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Test Questions Cost of Capital

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.

 

 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

[Market value weights]
            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.

 

Solution :

 

      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 :

 

(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

 

         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

 

 

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

 

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.

 

 

 

 

Solution :

 

(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%