proposal to construct a Toll Road in Nepal is under consideration of the Management.
The following information is available:
The initial investment will be in purchase of equipment costing USD 250 lakhs. The economic
life of the equipment is 10 years. The depreciation on the equipment will be charged on straight
line method.
EBIDTA to be collected from the Toll Road is projected to be USD 33 lakhs per annum for a
period of 20 years.
To encourage investment Nepalese government is offering a 15 year term loan of USD 150
lakhs at an interest rate of 6 per cent per annum. The interest is to be paid annually. The loan
will be repaid at the end of 15 year in one tranche.
The required rate of return for the project under all equity financing is 12 per cent per annum.
Post tax cost of debt is 5.6 per cent per annum.
Corporate Tax Rate is 30 per cent.
All cash Flows will be in USD.
Ignore inflation.
You are required to advise the management on the viability of the proposal by using Adjusted
Net Present Value method.
Given
PVIFA (12%, 10) = 5.650, PVIFA (12%, 20) = 7.469, PVIFA (8%,15) = 8.559, PVIF (8%, 15) =
0.315.
(8 Marks)
(c) Distinguish between Pass Through Certificates (PTC) and Pay Through Securities (PTS).
OR
Differentiate between Economic Value Added (EVA) and Market Value Added (MVA)
(4 Marks)
20.1
Exam Papers
Final (New) Examination : January 2021
Question 1
(a) Mr. X is of the opinion that market has recently shown the Weak Form of Market Efficiency. In
order to test the validity of his impression he has collected the following data relating to the
movement of the SENSEX for the last 20 days.
Days Open High Low Close
1 33470.94 33513.79 33438.03 33453.99
2 33453.64 33478.11 33427.82 33434.83
3 33414.06 33440.29 33397.65 33431.93
4 33434.94 33446.18 33377.78 33383.41
5 33372.92 33380.27 33352.12 33370.93
6 33375.85 33389.49 33331.42 33340.75
7 33340.89 33340.89 33310.95 33330.98
8 33326.84 33340.91 33306.17 33335.08
9 33307.16 33328.22 33296.43 33301.97
10 33298.64 33318.60 33254.28 33259.03
11 33260.04 33228.85 33241.66 33251.53
12 33255.92 33289.46 33249.46 33285.89
13 33288.86 33535.67 33255.98 33329.28
14 33335.00 33346.21 33276.72 33284.17
15 33293.83 33310.86 33278.54 33298.78
16 33300.02 33337.79 33300.02 33325.38
17 33323.36 33356.34 33322.44 33329.95
18 33322.81 33345.98 33317.44 33319.67
19 33317.51 33321.18 33294.19 33302.32
20 33290.86 33324.96 33279.62 33319.61
You are required:
To test the Weak Form of Market Efficiency using Auto-Correlation test, taking time lag of 10
days.
(8 Marks)
(b) A proposed foreign investment involves creation of a plant with an annual output of 1 million
units. The entire production will be exported at a selling price of USD 10 per unit.
At the current rate of exchange dollar cost of local production equals to USD 6 per unit. Dollar
is expected to decline by 10% or 15%. The change in local cost of production and probability
from the expected current level will be as follows:
Decline in value of USD (%) Reduction in local cost of Probability
production (USD/unit)
0 - 0.4
10 0.30 0.4
15 0.15 Additional reduction 0.2
20.2
The plant at the current rate of exchange will have a depreciation of USD 1 million annually.
Assume local Tax rate as 30%.
(i) Annual Cash Flow After Tax (CFAT) under all the different scenarios of exchange rate.
(ii) Expected value of CFAT assuming no repatriation of profits.
(iii) Viability of the investment proposal assuming an initial investment of USD 25 million
on plant and working capital with a required rate of return of 11% on investment and on the
basis of CFAT arrived under option (ii). The CFAT will grow @ 3% per annum in perpetuity.
(8 Marks)
(c) As a financial strategist you will depend on certain key financial decisions. Discuss.
(4 Marks)
Question 2
(a) On 1st January, 2020, an open ended scheme of mutual fund had outstanding units of 300
lakhs with a NAV of ₹ 20.25. At the end of January 2020, it had issued 5 lakhs units at an
opening NA V plus a load of 2%, adjusted for dividend equalisation. At the end of February
2020, it had repurchased 2.5 lakhs units at an opening NAV less 2% exit load adjusted for
dividend equalisation. At the end of March 2020, it had distributed 70 per cent of its available
income.
In respect of January - March quarter, the following additional information is available:
Value appreciation of the portfolio ₹ 460 lakhs
Income for January ₹ 24 lakhs
Income for February ₹ 36 lakhs
Income for March ₹ 47 lakhs
(i) Income available for distribution
(ii) Issue price at the end of January
(iii) Repurchase price at the end of February
(iv) Closing Value of Net Assets at the end of March.
(8 Marks)
(b) X Ltd., an Indian company, is considering a proposal to make an investment of USD 1,65,00,000
in Latin America. The project will have a life of 5 years. The current spot exchange rate is
INR/USD 72. All investments and revenues will occur in USD. The USD and INR risk free rates
are 8% and 12% respectively. The following cash flow is expected form the project.
Year Cash inflow (USD)
1 30,00,000
2 37,50,000
3 45,00,000
4 60,00,000
5 75,00,000
Assume required rate of return on the project as 14%. You are required to calculate:
(i) The viability of the project using foreign currency approach.
(ii) What will be the impact if there is a withholding tax of 10% applicable on the project.
(8 Marks)
20.3
(c) "The process of securitisation can be viewed as process of creation of additional financial product
of securities in the market backed by collaterals." What are the other features? Describe.
(4 Marks)
Question 3
(a) The price of March Nifty Futures Contract on a particular day was 9170. The minimum trading
lot on Nifty Futures is 50. The initial margin is 8 and the maintenance margin is 6%. The index
closed at the following levels on next five days:
Day 1 2 3 4 5
Settlement Price (₹) 9380 9520 9100 8960 9140
(i) Mark to market cash flows and daily closing balances on account of
(a) An investor who has taken a long position at 9170
(b) An investor who has taken a short position at 9170
(ii) Net profit/ loss on each of the contracts
(8 Marks)
(b) M/s. Sky products Ltd., of Mumbai, an exporter of sea foods has submitted a 60 days bill for
EUR 5,00,000 drawn under an irrevocable Letter of Credit for negotiation. The company has
desired to keep 50% of the bill amount under the Exchange Earners Foreign Currency Account
(EEFC). The rates for ₹/USD and USD/EUR in inter-bank market are quoted as follows:
₹/ USD USD/EUR
Spot 67.8000 - 67.8100 1.0775 - 1.8000
1 month forward 10/11 Paise 0.20/0.25 Cents
Transit Period is 20 days. Interest on post shipment credit is 8 % p.a. Exchange Margin is 0.1%.
Assume 365 days in a year.
(i) Exchange rate quoted to the company
(ii) Cash inflow to the company
(iii) Interest amount to be paid to bank by the company.
(8 Marks)
(c) Following are the yields on Zero Coupon Bonds (ZCB) having a face value of ₹ 1,000
Maturity (Years) Yield to Maturity (YTM)
1 10%
2 11%
3 12%
Assume that the term structure of interest rate will remain the same.
You are required to
(i) Calculate the implied one year forward rates
(ii) Expected Yield to Maturity and prices of one year and two year Zero Coupon Bonds at
theend of the first year.
(4 Marks)
20.4
Question 4
(a) The following are the financial statements of A Ltd., and B Ltd. for the financial year ended 31st
March, 2020. Both the companies are working in the same industry.
Balance Sheets (₹)
Total Net Fixed Assets 12,00,000 6,00,000
Total Assets 27,00,000 18,00,000
Equity Capital (Face Value ₹ 10) 10,00,000 8,00,000
Retained Earnings 3,00,000 ---
14% Long Term Debt 7,00,000 5,00,000
Total Liabilities 27,00,000 18,00,000
Income Statement (₹)
Net Sales 33,10,000 16,60,000
Gross Profit 6,90,000 3,40,000
Interest 98,000 70,000
EBT 3,92,000 1,70,000
Tax @ 30% 1,17,600 51,000
PAT 2,74,400 1,19,000
Additional information :
Dividend Pay-out Ratio 40% 60%
Market Price per Share 40 15
(i) Earnings Per share (EPS), Profit Earning Ratio (PER), Return on Equity (ROE) and Book Value
Per Share (BVPS) for both the firms.
(ii) Estimate future EPS growth rate for both the firms.
(iii) If on acquisition of B Ltd. by A Ltd., intrinsic value of B Ltd., will be ₹ 20 per share, develop
range of justifiable Exchange Ratio (ER) that can be offered by A Ltd., to shareholders of B
Ltd.
(iv) Based on your analysis in (i) and (ii) whether the negotiated ratio will be close to upper or
lower range. Justify.
(v) Post-merger EPS on an ER of 0.4: 1. What will be immediate accretion or dilution to EPS to
the shareholders of both the firms?
(vi) Post-Merger MPS on the basis of ER of 0.4 : 1
(12 Marks)
(b) Shyam buys 10,000 shares of X Ltd., @ ₹ 25 per share and obtains a complete hedge of shorting
400 Nifty at ₹ 1,100 each. He closes out his position at the closing price of the next day when
the share of X Ltd., has fallen by 4% and Nifty Future has dropped by 2.5%.
What is the overall profit or loss from this set of transaction?
(4 Marks)
(c) Venture Capital Funding passes through various stages. Discuss.
(4 Marks)
20.5
Question 5
(a) Ramesh has identified stocks of two companies A and B having good investment potential:
Following data is available for these stocks:
Year A (Market Price per Share in ₹) B (Market Price per Share in ₹)
2013 19.60 8.70
2014 18.75 12.80
2015 33.42 16.20
2016 42.64 18.25
2017 43.25 15.60
2018 44.60 13.25
2019 34.75 18.60
(i) The Risk and Return by investing in Stock A and B
(ii) The Risk and Return by investing in a portfolio of these Stocks if he invests in Stock A and
B in proportion of 6 : 4.
(iii) The better opportunity for investment
(10 Marks)
(b) M/s. Roly Ltd. wants to acquire M/s. Poly Ltd. The following is the Balance Sheet of Poly Ltd. as
on 31st March, 2020 :
Equity Capital (₹ 10 per share) 10,00,000 Cash 20,000
Creditors and other liability 3,20,000 Plant & Machinery 16,50,000
Total 19,20,000 Total 19,20,000
Shareholders of Poly Ltd. will get one share of Roly Ltd. at current Market price of ₹ 20 for every
two shares. External liabilities are expected to be settled at a discount of ₹ 20,000. Sundry
debtors and Inventories are expected to realise ₹ 2,00,000.
Poly Ltd. will run as an independent unit. Cash Flow After Tax is expected to be ₹ 4,00,000 per
annum for next 6 years. Assume the disposal value of the plant after 6 years will be ₹ 1,50,000.
Poly Ltd. requires a return of 14%
n 1 2 3 4 5 6
PVIF (14%, n) 0.877 0.769 0.675 0.592 0.519 0.456
Advise the Board of Directors on the financial feasibility of the Proposal.
(6 Marks)
(c) Non-bank Financial Sources are becoming popular to finance Start-ups. Discuss.
(4 Marks)
20.6
Question 6
(a) The Balance Sheet of M/s. Sundry Ltd. as on 31-03-2020 is follows:
(₹ in lakhs)
Share Capital 300 Fixed Assets 600
Reserves 200 Inventory 500
Long Term Loan 400 Receivables 240
Short Term Loan 300 Cash 60
Payables & Provisions 200
Total 1400 Total 1400
Sales for the year was ₹ 600 lakhs. The sales are expected to grow by 20% during the year. The
profit margin and dividend pay-out ratio are expected to be 4% and 50% respectively.
The company further desires that during the current year Sales to Short Term Loan and Payables
and Provision should be in the ratio of 4 : 3. Ratio of fixed assets to Long Term Loans should
be 1.5. Debt Equity Ratio should not exceed 1.5.
(i) The amount of External Fund Requirement (EFR)
(ii) The amount to be raised from Short Term, Long Term and Equity funds.
(8 Marks)
(b) XYZ has taken a six-month loan from its foreign collaborator for USD 2 millions. Interest is
payable on maturity @ LIBOR plus 1%. The following information is available:
Spot Rate INR/USD 68.5275
6 months Forward rate INR/USD 68.4575
6 months LIBOR for USD 2%
6 months LIBOR for INR 6%
(i) Calculate Rupee requirements if forward cover is taken.
(ii) Advise the company on the forward cover.
What will be your opinion if spot rate of INR/USD is 68.4275 ?
(8 Marks)
(c) Participants are required for the success of the securitisation process. Discuss their roles.
OR
Risks are inherent and integral part of the market. Discuss.
(4 Marks)
21.1
Table I
NATURAL LOGS, 𝒆𝒙 AND 𝒆−𝒙 VALUES
𝒙 𝑰𝒏 𝒙 𝒆𝒙 𝒆−𝒙 𝒙 𝑰𝒏 𝒙 𝒆𝒙 𝒆−𝒙
0.0 -4.6052 1.0101 0.9900 0.36 -1.0217 1.4333 0.6977
0.02 -3.9120 1.0202 0.9802 0.37 -0.9943 1.4477 0.6907
0.03 -3.5066 1.0305 0.9704 0.38 -0.9676 1.4623 0.6839
0.04 -3.2189 1.0408 0.9608 0.39 -0.9416 1.4770 0.6771
0.05 -2.9957 1.0513 0.9512 0.40 -0.9163 1.4918 0.6703
0.06 -2.8134 1.0618 0.9418 0.41 -0.8916 1.5068 0.6637
0.07 -2.6593 1.0725 0.9324 0.42 -0.8675 1.5220 0.6570
0.08 -2.5257 1.0833 0.9231 0.43 -0.8440 1.5373 0.6505
0.09 -2.4079 1.0942 0.9139 0.44 -0.8210 1.5527 0.6440
0.10 -2.3026 1.1052 0.9048 0.45 -0.7985 1.5683 0.6376
0.11 -2.2073 1.1163 0.8958 0.46 -0.7765 1.5841 0.6313
0.12 -2.1203 1.1275 0.8869 0.47 -0.7550 1.6000 0.6250
0.13 -2.0402 1.1388 0.8781 0.48 -0.7340 1.6161 0.6188
0.14 -1.9661 1.1503 0.8694 0.49 -0.7133 1.6323 0.6126
0.15 -1.8971 1.1618 0.8607 0.50 -0.6931 1.6487 0.6065
0.16 -1.8326 1.1735 0.8521 0.51 -0.6733 1.6653 0.6005
0.17 -1.7720 1.1853 0.8437 0.52 -0.6539 1.6820 0.5945
0.18 -1.7148 1.1972 0.8353 0.53 -0.6349 1.6989 0.5886
0.19 -1.6607 1.2092 0.8270 0.54 -0.6162 1.7160 0.5827
0.20 -1.6094 1.2214 0.8187 0.55 -0.5978 1.7333 0.5769
0.21 -1.5606 1.2337 0.8106 0.56 -0.5798 1.7507 0.5712
0.22 -1.5141 1.2461 0.8025 0.57 -0.5621 1.7683 0.5655
0.23 -1.4697 1.2586 0.7945 0.58 -0.5447 1.7860 0.5599
0.24 -1.4271 1.2712 0.7866 0.59 -0.5276 1.8040 0.5543
0.25 -1.3863 1.2840 0.7788 0.60 -0.5108 1.8221 0.5488
0.26 -1.3471 1.2969 0.7711 0.61 -0.4943 1.8404 0.5434
0.27 -1.3093 1.3100 0.7634 0.62 -0.4780 1.8589 0.5379
0.28 -1.2730 1.3231 0.7558 0.63 -0.4620 1.8776 0.5326
0.29 -1.2379 1.3364 0.7483 0.64 -0.4463 1.8965 0.5273
0.30 -1.2040 1.3499 0.7408 0.65 -0.4308 1.9155 0.5220
0.31 -1.1712 1.3634 0.7334 0.66 -0.4155 1.9348 0.5169
0.32 -1.1394 1.3771 0.7261 0.67 -0.4005 1.9542 0.5117
0.33 -1.1087 1.3910 0.7189 0.68 -0.3857 1.9739 0.5066
0.34 -1.0788 1.4049 0.7118 0.69 -0.3711 1.9937 0.5016
0.35 -1.0498 1.4191 0.7047 0.70 -0.3567 2.0138 0.4966
21.2
Table II
NATURAL LOGS, 𝒆𝒙 AND 𝒆−𝒙 VALUES
𝒙 𝑰𝒏 𝒙 𝒆𝒙 𝒆−𝒙 𝒙 𝑰𝒏 𝒙 𝒆𝒙 𝒆−𝒙
0.71 -0.3425 2.0340 0.4916 1.06 0.0583 2.8864 0.3465
0.72 -0.3285 2.0544 0.4868 1.07 0.0677 2.9154 0.3430
0.73 -0.3147 2.0751 0.4819 1.08 0.0770 2.9447 0.3396
0.74 -0.3011 2.0959 0.4771 1.09 0.0862 2.9743 0.3362
0.75 -0.2877 2.1170 0.4724 1.10 0.0953 3.0042 0.3329
0.76 -0.2744 2.1383 0.4677 1.11 0.1044 3.0344 0.3296
0.77 -0.2614 2.1598 0.4630 1.12 0.1133 3.0649 0.3263
0.78 -0.2485 2.1815 0.4584 1.13 0.1222 3.0957 0.3230
0.79 -0.2357 2.2034 0.4538 1.14 0.1310 3.1268 0.3198
0.80 -0.2231 2.2255 0.4493 1.15 0.1398 3.1582 0.3166
0.81 -0.2107 2.2479 0.4449 1.16 0.1484 3.1899 0.3135
0.82 -0.1985 2.2705 0.4404 1.17 0.1570 3.2220 0.3104
0.83 -0.1863 2.2933 0.4360 1.18 0.1655 3.2544 0.3073
0.84 -0.1744 2.3164 0.4317 1.19 0.1740 3.2871 0.3042
0.85 -0.1625 2.3396 0.4274 1.20 0.1823 3.3201 0.3012
0.86 -0.1508 2.3632 0.4232 1.21 0.1906 3.3535 0.2982
0.87 -0.1393 2.3869 0.4190 1.22 0.1989 3.3872 0.2952
0.88 -0.1278 2.4109 0.4148 1.23 0.2070 3.4212 0.2923
0.89 -0.1165 2.4351 0.4107 1.24 0.2151 3.4556 0.2894
0.90 -0.1054 2.4596 0.4066 1.25 0.2231 3.4903 0.2865
0.91 -0.0943 2.4843 0.4025 1.26 0.2311 3.5254 0.2837
0.92 -0.0834 2.5093 0.3985 1.27 0.2390 3.5609 0.2808
0.93 -0.0726 2.5345 0.3946 1.28 0.2469 3.5966 0.2780
0.94 -0.0619 2.5600 0.3906 1.29 0.2546 3.6328 0.2753
0.95 -0.0513 2.5857 0.3867 1.30 0.2624 3.6693 0.2725
0.96 -0.0408 2.6117 0.3829 1.31 0.2700 3.7062 0.2698
0.97 -0.0305 2.6379 0.3791 1.32 0.2776 3.7434 0.2671
0.98 -0.0202 2.6645 0.3753 1.33 0.2852 3.7810 0.2645
0.99 -0.0101 2.6912 0.3716 1.34 0.2927 3.8190 0.2618
1.00 0.0000 2.7183 0.3679 1.35 0.3001 3.8574 0.2592
1.01 0.0100 2.7456 0.3642 1.36 0.3075 3.8962 0.2567
1.02 0.0198 2.7732 0.3606 1.37 0.3148 3.9354 0.2541
1.03 0.0296 2.8011 0.3570 1.38 0.3221 3.9749 0.2516
1.04 0.0392 2.8292 0.3535 1.39 0.3293 3.0149 0.2491
1.05 0.0488 2.8577 0.3499 1.40 0.3365 3.0552 0.2466
21.3
Table III
CUMULATIVE DISTRIBUTION FUNCTION FOR THE STANDARD NORMAL RANDUM VARIABLE N (D) +
d 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6046 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9425 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9555 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998
3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.00000 1.0000 1.0000
4.0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.00000 1.0000 1.0000
21.4
Table IV
CUMULATIVE DISTRIBUTION FUNCTION FOR THE STANDARD NORMAL RANDUM VARIABLE N (D) -
d 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681
-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
-1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
-2.0 0.0228 0.0222 0.0271 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
-2.3 0.0107 0.0104 0.0102 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
-2.5 0.0068 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
-2.9 0.0019 0.0018 0.2218 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007
-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002
-3.5 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002
-3.6 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
-3.7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
-3.8 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
-3.9 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
-4.0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
21.5
Table V
AREA UNDER THE NORMAL CURVE AREA UNDER THE STANDARD NORMAL DISTRIBUTION
d 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.3059
0.1 0.0398 0.0438 0.0478 0.0157 0.0557 0.0596 0.0636 0.2675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1798 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389
1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3819 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3825 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4060 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890
2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916
2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4029 0.4931 0.4932 0.4934 0.4936
2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964
2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4963 0.4974
2.8 0.4974 0.4375 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986
3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990
3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993
3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 044995 0.4995 0.4995
3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997
3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998
3.5 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998 0.4998
3.6 0.4998 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.7 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.8 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999
3.9 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
4.0 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000
21.6

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1.

Time Value of Money

Expected Inflation Rate

LOS 2 : Future Value of a Single Cash Flow

LOS 3 : Present Value of a Single Cash Flow

LOS 4 : Future Value of a Multiple Unequal Cash Flow

1000 × (1 + 0.10) 3 = 1331

LOS 5 : Present Value of a Multiple Unequal Cash Flow

LOS 6 : Present Value of a Multiple Equal Cash Flow (Period Defined)

Note: If question is silent always assume Deferred Annuity.

LOS 7 : Present Value of Equal Cash Flow upto infinity (Perpetuity/

Where CF1 = Cash Flow at the end of year 1.

Note: Total Earnings mean Earnings available to equity share holders

LOS 2 : SOME BASIC RATIOS

𝐓𝐨𝐭𝐚𝐥 𝐝𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐩𝐚𝐢𝐝 𝐭𝐨 𝐞𝐪𝐮𝐢𝐭𝐲 𝐬𝐡𝐚𝐫𝐞𝐡𝐨𝐥𝐝𝐞𝐫𝐬

𝐓𝐨𝐭𝐚𝐥 𝐌𝐚𝐫𝐤𝐞𝐭 𝐕𝐚𝐥𝐮𝐞/ 𝐌𝐚𝐫𝐤𝐞𝐭 𝐂𝐚𝐩𝐢𝐭𝐚𝐥𝐢𝐳𝐚𝐭𝐢𝐨𝐧/ 𝐌𝐚𝐫𝐤𝐞𝐭 𝐂𝐚𝐩

𝐓𝐨𝐭𝐚𝐥 𝐑𝐞𝐭𝐚𝐢𝐧𝐞𝐝 𝐞𝐚𝐫𝐧𝐢𝐧𝐠𝐬

 REPS = EPS - DPS

𝐃𝐢𝐯𝐢𝐝𝐞𝐧𝐝 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞

𝐄𝐚𝐫𝐧𝐢𝐧𝐠 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞

 Retention Ratio = 1 – Dividend Payout Ratio

 Relationship Between DPR & RR:

LOS 3 : Define Cash Dividends, Stock Dividend ,Stock Split

LOS 4 : RETURN CONCEPTS

Required Rate of Return:

LOS 5 : Ex – Dividend and Cum – Dividend Price of a share

LOS 6 : Valuation Models based on Earnings & Dividends

LOS 7 : Gordon’s Model/Growth Model/ Dividend discount Model

𝐃𝟎 (𝟏 𝐠) 𝐃𝟏 (𝐧𝐞𝐱𝐭 𝐞𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐝𝐢𝐯𝐢𝐝𝐞𝐧𝐝) 𝑬𝑷𝑺𝟏 ( 𝟏 𝒃)

P0 = Current market price of share.

2. If EPS = DPS, RR = 0 then g = 0

3. Calculation of P1 (Price at the end of year 1)

Price at the beginning = PV of Dividend at end + PV of market price at end

Earnings per Share (EPS) ₹ 10

Required rate of return of investors 15%

LOS 8 : Determination of Growth rate

LOS 9: Calculation of Ke in case of Floating cost is given

 If floating Cost is expressed in Absolute Amount i.e. P0 – f =

EPS = BVPS × ROE

LOS 11 : Over – Valued & Under – Valued Shares

LOS 12 : Holding Period Return (HPR)

(Capital gain Yield / Return) (Dividend Yield / Return)

LOS 13 : Multi-stage Dividend discount Model [ If g >K e ]/ Variable Growth

You are required to determine:

LOS 14 : IRR Technique & Growth Model

LOS 15 : Price at the end of each year

Los 16 : Negative Growth

a) Calculate the present value of the stock.

LOS 17 : Valuation Using the H-Model

LOS 19 : Calculation of Maximum price of a share

LOS 20 : Cash Flow Base Models

a) Based on its Net Income:

d) Based on Free Cash Flow to Equity (FCFE):

a) Calculating FCFE from FCFF

QUESTION NO. 13B : Calculation of FCFF & FCFE

Account Payable $20 $20

LOS 21 : Valuation Based on Multiples

1. P/E Multiple Approach MPS = EPS × P/E Ratio

LOS 2 : Dividend Yield Valuation Method