99700905 cost-of-capital-solved-problems

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1. FINANCIAL MANAGEMENT Solved Problems

Rushi Ahuja 1

SOLVED PROBLEMS – COST OF CAPITAL

Problem 1

Calculate the cost of capital in the following cases:

i) 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%.
ii) 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 = Annual interest to be paid i.e. Rs. 12
t = Company’s effective tax rate i.e. 50% or 0.50
RV = Redemption value per Debenture i.e. Rs. 110
N = Number of years to maturity = 10 years
SV = issue price per debenture minus floatation cost i.e. Rs. 95

[12 + (110 – 95) / 10] (1 – .5)
kd =
(110 + 95) / 2

[12 + 2.5](0.5) 7.25
= = = 7.43%
97.50 97.50


(ii) Cost of preference capital


D + (RV – SV) / N
kp
(RV + SV) / 2


Where,
D = Dividend on Preference share i.e. Rs. 14
SV = Issue Price per share minus floatation cost Rs. 92
N = No. of years for redemption i.e. 12 years
RV = Net price payable on redemption Rs. 100

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14 (100 – 92) / 12
kp =
(110 + 95) / 2

14 + .67
=
95

= 15.28%

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 6the end of 10
th
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

= 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

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In this case D = 10
RV = 100
SV = 100 – 2 = Rs. 98

10 + (100 – 98) / 10
kp =
(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% non-convertible 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.



Effective cost of 13% NCD : In this case,

Annual Interest, I = Rs. 13
SV = 100 – 2.50 – 1.00
= 96.50

13 (1 – 5)
kd =
96.50%

= 6.74%

The effective cost of capital is lesser in case of 13% NCD.

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Problem 4

The following figures are taken from the current balance sheet of Delaware & Co.

Capital Rs. 8,00,000
Share Premium 2,00,000
Reserves 6,00,00
Shareholder’s funds 16,00,000
12% irredeemable debentures 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 Rs. 2 x 1.10
ke = + g = + 10 = 18%
P0 Rs. 27.50

The market value of equity is 80,000 x Rs. 27.50 = Rs. 22,00,000

I Rs. 12
kd = = = 15%
SV Rs. 80

The market value of debt is 4,00,000 x .80 = Rs. 3,20,000.
Now, the WACC is
(22,00,000 / 25,20,000) x .18 + (3,20,000/25,20,000) x .15 = .176 = 17.6%

Note: In this case, the dividend of Rs. 2 has just been paid. So, D0 = Rs. 2 and the D1, i.e. dividend
expected after one year from now will be D0 x (1 + g) = Rs. 2 x 1.10.

Problem 5

The following information has been extracted from the balance sheet of Fashions Ltd. as on 31-12-1998:

Rs. in Lacs
Equity share capital 400
12% debentures 400
18% term loan 1,200
2,00

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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 Cost of capital Proportion of total Weighted cost of
capital
Equity share capital 20% 4/20 4.00
12% debenture 12% 4/20 2.40
Term loan 18% 12/20 10.80
WACC 17.20

Therefore, weighted cost of capital (without consideration of the market price of Equity and not taking
into consideration the effect of Income Tax) is = 17.2% per annum.





b) When market price of equity shares is Rs. 160 (Face value Rs. 100), the cost of capital is:

D1 20
ke = =
p 160

= 12.5%

Weighted average cost of capital will therefore be:

Sources of capital Cost of capital Proportion of total Weighted cost of
capital
Equity share capital 12.5% 4/20 2.5%
12% debenture 12% 4/20 2.4%
18% Term loan 18% 12/20 10.8
WACC 15.7%

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%

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The cost of capital after tax benefit (as per premises – a):

Sources Cost Proportion Weighted cost (Rs.)
Equity 20% 4/20 4.00
12% debenture 7.2% 4/20 1.44
18% Term loan 10.8% 12/20 6.48
WACC 11.92

The cost of capital after tax benefit (as per premises – b):

Sources Cost Proportion Weighted cost (Rs.)
Equity 12.5% 4/20 2.50
12% debenture 7.2% 4/20 1.44
18% Term loan 10.8% 12/20 6.48
Weighted average cost= 10.42


Problem 6

The following information is available from the Balance Sheet of a company

Equity share capital – 20,000 shares of Rs. 10 each Rs. 2,00,000
Reserves and Surplus Rs. 1,30,000
8% Debentures 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. Proportion of capital
structure
Equity share capital 2,00,000 40%
Reserves and surplus 1,30,000 26%
Net worth 3,30,000 66%
8% debentures 1,70,000 34%
5,00,000 100%

Capital structure Amount
Rs.
Proportion
(weight)
After tax
cost
Weighted cost
Equity 2,00,000 40% 12% 12%x40%= 4.80%
Reserves and surplus 1,30,000 26% 12% 12%x26%= 3.12%
8% debentures 1,70,000 34% 4% 4%x34%= 1.36%
Total 5,00,000 100% 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%.

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The opportunity cost of retained earnings is the dividends foregone by shareholders. Therefore, the firm
must earn the same rate of return on retained earnings as on the Equity Share Capital. Thus, the
minimum cost of retained earnings is the cost of equity capital i.e. kr = ke.

Problem 7

A Limited has the following capital structure:

Equity share capital (2,00,000 shares) Rs. 40,00,000
6% preference shares 10,00,000
8% Debentures 30,00,000
80,00,000


The market price of the company’s 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 Rs. 2
ke = + g = + 0.07
P0 Rs. 20

= 0.1 + 0.07 = .17 or 17%

The cost of 8% debentures, after tax is 8 (1 – 5) = 4%

STATEMENT SHOWING WEIGHTED COST OF CAPITAL

Existing
Amt.
After-tax
Cost
Weights Weighted
cost
Equity share capital 40,00,000 .17 .500 .0850
Preference share capital 10,00,000 .06 .125 .0075
Debentures 30,00,000 .04 .375 .0150
.1075
So, Weighted Average cost of capital (K0) is 10.75%

b)
D1 Rs. 3
ke = + g = + .07
P0 Rs. 15

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= .20 + 0.7 = .27 or 27%

The cost of capital of new debenture (after tax) is 10% (1 - .5) = 5%





STATEMENT OF SHOWING WEIGHTED AVERAGE COST OF CAPITAL

Amt. After-tax
Cost
Weights Weighted
Cost
Equity share capital 40,00,000 .17 .40 .108
6% preference share capital 10,00,000 .06 .10 .006
8% debentures 30,00,000 .04 .30 .012
10% debentures 20,00,000 0.5 .20 .010
.136

c)
D1 Rs. 3
ke = + g = + .10
P0 Rs. 15

= .20 + 0.7 = .30 or 30%

STATEMENT OF SHOWING WEIGHTED AVERAGE COST OF CAPITAL

Amt. After-tax
Cost
Weights Weighted
Cost
Equity share capital 40,00,000 .30 .40 .120
6% preference share capital 10,00,000 .06 .10 .006
8% debentures 30,00,000 .04 .30 .012
10% debentures 20,00,000 0.5 .20 .010
.148

So, weighted average cost of capital (k0) 14.80%

Problem 8
The following is the extract from the financial statement of ABC Ltd.

Operating profit Rs. 105 lacs
- Interest on debentures Rs. 33 lacs
- Income tax Rs. 36 lacs
Net Profit Rs. 36 lacs
Equity Share Capital (of Rs. 10 each) Rs. 200 lacs
Reserves and Surplus Rs. 100 lacs
15% debentures (Rs. 100 each) Rs. 220 lacs
Total Rs. 520 lacs

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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 = Rs. 36,00,000
No. of equity shares = Rs. 20,00,000
EPS = Profit after tax / No. of shares
= 36,00,000 / 20,00,000
= Rs. 1.80

(ii) Cost of debentures, kd :
(based on market value)

kd = Interest (1 – t) / Market value
= 15 (1 – 5) / 93.75
= 8%

(based on Face Value)

kd = Interest (1 – t) / Face Value
= 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 company’s present book value capital structure is: Rs.
Preference shares (Rs. 100 per share) 2,00,000
Equity shares (Rs. 10 per share) 10,00,000
Debentures (Rs. 100 per debenture) 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

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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 = Rs. 13
SV = 100 – 4 = Rs. 99
RV = Rs. 100
t = .50
N = 10 year

[I + (RV – SV) / N] (1 – t)
kd =
(RV + SV) / 2

[13 + (100 – 96) / 10] (1 – .5)
=
(100 + 95) / 2
= 6.8%

Cost to Pref. Shares:

PD = Rs. 14
RV = 100
SV = 100 – 5 = Rs. 95
N = 10 years

D + (RV – SV) / N
kp =
(RV + SV) / 2

14 + (100 – 95) / N
=
(100 + 95) / 12

= 14.9%

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Cost to Equity Shares:

P0 = 22 – 2 = 20
D1 = 2
g = .07

D1
ke = + g
P0

2
ke = + .07
20

= 17%

Calculation of WACC (Book Value)

Source Amount Weight C/C WxC/C
Pref. of shares Rs. 2,00,000 .10 .149 .0149
Equity shares Rs. 10,00,000 .50 .170 .0850
Debentures Rs. 8,00,000 .40 .070 .0280
Rs. 20,00,000 1.00 .1279

So, WACC (BV) is 12.79 or 12.8%

Calculation of WACC (Market Value)

Source Amount Weight C/C WxC/C
Pref. of shares Rs. 2,40,000 .072 .149 .0107
Equity shares Rs. 22,00,000 .663 .170 .1127
Debentures Rs. 8,80,000 .265 .070 .0186
Rs. 33,20,000 1.000 .1420

So, WACC (MV) is 14.2%

Problem 10

The ABC Company has the total capital structure of Rs. 80,00,000 consisting of:
Ordinary shares (2,00,000 shares) 50.0%
10% preference shares 12.5%
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:

a) Computed a weighted average cost of capital structure.

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b) Compute the new weighted average cost of capital if the company raises an additional Rs. 20,00,000
debt by issuing 15% debenture. This 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) Compute the cost of capital if in (b) above, growth rate increases to 10%.

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 W C/C WxC/C
Ordinary shares .500 .17 .0850
10% Pref. Shares .125 .10 .0125
14% Debentures .375 .07 .0262
1.000 .1237

The WACC of the firm is 12.37%

(b) Cost of capital of additional debt

kd = 15 (1 - .5)
= 7.5%

New cost of equity share capital

ke = D1 / P0 + g

= 3 / 1.5 + 0.07

= 27%



Source W C/C WxC/C
Ordinary shares .40 .27 .108
10% Pref. Shares .10 .10 .010
14% Debentures .30 .07 .021
15% Debt. .20 .075 .015
1.000 .154

The WACC of the firm would be 15.4%

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If the growth rate in (b) is increased to 10%

ke = D1 / P0 + g

= 3 / 15 + .10

= 30%

Calculation of WACC of the firm

Source W C/C WxC/C
Ordinary shares .40 .30 .120
10% Pref. Shares .10 .10 .010
14% Debentures .30 .07 .021
15% Debt. .20 .075 .015
1.000 .166

The WACC of the firm would be of 16.6%.

Problem 11
ABC Ltd. has the following capital structure

4,000 Equity shares of Rs. 100 each Rs. 4,00,000
10% preference shares 1,00,000
11% Debentures 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 = D1 / P0 + g

= 10 / 102 + .10

= 19.8%

Calculation of Weighted Average Cost of Capital

Source Amount W C/C WxC/C
Equity capital Rs. 4,00,000 .4 .198 .0792

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10% Pref. Capital 1,00,000 .1 .100 .0100
11% Debentures 5,00,000 .5 .055 .0275
10,00,000 1.00 .1167

WACC = 11.67 OR 11.7%

(ii) Cost of Equity Capital is

ke = D1 / P0 + g

= 12 / 98 + .08

= 20.2%

Calculation of Weighted Average Cost of Capital (New)

Source Amount W C/C WxC/C
Equity capital Rs. 4,00,000 .308 .202 .0622
10% Pref. Capital 1,00,000 .077 .100 .0077
11% Debentures 5,00,000 .385 .055 .0212
12% Debentures 3,00,000 .230 .060 .0138
13,00,000 1.000 .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

Liabilities Rs. Assets Rs.
Equity shares capital 12,00,000 Fixed Assets 25,00,000
Pref. share capital 4,50,000 Current Assets 15,00,000
Retained Earnings 4,50,000
Debentures 9,00,00
Current Liabilities 10,00,000 ________
40,00,000 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.

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Solution

Specific Costs
_______


Sources Weights Specific cost Weighted cost
Equity funds 0.55 0.1800 0.09900
15% preference shares 0.15 0.1530 0.0229
14% debentures 0.30 0.655 0.0196

So, weighted average cost of capital, (k0), is 14.15%.

Problem 13

The capital structure of Hindustan Traders Ltd. as on 31-3-1999 is as follows:

Equity capital: 100 lacs equity shares of Rs. 10 each Rs. 10 crores
Reserves Rs. 2 crores
14% debentures of 100 each Rs. 3 crores

For the year ended 31-3-1999 the company has paid equity dividend at 20%. As the company is a
market leader with good future, dividend is likely to grow by 5% every year. The equity shares are now
traded at Rs. 80 per share in the stock exchange. Income tax rate applicable to the Company is 50%.



Required:
a) The current weighted cost of capital
b) The company has plans to raise a further Rs. 5 crores by way of long-term loan at 16% interest.
When this takes place the market value of the equity shares is expected to fall to Rs. 50 per
share. What will be the new weighted average cost of capital of the Company?

Solution

Cost of Debt Capital = kd = Int (1 – t)
Kd = 14 (1 – 0.5) = 7%

Cost of equity capital applying dividend growth model

ke = D1 / P0 +g
ke = 2 (1.05) / 80 + .05 = 7.63%

Weighted Average Cost of Capital (WACC)

BV (Rs. Crores) W C/C W x C/C
Shareholders funds
Equity capital 10
Reserves 2 12 80% 7.63% 6.104
Debentures 3 20% 7.00% 1.400

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Total 5 100% 7.504

WACC = 7.50%

Weighted average cost of capital after raising further debt of Rs. 5 crores

(i) Cost of existing debt of Rs. 3 crores = 7%
(ii) Cost of new debt of Rs. 5 crores = 16 (1 – 0.5) = 8%
(iii) Cost of Equity

D1 2 (1.05)
ke = + g = + 0.05 = 9.2
P0 50

WACC of New Capital Structure
Particulars BV (Rs.
crores)
W C/C W x C/C
Shareholder funds 12 60% 9.2% 5.52
Debentures 3 15% 7.0% 1.05
Long term loan 5 25% 8.0% 2.00
Total 20 100% 8.57

New WACC = 8.57%