BFD Notes

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Contents
Chapter No Name Page no

1 Dividend Policy 4
2 Mutual Funds 8
3 Leasing 12
4 Financial Services 18
5 Capital Budgeting 21
6 International Capital Budgeting 27
7 Bond Valuation 30
8 Risk Analysis 35
9 Business Valuation 42
10 Mergers & Acquisition 47
11 Portfolio Management 51
12 Derivatives 62
13 Forex Derivatives 74
14 International Finance – Basics 77
15 International Finance – Risk & Hedging 82
1. DIVIDEND POLICY
1. Expression of Dividend
a) Dividend Dates:
Declaration Date Dividend is announced

Last-cum-dividend Date Shares can be bought inclusive of dividend
First Ex-dividend Date Shares can be bought without being eligible for dividend. On this date
stock price will fall by quantum of dividend.
Record Date Register of members is closed as per Companies Act
Payment Date Dividend cheque is written
b) Dividend Ratios:
Dividend Rate (DPS / FV ) X 100 FV - Fair value

Dividend Yield (DPS / MPS) X 100 MPS - Market price per share
Payout Ratio (DPS / EPS) X 100 EPS - Earnings per share
DPS - Dividend per share
DPS – Investor point of view = Equity Dividend
DPS – Company point of view = Dividend + Dividend distribution tax
Retention Ratio 100 – Payout Ratio (OR)
(Retained Earnings / Equity Earning) X 100
DPS EPS X Payout Ratio
MPS Market Capitalization / No. of shares
Cost of Capital Ke = Inverse of P.E.Multiple (i.e 1 / P.E.Ratio)
2. Growth Rate
Stock Valuation – Dividend Growth Model
P.E.Multiple Approach MPS = EPS X PE Multiple

Earning Growth Model MPS = [ EPS X (1 + G ) ] / (Ke - G)
Compare MPS with AP (Actual stock price)
Relationship Valuation Decision

AP > MPS Overvalued Sell
AP < MPS Undervalued Buy
AP = MPS Correctly Valued Hold
Future Growth Rate
G=bXr
b = Retention Ratio, r = Return on Investment
Implied Growth Rate
G = Ke – (D1/P)
Implied Return on Equity
ROE = Implied growth rate / Earnings retention rate
3. Common Sense Approach (OR) All-Or-Nothing Approach
Nature of Firm Relationship Payout

Growth Company K<r 0%
Declining Company K>r 100%
Normal Company K=r Indifference
K = Cost of Equity (or) Shareholder's expectation

r = Rate of return
4. Dividend Models
a. Walter’s Model Po = (D / Ke) + [ (E - D) X ( r / Ke)] / Ke

b. Gordon’s Model Po = D1 / (Ke - g)
c. Graham & Dodd Model Po = m X (D + E/3) m = multiplier
d. Lintner’s Model D1 = Do + [ (EPS X Target payout) - Do ] X AF
(AF = Adjustment Factor)
e. Modigliani-Miller Model nPo = [ (n+m)P1 - I1 + X1 ] / (1 + Ke)
Steps in MM Model:
1. P1 = Po ( 1 + Ke ) - D1
2. Retained Earnings (or) Money Available = PAT - ( n X D1 )
3. Money to be raised = Investment in year one (I1) - Step 2
4. No. of shared to be issued at year end (m) = Step 3 / Step 1
5. LHS = nPo
6. RHS = [ (n+m)P1 - I1 + X1 ] / (1 + Ke)
7. LHS = RHS
Principle: Declaration or Non-declaration of dividend affects the market price P1 and does not affect the market
capitalization nPo.
5. Pricing of Buy- Back
Buy back Price = (S X Po) / (S - N)
N = Money available for buy back / Buy back price

S = No of shares outstanding before buy back
Po = Current Market price
Market Capitalization after buy back =Buy back price X ( original shares - shares bought back)
6. Alternatives to Dividend
Bonus Issue Capitalisation of reserves

Stock Split Reduction in Face value
Reverse Split Increase in Face value
Post MPS after bonus/ stock split/ reverse split:
Post MPS= Old Market capitalization / Revised number of shares
7. Effect of change in Dividend
Increase in dividend Decrease in dividend

Shareholder not want to spend extra cash Shareholder want to maintain his composition
Investment in shares of the company Sell the shares of the company
Investment in no of shares = Incremental No. of shares to be sold = Difference in dividend /
dividend / current MPS current MPS
8. Post Bonus price
Theoretical post rights price per share
P = (MN + Sr) / (N + r)
Theoretical value of rights
R = [r / (N + r)] X (M - S) OR
Current MPS - Theoritical post rights price per share
S = Subscription per share

M = Market price per share
N = No. of existing shares
r = No. of right shares
No. of Right shares = Existing No. of shares / Ratio of Rights

Ratio of Rights = Ex-rights price per share / Subscription price
Ex-rights price per share = Share capital after Right issue / No. of Right shares
Subscription price = Money to be raised / No. of Right shares
Effect of Right issue
i. Value of shares before Right issue = No. of existing shares X Old MPS
ii. Value of shares after Right issue =No.of existing shares X Theoretical post right price per share (+) Sale
proceeds (No. of Right shares X Theoretical value of Rights)
iii. Compare the values of step I & step ii
Effect on wealth of Shareholder

Step I = Step ii – Nil
Step I > Step ii – Loss
Step I < Step ii – Profit
9. Flotation Cost
 Cost associated with issue of new share.

 Hence flotation cost for Existing Equity share & Retained earning = Zero
Flotation Cost %
Po X (1 - f) = D1 / (Ke - g)
10. Corporate Dividend Tax (CDT)
 Company is required to pay CDT on behalf of Equity shareholder.
 Dividend should not be taken after tax.
 Hence while calculated dividend consider CDT
 i.e., Dividend Per Share(DPS) X (1 + CDT)
11. Approaches to Dividend
a) Constant dividend
Fixed amount of dividend is paid each year irrespective of the earnings
b) Constant Payouts
Dividend Payout Ratio is kept constant
c) Constant Dividend plus
Fixed Low DPS is paid constant + Additional DPS paid in years of good profit
d) Residual Approach
Capital Structure altered Capital Structure un-altered

Dividend = PAT - Upcoming Capital expenditure Dividend = PAT - Capital expenditure funded by equity
e) Compromise Approach
Finance manager has to consider the following while declaring dividends

i. Projects with positive NPV are not to be cut to pay dividends
ii. Avoid dividend cuts
iii. Avoid the need to raise fresh equity
iv. Maintain a long term Target Debt Equity ratio
v. Maintain a long term Target Dividend Payout ratio
2. MUTUAL FUNDS
A. Net Asset value
NAV per unit = Net Asset value of the fund / No. of units outstanding
Market value of Investment XXX

Add:
Receivables XXX
Accrued income XXX
Other assets XXX
Less:
Accrued expenses XXX
Payables XXX
Other liabilities XXX
Net Asset Value XXX
Net Asset of the scheme = Total Assets - Total External Liability
B. Valuation Rules - "Mark - To - Market" Basis
Nature of Asset Valuation Price

Liquid asset like cash Book Value
All Listed & Trade securities other than those Closing Market price
held as not for resale
Debentures & Bonds Closing Traded price / yield
Liquid shares or debentures Last known price or Book value whichever is lower
Fixed income securities Current yield
C. Costs of Mutual fund
Expense Ratio = Total Expenses / Average value of portfolio
Expense per unit = Total Expenses / No. of Units

Average value of portfolio = (Opening NAV + Closing NAV ) / 2
R2 = [(1 / 1- Initial Expenses %) X R1 ] + Recurring Expenses%
R1 = Personal Earnings
R2 = Mutual Fund Earnings
Expenses include management and advisory fees, travel cost, consultancy etc.
Expense exclude brokerage cost for trading
D. Evaluation Models
A. Reward -to-variability / Volatility Ratio = Sharpe Ratio & Treynor Model
I. Sharpe Ratio = ( Rp - Rf ) / σp
Rp = Yield / Opening NAV
II. Treynor Model = ( Rp - Rf ) / βp
B. Measures of Excess Return
I. Jensen Alpha = Rp - [ Rf + β ( Rm - Rf ) ]
α = Return on portfolio - Return as per CAPM
Alpha is Positive Fund is undervalued, outperformed the market

Alpha is Negative Fund is overvalued, better the performance
II. Morning Star Index = Average Return - Average Risk of loss
Risk of loss = Lower of (Rf - Return) or zero
III. FAMA net selectivity = (Rp - [Rf+ (σj/σm)x(Rm-Rf)]
Steps:
1. Risk premium from Portfolio = Rp-Rf

2. Risk premium from Market = Rm-Rf
3. Total Risk premium = β x (Rm-Rf)
4. Total gain = Step 1 - Step 3
5. Appreciation premium for diversification = (σj/σm)x(Rm-Rf)
6. Net gain = Step 1 - Step 5
Systematic risk = σpxβp

Unsystematic risk = Total risk - Systematic risk
Beta (β) =(σj/σm)x Correlation

Always β for Market Portfolio = 1
Rp = Return on Portfolio
Rf = Risk free Return
σp = Standard deviation on Portfolio
βp = Beta of stock
Rm = Market return
7. Returns
Holding Period Return = [Cash dividend + capital appreciation + capital gains ]

Opening NAV per unit
Annualized Return = (Total Return / period) X 365
Monthly return = Annual Return / 12
Capital appreciation = Closing NAV per unit - Opening NAV per unit
Return from Mutual fund = [Investor expectation/100 - Issue expenses]+ Annual recurring expenses
Effective Yield in percentage = [Total Yield/Opening NAV] = [365/No. of days holding] X 100
Portfolio Turnover = Lower of (Annual Purchase or Sale) / Average value of portfolio
TWR vs. RWR
Time Weighted Return (TWR) Rupee Weighted Return (RWR)

Ignores intervening inflows & outflows of cash considers intervening inflows &
outflows of cash
(Closing value - Opening value)/opening value x100 Calculate using IRR method
8. Average Rate of Return
Plan A - Dividend Re-investment plan
Date Dividend % Investment = Cumulative Rate (as given Units Cumulative

(as given in units x Face value x in the problem) (Investment/rate) units
the problem) Dividend %
Plan B - Bonus plan
Bonus ratio (as given Units = Cumulative units x Cumulative NAV / Unit (as given in the
Date in the problem) Bonus ratio units problem)
Redemption value = Cumulative units on closing date x rate on closing date

Less
Short term capital gain tax = Units on closing date x Tax % x difference between closing and previous date
rate
Security transaction tax = Redemption value x tax rate
Investment
Net return from investment
Plan C - Growth plan
Redemption value = IPO units x rate on closing date

Less
Security transaction tax = Redemption value x tax rate
Investment
Net gain
Note : In growth plan alone, we won’t deduct short term capital gain.
Holding period is more than one year, hence short term capital gain
wont arise
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9. Investment Decision
Slope of Capital Market = [ Expected Return - Opportunity cost ]/ Standard Deviation

Fund having higher slope is preferable.
10. Entry load vs Exit load
Entry Load Exit Load

Front End Load Back End Laod
Total amount paid by the investor Total amount received by the investor
Sale price per unit = NAV X (1 + Entry Load) Repurchase price / Buyback price = NAV X (1 - Exit Load)
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3. LEASING
1. Terms
Particulars Lessor Lessee

Asset Legal owner User
Lease Rent Income Expense
Tax Taxable Tax deductible
Depreciation Yes No
Investment/ Capital Financing / Capital structuring/
Decision Budgeting planning
Appropriate Discount rate WACC Opportunity cost
2. Lessor point of view
STEPS:
i. Identify Initial Outflow

ii. Discount In-between cashflows after tax
iii. Discount Terminal flow
iv. Compute NPV
v. NPV is positive - Lease
NPV is negative - Don’t Lease
NPV - Net Present Value
NPV - Net Present Value
Discounted
Cash Lease Lease rent - CFAT = Lease Discoun Cash flow
Year Flow Rent Depreciation Depreciation Tax rent - Tax t Factor after tax
Lease Rental
Received in Advance Received in Arrears
Received at the beginning of the period Received at the end of the period
Tax on lease rental will be considered as & when the cash flow in or rent accrues whichever is earlier
Finance or Operating Lease

All lease rental payments are tax deductible, hence the distinction of Finance or operating is irrelevant
while evaluating Lease option
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3. Lessee Point of view
A. PRESENT VALUE MODEL
Step 1: BORROW & BUY OPTION
Purchase price
Less: Present value of tax saved on depreciation
Less: Present value of Net salvage value
Present value of Buying option
Step 2: LEASE OPTION
Lease Rental
Less: Tax on Lease rent
Lease rent after tax
Present value of Lease option
Step 3: Compare step1 & 2
Select the option with lower PV of outflows
Step 1 < Step 2 = Borrow & Buy

Step 1 > Step 2 = Lease
Net salvage value = Residual value + Tax saving on loss from sale
Tax Savings on depreciation
Discounted Tax
Opening Closing Tax savings on Discoun savings on
Year balance Depreciation balance depreciation t Factor depreciation
Implication of Target Debt Ratio
i. Compare Leasing with borrowing

ii. Target Debt ratio is increased - By leasing or borrowing
iii. Target Debt ratio is decreased - By funding the asset by equity rather than leasing or borrowing
B. IRR MODEL
i. Internal Rate of Return = IRR

ii. IRR - Discount rate at which NPV = 0
iii. We discount cash flows under two rates i.e., higher rate & lower rate.
iv. Higher discount rate gives positive NPV
v. Lower discount rate gives negative NPV
vi. Find exact discount rate IRR using the following formula
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IRR = Lower Rate + { [Lower rate NPV / (Lower rate NPV - Higher rate NPV)] X Difference in rates }
Borrow & Buy Lease option
Initial Tax saved on Salvage Lease

Year cost Depreciation depreciation value Rental Lease after tax NET
Buying instead of Leasing
NET = Initial cost + Tax saved on depreciation + Salvage value - After tax Lease rental
Leasing instead of Buying
NET = After tax Lease rental - Initial cost - Tax on depreciation - salvage value
Investment decision Outflow followed by Inflow IRR < Opportunity cost Not good to Invest
Financing Decision Inflow followed by outflow IRR < Opportunity cost Good to finance
C. WEINGARTNER'S MODEL or CAPITAL BUDGETING MODEL
Steps:
i. Compute NPV under Lease option

ii. Compute NPV under Purchase option
iii. Select the option that has the higher NPV
D. ADJUSTED PRESENT VALUE METHOD (APV)
Steps:
i. Compute Base case NPV

ii. Compute Present value of tax saved on Interest paid
iii. Compute APV = Step (i+ii)
iv. If APV of Borrow & buy option is positive - BORROW & BUY otherwise Lease.
E. NET ADVANTAGE TO LEASING
1.Initial Outlay 3. Present value of Lease Rental
2. Tax Shield on Lease Rental 4. Present value of Tax benefit on depreciation
5. Present value of Tax benefit on Interest
6. Present value of Net Salvage value

A=1+2 B=3+4+5+6
Net Advantage to Leasing (NAL)= A - B
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Relationship Decision
A>B Lease
A<B Borrow & Buy
F. BOWER - HERRINGER - WILLAISMON (BHW) MODEL
Evaluation:
Financing Part Tax Shield Part
Financial Advantage of Leasing (FAL) Operating Advantage of Leasing (OAL)
FAL = PV of loan payment - PV of OAL = PV of lease related tax shields - PV of loan related
Lease payments tax shields - PV of Residual value
If (FAL + OAL) is positive - Lease

If (FAL + OAL) is negative- Borrow & Buy
G. BOWER MODEL
i. Same as Present Value Model

ii. Cost of Purchase - COP = PV of Borrow & Buy
option
iii. Cost of Lease - COL = PV of Lease option
COL < COP Lease

COL > COP Borrow & Buy
4. Break Even Lease Rental (BELR)
Lessee’s point of view
Initial Outlay
Less: Present value of Lease Rental
Add: Tax Shield on Lease Rental
Less: Present value of Tax benefit on depreciation
Less: Present value of Tax benefit on Interest
Less: Present value of Net Salvage value
Net Advantage to Leasing (NAL)
Equate NAL = 0 to compute BELR
Lessor's point of view
Cost of Machinery
Less: Present value of Salvage value
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Less: Present value of Tax benefit on depreciation
Less: Present value of Tax saving on short term capital gain
Cash Flow
After tax BELR = Cash Flow / Present value Annuity

factor
Before tax BELR = After tax BELR - ( 1 - Tax Rate)
5. Irrelevant Cash flows
While evaluating under Lessee's point of view, the following cash flows are irrelevant
Since these cash flows are COMMON for both buying & leasing options
a) Operating Cost
b) Forecast revenues
c) Training cost
d) Difference between Principle & Interest
e) Inflows from operations
f) Interest ( Irrelevant since considered while discounting)
6. Sensitivity of Residual Value
[Present Value of Lease option / Present value of Salvage value ] X 100

Up to this % Residual value to lease is Economical
7. Equated Annual Installment
=Loan Amount / Annuity factor
Annual cash inflow =

Cost of asset / Annuity factor at Lessor's expected ROR for the lease period
Appropriate Discount Rate

Monthly Rate - LR & Tax shelter
Yearly Rate - Purchase price & Salvage value of asset
8. Salvage Value
WDV of asset > Net Sale value Loss on sale Salvage value + (Loss on sale X Tax rate)
WDV of asset < Net Sale value Profit on sale Salvage value - (Profit on sale X Tax rate)
WDV of asset
Less: Net sale value
Terminal flow
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9. Treatment of Depreciation
Steps (Common for both SLM & WDV)
i. Compute depreciation amount
Closing WDV =
Opening Opening WDV -
Year WDV Depreciation depreciation
ii. Tax saving on depreciation
iii. Present value of tax saved on depreciation
Tax saving on Discoun Discounted Tax

Depreciation t Factor savings
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4. FINANCIAL SERVICES
1. Flat rate
Simple Interest = (Principal X Time X Rate)/100

EMI = Total Repayment amount /No of
Installments
Interest = Total repayment amount - amount
borrowed
Flat rate = (Interest/ Total borrowing)X 100 X
1/n
Effective Interest rate = [n/(n+1)]X 2F
n = No. of installments
F = Flat rate of interest
F = [Installment amount - (Sale price - downpay)]/ (Sale price - downpay) X 100
2. Annuity factor
Annuity factor = Cost of Asset/Lease rental per year
3. Decision on whether to avail discount
In case of cash sales, there will be discount. In case of credit sales, there will not be any discoun t.
A. Company having Surplus
After Investment rate > IRR - Not avail discount - Opt for higher purchase/credit purchase
After Investment rate < IRR - Avail discount
B. Company having Deficit
After borrowing rate > Discount rate - Not avail discount - Pay in installments
After borrowing rate < Discount rate - Avail cash discount
4. Loans swap
i. Compute cost of existing loan

ii. Compute cost of new loan
iii. Decide
Cost of existing loan > Cost of new loan - Swap
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Cost of existing loan < Cost of new loan - Don’t Swap
5. Factoring vs Bank borrowings
a) Savings on factoring
Savings in cost of administering debtors

(+) Reduction in bad debts
(+) Savings in interest on borrowings
(-) Cost of factoring
Net benefit of factoring
Effective rate of interest = (Net cost to the firm/Advance paid) X 100
b) Interest saved on bank borrowings
Existing average debtors

(-) Average new debtors
Reduction in debtors
Cost included in debtors = Amount of borrowings reduced % X Reduction in debtors
Interest saving = Interest % X Cost included in debtors
c) Compare a & b above and decide
6. Cost of fund
Basic Interest cost + Brokerage + Rating charges + Stamp duty = Final cost
Basic Interest cost = [(Face value - Issue price)/Issue price] X 12 months
7. Analysis of Receivables - Computation of finance amount
i. Determine eligible outstanding amount
Eligible amount will be considered as collateral only if;

a) Days outstanding is within due date and
b) Average payment period or historic payment date is within due date
If any one of the conditions is not satisfied, then don’t consider the receivable as outstanding amount
ii. Computation of amount which can be lend
Invoice amount (-) cash discount or allowance = Net amount considered for bank finance
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Eligible bank finance = % on Net amount considered for bank finance
8. Computation of factoring cost
i. Computation of net amount paid to firm
Receivables = Total sales X Collection period/365
Trade receivable period = Trade receivable/ Turnover X 365
Receivables
(-) Factor margin money or factoring reserve
Amount of finance offered by Factor
(-) Factor commission
Amount available for advance
(-) Interest
Net amount paid to the firm (Advance to be paid)
ii. Computation of effective cost of factoring
a) Annual cost of factoring

Factoring commission + Interest on factored debts
( - ) b) Savings on account of factoring
Cost of credit administration + bad debts avoided
c) Net cost of factoring
Effective rate of factoring = (Effective cost/ Net amount advanced) X 100
9. Beneficial Usage of Credit Card
i. Deferment of payment per month

ii. Effective deferment or savings per year
iii. Notional interest earnings on such savings = Step ii X Interest Rate
iv. Annual credit card charges
v. Benefit derived due to usage of credit card = Step iii - Step iv.
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5. CAPITAL BUDGETING
1. Time Value of Money
n
Future Value = Present Value X ( 1 + TVM)
FV = Today's Investment X FVF
n
PV = FV / (1 + TVM)
Future Value of Annuity = Annuity X FVAF
FVAF = (FVF -1) / R
Present value of Annuity = Annuity X PVAF
PVAF = ( 1 - PVF) / R
Future Value of Annuity Immediate = Future value regular X (1 + r)
Present value of Perpetuity = Perpetuity / Time value of money

Present value of Growing Perpetuity = Perpetuity / (Time value of money - Inflation rate)
Effective Annual Rate (EAR) = [1 + (Stated Rate / n)]n -1
n - No of times the interest is compounded during the year

FV - Future value
PV - Present value
FVF - Future value factor
TVM - Time value of money
FVAF- Future value Annuity factor
PVAF - Present value annuity factor
R – Rate
2. Investment Decisions
Steps:
i. Identify Initial investment
a. Initial capital expenditure
b. Initial investment in working capital
ii. Identify In-between cash flow

a. Operating cash flows
b. Increase / Decrease in working capital need to be added / subtracted
Working
Capital Increase Decrease
Debtors Overstate Understate
Creditors Understate Overstate
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Stock Overstate Understate
c. Additional investment in capital assets

d.Include Opportunity cost & ignore Sunk cost
iii. Identify Terminal cash flow

a. Net sale value of asset
b. Re-capture of working capital
iv. Discount the cash flows after tax & compute NPV
Consider the following while computing Cash flow after tax(CFAT)
a. Depreciation is initially deducted while calculating tax, then added back while calculating CFAT
b. If cash flows include inflation then discount rate also include inflation
c. If cash flows exclude inflation then discount rate also exclude inflation
d. Tax shelter = Tax rate X Loss adjusted
e. Capital gain - if Sale value > Written down value of asset
v. Project with positive NPV should be accepted
Evaluation of cash flows
Equity Shareholder's Perspective Lender's Perspective
Equity NPV = NPV of Equity shareholders Project NPV = NPV of term lenders
IRR of Equity shareholders = Equity IRR IRR of term lenders = Project IRR
Profit after tax(PAT) computed after The post tax interest cost must be
deducting the interest cost added back in arriving at cash flow
Interest & Principal need to be deducted Interest & Principal are not deducted
while arriving cash flows while arriving cash flows
3. Replacement Analysis
Terms
Abandonment Purchase Replacement

Abandoning the existing asset
Giving up existing asset Buying a new asset
& replacing it with new one
Abandonment Decision
Value of Asset Action Status
Disposal value < Fair Value Retain Undervalued in the market

Disposal value > Fair Value Abandon Overvalued in the market
STEPS:
i. Opportunity outflow ( today's net sale value of existing asset)
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ii. Compute future cash flows across balance life of asset
iii. Compute terminal flow
iv. Discount the cash flows to compute NPV
v. NPV is positive - Continue with the asset
NPV is negative - Abandon the asset
Purchase Decision
STEPS:
i. Find Initial outflow of new machine in the market

ii. Cash flows after tax across its useful life
iii. Compute terminal flow
iv. Discount the cash flows at after tax Cost of capital to arrive NPV
v. NPV is positive - Buy the asset
NPV is negative - Don’t buy the asset
Replacement Decision
NPV of PO > NPV of CO Purchase new asset & Discard old
NPV of PO < NPV of CO Continue with old asset & not buy new one
PO - Purchase Option
CO - Continuing Option
Method 1: Equated Annual Benefit Method
Equated Annual Benefit (EAB) Equated Annual Cost (EAC)

EAB = NPV / PVAF EAC = PVO / PVAF
Based on NPV Not based on NPV
Annual cash flow = EAB Present value of cost = EAC
Project with Higher EAB is selected Project with Lower EAC is selected
Method 2: Incremental cash flow Method
Steps:
i. Compute incremental initial outflow
Purchase price of new asset

Less: Net sale value of old asset
ii. Compute incremental operational flows
Operational flow from new asset

Less: Operational flow from old asset
iii. Compute incremental terminal flows
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Net sale value of new asset
Less: Net sale value of new asset
iv. Consolidate Step i ,ii & iii cash flows & discount at after tax cost of capital
v. Compute NPV
If NPV is positive - Replace the asset

If NPV is negative - Don't Replace the asset
4. Inflation
Money Cash flow

Includes Future Inflation
Money Discount rate
Real Cash flow
Excludes Future Inflation
Real Discount rate
(1 + MDR) = (1 + RDR) X ( 1 + IR)

RCF = MCF / IR
MDR - Money Discount Rate

RDR - Real Discount Rate
IR - Inflation Rate
RCF - Real Cash flow
MCF - Money Cash flow
Present Value
MCF discounted at MDR

RCF discounted at RDR
Conversion
MCF converted into RCF Discount at IR

RCF converted into MCF Compound at IR
Types of Inflation Rates(IR)
Symmetrical IR Asymmetrical IR
All items have same level of inflation All items have different rates of inflation
Convert: i. cash flows into terms in which discount rates are ii. Convert cash flows into terms in which the
Discount rates into terms in which cash flows are discount rate is
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Note: Depreciation is a non-cash item considered with Zero inflation while calculating NPV
5. Capital Rationing
Capital Rationing = Money is in short supply
Requirement < Availability No Short supply

Requirement > Availability Short supply
Types of Capital Rationing
Single Period Multiple Period

Short supply in one year only Short supply in more than one year
Nature of Projects
Divisible project Indivisible project
Permit fractional investments Do not Permit fractional investments
They can be taken up in parts They have to be taken up in full or dropped
A. Single period, Divisible projects
Steps:
i. Identify projects with positive NPV

ii. Identify that capital rationing exist i.e., Requirement > Availability
iii. Rank the projects in the Profitability Index ratio (NPV / Initial outlay)
iv. Assign money to the projects on the basis of rank.
If money is not adequate to fully cover the project then part of the project would be undertaken
v. Aggregate the NPV of selected projects
B.Single period, Indivisible projects
Steps:
i. Identify projects with positive NPV

ii. Identify that capital rationing exist i.e., Requirement > Availability or Supply < Demand
iii. Rank the projects in the ratio (NPV / Initial outlay)
iv. Identify various feasible combinations using trial & error method.
If money is available but cannot be allotted to any project, it will be dealt with as surplus cash.
v. Compute NPV of feasible combinations & select the one with highest aggregate NPV.
vi.Assume NPV of surplus cash as Zero.
Investing Surplus cash
Investment Rate > Cost of capital NPV is positive
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Investment Rate = Cost of capital NPV is Zero
Investment Rate < Cost of capital NPV is negative
Select the rate at which highest NPV is possible
C.Multi period, Divisible & Indivisible projects
Steps:
i. Establish the Maximization NPV equation

ii. Lay down the constraints
iii. Solve the Linear Programming Equation
6. Adjusted NPV
Base case NPV XXX

Less: Issue Cost (XXX)
Add: Present value of tax shield on interest XXX

Adjusted NPV XXX
Adjusted IRR - Rate at which Adjusted NPV = Zero
(Cash flow / Cost of capital) - Investment + Present value of tax shield on Interest = 0
7. Financial Terms
I. Operating Leverage = Contribution / EBIT
II.Financial Leverage = EBIT / EBT
III.Return on Capital Employed (ROCE) = (EBIT / Capital employed) X 100
IV.Interest Coverage ratio = (EBIT / Interest charges) X 100 or [(PAT + Depreciation + Interest)/Interest]
V.Debt Service Coverage Ratio (DSCR) = [(PAT + Depreciation + Interest) / (Interest + Principle repayment) ]
VI.EBIT - Earnings before Interest & Tax
VII.EBT - Earnings before Tax
VIII.PAT - Profit after Tax
26
6. INTERNATIONAL CAPITAL BUDGETING
1. Computation of NPV
Home Currency Approach Host Currency Approach

Home country - who makes investment Host country - country in which investment is made
Investor country Investee country
Discount at Home country discount rate Discount at Host country discount rate
Host Currency Approach
Steps:
i. Compute host currency cash flow
ii.Compute host currency discount rates
iii. Compute host currency NPV
iv. Convert at Spot rate to arrive at home country NPV
Home Currency Approach
Steps:
i. Compute host currency cash flow
ii.Convert to home country cash flows, by applying Spot rate on different dates
iii. Identify home currency discount rate
iv. Compute home currency NPV
2. Discount Rate Computation
Risk Free Rate Risky Rate

Forward rate = [ (1 + Rh) /(1 + Rf) ] X Spot rate Risky Rate = (Spot rate / Forward rate) X (1 + Rh)
Rh - Rate of 1st currency (Home )

Rf - Rate of 2nd currency (Foreign)
Risk Premium
Time value of money Nominal Rate of return

(1 + Rn) = (1 + Rf) X (1 + Rp)
= Real Rate of investment on risk free return
+ Risk premium
27
Situation Appropriate Discount rate
i. Home country invests only in Equity Discount @ Ke Cost of Equity
ii.Home country invests in both Equity & Debt Discount @ Weighted Average Cost of Capital
iii. Host country invests in Equity Discount cash flows to the extent repatriable @ Rate
of Return desired by Home country investor
iv. Host country invests in debt Discount rate reflects project's business risk +
financial risk arising from gearing. Ascertain discount
rate using CAPM & gearing
3. Tax Implication
Methods:
i. Discount the after tax cash flows at after tax discount rate OR
ii. Use Adjusted Present Value Method
Base case NPV XXX

Less: Issue Cost (XXX)
Add: Present value of tax shield on interest XXX
Adjusted NPV XXX
4. Repatriation Restrictions
When one entity invests in another country there could be restrictions on

how much profits can be taken back to the home country. These restrictions
are called Repatriation Restrictions
Cash
Particulars flows
Year 1 2 3
a. Project cash flows (Balance held (f) of previous year)
b. Amount repatriated (remitted)
c. Opening investment
d. Additional investment (a - b)
e. Interest on Opening investment
f. Balance held(given) XX XX XX
g. cash flows from parent point of view (b) XX XX XX
i.e., Amount Repatriated
h. Final year cash flow XX
28
With Repatriation
Discoun Present
Year Cash flows t factor value
value as given in
0 the problem
1
Amount repatriated
2 ( b ) as per above
3 table
Final year cash

3
flow ( h ) as per
above table
NPV
Without Repatriation
Discoun Presen
Year Cash flows t factor t value
0
1 Values as given in
2 the problem
3
NPV
Compare NPV with repatriation & without repatriation restrictions and decide
29
7. BOND VALUATION
1. Value of Bond
If interest is paid half yearly,
Calculate Interest = Face value X coupon rate X 6/12 months
i) Present Value of Interest =

Interest amount X Present value of (Rate of return X 1/2)% for (Maturity period X 2) years
ii) Present value of Maturity value =

Face value X Present value of (Rate of return X 1/2)% for (Maturity period X 2) years
iii) Bond value = i) + ii)
Fair Market Price (FMP) vs. Actual Market Price (AMP)
Fair Market value = Present value of Interest + Present value of Principal

Quarterly compounding = (Coupon rate & YTM)/4
Relationship Valuation Action

AMP < FMP Under Buy
AMP > FMP Over Sell
AMP = FMP Correct Hold
Amount of Investment
Amount required for making payment on maturity date =

Amount to be invested X [1+(Rate of Interest X No of days to maturity/365)]
{(Face Value - Issue price)X 12/m X 100} / Issue Price
m = No of months (Maturity period)
Cost of funds (p.a) = Effective rate of Interest + Brokerage + rating charge + stamp duty
2. Effective Rate of Interest
Actual Interest per annum that an investor earn during his period of holding
{(Face Value - Issue price)X 12/m X 100} / Issue Price
3. Yield to Maturity (YTM)
{(Redemption price - Current price) X 365/ No of days } / Current price
YTM = (Coupon return + Prorated discount)

(Redemption price + purchase price)/2
30
Coupon return = Face value or Maturity value X Coupon rate
Pro rated discount = Net capital appreciation/No of years to maturity
Net capital appreciation = Redemption price - Issue price
Face value = Issue price/(100- discount rate) , if it is issued at discount
Face value = Issue price/(100+premium rate) , if it is issued at premium
4. Effective Annual Return
Use periodic compounding

360/days
EAR = [1+(Yield/Period)]
5. Computation of Issue Price

Issue price = Present value of future cash outflows
Discount Discounted
Year Nature Cash flows factor cash flow
Interest Rate of Interest X Face value

Face value ± Premium or
Maturity proceeds discount amount
If current market rate or Yield rate of return are given, then consider only yield rate of return for
discount factor
6. Immunization
Duration of assets = Duration of liability
Maturity Coupon Duration DXW=

Stock Weight (W) Immunized
years rate (D)
Liability
Based on
Investment
7. Duration
1+Y (1+ Y)+Period X (C-Y)

(-)
period
Y C[(1+Y) - 1]+Y
Y = YTM
C=Coupon rate
31
Tabular form
Year Cash flows Present value Discounted % of Present Weighted

factor @ YTM rate cash flow value average time
1 2 3 4= 2X 3 5= 4/(Total of 6= Weights X 5
4 X 100)
Total of 6 =
Duration
Fall by basis points Rise by basis points
Sell - Less duration bonds Sell - More duration bonds
Buy - More duration bonds Buy - Less duration bonds
8. Volatility
Duration /(1+ Yield)
For every % change in yield, price of bond will vary by volatility
9. Holding period Return
Total return earned on bond over a period held by an investor
{(Price gain + Coupon payment)/Purchase price }X 100
Price gain = Redemption price - Issue price
10. Yield with tax & capital gains
i) coupon return
Less tax on coupon return
Net coupon return(Interest)
ii) Redemption price

Less Issue price
Capital gains
Less tax on capital gains
Net capital gains or capital appreciation
iii) Net cash flow on maturity = Redemption price - Tax on capital gains
iv) YTM = Net coupon return + (Pro rated discount/period of maturity)

(Net cash flow on maturity + Issue price)/2
32
11. YTM considering the time value of money (IRR)
V2-VM
YTM = R2 + X (R1 - R2)
V2-V1
VM = Investment value or Issue price
R1 R2
R1 discounted R2 discount
Cash flow discount discounted
Cash flow factor
Year factor Cash flow
1 to n Coupon
return
nth year Net
maturity
proceeds
Total of R1 discounted cash flow = V1

Total of R2 discounted cash flow = V2
YTM (Annualized) =
Half yearly coupon return + [Pro rated discount/(2 Period of maturity)]
2 X
(Redemption price + Purchase price)/2
To compute market price

i) substitute the values in the above formula & equate it to YTM
ii) consider Pro-rated discount = Redemption price + Market price
iii) under denominator, in place of purchase price, put MP & form a equation
& solve it to get the value of MP
If purchase is made in a period other than beginning or end of the year

then MP = MP calculated as above as on beginning of the year of purchase +
Accrued Interest for the period (Beginning of the year of purchase to date of purchase)
12. Value of Deep Discount Bond
Expected value = Present value of Maturity value for maturity period @ YTM rate
13. Refunding a Bond
Ahead of time because you may awash with money
Steps
i) Current repayment is an outflow
ii) Annual inflows are interest cost saved net of costs
iii) Terminal flow is savings in principal repayment in original terminal year
iv) Appropriate discount rate
33
v) NPV is positive, refund. Otherwise, retain
Ahead of time & is replaced with new bond offering
Steps
i) Incremental initial flow
ii) Incremental in-between flow
iii) Incremental terminal flow
iv) NPV is positive, refund. Otherwise, retain
v) Cost of bond less than rate of alternative investment, don’t refund
Cost of bond > rate of alternative investment, refund
14. Effect of increase or decrease in yield to Current market price
Increase in Yield
CMP - (CMP X Increase in Yield X Volatility)
Decrease in Yield
CMP + (CMP X Decrease in Yield X Volatility)
15. Pricing of bond
Relationship Price of bond

Coupon rate < Yield At Discount
Coupon rate = Yield At Par
Coupon rate > Yield At Premium
34
8. RISK ANALYSIS
1. Real options in Capital budgeting
a) Investment Timing Option

An option to wait before making additional Investment
Steps:
i. Compute NPV as of now
ii. Compute NPV after waiting period
iii. If NPV is positive then accept the option
iv. Real option value = Positive NPV after deferment(waiting period)
v. Option premium = Price reduction / Erosion in margin
b) Growth Option
An option to expand or vary the output
Steps:
i. Compute NPV for initial investment
ii. Compute NPV for option to expand the investment
iii. Worth of project with option = NPV for initial investment + Value of option
iv. Compare the worth of project with & without option and select which is having positive
NPV
c) Put Option
An option to shrine or abandon an investment
Steps:
i. Compute NPV of project
ii. Abandon at the end of year
Compute the NPV if project is Successful & Unsuccessful
iii. Expected value with option
Event NPV Probability Expected NPV

Successful
Unsuccessful
iv. Value of option = NPV of project without option + Expected value of option
v. If value of option is positive then accept the project
2. Z Values
Z=(X-Ẍ )/σ
X - Desired NPV
Ẍ - Originally estimated NPV
o - Standard deviation of possible NPVs
35
Value of Z Impact
Positive Z falls in Right Tail
Negative Z falls in Left Tail
Tail Requirement Action Add / deduct to arrive Z value

Left Greater than Add to 0.5
Left Less than Deduct from 0.5
Right Greater than Deduct from 0.5
Right Less than Add to 0.5
3. Hiller's Model
Types of Cash flow
Independent Cash flow Dependent cash flow

Cash flow of succeeding years Cash flow of succeeding years
not depend on earlier years are perfectly correlated to earlier years
Uncorrelated Cash flows Correlated Cash flows
Less Risk High Risk
Steps:
A. Independent Cash Flows
i. Compute Expected cash flows
Cash Probability Expected Cash Flow =

Year flows (P) Cash flow X P
ii. Compute NPV
Year Expected cash flow Discount factor Discounted cash flow
iii. Compute Variance of cash flows
Cash
Year flows Deviation (D) Probability (P) PD²
iv. Double discount the variance
Year Variance Double discount factor (1+r)²ᶯ Value
36
v. Standard Deviation = √ Total value of discounted variance
Steps:
B.Dependent Cash Flows
i. Compute Expected cash flows
Expected Cash Flow

Year Cash flows Probability (P) = Cash flow X P
ii. Compute NPV
Discoun Discounted cash

Year Expected cash flow t factor flow
iii. Compute Variance of cash flows
Year Cash flows Deviation (D) Probability (P) PD²
iv. Compute Standard Deviation = √ PD²
v. Discount the Standard Deviation (σ)
Year σ Discount Factor Discounted σ
4. Probability
Probability Distribution - Indicates the range of possible outcomes
Steps:
i. Chance of occurrences is assigned a numerical value
ii. Expected Value = Simple Average of Possible values
iii. ∑ P X R
P = Probability
R = Value
Cas Probability Expected Value =

Year h (P) Cash flow X P
flow
Statistical Formula of Expected value:
[Most Optimistic value + 4 times Realistic value + Most Pessimistic value] / 6
37
[Expected value of worst case + (4 X Expected value of Most Likely case)+Expected value of Best case] / 6
5. Standard Deviation (σ )
Measure of Risk
σ = √ ∑PD²
Cas Expected PXDX

Year h Probability Cash flow Deviation D
Flow
CF P X D=X-Ẍ PD²
Higher σ High Risk

Lower σ Low Risk
Decision:
Aggressive Investor Prefer project with Higher Return

Conservative Investor Prefer project with Lower Risk
Project Selection:
Two projects having-

A. Same Return - Select project with Lower Risk
B. Same Risk - Select project with Higher Return
C. Different levels of Risk & Return - Choice depend on risk preference of investor
6. Risk Adjusted Discount Rate (RADR)
 All projects are not discounted at same rate.

 Cut-off discount rate should be adjusted upward/ downward to take care of additional/lower risk
element.
RADR = Cut-off rate + Risk Premium
Cut-off rate = Regular Cost of Capital based on capital structure
Irving Fisher Model
(1 + Base discount rate) X (1 + Risk premium) = (1 + RADR)
RADR Vs CEF
Particulars CEF RADR

Adjusting Factor Cash flows Discount Rate
38
Discount Rate Risk free rate Risky rate
7. Certainty Equivalent Factor (CEF)
CEF = CCF / UCF

CCF = Cash Flow X Certainty Factor
UCF = CCF X CEF
CCF - Certain Cash Flow

UCF - Uncertain Cash Flow
Steps:
i. Compute CCF
Year Cash flow Certainty Factor CCF
ii. Compute NPV by discounting certain (assured) cash flows at risk free rate
Year CCF Discount Factor Discounted CCF
iii. NPV is positive - Accept the project
iv. NPV is negative - Reject the project
8. Simulation
Steps:
i. Define the problem & lay down the NPV model
ii. Identify the parameters & exogenous variable

Parameters: a)Initial Investment)Project life & c) Cost of Capital
Exogenous Variable: Revenue & Cost (Cash flows)
iii.Specify Rupee value & Probability
Sl.No Cash flow Probability Cumulative Probability
iv. Generate random number class intervals for exogenous variable
Sl.No Probability Cumulative Probability Random digit allocation
39
v. Assign random numbers & ascertain value
Random Number Range Cash flow
vi. Solve the model & compute NPV
9. Sensitivity Analysis
Measure the % of change in input parameter which lead to reversal of investment decision
i.e., NPV turns Zero
Parameter Direction of change

Size ↑
Cash flows ↓
Life ↓
Discount Rate ↑
Sensitivity % = ( Change / Base) X 100
Sales - Sensitivity % = ( NPV / PV of sales) X 100

Cost - Sensitivity % = (NPV / PV of Cost) X 100
Initial Outlay - Sensitivity % = (NPV / Initial Outlay) X 100
Project is more sensitive when Sensitivity % is Lower

Project is least sensitive when Sensitivity % is Higher
10. Joint Probability
Steps:
i. Identify the various paths or outcome
ii. Compute Joint probability = eg., Year 1 probability X Year 2 Probability
iii. Compute NPV of each path
Particulars Path 1 Path2 Path3

Year 1
PV of Cash flows
NPV of the year
Joint Probability
Expected Outcome =
NPV X Joint Probability
iv. Compute Expected NPV = Sum of Expected outcome
40
v. If Expected NPV is positive - Accept the project
vi. If Expected NPV is negative - Reject the project

11. Selection of Project
Select the project having-
i. Higher Expected NPV

ii. Lower Standard Deviation
iii. Higher Profitability Index
iv. Lower Risk
v. Lower Pay back period
vi.Higher Accounting Rate of Return
Profitability Index = Present value of Inflow / Present value of Outflow

Present value of Inflow = NPV + Present value of Outflow
Pay Back period
Even Cash flows Uneven Cash flows

Pay Back period = Initial Investment / Completed years + (Remaining Amount /
Annual cash inflows Available Amount)
Accounting Rate of Return (ARR)
Average Annual PAT / Average Investment

Average Investment = (Initial Investment + Salvage value) / 2
12. Risk Analysis
Higher Standard Deviation

Higher Discount Rate
Higher
Lower Certainty Equivalent Factor Risk
Correlated Cash flows
Higher Co-efficient of Variation
Lower
Uncorrelated Cash flows Risk
13. Co-efficient of Variation
Standard deviation / Expected NPV

i.e., σ / (NPV X Probability)
41
9. BUSINESS VALUATION
1. Asset based valuation
Value of assets
(-) Value of liabilities
(-) Preference share capital
Net assets available to equity shareholders
Value per equity share = Net assets available to equity shareholders/ No. of equity shares
Basis of valuation
A. Assets
1. Tangible fixed assets - Current cost
2. Intangible fixed assets - Current cost
3. Goodwill - Ignore book value, consider new value
4. Quoted investments - Market price
5. Unquoted investments - Book value after adjusting loss
6. Inventories -Cost or market price
7. Debtors - Realizable value (Adjust bad debts)
8. Development expenses - Under expansion of old project or entering new project
9. Value of capital WIP - Current cost
10. Miscellaneous expenses & Losses - Fictitious assets (hence ignored)
B.Liabilities -All liabilities are considered at redemption amount i.e. considering discount or premium
1. Short term liability (current liability)
2. Long term liability (debenture/loan)
3. Provision for tax
4. Contingent liability
5. Prior period adjustments
6. Preference share capital
7. Arrears and proposed preference dividend
8. Proposed equity dividend (Only in case of computing ex-dividend value of shares)
Proposed equity dividend
Compute value per share on the basis of
Ex dividend Cum dividend

Deduct proposed dividend Don’t deduct proposed dividend
from the asset value and from the asset value while
derive net asset value deriving net asset value
42
2. Earnings Yield method
PE ratio model
Steps:
1. Compute FMOP = Future Maintainable Operating Profits (after deducting pref. dividend)
2. Determine NRR/market return expectation %
3. Adjust the industry NRR for the risk factors applicable to the company
4. Capitalized value of FMOP = Step 1 / Step 3
5. Total assets available to equity shareholder = Step 4 + Non trade investments
6. Value per equity share = Step 5 / No of equity shares
Return on capital employed (ROCE)
Steps:
1. Compute current return on capital employed
2. Compute latest capital employed
3. Compute return by multiplying capital employed with return on capital employed
4. Capitalize the value of step 3 at market rate of return to arrive the value of the firm
ROCE is meaningful only if expressed in current cost figures
3. Dividend Yield Method
Steps:
1. Compute Future maintainable dividend rate or dividend rate for the current year =
Distributable profits/Paid up value of equity capital
2. Normal rate of dividend/market dividend expectation for the industry as a whole
3. Adjusted for the risk factors - Risk adjusted dividend rate
4. Value per share = Paid up value per share X Company's dividend rate/Step 3
Note: Dividend yield method & earnings capital method will have same NRR
When company has 100% dividend payout ratio
Dividend based valuation
1. No growth in dividend
Current share price = D1/Ke
2. Constant growth in dividends
Current share price = D1/(Ke - g)
3. Stepped up growth
43
a) compute dividend till the end of the year in which the final change in dividend takes place
b) Assume certain Ke at the beginning of the year in which the final change in dividend takes place
Price at the beginning of the year = Dn/(Ke - g)
c) compute the present value of dividend and market price at assumed Ke

If this equals current market price, the assumed Ke is final Ke.
D1 = Do X (1+g)
4. Productivity factor method
Steps:
1. Simple average or weighted average of return on capital employed
Return on capital employed = PBIT/Capital employed
2. Capital employed on valuation date
3. Future Maintainable profit before interest and tax
= Step 2 X Step 1
4. FMOP = Step 3 - Interest on debt - tax - preference dividend
5. Determine NRR/Market return expectation for the industry as a whole
6. Capitalized value of FMOP = FMOP/Risk adjusted NRR
7. Total asset available to equity share holder = Step 6 + Non trade investments
8. value per share = Step 7/ No of equity shares
5. Price earning multiple method
Steps:
1. Compute present EPS or future maintainable EPS
EPS = Profits after tax/No of equity shares
2. PE ratio should be ascertained for the representative company in the industry are being valued
and not for the company whose shares.
PE ratio = Market price per share/ Earnings per share
3. Value per share = Step 1 X Step 2
Note:
Productivity factor method & PE multiple method - Variant of earnings capitalized method
i.e. NRR = 1/ PE ratio
6. Discounted cash flow method
Steps:
1. Computation of free cash flows
2. Determination of discount rate
3. Computation of present value
44
4. Estimation of terminal value
5. Value of firm = Step 3 + Step 4
7. Terminal value
Perpetuity Growing
Multiplier approach approach perpetuity Book value
Forecasted book
Last year profit X PE Free cash cash flow X value of capital X
multiple flow/Discount rate (1+g)/(Ke-g) Market to book ratio
8. Valuation
Calculation of Profit After Tax(PAT) XXX

Profit before interest & tax (PBIT) XXX
Less: Debenture Interest XXX
Profit before tax (PBT) XXX
Less: Tax XXX

Profit after tax (PAT) XXX
Less: Preference dividend XXX
Less Equity dividend XXX
Retained Earnings XXX
Interest & Fixed Dividend coverage=(PAT + Debenture interest) /(Debenture interest + Preference
dividend)
Capital Gearing Ratio = Fixed Interest bearing funds / Equity shareholders funds
Fixed Interest bearing funds = Preference share capital + Debentures
Equity shareholders funds = Equity share capital + Reserves
Yield on Equity shares % = (Yield on shares / Equity share capital) X 100
Expected Yield on Equity shares

Assume Risk premium as
1% for every one difference for Interest & fixed dividend coverage
2% for every one difference for Capital Gearing ratio
Risk premium =Given Average Ratio - (Calculate ratio X % for difference)

Normal return expected
+ Risk premium for low interest & fixed dividend coverage
+ Risk premium for high Interest gearing ratio
45
Value of Equity share = (Actual yield / Expected yield) X Paid-up value of share
Ke = (1/PE ratio) X 100
9. CAPM based valuation
CAPM is used to arrive at the initial listing price of share and market price of unlisted firm
Steps:
1. Determination of Beta
2. Return using CAPM
Rf + β ( R m - Rf )
3. Compute market price using dividend growth model
4. Assessing the price payable Step 3 X (estimated market price - discount)
5. Value of shares = Price per share X Number of shares
Fair value
It is ascertained under Berliner method
Berliner method = Average of net asset value & EPS capitalization
10. Chop-Shop approach/Break even value approach
 Identify firm's business segments.

 Calculate average capitalization ratios.
 Calculate theoretical market value based on each of average capitalization ratio.
 Average the theoretical values to determine Chop-shop value.
46
10. MERGERS & AQUSITION
1. Present EPS & PE Ratio
Acquirin Target
Particulars
g company
company
No of equity shares
EAT or PAT
EPS = EAT/No of equity shares
Current market price = EPS X
PE ratio
PE ratio = MPS/ EPS
Market value after Merger = Earning X
PE ratio
EAT - Earning after tax

EPS - Earnings per shares
MPS - Market price per share
2. Shares issued to targeted company
No of shares outstanding in targeted company X Exchange ratio or Swap ratio
3. Equivalent EPS of target company after Merger
= EPS of merged company/Swap ratio
4. Exchange ratio
Based on any one of the following factors
Methodology
Exchange ratio/Swap ratio = Relevant factor of target company/Relevant factor of acquiring compa ny
a) Earnings per share = EPS of Target firm / EPS of Acquiring firm

b) Book value per share = BV per share of Target Co., / BV per share of Acquiring Co.,
c) Market price per share = MPS of Target Co., / MPS of Acquiring Co.,
d) Fair value per share = FV per share of Target Co., / FV per share of Acquiring Co.,
e) any other basis
Book value per share = Total Equity shareholder's fund / Total number of Equity share
Return on Equity (ROE)= (Earnings for Equity shareholder / Total Equity shareholder fund) X 100
EPS = Book value per share X ROE
47
Compute Exchange ratio = EPS of two companies before merger in the following cases
a) Earnings available to shareholders will not be diminished by the merger
b) Acquiring company's pre merger and post merger EPS are to be same
c) Acquiring company wants to ensure the earnings to the members as before the merger takes place
d) Without dilution of EPS
In the above cases, EPS before merger = EPS after merger
5. Terminal cash flow
Cash flow X (1 + growth)/(ke - g)
6. Minimum & Maximum exchange ratio
Exchange ratio = [(Value + gain) of target company] X outstanding shares of acquiring company
[(Value + gain) of acquiring company] X outstanding shares in target company
Minimum exchange ratio = [(Value + gain) of target company] X outstanding shares of acquiring co mpany
[(Value) of acquiring company] X outstanding shares in target compa ny
Maximum exchange ratio = [(Value) of target company] X outstanding shares of acquiring company
[(Value) of acquiring company] X outstanding shares in target company
7. Impact of EPS under 2 alternatives
Particulars Alternative 1 Alternative 2
a) Perspective of shareholders of acquiring company

EPS after merger
(-) EPS of acquiring company before merger
Change in EPS
Effect for shareholders of acquiring company - No change or
increase/decrease
b) Perspective of shareholders of target company

EPS after merger
EPS originally held in target company
(EPS after merger X exchange ratio)
(-) EPS of target company before merger
Change in EPS
Effect for shareholders of target company - No change or
increase/decrease
48
8. Evaluation from acquiring company's perspective
From the point of view of acquiring company, the method under which preferred
lowest shares are issued to target company is
9. Capital budgeting decision
Ke = (D1 / P) + g
Ke - cost of capital, D1 - expected dividend, P - current market price (MPS), g = growth
P = D1/(Ke - g)
10. Weighted average PE multiple = Combined market capitalization/Combined earnings
Steps:
1. Compute NPV
2. IF NPV is positive, merge two companies. If it is negative, don’t merge.
11. Steps in case of cash deal
1. Synergy gain
2. Less true cost of acquisition
3. Net gain to acquiring company
True cost of acquisition = Consideration (-) Market value of target company
12. Steps in case of stock alternative
1. Synergy gain
2. Less true cost of acquisition
3. Net gain to acquiring company
True cost of acquisition = (Theoretical post merger price X shares issued) - Market value of target company
Theoretical post merger price = New EPS of merged entity
New EPS of merged entity = (Market value of Acquiring Co., + Market value of Target Co., + Synergy Gain)
Shares of Acquiring Company + Shares issued to Target Company
13. Free float capitalization
Total market capitalization of merged entity

Less: Promoter's holding
Free float market capitalization
49
14. Factors determining acquiring company to be financially stronger or better performing company
If a company has higher
 EPS
 PE ratio
 Return on Equity = Profit after tax/(Share capital + Reserves)
 Book value or intrinsic value = Net worth/No of shares
 Growth rate = Return on equity X Retention ratio
 Retention ratio = 100% - Dividend payout ratio
If all the above are higher, then the company is considered as financially stronger.
Financially stronger companies considered as acquiring company
15. Price offered for cash offer
Price offered for cash offer < price determined under share offer
Cash offer - Less risk
Share offer - More risk
50
11. PORTFOLIO MANAGEMENT
1. Return
Methods to compute Return
i) Arithmetic mean
(R1 + R2 + R3 +…..RN) / N
R1= Return in Year 1, N =No of years
ii) Holding Period Return (HPR)
(1+R1) X (1+R2) X …….X (1+ RN)
iii) Annual Simple Return (ASR)
HPR/N
iv) Compounded Annual Rate of Growth (CARG)
IRR (Most accurate representation of return)
Return from Listed securities
R = { (P1 - P0 ) + D1 } / P0
R - Return from Investment during the period

P1 - Market price at the end of the period
P0 - Market price at the beginning of the period
D1 – Dividend
Note: Capital appreciation = P1 - P0

If period is less than 1 year, annualize the result
Expected return
Weighted average return with probability being assigned weights = ∑ P X R
P - Probability, R – Return
Note: Other things remaining the same, Securities with higher return should be preferred.
51
2. Risk
2
Standard deviation = √∑ Pd
Ṝ - Arithmetic Mean
d = R-Ṝ
σ2=Variance
σ=Std
deviation
P=Probability
Note: Other things remaining the same, Securities with lower risk should be preferred.
Probability distribution of possible outcome is;
Symmetrical - Std deviation is an acceptable measure
Not Symmetrical - Std deviation is not an acceptable measure
Risk includes both positive & negative deviation from anticipated levels
Deviation - Positive - Upside Risk Deviation - Negative - Downside Risk

Actual Return > Expected Return Actual Return < Expected Return
3. Diversification (Defensive strategy)
i) Investing in more than one security; one line of business

ii) Only reduces risk & not enhance returns
4. Dominance
Rules:
i. If return of two security are different but their risk (Standard deviation) are same
Decision: Security with higher return is preferred
ii. If return of two security are same but their risk (Standard deviation) are different
Decision: Security with lower risk is preferred
iii. If risk and return of two security are different
Decision: Security with lower Co-efficient of variation is preferred
A dominates B: A= Dominating / Efficient stock , B = Dominated / Inefficient stock
All dominates stocks will be rejected & only the efficient stocks will form part of the Portfolio
Efficiency frontier
52
If the efficient stocks are plotted on a graph with Return on Y axis and Risk on X axis are joined by a line,
the resultant line is called Efficiency Frontier.
This helps to decide whether a new stock can be selected or rejected
Above the frontier Below the frontier On the frontier

Stock dominates some Stock is dominated by Stock is an efficient
security on previously some security - Reject stock - Select the
drawn frontier – Frontier the stock new stock
will have to be redrawn
Co-efficient of Variance (%)
CV = σ/R X 100
o - Std deviation
R - Mean of return
Stock with lower CV will be selected
5. Alpha
i) indicator of the extent to which the actual return of a stock deviates from those predicted by its beta value
ii) A share's alpha value is a measure of its abnormal return & represents the % by which the share's
returns are currently above or below the required return given its systematic risk
Alpha = Return mandated by CAPM - Actual return earned

i.e simple average of (Return by CAPM - Actual return)
If CAPM holds good, then Alpha = Zero

Alpha of a well diversified portfolio = Zero
Alpha Valuation Action

Positive Under Buy
Zero Correct Hold
Negative Over Sell
Current Return = Expected CAPM return + Alpha value
6. Non Diversifiable Risk
- Diversification helps in reducing specific risk
- Portfolio risk per se, in which behavior of returns of two or more securities bears a dominant factor,
cannot be diversified away
Total Risk
Diversifiable Risk Non-Diversifiable Risk
Unsystematic risk = Total Risk - Systematic Risk Systematic Risk = β X σm
53
Systematic Risk = σj/σm
X Cor.jm
σj, σm - Risk element in stock
(σj) Risk element in stock
market (σm)
Cor. Jm - Correlation between stock & market
Capital Market Line
Common Sense
approach Graphical approach
[Rf +(σj/σm) X (Rm-Rf)] (Ep - Rf)/σp
λ = (Rm - Rf)/σm
λ - Market price of risk
Rm - Return from market
Rf - Risk free ROR
σm - Standard deviation of Market
Attitude of market to Risk-Return trade-off = Rf + (λ X σj)
7. Beta
Natur
β e Investor Risk Speed Preference
>1 High Aggressive Higher Faster Rising market
Same
=1 Unity Copy cat Same pace Sideway market
<1 Low Conservative Lower Slower Falling market
i) To calculate Beta of single security
β= ∑ xy - n Ẍ Ÿ
2 2
∑y - nŸ
X - Return from stock

Y - Return from market
Ẍ - Arithmetic mean of ROR of stock
Ÿ - Arithmetic mean of ROR of market
n- no of observations
Observation Y x xy y2
ii)
β= Covariance jm/Variance m
2
= Cov jm /σ m
54
= ∑ dxdy
2
σ y
2
Observation Y x Deviation dy Variance d dy Cov. (dxdy)
y
2
Total σy Cov.xy
β= Covariance between stock & market

Variance of market
iii)
β= σj/σm X Correlation
jm
σj - S.D of stock
σm - S.D of market
Correlation jm - Correlation between returns from stock & market
Correlation co-effcient (Cor jm) = Cov jm/(σj X

σm)
2 2
Observation y x dy dx dy dx dxdy
Total
2
σy = √∑dy
2
σx = √∑dx
Correlation = ∑dxdy
σx X σ y
x- Stock, y – Market
Beta of a Portfolio
i) compute value weights
ii) compute weighted Beta
Security Weighted Investment Beta Weight X Beta
Slope (Beta) Indicate

>1 Change in risk premium > Rate of change in market
<1 Change in risk premium < Rate of change in market
=1 Change in risk premium = Rate of change in market
55
8. Capital Asset Pricing Model
Rj = Rf + β (Rm-Rf) Rj
= Expected return
Revised expected return = Expected return (Rj) + [ β X Increase or decrease in risk premium]
Risk premium = β X Market risk premium
Security Market Line

If Beta is higher, risk premium to market will be high.
SML shows how expected ROR depends on Beta
Risk free rate

In CAPM, there is only one risk free rate
If there are two rates in the problem,
Aggressive approach Consider higher rate
Conservative approach Consider lower rate
Moderate approach Consider simple average of higher & lower rates
Undervalued & Overvalued stocks
Price relationship Return relationship Valuation Action

AMP < FMP CAPM < Expected return Under Buy
AMP = FMP CAPM = Expected return Correct Hold
AMP > FMP CAPM > Expected return Over Sell
AMP - Actual Market Price, FMP - Fair Market Price
9. Portfolio
i) Return of Portfolio ( Weighted average return of the security)
First principle
i) convert securities into portfolio with help of
investment weight & arrive the return
R = ∑(W X R)
ii) Now portfolio resembles single stock,
compute return = ∑(P X R)
R = Return
RA X W + RB X W and Probability
No RA RB so on P PXR
56
Formula based
i) compute the expected return by taking into account
the probability of occurrence
R=∑(W X R)
ii) compute return of portfolio = ∑(W X R)
Weight Return
No Security W R WXR
ii) Risk of portfolio
Risk can be measured using two statistical tools

i) covariance
ii) coefficient of correlation
i) Covariance
Measurement of co-movement between 2 variables
Covariance Return of 2 securities/assets

Positive value Tend to go together
Negative value Tend to offset each other
Zero value No distant relationship between movements in returns
Covariance=∑Pdxdy
Security Probability P Return X Return Y dx= X-Ẍ Dy= Y-Ÿ
ii) Correlation coefficient
Measure of closeness of relationship between two random variables

Ranges between -1 & +1
Correlation coefficient Relationship

0 Returns are unrelated
-1 Perfect negative correlation
+1 Perfect positive correlation
Correlation coefficient= Covariance xy/(σx Xσy)
57
Measuring risk in portfolio of 2 securities
Two methods
i) First principle
First principle
i) compute return of each outcome using
∑(W X R)
ii) Compute portfolio return
2
iii) compute S.D = √∑Pd
R = Return
R A X W + RB X
2
No RA RB W and so on Probability P PXR Deviation d Pd
ii) Formula based
i) consider S.D of each security

ii) proportion/weight of investment in each security
iii) covariance of pair of securities
σ= √[σx2 X Wx2]+[σy2 X Wy2]+ [2 X σx X σy X Wx XWy X Covariance of

XY]
Risk reduction
Actual risk of portfolio is less than the weighted average risk of securities that constitute the portfolio
Relationship between correlation & risk reduction
Value of Nature of
correlation correlation Movement of return Risk reduction
+1 Perfect positive same direction Not possible
-1 Perfect negative opposite direction Can be reduced to zero
same direction but not
0 to +1 Positive in same proportion Possible but not to zero
opposite direction but
0 to -1 Negative not in same proportion Possible but not to zero
Determination of portfolio in which risk is lowest
2
W x= o y - Covariance of XY
2 2
σx +σy - 2 Covariance of XY
with the given correlation, compute covariance of XY =
σX X σy X Correlation of XY
58
W y = 100% - W x
Risk in portfolio of N securities
2 2 2 2
(a+b+c) = a + b +c + 2ab+ 2bc+2ca
2
S. D = √(a+b+c)
2
a = (W X σa
2
)2
b = (W X σb
2
)2
c = (W X σc
2
)
2ab = 2 X Wσa x Wσb X Correlation of
ab 2bc = 2 X Wσb x Wσc X Correlation of
bc 2ca = 2 X Wσc x Wσa X Correlation of
ca
10. Factor model
Arbitrage pricing theory model
Steps:
i) Identify the macro economic factors
i.e inflation, GNP etc
ii) Assess risk premium for taking on factor risk
iii) re adjust the risk premium to fall in line with sensitivity of selected firm to each of these factors
Rj = Rf + β1 ( Rm-Interest - Rf) +β2 ( Rm-Inflation - Rf)+β3 ( Rm-GNP - Rf)
Sensitivity factor (Beta)
Stock Forex Interest GNP

A
B
Total
Beta = Weighted Beta = Weighted Beta = Weighted Beta = Weighted

average of total average of total average of total average of total
Market Model
i) Rj = CAPM + Alpha
Rj = [Rf + β(Rm-Rf)] + α
59
ii) Situations
If risk adjusted Alpha value is greater than zero or Alpha value is greater than Rf then,
Risk premium =
Rj-Rf= α - (Rf X (1-β)) + (β X (Rm-Rf)
If(Rf X (1-β) = α, then risk premium as per CAPM = Risk premium as per market
model
Computation of component of non-diversifiable risk of shares
Steps:
i) Expected return of the company
Rj = Rf + λ (σ AB X
PAB,m)
λ = Market attitude to risk and risk - return trade off

o AB = Standard deviation of returns of company AB limited
PAB,m = Degree of correlation between AB limited & Market
Rf = Risk free rate
ii) Excess return over risk free rate = Rj-Rf
iii) Risk premium = σAB X PAB,m
iv) Return for non-diversifiable risk= Step ii) - iii)
Expected return
CML Priniple
[Rf +(σj/σm) X (Rm-Rf)]
SML equation
[Rf +(σj/σm) X (Rm-Rf) X Correlation of jm]
11. Beta of the firm
Unlevered & Levered
Unlevered - Only equity
i) Singe project
60
βL = βA = βO
ii) Many project

βL = βA = βO
βA = β of Weighted average assets
Project Weight CAPM return Weight X Return

A
B
C
Total XX = βA
Levered firm - Both equity & debt
i) single project
βO = β of weighted average liability
βWL = βd ( D/V) + βe (E/V)
V (Value of firm) = D (Debt) + E (Equity)
D = after tax debt if tax rate is given
ii) many project

βO = βWA = βWL
βWA = β of weighted average of assets
βWL = β of weighted average of liabilities
Proxy Beta
i) Compute Beta of Un levered company from Beta of 1st levered company

ii) compute Beta of 2nd levered company from Beta of unlevered company
βu = βg X E/(E+D(1-t))
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12. Derivatives
Derivative contract
It is a financial instrument whose payoff structure is derived from the value of the underlying
asset
Forward contract
It is an agreement entered today under which one party agrees to buy and the other party agrees to sell
a specified assest on a specified future date at an agreed price
Futures contract
It is a standardised contract between two parties where one of the parties commits to buy and the other
commits to sell, a specified quantity of a specified asset at an agreed price on a given date in the future
Options contract
An option is a contract between two parties under which the buyer of the option buys the right, and not
the obligation, to buy or sell a standardised quantity (contract size) of a financial instrument (underlying
asset) at or before a pre-determined date (expiry date) at a price decided in advance (exercise price or
strike price)
Derivative instruments
Particulars Forward Futures Option

Standardization No Yes Yes
Price Negotiation Between buyer Market determined Option price Is market
& seller determined. Strike price is
exchange determined
Liquidity No Yes Yes
Contract closure By delivery By delivery or by paying the By delivery or by paying the
price differential or by taking price differential or by taking
an offsetting position an offsetting position
Margins None Yes Yes
Guarantor None Clearing house Clearing house
Obligation to perform Both parties Both parties Writer
Option writer collects premium
Profit settlement End of contract Daily on T +1
1. Options
A) Parties
Holder Writer
Buyer Seller
One who buys the right One who grants the right
Right to buy & sell Obligation to buy & sell
B) Types
Call option Put option
62
Right to sell by the buyer Right to buy by the buyer
Obligation to buy by the writer Obligation to sell by the writer
American option European option
Exercised on any date on or before the expiry date Exercised only on the expiry date
Party Increase in price Decrease in price

Call holder Favourable Adverse
Call writer Adverse Favourable
Put holder Adverse Favourable
Put writer Favourable Adverse
Option Right to EP < MP EP > MP

Call Buy Exercise Lapse
Put Sell Lapse Exercise
C) In-At-Out Money relationship
Relationship Call option Put option

EP < MP Exercise - In the money Lapse - Out the money
EP = MP Indifference - At the money Indifference - At the money
EP > MP Lapse - Out the money Exercise - In the money
EP - Exercise Price, MP - Market Price
D) Kinds of Market
Relationship Nature of market Suitable option

Expected MP > EP Bullish Call
Expected MP = EP Neutral -
Expected MP < EP Bearish Put
E) Intrinsic value
Option Relationship Intrinsic value(IV)

Call MP > EP IV = MP - EP
Put MP < EP IV = EP - MP
IV arise only in case of "in the money"
IV for cases having OTM & ATM = Zero
F) Time Value
Time value = Option premium - Intrinsic value
Option premium< Intrinsic value, Time value = 0
G) Pay-off table
63
Steps:
1. Projected Market price or expected Market price
2. Exercise price
3. Action - exercise or indifference or lapse (Compare step 1 & 2)
4. Status in/at/out of the money
5. GPO - Gross Pay Off
GPO = Difference between Market price & Exercise price only in case of ITM
GPO for cases having OTM & ATM = Zero
6. Option premium
7. Net Pay Off (NPO) = GPO + Option premium
8. Draw Pay Off graphs based on the NPO values
Relationship Buyer Writer

GPO Positive Negative
Option Premium Negative Positive
Note: Amount of GPO & Premium will be same for buyer & writer but sign differs
GPO
Call Option, GPO = MP – EP
Put Option, GPO = EP- MP
Party Gains Loss

Call Buyer Unlimited Limited
Put Buyer Limited Limited
Call writer Limited Unlimited
Put writer Limited Limited
Status Value of Call Value of Put

EP > MP Zero E - S1
EP = MP Zero Zero
EP < MP S1 – E Zero
H) Breakeven price
BEP = Market price at which option parties makes no profit or loss

Call Option - BEP = Exercise price + Option Premium
Put Option - BEP = Exercise price - Option Premium
Call Put
Buyer MP - EP - P = 0 EP - MP - P = 0
Seller EP - MP + P = 0 MP - EP + P = 0
64
I) Value of option contract on expiry
Call option (C1) = Max (0, S1 - E)

Put option (P1) = Max (0, E - S1)
C1 - Value of call on expiry

P1 - Value of put on expiry
E - Exercise price
S1 - Spot price on expiry date
J) Value of option before expiration
Call option - Under valued - Buy in derivative market & sell in spot market
Put option - Over valued - Sell in derivative market
Under valued - If Premium < intrinsic value
Over valued - If Premium > intrinsic value (No time value of money)
2. Strategies of option
Note: Write the exercise price in ascending order, if it is not given in that order
Spread
Option Exercise price low Exercise price high

Call Higher premium Lower premium
Put Lower premium Higher premium
A) Bull Spread
Buying at E1 & Selling at E2
Call Option Put option

Relationship E1 E2 E1 E2
S1 < E1 Lapse = zero Lapse = zero Exercise = (-)(S1-E1) Exercise = (S1-E2)
E1 < S1 < E2 Exercise = (S1-E1) Lapse = zero Lapse = zero Exercise = (S1-E2)
S1 > E2 Exercise = (S1-E1) Exercise = (-)(S1-E2) Lapse = zero Lapse = zero
B) Bear Spread
Selling at E1 & Buying at E2

Relationship E1 E2 E1 E2
S1 < E1 Lapse = zero Lapse = zero Exercise = (S1-E1) Exercise = (-)(S1-E2)
E1 < S1 < E2 Exercise = (-) (S1-E1) Lapse = zero Lapse = zero Exercise = (-)(S1-E2)
S1 > E2 Exercise = (-) (S1-E1) Exercise = (S1-E2) Lapse = zero Lapse = zero
65
Spread E1 E2 Option Initial
Bull Buy Sell Call Cost or debit
Bull Buy Sell Put Credit
Bear Sell Buy Call Credit
Bear Sell Buy Put Debit or cost
C) Butterfly Spread

Relationship E1 E2 E3 E1 E2 E3
Lapse = Lapse = Lapse = Exercise = Exercise = Exercise = (-)
S1 < E1 zero zero zero (-) (S1-E1) (S1-E2) (S1-E3)
Exercise = Lapse = Lapse = Lapse = Exercise = Exercise = (-)
E1 < S1 < E2 (S1-E1) zero zero zero (S1-E2) (S1-E3)
Exercise = Exercise = Lapse = Lapse = Lapse = Exercise = (-)
E2 < S1 < E3 (S1-E1) (-)(S1-E2) zero zero zero (S1-E3)
Exercise = Exercise = Exercise Lapse = Lapse =
S1 > E3 (S1-E1) (-)(S1-E2) = (S1-E3) zero zero Lapse = zero
Premium of E2 = Premium E1 & E3
D) Straddle
It involves simultaneous purchase or sale of options with same strike price & same expiry date
Straddle Call Put

Long Buy Buy
Short Write Write
Same number, same Exercise price, same expiry date
E) Strips & Straps
When an investor expects huge change in price, he might either set up strip or strap depending
on whether a price fall is more imminent or a price rise
Put is more profitable when price decrease occurs

Call is more profitable when price increase occurs
Call Put
Strip Buy Buy 2
Strap Buy 2 Buy
Same exercise price, same expiry date
F) Strangle
It involves simultaneous purchase or sale of options with same expiry date but with different exercise
price
66
Strangle E1 E2
Long Buy Put Buy Call
Short Write Put Write Call
G) Box Spread
Simulataneous opening of bull spread & bear spread on same underlying asset
Limited profit can be earned if stock moves in either direction
H) Condors
Involves four call options or four put options

Long condor - Buying Calls or Buying Puts
Short condor - Writing Calls or writing Puts
Exercise price are selected in such a way to satisfy both the following 2 equations
E2 - E1 = E4-E3
E3-E1 = 2 X (E2-E1)
Condor Options
Long Call Buy Call at E1 & E 4 Write Call at E2 & E3
Long Put Buy Put at E1 & E 4 Write Put at E2 & E3
Short Call Write Call at E1 & E4 Buy Call at E2 & E3
Short Put Write Put at E1 & E4 Buy Put at E2 & E3
Condor Limited profits Limited loss

Long Middle zone Lower & Upper zone
Short Lower & Upper zone Middle zone
I) Caps, Floor & Collar
Caps - Setting the upper limit by strike price of call purchased

Floor - Setting the lower limit by strike price of put sold
Collar - Combination of Caps & Floor
3. Setting up Put
a) when puts are traded, Quote the price

P = C + PVEP - S
-rt
Present Value of Exercise Price(PVEP) = EP X e
b) when puts are not traded;
i) Want to buy - Buy a call & sell a share
Investment @ PVEP
ii) Want to sell - Write a call & buy a share
Sell Investment @ PVEP
67
4. Valuation of option
I. Portfolio Replicating Model
a. Stock Equivalent Approach
i) computation of Call option premium
Only ITM
Steps:
i) Compute intrinsic value of Judgement Prices (JP) on expiry date
ii) No of calls bought = Difference in Stock price (JP)/Difference in Intrinsic values of JP
-rt
iii) Present Value of Exercise Price(PVEP) = EP X e
iv) Call option premium (Co) = CMP (So) - PVEP
So = (Co X no of calls) + PVEP
Only OTM
Steps:
No one is willing to buy this call
Hence Option premium = Zero
Both ITM & OTM

Steps:
ii) No of calls bought = Difference in Stock price (JP)/Difference in Intrinsic values of JP
-rt
iii) Present Value of lowest stock price/Judgement Price = Lowest Judgement Price (LJP) X e
iv) Call option premium (Co) = So - PVLJP
So = (Co X no of calls) + PVLJP
ii) computation of Put option premium

Put call parity therory is used to compute put option premium
So + P = Co + PVEP
Note: Same for Stock Equivalent & Option Equivalent approach
b. Option Equivalent Approach
i) computation of Call option premium
Only ITM
ii) No of shares bought = Difference in Intrinsic values/Difference in Stock price/JP
iii) Amount of borrowing = PV[(No of shares bought X LJP) (-) Intrinsic value of J1 price]
-rt
[(No of shares bought X LJP) (-) IV at J1] X e
iv) Co = (No of shares bought X So) (-) amount of borrowing
68
Both ITM & OTM
Same procedures as "Only ITM"
Only OTM
No Option premium
II. Risk Neutral Model
Applicable only to Call option premium
To compute put option premium, use put call parity theory
Steps:
i) Compute intrinsic value of JPs
ii) Compute the % of change - by comparing JP & Current Market Price (CMP)
iii) Compute probability
assume upside probability = P
assume downside probability = 1-P
Upside - Increase in % of change
Downside - Decrease in % of change
iv) Solve the equation
(Downside % of change X P) + (Upside % of change X (1-P)) by equating it to the risk free return
v) Substitute the value of P in step iv equation to get expected value of Intrinsic value on expiry da te
-rt
vi) Fair call = Present Value of Expected IV (Step v value X e )
III. Binominal Model
American Call & Put European Call & Put

i) Draw the sketch of possible movement in i) Draw the sketch of possible movement in stock
stock price price
ii) Compare EP & MP and identify the status ii) Compare EP & MP and identify the status and
and action action
iii) Compare IV iii) Compare IV
iv) Consider higher of Expected Value at Later iv) From Right to Left in the sketch - compute the
exercise and Value at Immediate exercise probability of IV & get the final expected MP
IV. Black Scholes Model
Co = [So X N (d1)] (-) [PVEP X N(d2)]

2
d1 = [NL X (So/EP) + [r + 0.5 X σ ] X t ]
o √t
2
d2 = [NL X (So/EP) + [r - 0.5 X σ ] X t ]
o √t
69
NL = Natural Log
N(d1) & N(d2) = Z values of d1 & d2 i.e by adding 0.5 to NL values
If dividend is paid, consider only adjusted So.
Adjusted So = So - PV of dividend paid
5. Futures
Long position Buys or holds an asset

Short position Sells an asset
Continuous compounding
rt
A=PXe
Continuous discounting
-rt
A=PXe
Equivalent rates
r1/m
Normal to continuous - r2 = m(e -1)
r1/m
Continuous to normal - r2 = m(e -1)
r1/m
= r2/m = e -1
r1/m
= r2/m + 1 = e
= log(r2/m+1)
e
= r1/m log e
r1 = m log (r2/m+1)
Y = Ln X, then X = ey
r1 - normal rate, r2 - continuous compounding rate, m - frequency of compounding, e -

exponential value (+X)
Ln = Natural logarithm
Borrow or Forward/
Relationship Valuation Invest Futures Spot Market
Actual Future price < Fair Future price Under valued Invest Buy Sell
Actual Future price > Fair Future price Over valued Borrow Sell Buy
n
[Future price/(1+ risk free rate)] = Spot price + PV of storage
cost - PV of convenience yield
Fair Future Price (FFP)
i) Security generating no income - No dividend

rt
FFP = So X e
ii) Dividend paid

Adjusted So = So - PV of dividend paid
70
rt
FFP = Adjusted So X e
iii) Yield - Ratios to dividend in companies & stock price

(r-y) X t
FFP = So X e
r - Rate of return, y = Yield
iv) Involve storage costs (Carry type)

rt
Whereas Adjusted So = So + PV of storage costs
v) Involve storage costs (Non Carry type)

(r-c) X t
Whereas Adjusted So = So + PV of storage costs
vi) Storage costs expressed as % of FFP

(r-y) X t
FFP = So X e
6. Hedging with Futures
a) Hedging ratio
Hedging ratio (Beta) = (σ Market /σ futures ) X Correlation
Price Impact on price increase/decrease

Spot Future increase/decrease
Spot Future
Increase Gain Loss
Long (Buy) Short (Sell)
Decrease Loss Gain
Increase Loss Gain
Short (Sell) Long (Buy)
Decrease Gain Loss
b) Cross Hedging
Steps:
i) price of Future contract
So X e(r-y) X t
ii) computation of no of contracts entered into

no units per Future contract = Future contract price - Index price
Value of Future contract = No of units X Future contract price
No of contracts to be entered = (Portfolio value X Beta of Portfolio)/Value of Future contracts
iii) computation of gain on short Future position

Contract Future price
Less index position
Gain per unit of index
No of units per contract
71
Gain per contract = Gain per unit of index X No of units per contract
Total Gain = No of contracts X Gain per contract
c) Hedging with index future
Index value or Future value = Portfolio amount X Hedge ratio or Beta ratio
Action in stock
Trend market Position in index market
Rise Buy/long Sell/short
Fall Sell/short Buy/long
d) Stock Hedging
i) No of future contract to be bought or sold

( β X No of units of spot position requiring hedging) /No of units underlying in Future contracts
ii) Increase or fall in index due to increase or decrease in share price
(Amount fallen or Amount increased )/β
Portfolio (Beta) - Increase in risk Portfolio (Beta) - Decrease in risk

A) Buy stock B) Buy Futures C ) Sell stock D) Sell Futures
Sell Risk free investment Keep portfolio intact Buy risk free investment Keep portfolio intact
Combination of A & C - Case I

Combination of B & D - Case II
Combination of A & C - Case I Steps

i) compute weights = (Price X Qty)/total value of stocks
ii) compute weighted Beta
iii) Assume
Weight of stock in new portfolio = W 1
Weight of risk free investment = 1-W 1
Weighted Beta of new portfolio = [ W 1 X (Step ii)] + [ (1-W 1) X 0] = Portfolio (Beta) given
iv) solve the above equation and get the values of W 1 & 1 - W 1
v) compute value of portfolio to be sold using
(1-W 1) values X No of index sold X weights (step i)
Combination of B & D - Case II Steps

No of index contract to be sold or bought
= [Portfolio value X (Old Beta - Desired Beta)]/Value of Future contract
72
7. Arbitrage
Option type Status Action on Option Action on stock

Call Under valued Buy Sell
Call Over valued Sell Buy
Put Under valued Buy Buy
Put Over valued Sell Sell
a) Call option
Theoretical minimum price = Current stock price (So) - Present value of exercise price (PVEP)
Cashflows to make profit for the arbitrager

i) sell stock at spot price - So
ii) Less buy call option (given)
iii) Invest the remaining proceeds of stock in risk free investment
rt
iv) Receive the maturity value of investment (Investment X e )
v) Less buy stock at exercise price
vi) net gain made (iv-v)
Theoretical minimum call price < price of call Call is under priced
Theoretical minimum call price > price of call Call is over priced
b) Put option
Cashflows to make profit for the arbitrager
i) Borrowed amount - (So + value of put option)

ii) Less buy put option (given)
iii) Buy stock at spot price So

iv) Exercise the put option
rt
v) Less repay the amount of borrowing (Borrowed amount X e )
vi) net gain made (iv-v)
Value of put option > Theoretical minimum price Put is under priced
Value of put option < Theoretical minimum price Put is over priced
73
13. Forex Derivatives
1. Forex Futures
Relationship Arbitrage Action

Forward Bid rate > Future rate No Buy at higher price & sell at lower price
Forward Ask rate > Future rate Yes Selling at a price higher than purchase price
Gain = No of contracts X (Forward Ask rate - Future
rate)
2. Forex Options
Cost of buying a call = Forward rate + Option premium + PV of Option premium
3. Forward Interest Rate
i) Zero rate (Implied interest rate at time 0)
1. Capital gain = Redemption price - Current Market price

2. Annual Interest = Capital gain X Interest rate
3. Total Interest = Annual Interest X Period (No of years)
4. Total Income to the bondholders = Capital gain + Total Interest
5. Income per annum = Total Income/ Period of bond
6. Implied Interest rate = Income per annnum/Current Market price
ii) Forward rate
For Year 1 = Implied Interest rate of Year 1

For Year 2 = [(R2 X T2) - (R1 X T1) ]/(T2-T1)
R1, R2 - Implied interest rate of Year 1 & Year 2
T1, T2 - Time period of Year 1 & Year 2
Continuous compounding rate = [(Rn X Tn) - (Rn-1 X Tn-1) ]/(Tn-Tn-1)
4. Interest Rate Futures
Term Means Interest

Buying Investing Receive
Selling Borrowing Pay
Interest rate expectation Asset Liability

Down Buy Sell
Up Sell Buy
74
5. Hedging with Interest Rate Futures
Expectation on Interest rate To go up To come down

Action Sell first, close out by buying Buy first, close out by selling
Effect, if interest rate rises Gain from futures Lose in futures
Effect, if interest rate falls Lose in futures Gain from futures
6. Interest Rate Swap
Situation Movement from Movement to

Strong Weak
∆ Fixed rate > ∆ Floating rate Fixed Floating
∆ Floating rate > ∆ Fixed rate Floating Fixed
From Fixed to Floating

Steps:
i) compute ∆ fixed rate
ii) compute ∆ floating rate
iii) compute net difference = i) - ii)
iv) Split the difference/gain between the strong & weak companies in an agreed ratio
v) perform sequence of operations
Strong company Weak company

a) Pay bank the contracted fixed rate e) pay bank the contracted floating rate
b) Receive from counterparty (a + share of gain) f) Receive from strong company (c)
c) Pay counterparty the floating rate which the strong
company is entitled to in the market g) Pay the strong company (b)
d) a + b + c h) e + f + g
From Floating to Fixed

Steps:
i) compute ∆ fixed rate
ii) compute ∆ floating rate
iii) compute net difference = i) - ii)
iv) Split the difference/gain between the strong & weak companies in an agreed ratio
v) perform sequence of operations
Strong company Weak company

a) Pay bank the contracted floating rate e) pay bank the contracted fixed rate
b) Receive from counterparty (a + share of gain) f) Receive from strong company (c)
c) Pay counterparty the fixed rate which the strong
company is entitled to in the market g) Pay the strong company (b)
d) a + b + c h) e + f + g
75
7. Interest Swap Vs Currency Swap
Interest Swap Currency Swap

Payment streams that are exchanged are Payment streams that are exchanged are
denominated in one single, common currency denominated in two different currencies
8. Interest Rate Options – Collar
Action Meaning
Buying a cap Buying a put
Buying a floor Buying a call
Collar for Buy Sell Buy/Sell

Investment Cap Floor Buy at Put; Sell at Call
Borrowing Floor Cap Buy at Call; Sell at Put
9. Money Market Hedging
Steps:
i) Identify foreign current asset or liability
ii) Settle - Encash the asset & settle the liability i.e. Realise and repay
iii) Invest the money borrowed
Investment = Step 1/Interest rate for the given period
iv) Convert the money borrowed into foreign currency
Step iii) X Ask Spot rate
v) Repay the loan = Step iv)+ Interest amount
76
14. International Finance - Basics
1. Direct & Indirect Quote
Nature of quotation Expression Price 1st currency Product 2nd currency

Direct quote HC per unit of FC HC FC
Indirect quote FC per unit of HC FC HC
Direct quote = 1/Indirect quote
American Terms - Direct quote in America

European terms - Indirect quote in America
Generally all currencies are expressed only in American terms except currencies like Pound, Euro,
New Zealand dollars, South African Rand, AUD dollars
2. Bid, Ask, Spread & Middle Rate
Bid - Banks buying rate

Ask - Banks selling rate
Spread = Ask – Bid
Middle rate = (Ask + Bid)/2
Spread
Narrow Wide
Exchange rate Stable Volatile
Market depth (volume of transactions in the market) Deep Shallow
Banks
Buy Sell
Bid Pdt Price
Ask Price Pdt
Bid comes 1st & Ask comes next

Bid never be greater than Ask
3. Cross Rate
Bid (A/B) = Bid (A/C) X Bid (C/B)

Ask (A/B) = Ask (A/C) X Ask (C/B)
Bid(A/B) = 1/(Ask(B/A))
Ask(A/B) = 1/(Bid(B/A))
Numerator – Price; Denominator – Product
77
4. Forward Rate
Relationship Price (HC) Product (FC)

Fwd rate > Spot rate Depreciate Appreciate
Fwd rate < Spot rate Appreciate Depreciate
Product = (F-S)/S X 100 X 12/m

Price = (S-F)/F X 100 X 12/m
If result is positive - Appreciating

If result is negative - Depreciating
n Xm
Forward rate = Spot Rate X (1+r/m)
r - Rate of interest p.a, m- no of compounding in a year, n - no of years
Forward rate = Spot rate X [(1+ home currency rate)/(1+foreign currency rate)]
Forward discount = (Fwd rate - Spot rate)/Spot rate X 100 X 12 months/Fwd period
Appreciate - Trading at Premium

Depreciate - Trading at Discount
Exchange rate on maturity xxx

Less: Purchase price xxx
Less: Premium xxx
Less: Interest cost xxx
Gain/Loss XXX
5. Swap Points
Forward Spot
Bid p R p-r = Swap bid
Ask q T q-t = Swap ask
q-p t-r
Fwd spread Spot spread
If swap points are in ascending order, Add

If swap points are in descending order, Deduct
i) Ask > Bid
Swap Ask > Swap Bid - Add Swap points

Swap Ask < Swap Bid - Deduct Swap points
i) Ask > Bid
ii) Fwd spread > Spot spread
78
Net Exposure of each foreign currency in Rs
Foreign currency Inflow Outflow Net Inflow Spread Net Exposure

1 2 3 4=2-3 5 = Fwd rate - spot rate 6= 4 X 5
If net inflow & spread are negative, then net exposure will be positive.
6. Interest Rate Parity Theory (IRPT)
(1 + Rh)/(1+ Rf) = F1/eo

F1 = Fwd rate, eo = Spot rate, Rh - Home country interest rate, Rf - Foreign country interest rate
How IRPT works

Steps:
i) Maturity value in the currency of first country
a) Invest the amount at given interest rate
b) Compute maturity value = Amount invested + Interest earned
ii) Maturity value in the currency of second country
a) Buy the currency of second country by applying spot rate
b) Invest the proceeds of step ii) a) at given interest rate
c) compute maturity value = Step ii(a) + Interest earned
iii) Convert the maturity value of Step ii (c) into the currency of first country by using I year forward rate
Step iii) = Step (i) b
7. Arbitrage
Fwd rate reflects IRPT

If Fwd rate did not reflect IRPT, arbitrage opportunities arise.
TYPES OF ARBITRAGE
a) Space
Price of the currency being different in 2 different banks
Bilateral currencies
i) express as currency A per unit of Currency B
ii) Buy from banks having lower ask rate
iii) Sell to banks having higher bid rate
iv) difference may be profit/loss ( between ii) - iii))
b) Time
Prices in 2 markets, spot & forward whether in same bank or in different banks
Interest rate = Borrowing rate
Bid rate = Ask rate
79
Relationship Arbitrage Money flow
from to
AFR > TFR Yes FC HC
AFR = TFR No
AFR < TFR Yes HC FC
Theoritical Home Risk Free Rate method

i) compute Theoritical Home Rate (THR) using IRPT
ii) compare Actual Home Rate (AHR) with THR
iii) identify the flow of arbitrage using the following table

from to
AHR > THR Yes FC HC
AHR = THR No
AHR < THR Yes HC FC
Theoritical Rh=
(1 + Rh)/(1+ Rf) = F1/eo
PROOF FOR EXISTENCE OF ARBITRAGE

i) Borrow money in the country from where money is identified to flow out
ii) Convert at spot rate
iii) Invest in the other currency
iv) Take forward cover
v) Realise the investment along with interest thereon
vi) Re-convert at forward rate
vii) Repay the borrowing along with interest thereon
viii) compute arbitrage gain or loss - Step vi) - Step vii)
8. Purchasing Power Parity Theory
PPPT lays down link between exchange rate and inflation rates
High inflation in one country will be set off by depreciation of currency of that country
Law of one price - Price of a commodity shall be same in two markets, else arbitrage opportunity arise.
If PPPT does not hold, then enter arbitrage
Steps in arbitrage
i) compute theoritical home rate using PPPT
ii) compare actual home rate & Theoritical(fair) home rate
iii) identify the flow of arbitrage using the following table
80
from To
Actual Ih > Fair Ih yes FC HC
Actual Ih = Fair Ih No
Actual Ih < Fair Ih yes HC FC
(1+ Ih)/(1+ If) = F1/Eo

Ih - Inflation in home country
If - Inflation in foreign country
F1 - Forward rate of foreign currency
E0 or So - Spot rate of foreign currency
% change = [(Ih-If)/(1+If)] X 100

% change is positive - Depreciation
% change is negative - appreciation
9. International Fischer Effect
Reinforces IRPT & PPPT by highlighting the inflation element in nominal interest rate
Changes in anticipated inflation produce corresponding changes in rate of interest
(1+ Money rate) = ( 1+ Real rate)X (1 + Inflation rate)
Exchange position/Currency position
Particulars Purchase Sales

Opening position over bought XX -
Purchased a bill XX -
Forward sale TT - XX
Forward purchase contract cancelled - XX
Remitted by TT - XX
Draft cancelled XX -
XXX XXX
Closing balance over sold XXX
XXX XXX
Cash position (Nostro A/c)
Particulars Credit Debit

Opening balance in credit (Nostro A/C) XX -
Remitted by TT - XX
XXX XXX
Closing balance XXX
81
15. International Finance – Risk & Hedging
1. Currency Invoicing
Foreign currency Invoice under which currency?

Importer Exporter
Appreciates Home currency Foreign currency
Depreciates Foreign currency Home currency
2. Leading & Lagging
Foreign currency Export Export Import

Depreciates Lead Lead Lag
Appreciates Investment Borrowing Surplus cash
Appreciation % < Alternative % Lead Lag Lag
Appreciation % > Alternative % Lag Lead Lead
3. Netting
Outstanding amount are adjusted against dues payable

Its enough to pay net amount
Bilateral (2 parties)
Multilateral (More than 2 parties)
4. Forward Cover
Relationship Export Import

Expected Spot rate > Forward rate No forward cover Take forward cover
Expected Spot rate < Forward rate Take forward cover No forward cover
Expected spot rate (as on date of maturity of forward contract) = Spot rate +
(appreciation) - (depreciation)
5. Cancellation of forward contract
Exporter Importer
due date Early due date early
Buy $ Buy $ Sell $ Sell $
Spot Forward Spot Forward
82
6. Honour
Exporter Importer
No action Cancelling old contract No action Cancelling old contract
i) Original position - Sell $ Forward i) Original position - Buy $ Forward
ii) Opposite position - Buy $ Forward ii) Opposite position - Sell $ Forward
iii) New contract - Sell $ Spot iii) New contract - Buy $ Spot
7. Roll over
Exporter Importer
i) Buy $ Spot i) Buy $ Forward i) Sell $ Spot i) Sell $ Forward
ii) Sell $ Forward ii) Sell $ Forward ii) Buy $ Forward ii) Buy $ Forward
Summary table
Honour Rollover Cancel

Due date Early Due date Early Due date Early
Importer No act
Buy Spot Forward Forward No act No act
Sell Forward Spot Forward Spot Forward
Exporter No act
Buy Forward Spot Forward Spot Forward
Sell Spot Forward Forward No act No act
Rules:
1. Honour on Due date - No action
2. Honour early
i) Identify original position
ii) Reverse original position - Forward rate is relevant
iii) Create new (Original) position now -Spot rate is relevant
3. Cancel
ii) Take opposite position -
Due date - Spot rate is relevant
Early - Forward rate is relevant
4. Rollover
ii) Take opposite position -
Due date - Spot rate is relevant
Early - Forward rate is relevant
iii) Create new (Original) position now -Forward rate is relevant
83
8. Money Market Hedge
Receivables Payables
Steps: Steps:
i) identify $ receivables asset i) identify $ liability
ii) Borrow $ (Principal + Interest) ii) Borrow in Rs.
iii) Convert the borrowed amount in $ to Rs iii) Convert the borrowed amount in Rs to $
iv) Invest the converted Rs including interest iv) Invest the converted $
v) Realise the Re - investment v) Realise the step iv investment along with interest
vi) Settle the $ liability of Step ii) with $ vi) Settle the $ liability of Step i) with realisation in Step
receivable of Step i) along with interest thereon v)
vii) pay the amount borrowed in step ii) along with
interest
Effective rate = Realised amount/$ Receivable Effective rate = Step vii/Step i
i.e Step v/Step i
Effective rate > Forward rate - Prefer Money Effective rate > Forward rate - Don’t Prefer Money
Market Hedge Market Hedge
Effective rate < Forward rate - Don’t prefer Effective rate < Forward rate - Prefer Money Market
Money Market Hedge Hedge
9. Comparison of forward cover with Money Market Hedge
Method Exporter Importer

Cashflow Whichever gives higher domestic Whichever gives lower domestic currency
currency inflow outflow
Effective rate Whichever gives higher effective
rate Whichever gives lower effective rate
Money Market Hedge for Possibility exists, if in absolute terms

Importer Borrowing and lending rates are lower in foreign currency than in
domestic currency - Domestic currency depreciating
Exporter Borrowing and lending rates are higher in foreign currency than in
domestic currency - Foreign currency depreciating
84
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1

Chapter No Name Page no

Declaration Date Dividend is announced

Dividend Rate (DPS / FV ) X 100 FV - Fair value

Stock Valuation – Dividend Growth Model

P.E.Multiple Approach MPS = EPS X PE Multiple

Compare MPS with AP (Actual stock price)

Relationship Valuation Decision

Future Growth Rate

b = Retention Ratio, r = Return on Investment

Implied Growth Rate

Implied Return on Equity

3. Common Sense Approach (OR) All-Or-Nothing Approach

Nature of Firm Relationship Payout

K = Cost of Equity (or) Shareholder's expectation

a. Walter’s Model Po = (D / Ke) + [ (E - D) X ( r / Ke)] / Ke

5. Pricing of Buy- Back

Buy back Price = (S X Po) / (S - N)

N = Money available for buy back / Buy back price

Bonus Issue Capitalisation of reserves

Post MPS after bonus/ stock split/ reverse split:

7. Effect of change in Dividend

Increase in dividend Decrease in dividend

8. Post Bonus price

Theoretical post rights price per share

Theoretical value of rights

S = Subscription per share

No. of Right shares = Existing No. of shares / Ratio of Rights

Effect of Right issue

Effect on wealth of Shareholder

 Cost associated with issue of new share.

10. Corporate Dividend Tax (CDT)

11. Approaches to Dividend

Fixed amount of dividend is paid each year irrespective of the earnings

Dividend Payout Ratio is kept constant

c) Constant Dividend plus

Capital Structure altered Capital Structure un-altered

Finance manager has to consider the following while declaring dividends

Market value of Investment XXX

Net Asset of the scheme = Total Assets - Total External Liability

B. Valuation Rules - "Mark - To - Market" Basis

Nature of Asset Valuation Price

C. Costs of Mutual fund

Expense Ratio = Total Expenses / Average value of portfolio

Expense per unit = Total Expenses / No. of Units

R2 = [(1 / 1- Initial Expenses %) X R1 ] + Recurring Expenses%

A. Reward -to-variability / Volatility Ratio = Sharpe Ratio & Treynor Model

II. Treynor Model = ( Rp - Rf ) / βp

B. Measures of Excess Return

α = Return on portfolio - Return as per CAPM

Alpha is Positive Fund is undervalued, outperformed the market

II. Morning Star Index = Average Return - Average Risk of loss

Risk of loss = Lower of (Rf - Return) or zero

III. FAMA net selectivity = (Rp - [Rf+ (σj/σm)x(Rm-Rf)]

1. Risk premium from Portfolio = Rp-Rf

Systematic risk = σpxβp

Beta (β) =(σj/σm)x Correlation

Holding Period Return = [Cash dividend + capital appreciation + capital gains ]

Annualized Return = (Total Return / period) X 365