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
- 3. Traditional 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
- 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).
- 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%.
Traditional Theory Approach
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:
- Firm uses no debt 10%
- Firm uses Rs. 4,00,000 as debt 11%
- 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:
| No Debt | Rs. 4,00,000 @ 5% | Rs. 6,00,000 @ 7% | |
| Net Operating income | 2,00,000 | 2,00,000 | 2,00,000 |
| Interest | – | 20,000 | 42,000 |
| Earning available to shareholders | 2,00,000 | 1,80,000 | 1,58,000 |
| Equity Capitalization Rate | 10% | 11% | 15% |
| Market value of Equity Shares | 20,00,000 | 16,36,363 | 10,53,333 |
| Market Value of Firm | 20,00,000 | 20,36,363 | 16,53,333 |
| Average Cost of Capital (Earning/Value of the Firm) | 10% | 9.82% | 12.09% |
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:
| Firm A | Firm B | |
| Net Operating Income (NOI) | 50,000 | 50,000 |
| Interest on debenture | – | 10,000 |
| Profit before taxes | 50,000 | 40,000 |
| Taxes (40%) | 20,000 | 16,000 |
| Profit after taxes | 30,000 | 24,000 |
| After-tax Capitalization Rate | 10% | 10% |
| Total market value of the equity(S) | 3,00,000 | 2,40,000 |
| Market value of debt (B) | – | 2,00,000 |
| Total Value (V) | 3,00,000 | 4,40,000 |
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
| Company A | Company B | |
| Net Income | 50,000 | 50,000 |
| Interest on debenture | – | 10,000 |
| Profit before taxes | 50,000 | 40,000 |
| Taxes (40%) | 20,000 | 16,000 |
| Profit after taxes | 30,000 | 24,000 |
| After-tax Capitalization Rate | 10% | 10% |
| Total market value of the equity(S) | 3,00,000 | 2,40,000 |
| Market value of debt (B) | – | 2,00,000 |
| Total Value (V) | 3,00,000 | 4,40,000 |
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.
| A | B | |
| No. Of Ordinary Shares | 1,00,000 | 1,50,000 |
| Debentures (8%) | 50,000 | – |
| Market Price/Share | Rs. 1.30 | Rs. 1 |
| Profit Before Interest | 20,000 | 20,000 |
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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