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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%. 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.
ii)
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
= = = = =
Annual interest to be paid i.e. Rs. 12 Company’s effective tax rate i.e. 50% or 0.50 Redemption value per Debenture i.e. Rs. 110 Number of years to maturity = 10 years 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) = 97.50
7.25 = 7.43% 97.50
(ii) Cost of preference capital
D + (RV – SV) / N kp (RV + SV) / 2
Where, D = SV = N = RV =
Dividend on Preference share i.e. Rs. 14 Issue Price per share minus floatation cost Rs. 92 No. of years for redemption i.e. 12 years Net price payable on redemption Rs. 100 Rushi Ahuja
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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 Rushi Ahuja
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D RV SV
= = =
kp
=
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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% 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 SV
= = =
Rs. 13 100 – 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. Rushi Ahuja
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Problem 4 The following figures are taken from the current balance sheet of Delaware & Co. Capital Share Premium Reserves Shareholder’s 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
The market value of equity is 80,000 x Rs. 27.50 = Rs. 22,00,000 I kd =
Rs. 12 =
SV
= 15% 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:
Equity share capital 12% debentures 18% term loan
Rs. in Lacs 400 400 1,200 2,00 Rushi Ahuja
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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
Equity share capital 12% debenture Term loan
20% 12% 18%
4/20 4/20 12/20 WACC
Weighted cost of capital 4.00 2.40 10.80 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 ke
20
=
= p
=
160
12.5%
Weighted average cost of capital will therefore be: Sources of capital
Cost of capital
Proportion of total
Equity share capital 12% debenture 18% Term loan
12.5% 12% 18%
4/20 4/20 12/20 WACC
Weighted cost of capital 2.5% 2.4% 10.8 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 18% Term loan
: :
12 x 0.60 18 x 0.60
= =
7.2% 10.8% Rushi Ahuja
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The cost of capital after tax benefit (as per premises – a): Sources Equity 12% debenture 18% Term loan
Cost 20% 7.2% 10.8%
Proportion 4/20 4/20 12/20 WACC
Weighted cost (Rs.) 4.00 1.44 6.48 11.92
The cost of capital after tax benefit (as per premises – b): Sources Equity 12% debenture 18% Term loan
Cost Proportion 12.5% 4/20 7.2% 4/20 10.8% 12/20 Weighted average cost=
Weighted cost (Rs.) 2.50 1.44 6.48 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 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.
Equity share capital Reserves and surplus Net worth 8% debentures
Capital structure Equity Reserves and surplus 8% debentures Total
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%
Proportion of capital structure 40% 26% 66% 34% 100%
After tax cost 12% 12% 4%
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%.
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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) 6% preference shares 8% Debentures
Rs. 40,00,000 10,00,000 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 ke
=
Rs. 2 +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
Equity share capital Preference share capital Debentures
Existing Amt. 40,00,000 10,00,000 30,00,000
After-tax Cost .17 .06 .04
Weights .500 .125 .375
Weighted cost .0850 .0075 .0150 .1075
So, Weighted Average cost of capital (K0) is 10.75% b) D1 ke =
Rs. 3 +g=
P0
+ .07 Rs. 15 Rushi Ahuja
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=
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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. Equity share capital 6% preference share capital 8% debentures 10% debentures
40,00,000 10,00,000 30,00,000 20,00,000
After-tax Cost .17 .06 .04 0.5
Weights .40 .10 .30 .20
Weighted Cost .108 .006 .012 .010 .136
c) D1 ke =
Rs. 3 +g=
+ .10
P0 =
Rs. 15
.20 + 0.7 = .30 or 30%
STATEMENT OF SHOWING WEIGHTED AVERAGE COST OF CAPITAL Amt. Equity share capital 6% preference share capital 8% debentures 10% debentures
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
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 - Interest on debentures - Income tax Net Profit Equity Share Capital (of Rs. 10 each) Reserves and Surplus 15% debentures (Rs. 100 each) Total
Rs. 105 lacs Rs. 33 lacs Rs. 36 lacs Rs. 36 lacs Rs. 200 lacs Rs. 100 lacs Rs. 220 lacs 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)
(ii)
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
= = =
Interest (1 – t) / Market value 15 (1 – 5) / 93.75 8%
= = =
Interest (1 – t) / Face Value 15 ( 1 - .5) / 100 7.5%
=
EPS / p0
=
1.80 / 12 = 15%
Cost of debentures, kd : (based on market value) kd
(based on Face Value) kd
(iii)
Cost of equity capital: ke
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: 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 Rushi Ahuja
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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 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%
Cost to Pref. Shares: PD RV SV N
= = = =
kp
=
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% Rushi Ahuja 10
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Cost to Equity Shares: P0 D1 g
= = =
ke
=
22 – 2 = 20 2 .07 D1 +g P0 2
ke
=
+ .07 20
=
17%
Calculation of WACC (Book Value) Source Pref. of shares Equity shares Debentures
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
So, WACC (BV) is 12.79 or 12.8% Calculation of WACC (Market Value) Source Pref. of shares Equity shares Debentures
Amount Rs. 2,40,000 Rs. 22,00,000 Rs. 8,80,000 Rs. 33,20,000
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 Ordinary shares 10% Pref. Shares 14% Debentures
W .500 .125 .375 1.000
C/C .17 .10 .07
WxC/C .0850 .0125 .0262 .1237
C/C .27 .10 .07 .075
WxC/C .108 .010 .021 .015 .154
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 Ordinary shares 10% Pref. Shares 14% Debentures 15% Debt.
W .40 .10 .30 .20 1.000
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 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
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 10% preference shares 11% Debentures
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) ii)
Find out the cost of equity capital and the WACC, and 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 Equity capital
Amount Rs. 4,00,000
W .4
C/C .198
WxC/C .0792 Rushi Ahuja 13
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1,00,000 5,00,000 10,00,000
.1 .5 1.00
.100 .055
.0100 .0275 .1167
C/C .202 .100 .055 .060
WxC/C .0622 .0077 .0212 .0138 .1049
Solved Problems
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 Equity capital 10% Pref. Capital 11% Debentures 12% Debentures
Amount Rs. 4,00,000 1,00,000 5,00,000 3,00,000 13,00,000
W .308 .077 .385 .230 1.000
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 Equity shares capital Pref. share capital Retained Earnings Debentures Current Liabilities
Rs. 12,00,000 4,50,000 4,50,000 9,00,00 10,00,000 40,00,000
Assets Fixed Assets Current Assets
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. Rushi Ahuja 14
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Solution Specific Costs _______
Sources Equity funds 15% preference shares 14% debentures
Weights 0.55 0.15 0.30
Specific cost 0.1800 0.1530 0.655
Weighted cost 0.09900 0.0229 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 Reserves 14% debentures of 100 each
Rs. 10 crores Rs. 2 crores 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) Shareholders funds Equity capital Reserves Debentures
10 2
BV (Rs. Crores)
W
C/C
W x C/C
12 3
80% 20%
7.63% 7.00%
6.104 1.400
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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 (ii) Cost of new debt of Rs. 5 crores = 16 (1 – 0.5) (iii) Cost of Equity D1 ke =
= 7% = 8%
2 (1.05) +g=
P0
+ 0.05 = 9.2 50
WACC of New Capital Structure Particulars Shareholder funds Debentures Long term loan Total
BV (Rs. crores) 12 3 5 20
W
C/C
W x C/C
60% 15% 25% 100%
9.2% 7.0% 8.0%
5.52 1.05 2.00 8.57
New WACC = 8.57%
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