Solved Numerical Problems of Capital Structure Approaches

Introduction

Capital Structure is the combination of all the long-term sources of finances. Capital structure theories relate the capital structure of firm, capital mix and value of the firm; basically capital structure theories relate financial leverage with value of the firm. There are four widely accepted theories on capital structure:

• 1. Net Income Approach
• 2. Net Operating Income Approach
• 4. Modigliani-Miller Approach

Some of the solved numerical problems of capital structure theories are presented below with solutions to have a better understanding on the theories.

Net Income Approach

Illustration 1

Mehta Company Limited is expecting an annual EBIT of Rs. 2,00,000. The company has Rs. 5,00,000 in 10% debentures. The cost of equity capital or capitalization rate is 12.5%. Compute the value of the firm.

Solution:

Net Income                                                                                           Rs. 2,00,000

Less: Interest on 10% Debenture of Rs. 5,00,000                         Rs.    50,000

Earnings available to equity shareholders                             Rs. 1,50,000

Market Capitalization Rate                                                             12.5%

Market Value of the Equity (S) = 1,50,000*               Rs. 12,00,000

Market Value of Debenture (D)                                         Rs. 5,00,000

Value of the Firm (S+D)                                                                  Rs. 17,00,000

Illustration 2

1. An organization expects a net income of Rs. 1,00,000. It has Rs. 1,50,000, 10 % debentures. The equity capitalization rate of the company is 12%. Calculate the value of the firm and overall capitalization rate according to the Net Income Approach (ignoring income-tax).
2. If the debenture debt increased to Rs. 2,00,000, what shall be the value of the firm and the overall capitalization rate ?

Solution:

Net Income                                                                                           Rs. 1,00,000

Less: Interest on 10% Debenture of Rs. 1,50,000                         Rs.    15,000

Earnings available to equity shareholders                                Rs.   85,000

Market Capitalization Rate                                                                    12%

Market Value of the Equity (S) = 85,000*                    Rs. 7,08,333

Market Value of Debenture (D)                                                    Rs. 1,50,000

Value of the Firm (S+D)                                                                 Rs. 8,58,333

Overall Cost of Capital (Ko) = =  11.65%

b.

Net Income                                                                                          Rs. 1,00,000

Less: Interest on 10% Debenture of Rs. 2,00,000                         Rs.    20,000

Earnings available to equity shareholders                      Rs.   80,000

Market Capitalization Rate                                                                       12%

Market Value of the Equity (S) = 80,000*                    Rs. 6,66,666

Market Value of Debenture (D)                                                   Rs. 2,00,000

Value of the Firm (S+D)                                                                 Rs. 8,66,666

Overall Cost of Capital (Ko) = =  11.53%

It is clearly evident that addition of debt to the capital mix has decreased the overall cost of capital increasing the value of the firm

Net Operating Income (NOI) Approach

Illustration 1

A manufacturing company is expecting the Net Operating Income of is Rs. 200,000. The company has debenture lending of Rs 6,00,000 at 10% interest payable. The overall capitalization rate is 20%. Calculate the value of the firm and the equity capitalization rate as per the NOI approach.

What will be the impact on value of the firm and equity capitalization firm if the debenture amount is increased to Rs. 7,50,000?

Solution

Net Operating Income                                                                            Rs. 2,00,000

Interest                                                                                                    Rs.    60,000

Capitalization Rate                                                                                       20%

Value of the firm                                 = EBIT/Ko = 2,00,000/.20 = Rs. 10,00,000

Equity Capitalization Rate                =(EBIT-I)/(V-D)

= (2,00,000-60,000)/(10,00,000-6,00,000)

= 35%

If the debenture amount is increased,

Value of the Firm                                  = EBIT/Ko = 2,00,000/0.20 = Rs. 10,00,000

Equity Capitalization Rate                  = (EBIT-I)/(V-D)

= (2,00,000-75,000)/(10,00,000-7,50,000)

= 50%

Here, the value of firm is irrespective of the capital mix. The benefit of adding the debt fund of Rs. 1,50,000 is nullified by the increase in equity Capitalization rate from 35% to 50%.

Illustrations 1

Compute the value of the firm, value of shares and average cost of  capital from the following information:

Net Operating Income                                        Rs. 2,00,000

Total investment                                                  Rs. 10,00,000

Equity Capitalization Rat, If:

1. Firm uses no debt                                     10%
2. Firm uses Rs. 4,00,000 as debt               11%
3. Firm uses Rs. 6,00,000 as debt               15%

Assume that Rs. 4,00,000 debt can be raised at 5% and Rs. 6,00,000 can be raised at 7% rate of Interest.

Solution:

From the solution above, we can conclude that the increasing the debt portion, over a certain limit, has increased the cost of capital eventually.

Modigliani-Miller (MM) Approach

Illustration I

Company A and B are two similar businesses with similar business risks. Company A is unlevered whereas Company B is levered with Rs. 2,00,000 debenture @ 5% interest rate. Both the companies earn Rs. 50,000 before tax income. The after-tax capitalization rate is 10% and the corporate tax-rate is 40%. Calculate the market value of two firms.

Solutions:

Illustration II

Company A and B are engaged in the same line of activity with similar business risk. Company A is unlevered and Company B is levered with Rs. 2,00,000 debentures carrying 5% rate of interest. Both the firms have income before interest and taxes of Rs. 50,000. The company’s tax rate is 40% and capitalisation rate 10% for purely equity firms. Compute the value of firm U and L using the NI and NOI approach.

Solution:

Under NI Approach

Under NOI Approach (Taxes are under consideration)

Value of unlevered Firm (Vu)    = [EBIT (1-Tc)]/Ke = [50,000*(1-0.4)]/0.10

=Rs. 3,00,000

Value of levered Firm (VL)                    = Rs. 3,00,000+ Rs. 2,00,000*0.40

= Rs. 3,80,000

Illustration III

Company A and B are homogeneous in all respects except that Company A is levered while Company B is unlevered. Company A has Rs. 5,00,000 assumptions are met and the tax rate is 50%. (3). EBIT is Rs. 50,000 and that equity-capitalisation rate for Company B is 12%. What would be the value for each firm according to M— M’s approach?

Solution:

Value of unlevered Firm (Vu)    = [EBIT (1-Tc)]/Ke = [50,000*(1-0.5)]/0.12

=Rs. 2,08,333

Value of levered Firm (VL)            = Rs. 2,08,333+ Rs. 5,00,000*0.50

= Rs. 4,58,33

Illustration IV

The following is the data regarding two companies A & B belonging to the same equivalent risk classes.

All profits after paying debenture interest are distributed as dividend. How, under MM approach, an investor holding 10% of shares in company A will be better off in switching holding to company B.

Solutions:

One sells 10% shares from A i.e. 10%* 1,00,000 = 10,000 shares

Amount after selling shares = Rs. 1.3*10,000 = Rs. 13,000

Amount of loan to be taken = 10% of 50,000 = Rs. 5,000

Total amount available for making investment in B: Rs. 18,000

Amount is invested in Company B

No. f share purchased of B @ Re. 1 per share = 18,000

Proportion of share in company B = 18,000/1,50,000 = 12%

Present Income of Company A

Profit Before Interest of the Company =  Rs. 20,000

Debenture Interest @8%                              =    (Rs. 4,000)

Profit After Interest                                   =    Rs 16000

Share Profit on Company A       (10%)               Rs. 1600

Present Income while switching to Company B

Profit Before Interest of the Company =  Rs. 20,000

Debenture Interest @8%                              =    –

Profit After Interest                                   =    Rs 20,000

Share Profit on Company B        (12%)               =Rs. 2400

Interest on Loan 8%*5,000                                = Rs. 400

Profit After Interest                                         = Rs. 2000

Hence, the investor is in a better position in switching the investment amount from Company A to Company B. The profitability has increased by Rs. 400

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