Cost Of Capital Problems.pdf

Find out the cost of equity capital given that the earnings are expected to remain same for coming years.. Solution a Weighted average cost of capital of the company is as follows: Sour

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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

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 10th

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)

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

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

P0 Rs 27.50 The market value of equity is 80,000 x Rs 27.50 = Rs 22,00,000

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

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

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

= 12.5%

Weighted average cost of capital will therefore be:

Sources of capital Cost of capital Proportion of total Weighted cost of

capital

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):

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

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

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

structure

Capital structure Amount

Rs

Proportion (weight)

After tax cost

Weighted cost

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

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

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

.1075

So, Weighted Average cost of capital (K0) is 10.75%

b)

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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

.136

c)

= 20 + 0.7 = 30 or 30%

STATEMENT OF SHOWING WEIGHTED AVERAGE COST OF CAPITAL

Amt After-tax

Cost

Weights Weighted

Cost

.148

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

Problem 8

The following is the extract from the financial statement of ABC Ltd

Equity Share Capital (of Rs 10 each) Rs 200 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:

= 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

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)

So, WACC (BV) is 12.79 or 12.8%

Calculation of WACC (Market Value)

Pref of shares Rs 2,40,000 072 149 0107

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%

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

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%

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

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

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

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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)

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

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