1. What is meant by cost of capital ?

2. Define cost of capital.

3. Describe the Importance of cost of capital in Decision making.

4. Explain the different types of costs related to the cost of capital.

5. Explain critically the different approaches for computing cost of equity.

6. Specific cost Vs composite cost.

7. What are the methods of computing cost of equity capital ?

8. Define the concept of cost of capital. State how you would determine the weighted Average cost of capital of a firm.

9. Write a detailed note on the cost of individual components of capital.

10. What is weighted average cost of capital ? Examine the rational behind the use of weighted

average cost of capital.

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** PROBLEMS AND SOLUTIONS**

**Problem 1**. From the following capital structure of a company calculate the overall cost

of capital using (a) Book value weights and (b) Market value weights

** (b) Computation of Weighted Average Cost of Capital**

Source
(1) Equity share capital Preference share capital Debentures |
Amount After tax cost
(2) $ (3) 90,000 14% 10,000 10% 30,000 5% 1,30,000 |
Total after tax $
Cost (4) = (2) x (3) 12,600 1,000 1,500 15,100 |

Weighted average cost of capital = 15,100/1,30,000 x 100

= 11.61%

**Problem 2.** A fir m has the following capital structure after tax costs for the different

sources of funds used.

Source of funds Amount ($) Proportion After tax cost %

Debt 15,00,000 25 5

Preference shares 12,00,000 20 10

Equity shares 18,00,000 30 12

Retained earnings 15,00,000 25 11

60,00,000 100

You are required to compute the weighted average cost of capital.

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**Solution :**

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** Computation of Weighted Average Cost of Capital**

Source of funds Amount ($) Proportion After tax cost %

(1) (2) $ (3) cost (4) =(2) x (30)

Debt 15,00,000 5% 75,000

Preference shares 12,00,000 10% 1,20,000

Equity shares 18,00,000 12% 2,16.000

Retained earnings 15,00,000 11 % 1,65,000

60,00,000 100 5,65,000

Weighted average cost of capital = 5,76,000 /60,00,000 x 100

**Problem 3.** The Servex company has the following capital structure on 30-6-2004.

Ordinary shares (2,00,000 Shares) 6% Preference shares 8% Debentures |
$
40,00,000 10,00,000 30,00,000 80,00,000 |

The share of the company sells for $ 20. It is expected that company will pay a current

dividend of $ 2 per share which will grow at 7% for ever. Assume the tax rate may be 50%.

(i) Compute the weighted average cost of capital based on existing capital structure.

(ii) Compute the new weighted average cost of capital if the company raises an additional $ 20,00,000 debt by issuing 10% debenture. This would result in increasing the expected dividend to $ 3 and leave the growth rate unchanged, but the price of share will fall to $ 15 per share.

(iii) Compute the cost of capital if in (ii) above growth rate increases to 10%

**Solution :**

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**(i) Statement showing Weighted Average Cost of Capital**

Source
(1) Equity share capital Preference share capital Debentures |
Amount
(2) $ 40,00,000 10,00,000 30,00,000 80,00,000 |
After tax cost
(3) 17% 6% 4% |
Total after tax $
Cost (4) = (2) x (3) 6,80,000 60,000 1,20,000 8,60,000 |

Weighted average cost of capital = 8,60,000/80,00,000 x 100

K_{ e} =10.75

**NOTE :** Computation cost of equity share is

K _{e} = D/MP +g =$ .2 /$ 20 =0.07 =.17 x 100

** (ii)Statement showing Weighted Average Cost of Capital**

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Source Amount After tax cost
(1) (2) $ (3) Equity s ha re capital 40,00,000 27% 6% Preference capital 10,00,000 6% 8% Debentures 30,00,000 (8-4) 4% 10% Debentures 20,00,000 (10-5) 5% 1,00,000,00 |
Total after tax $
Cost (4) = (2) x (3) 10,80,000 60,000 1,20,000 1,00,000 13,60,000 |

Weighted average cost of capital ke = 13,60,000 /1,00,00 ,000 x 100

=13.6

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**NOTE :** Computation cost of equity share is

=ke =D/MP +g

=3/15 +0.07

=.20 +.07 =27 x 100

=17%

** (iii) Statement showing Weighted Average Cost of Capital**

Source Amount After tax cost
(1) (2) $ (3) Equity share capita l 40.00,000 30% 6% Preference capital 10,00,000 6% 8% Debentures 30,00,000 (8-4) 4% 10% Debentures 20,00,000 (10-5) 5% 1,00,000,00 |
Total tax $
Cost (4) = (2) x (3) 12,00,000 60,000 1,20,000 1,00,000 14,80,000 |

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Weighted average cost of capital ke = 14,80,000 /1,00,00 ,000 x 100

= 14.80 %

**NOTE :** Computation of cost of equity share i s :

=Ke = D /MP g

=3 /15 +.10

.30 i.e., 30% (.30 x 100)

**NOTE :** Tax R ate i.e., 50% to adjust only on Debenture after tax cost.

(i) Table= 10% : 50% of 10%= 5% – 5%= 5%

(ii) Table= 10% : 50% of 10%= 5% – 5%= 5%

(iii) Table= 8% : 50% of 8%= 4% – 4%= 4%

**Problem 4.** Following are the details regarding the capital structure of Sridhar & Co Ltd.

Type of Capital Book value Market value Specific cost

$ $

Debentures 40,000 38,000 5%

Preference capital 10,000 11,000 8%

Equity capital 60,000 1,20,000 13%

Retained earnings 20,000 _ 9%

1,30,000 1,69,000

You are requested to determine the weighted average cost of capital using (i) Book value as weights (ii) Market value as weights. Do you think t he re can be a situation where weighted average cost of capital would be the same irrespective of the weights used.

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**Solution :**

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**(i) Statement showing Weighted Average Cost of Capital**

(Book value)

Sources Amount
(1) (2) $ Debentures 40,000 Preference capital 10,000 Equity capital 60,000 Retained earnings 20,000 1,30,000 |
After tax cost
I X 100 (3) 5% 8% 13% 9% |
Total after tax Rs.
Cost (4) = (2) x (3) 2,000 800 7,800 1,800 I 12,400 |

Weighted average cost of capital = 12,400/1,30,000 x 100

= 9.53 %

**(ii) Statement showing Weighted Average Cost of Capital**

(market value)

Sources
(1) Debentures Preference capita l Equity capita l |
Amount
(2) $ 38,000 11,000 1,20,000 1,69,000 |
After tax cost Total after tax $
(3) Cost (4) = (2) x (3) 5% 1,900 8% 880 13% 15,600 18,380 |

Weighted average cost of capital = 18,380/1,69.000 x 100

= 10.87%

**Result and Comments :**

Cost of capital would be the same irrespective of the weights in case the Book value and

the Market value of the securities are the same.

**Problem 5.** Your company’s share is quoted in the market at $ 20 currently. The company pays a dividend of $ 1 per share and the invest or expects a growth rate of 5% per year. Compute :

(a) The company’s cost of equity capital.

(b) If the anticipated growth rate is 6% p.a. calculate the indicated market price per share.

(c) If the company’s cost of capital is 8% and the anticipated growth rate is 5% p.a., calculate the indicated market price if the dividend of $1 per share is to be maintained.

**Solution :**

(a) Cost of equity capital = Dividend /prince x 100 + Growth rate

=1/20 x 100 +5%

= 5% +5%

= 10%

( b) Market price =Dividend /Cost of equity capital – Growth rate %

=1/10% -6%

=1/4%

=.25 x 100 =$ .25

(c) Market prince = $ 1 /8% -5% = $ 33.33

**Problem 6. **The capital structure of Reliance Ltd is as follows :

3000 12% Debentures of $ 100 each 3,00,000

2000 10% Preference shares of $ 100 each 2,00,000

4000 Equity shares of $ 100 each 4,00,000

Retained Earnings 1,00,000

The earnings per share of the company for the past years have been $ 15. The shares of the company are sold in the market at Book value. The company’s tax rate is 50%. The shareholder’s tax liability may be assumed as 25%. Find out the weighted average cost of capital.

**Solution :**

(i) Cost of Debentures

Kd =I/NP 9I-T)

= 36,000 /3,00,000 x .50 = 6%

(ii) Cost of preference share capital 10%

(iii) Cost of equity share capital 12%

(iv) Cost of Retained Earnings 9%

**Statement showing Weighted Average Cost of Capital**

Source Amt ($) Weights Specific cost
% Debentures 3,00,000 .3 6 Preference capital 2,00,000 .2 10 Equity capital 4,00,000 .4 12 Retained earnings 1,00,000 .1 9 10,00,000 |
Weighted
Average cost 1.8 2.0 4.8 0.9 9.5 |

**Problem 7**. Calculate the cost of equity for a fir m whose shares are quoted at $ 120. The dividend at the end of the year is expected to be Rs. 9. 72 per share and the growth rate is 8%.

**Solution :**

Cost of equity for a firm

Ke =DPS /MP +g

Ke = Cost of equity capital

DPS = Dividend per Equity share

MP = Market price of an equity share

g = growth rate of dividend

Ke = 9. 72 /120 x 100 + 8%

= 8.1% + 8.00% = 16.1%

**Problem 8.** The current market price of an equity share of a company is $. 90. The current dividend per share is $ 4.50. In case. the dividends are expected to grow at the rate of 8%, what is the shareholders’ required rate of return ?

**Solution :**

Shareholders’ required rate of return :

Ke =DPS /MP +g

Ke =4.50 /90 +8%

.05 + .08 = 0.13

i.e., .13 x 100 = 13%

Shareholders’ required rate of return is 13%.

**Problem 9.** (a) A company plans to issue 1,000 new shares of $ 100 each at par. The floatation costs are expected to be 5% of the share price. The company pays a dividend of $ 10 per share initially and the growth in dividends is expected t o be 5%. Compute t he cost of new issue of equity shares. (b) If the current market price of an equity share is $ 150. Calculate the cost of existing equity share capital.

**Solution :**

Ke =DPS /MP +g

=10 /100-5 + 5% = 15.53%

= Ke = D /MP +G

=10/150-5 +5% =10 /145 +5%

= 11 .89%