Solved Problems Cost of Capital
Solved Problems Cost of Capital
Solved Problems Cost of Capital
PGDM
Problem 1
FINANCIAL MANAGEMENT
ii
X Ltd. issues 12% Debentures of face value Rs. 100 each and realizes Rs.
95 per Debenture. The Debentures are redeemable after 10 years at a
premium of 10%.
Y. Ltd. issues 14% preference shares of face value Rs. 100 each Rs. 92 per
share. The shares are repayable after 12 years at par.
Note: Both companies are paying income tax at 50%.
Solution
(i) Cost of Debt
[Int + (RV SV) / N] (1 t)
kd
(RV + SV) / 2
Int
t
RV
N
SV
=
=
=
=
=
kd =
(110 + 95) / 2
[12 + 2.5](0.5)
7.25
=
50 97.50
ii
=
=
=
=
kp =
(110 + 95) / 2
14 + .67
15.28%
95=
Problem 2
a) A company raised preference share capital of Rs. 1,00,000 by the issue of
10% preference share of Rs. 10 each. Find out the cost of preference share
capital when it is issued at (i) 10% premium, and (ii) 10% discount.
b) A company has 10% redeemable preference share which are redeemable at
th
6the end of 10 year from the date of issue. The underwriting expenses are
expected to 2%. Find out the effective cost of preference share capital.
c) The entire share capital of a company consist of 1,00,000 equity share of Rs. 100
each. Its current earnings are Rs. 10,00,000 p.a. The company wants to raise
additional funds of Rs. 25,00,000 by issuing new shares. The flotation cost is
expected to be 10% of the face value. Find out the cost of equity capital given that
the earnings are expected to remain same for coming years.
Solution
(a) Cost of 10% preference share capital
(i) When share of Rs. 10 is
issued at 10% premium Kp
= D / P0
= 10 / 11 x 100
= 9.09%
(ii) When share of Rs. 10 is
issued at 10% discount kp
= PD / P0
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= 10 / 9 x 100
= 11.11%
(b) The cost of preference share (face value = Rs. 100) may be found as follows:
D + (RV SV) / N
kp =
(RV+ SV) / 2
In this case D
=
RV
=
SV
=
=
kp
10
100
100 2 = Rs. 98
10 + (100 98) / 10
(100 + 98) / 2
= 10.3%
(c) In this case, the net proceeds on issue of equity shares are Rs. 100 10 =
Rs. 90 and earnings per share is Rs. 10.
Cost of new equity is:
ke
D1 / p0
10 / 90 11.%
Problem 3
A company is considering raising of funds of about Rs. 100 lakhs by one
of two alternative method, viz., 14% institutional term loan or 13% nonconvertible debentures. The term loan option would attract no major
incidental cost. The debentures would have to be issued at a discount of
2.5% and would involve cost of issue of Rs. 1,00,000.
Advise the company as to the better option based on the effective cost of
capital in each case. Assume a tax rate of 50%.
Solution
Effective cost of 14% loan: In this case, there is no other cost involved and
the company has to pay interest at 14%. This interest after tax shield @
50% comes to 7% only.
=
=
=
kd
Rs. 13
100 2.50 1.00
96.50
13 (1 5)
96.50%
6.74%
The following figures are taken from the current balance sheet of Delaware & Co.
Capital
Share Premium
Reserves
Shareholders funds
12% irredeemable debentures
Rs. 8,00,000
2,00,000
6,00,00
16,00,000
4,00,00
An annual ordinary dividend of Rs. 2 per share has just been paid. In
the past, ordinary dividends have grown at a rate of 10 per cent per
annum and this rate of growth is expected to continue. Annual interest has
recently been paid on the debentures. The ordinary shares are currently
quoted at Rs. 27.5 and the debentures at 80 per cent. Ignore taxation.
You are required to estimate the weighted average cost of capital
(based on marker values) for Delaware & Co.
Solution
In order to calculate the WACC, the specific cost of equity capital and debt
capital are to be calculated as follows:
D1
ke =
Rs. 2 x 1.10
+g=
P0
+ 10 = 18%
Rs. 27.50
Rs. 12
=
SV
= 15%
Rs. 80
Rs. in Lacs
400
12% debentures
18% term loan
400
1,200
2,00
a) Determine the weighted average cost of capital of the company. It had
been paying dividends at a consistent rate of 20% per annum.
b) What difference will it make if the current price of the Rs. 100 share is Rs.
160?
c) Determine the effect of Income Tax on the cost of capital under both premises
(Tax rate 40%).
Solution
a) Weighted average cost of capital of the company is as follows:
Sources of capital
Equity share capital
12% debenture
Term loan
b) When market price of equity shares is Rs. 160 (Face value Rs. 100), the cost
of capital is:
D
1
20 ke
=
p 160
= 12.5%
Weighted average cost of capital will therefore be:
Sources of capital
Equity share capital
12% debenture
18% Term loan
The above WACC is without taking into consideration the effect of Income Tax.
c) As interest on debenture and loans is an allowable deductible expenditure
for arriving at taxable income, the real cost to the company will be interest
charges less tax benefit (assuming that the company earns taxable income).
So, interest cost will be : Rate of interest (1 t)
12% Debenture
:
12 x 0.60
=
7.2%
18% Term loan
:
18 x 0.60
=
10.8%
Problem 6
The following information is available from the Balance Sheet of a company
Equity share capital 20,000 shares of Rs. 10 each
Reserves and Surplus
8% Debentures
Rs. 2,00,000
Rs. 1,30,000
Rs. 1,70,000
The rate of tax for the company is 50%. Current level of Equity Dividend is
12%. Calculate the weighted average cost of capital using the above
figures.
Solution
Capital structure
Rs.
2,00,000
1,30,000
3,30,000
1,70,000
5,00,000
Amount
Rs.
2,00,000
1,30,000
1,70,000
5,00,000
Proportion
(weight)
40%
26%
34%
100%
After tax
cost
12%
12%
4%
Proportion of capital
structure
40%
26%
66%
34%
100%
Weighted cost
12%x40%= 4.80%
12%x26%= 3.12%
4%x34%= 1.36%
9.28%
1. As the current market price of equity share is not given, the cost of capital of equity
share has been taken with reference to the rate of dividend and the face value of
the share. So, ke = 12/100 = 12%.
Rs. 40,00,000
10,00,000
30,00,000
80,00,000
The market price of the companys equity share is Rs. 20. It is expected
that company will pay a dividend of Rs. 2 per share at the end of current
year, which will grow at 7 per cent for ever. The tax rate may be presumed
at 50 per cent. You are required to compute the following:
a) A weighted average cost of capital based on existing capital structure.
b) The new weighted average cost of capital if the company raises an additional
Rs. 20,00,000 debt by issuing 10 per cent debentures. The would result in
increasing the expected dividend to Rs. 3 and leave the growth rate unchanged
but the price of share will fall to Rs. 15 per share.
c) The cost of capital if in (b) above, growth rate increases to 10 per cent.
Solutions
a) The cost of equity capital is
D1
ke
Rs. 2
+g=
+ 0.07
P0
Rs. 20
Existing
Amt.
40,00,000
10,00,000
30,00,000
After-tax
Cost
.17
.06
.04
D1
P0
+g=
Rs. 3
Rs. 15
+ .07
Weights
.500
.125
.375
Weighted
cost
.0850
.0075
.0150
.1075
c)
40,00,000
10,00,000
30,00,000
20,00,000
D1
ke =
Weights
Weighted
Cost
.108
.006
.012
.010
.136
.40
.10
.30
.20
Rs. 3
+g=
P0
After-tax
Cost
.17
.06
.04
0.5
+ .10
Rs. 15
40,00,000
10,00,000
30,00,000
20,00,000
After-tax
Cost
.30
.06
.04
0.5
Weights
.40
.10
.30
.20
Weighted
Cost
.120
.006
.012
.010
.148
Total
Rs. 520 lacs
The market price of equity share and debenture is Rs. 12 and Rs. 93.75
respectively. Find out (i) EPS, (ii) % cost of capital of equity and
debentures.
Solution
(i) Earnings per share
Profit after tax
No. of equity shares
EPS
=
=
=
=
=
Rs. 36,00,000
Rs. 20,00,000
Profit after tax / No. of shares
36,00,000 / 20,00,000
Rs. 1.80
= 15 (1 5) / 93.75
= 8%
(based on Face Value)
kd
= 15 ( 1 - .5) / 100
= 7.5%
(iii)Cost of equity capital:
ke
EPS / p0
= 1.80 / 12 = 15%
Problem 9
As a financial analyst of a large electronics company, you are required to
determine the weighted average cost of capital of the company using (i)
book value weights and (ii) market value weights. The following
information is available for your perusal:
The companys present book value capital structure is:
Preference shares (Rs. 100 per share)
Equity shares (Rs. 10 per share)
Debentures (Rs. 100 per debenture)
Rs.
2,00,000
10,00,000
8,00,000
All these securities are traded in the capital market. Recent prices are:
Debentures @ Rs. 110 per debenture
Preference shares @ Rs. 120 per share
Equity shares @ Rs. 22 per share
Anticipated external financing opportunities are:
i) Rs. 100 per debenture redeemable at par; 10 year-maturity, 13% coupon
rate, 4% flotation costs, sale price Rs. 100.
ii) Rs. 100 preference share redeemable at par; 10 year-maturity, 14% dividend
rate, 5% flotation costs, sale price Rs. 100.
iii)
Equity shares: Rs. 2 per share flotation costs, sale price @ Rs. 22.
In addition, the dividend expected on the equity share at the end of the year is Rs. 2
and the earnings are expected to increase by 7% p.a. The firm has a policy of paying
all its earnings in the form of dividends. The corporate tax rate is 50%.
Solution
In order to find out the WACC, the specific cost of capital of different sources may be
calculated as follows:
Cost to debenture:
Int, I
SV
RV
t
N
=
=
=
=
=
kd
Rs. 13
100 4 = Rs. 99
Rs. 100
.50
10 year
[I + (RV SV) / N] (1 t)
(RV + SV) / 2
[13 + (100 96) / 10] (1 .5)
=
=
(100 + 95) / 2
6.8%
=
=
=
=
=
Rs. 14
100
100 5 = Rs. 95
10 years
D + (RV SV) / N
(RV + SV) / 2
14 + (100 95) / N
=
(100 + 95) / 12
=
14.9%
=
=
=
22 2 = 20
2
.07
D1
ke
+g
P0
2
ke
+ .07
20
17%
Amount
Rs. 2,00,000
Rs. 10,00,000
Rs. 8,00,000
Rs. 20,00,000
Weight
.10
.50
.40
1.00
C/C
.149
.170
.070
WxC/C
.0149
.0850
.0280
.1279
Weight
.072
.663
.265
1.000
C/C
.149
.170
.070
WxC/C
.0107
.1127
.0186
.1420
Amount
Rs. 2,40,000
Rs. 22,00,000
Rs. 8,80,000
Rs. 33,20,000
14% debentures
37.5%
The shares of the company sells for Rs. 20. It is expected that company will pay next
year a dividend of Rs. 2 per share which will grow at 7% forever. Assume a 50% tax rate.
You are required to:
Solution
(a) WACC of the existing capital structure
ke =
D1 / P0 +g
= 2 / 20 + 0.07
= 17%
Calculation of weighted average cost of capital
Source
Ordinary shares
10% Pref. Shares
14% Debentures
W
.500
.125
.375
1.000
15 (1 - .5)
= 7.5%
D 1 / P0 + g
= 3 / 1.5 + 0.07
= 27%
C/C
.17
.10
.07
WxC/C
.0850
.0125
.0262
.1237
Source
Ordinary shares
10% Pref. Shares
14% Debentures
15% Debt.
W
.40
.10
.30
.20
1.000
C/C
.27
.10
.07
.075
WxC/C
.108
.010
.021
.015
.154
D 1 / P0 + g
= 3 / 15 + .10
= 30%
Calculation of WACC of the firm
Source
Ordinary shares
10% Pref. Shares
14% Debentures
15% Debt.
W
.40
.10
.30
.20
1.000
C/C
.30
.10
.07
.075
WxC/C
.120
.010
.021
.015
.166
Rs. 4,00,000
1,00,000
5,00,000
The current market price of the share is Rs. 102. The company is expected to
declare a dividend of Rs. 10 at the end of the current year, with an expected
growth rate of 10%. The applicable tax rate is 50%.
i) Find out the cost of equity capital and the WACC, and
ii) Assuming that the company can raise Rs. 3,00,000 12% Debentures, find
our the new WACC if (a) dividend rate is increased from 10 to 12%, (b)
growth rate is reduced from 10 to 8% and (c) market price is reduced to Rs.
98.
Solution
(i) Cost of Equity Capital is
ke =
D 1 / P0 + g
= 10 / 102 + .10
= 19.8%
Calculation of Weighted Average Cost of Capital
Source
Equity capital
10% Pref. Capital
11% Debentures
Amount
Rs. 4,00,000
1,00,000
.1
5,00,000
.5
10,00,000
1.00
W
.4
C/C
.198
.100
.055
D1 / P0 + g
= 12 / 98 + .08
= 20.2%
Amount
Rs. 4,00,000
1,00,000
5,00,000
3,00,000
13,00,000
W
.308
.077
.385
.230
1.000
C/C
.202
.100
.055
.060
WxC/C
.0622
.0077
.0212
.0138
.1049
Problem 12
An electric equipment manufacturing company wishes to determine the weighted average
cost of capital for evaluating capital budgeting projects. You have been supplied with the
following information:
BALANCE SHEET
WxC/C
.0792
Liabilities
Equity shares capital
Pref. share capital
Retained Earnings
Debentures
Current Liabilities
Rs. Assets
12,00,000 Fixed Assets
4,50,000 Current Assets
4,50,000
9,00,00
10,00,000
40,00,000
Rs.
25,00,000
15,00,000
________
40,00,000
Additional Information:
i) 20 years 14% debentures of Rs. 2,500 face value, redeemable at 5%
premium can be sold at par, 2% flotation costs.
ii) 15% preference shares: Sale price Rs. 100 per share, 2% flotation costs
iii) equity shares: Sale price Rs. 115 per share, flotation costs, Rs. 5 per share
The corporate tax rate is 55% and the expected growth in equity dividend is 8% per
year. The expected dividend at the end of the current financial year is Rs. 11 per
share. Assume that the company is satisfied with its present capital structure and
intends to maintain it.
Solution
Specific Costs
_______
Sources
Equity funds
15% preference shares
14% debentures
Weights
0.55
0.15
0.30