THEORIES OF CAPITAL STRUCTURE - Compiled By- Sapna Bhupendra Jain; 98112-55704 There are only two main sources of funds one are equity and other is debt. Both sources are used by the firms to finance their business activities. The proportion of debt and equity may differ according to requirement. Theories of capital structure explain the impact of proportion of debt and equity on the overall cost of capital and value of the firm. To be more specific, these theories explain the impact of debt on the overall cost of capital and value of the firm. These theories try to answer the question: whether a firm can affect its valuation and its overall cost of capital by varying the proportion of debt and equity i.e. whether financial leverage affect overall cost of capital and value of firm or not. There are four theories – (1) Net Income Approach – (NI approach) This approach suggests that there is a relationship between capital structure and the value of the firm and therefore the firm can affect its value by increasing or decreasing the debt proportion in the overall financing mix. The NI approach makes the following additional assumption – (1) That the total capital requirement of the firm is given and remains constant. (2) That Kd is less than Ke. (3) Both Kd and Ke remain constant and increase in financial leverage i.e. use of more and more debt financing in the capital structure does not affect the risk perception of the investors. The NI approach starts from the argument that change in financing mix of a firm will lead to change in weighted average cost of capital (Ko) of the firm resulting in the change in value of the firm. As Kd is less than Ke, the increasing use of cheaper debt in the overall capital structure will result in the magnified return available to the shareholders. The increased returns to the shareholders will increase the total value of the equity and thus increases the total value of the firm. %Cost of Capital of
Ke Ko Kd
Leverage (degree) With the judicial use of debt and equity; a firm achieve an optimal capital structure. Optimal capital structure is one at which the weighted average cost of capital is minimum resulting in the maximum value of firm. EXAMPLE: The expected EBIT of a firm is Rs. 2,00,000. It has issued equity share capital with Ke @ 10% and 6% debt of Rs. 5,00,000. Find out the value of the firm and the overall cost of capital. Solution: EBIT 2,00,000 (-) Interest 30,000 Net Profit 1,70,000 Ke 10% 1
Value of equity 1,70,000 / 10 Value of debt (D) Total value of firm (V) Ko EBIT / V
17,00,000 5,00,000 22,00,000 2,00,000 = 0.09 or 9% 22,00,000 Now, if the firm has issued 6% debt of Rs. 7,00,000 instead of Rs. 5,00,000, the position would have been as follows: EBIT 2,00,000 (-) Interest 42,000 Net profit 1,58,000 Ke 10% Value of equity 1,58,000 / .10 15,80,000 Value of debt. (D) 7,00,000 Total value of firm, (V) 2 2,80,000 Ko EBIT / V 2,00,000 = 0.87 or 8.7% 22,80,000 So when the 6% debt is increased from Rs. 5,00,000 to Rs. 7,00,000 the value of the firm increases from 22,00,000 to 22,80,000 and weighted average cost of capital decrease from 9% to 8.7%. Now, say the firm has issued 6% debt of Rs. 2,00,000 only instead of s. 5,00,000. The position would be as follows: EBIT 2,00,000 (-) Interest 12,000 Net profit 1,88,000 Ke 10% Value of equity 1,88,000 / .10 18,80,000 Value of debt (D) 2,00,000 Total value of the firm (V) 20,80,000 Ko EBIT / V 2,00,000 = 0.096 or 9.6% 20,80,000 So, when the proportion of 6% debt is reduced to Rs. 2,00,000 only, the value of the firm reduces to Rs. 20,80,000 and the weighted average cost of capital increases from 9% to 9.6%. Thus as per the NI approach, a firm is able to increase its value and to decrease its weighted average cost of capital by increasing the debt proportion in the capital structure. (2) NET OPERATING INCOME APPROACH – (NOI)
This approach suggests that the market value of the firm depend upon the net operating profit or EBIT and the overall cost of capital. The financing mix or capital structure is irrelevant and does not affect the value of the firm. The NOI approach makes the following assumptions – (i) The investors see the firm as a whole and thus capitalise the total earnings of the firm to find the value of the firm as a whole. (ii) Ko of the firm is constant and depends on the business risk, which also is assumed to be unchanged. (iii) Ke is also taken as constant.
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(iv)
The use of more and more debt in the capital structure increases the risk of the shareholders and thus results in the increase in the Ke. The increase in Ke is such as to completely off set the benefit of employing cheaper debt; and (v) That there is no tax. This approach based on the concept that, for a given value of EBIT, the value of the firm remain same irrespective of the capital composition and instead depends on the Ko. V = EBIT Ko And value of equity = Value – Debt (V – D) Ke = EBIT V-D Ke Cost of Capital %
Ko Kd
Leverage (degree) This diagram shows that Kd and Ko are constant for all level of leverage. As the debt proportion or the financial leverage increases, the risk of the shareholders also increases and thus Ke also increases. EXAMPLE – A firm has an EBIT of Rs. 2,00,000 and belongs to a risk class of 10%. What is the value of Ke if it employees 6% debt to the extant of 30%, 40% or 50% of the total capital funds of Rs. 10,00,000. Computation of Ke and value of shares: 30% debt 40% debt 50% debt EBIT 2,00,000 2,00,000 2,00,000 Ko 10% 10% 10% Value of firm (V) 20,00,000 20,00,000 20,00,000 Value of 6% debt (D) 3,00,000 4,00,000 5,00,000 Value of equity (V-D) 17,00,000 16,00,000 15,00,000 Net profit (EBIT-Interest) 1,82,000 1,76,000 1,70,000 Ke (Net Profit/value of equity) 10.7% 11% 11.33% The Ke of 10.7%, 11% and 11.33% can be verified for different proportion of debt by calculating Ko as follows: For 30% debt, Ke = [D/(D+E)] Kd + [E/(D+E)] Ke = [3 /(3+17)] 0.06 + [17/(3+17)] 0.107 = 10% For 40% debt, Ko = [D/(D+E) Kd + [E/(D+E)] Ke = [4/(4+16)] 0.06 + [16/(4+16)] 0.11 = 10% For 50% of debt, Ko = [D/(D+E)] Kd + [E/(D+E)] Ke = [5/(5+15)] 0.06 + [15/(5+15)] 0.113 = 10% This calculation shows that employment of more and more debt in the capital structure is off set by the increase in Ke.
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(3) TRADITIONAL APPROACH Value of firm can be increased and overall cost of capital is lowered by using judicious mix of debt and equity. The use of debt will achieve these objectives (increasing value of firm and reducing Ko) upto a certain point. Upto this point, with increase in financial leverage there may be slight increase in Ke (because of increase in financial risk) but the benefit of using cheaper debt funds is more than the increase in Ke. Hence Ko is lowered resulting in increase in value of firm. Beyond this point, with increase in degree of financial leverage, Ke exceeds the benefit of use of debt funds. The result is increased Ko and lowered value of firm. The optimum capital structure is one at which Ko is minimum i.e. value of firm is maximum. Cost of Capital %
Range of optimal capital structure. Leverage (degree) EXAMPLE – A firm’s total requirement of funds Rs. 1,00,000; expected EBIT = 20,000; Kd is 5% if the amount of debt does not exceed Rs. 50,000. It is so exceeds, Kd is 8% on total amount of debt. If the proportion of debt to total funds is upto 50%, Ke is 10%, otherwise 15%. Find Ke and value of firm if % of debt to total funds is 10%, 40% and 70%. Computation of Ko and value of firm at various level of financial leverage % of debt to total funds: 10 40 70 EBIT 20,000 20,000 20,000 Interest 500 2,000 5,600 Profit for equity 19,500 18,000 14,400 Value of equity 1,95,000 1,80,000 96,000 Value of debt 10,000 40,000 70,000 Value of firm 2,05,000 2,20,000 1,66,000 Ko 9.76% 9.09% 12.05% (4) MODIGLIANI – MILLER MODEL – (MM Model) MM maintain that choice of capital structure (i.e. degree of financial leverage) has no effect on the overall cost of capital and value of firm. They fully agree with the conclusions of Net Operating Income approach but they provide theoretical argument in support of these conclusions. In other works, MM has suggested a mechanism to prove their point. This mechanism is called ARBITRAGE PROCESS. The arbitrage process is a balancing operation. It suggests that investors buy undervalued shares and sell over valued shares. They may create home made leverage or they may undo the leverage. (By creating home made leverage we mean borrowing money. MM assume that investors are able to borrow in identical proportion to companies at identical interest rate. By “undoing the leverage” we mean investing in debt securities). This process goes on till the market achieves equilibrium i.e. both the firms achieve same value. MM
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assumes that capital markets are perfect, there is no transaction cost, no taxes and payout ratio is 100%. EXAMPLE – Two companies A & B have same business risk. Face value of shares of the companies Rs. 1.00 each. Other relevant data for the two companies are given below. A B No of ordinary shares. 90,000 1,50,000 Market price per share 1.20 1.00 6% Debentures 60,000 ---EBIT 18,000 18,000 An investor holds 900 shares of A. Explain and illustrate the process by which, through investors’ actions, the market values of the two companies might be brought into equilibrium. Answer – DPS is Rs. 0.16 and Rs. 0.12 in the case of firm A and B respectively. A gets annual divided of Rs. 144. It would be in his interest to move from A (levered firm) to B (unlevered firm). To maintain the risk at the levels of A he may borrow Rs. 600 at 6% (MM assume that inventors are able to borrow in identical proportions to companies at identical interest rates. The investors is holding 1% shares of A. hence, he can borrow 1% of Rs. 60,000 i.e. total debt of A at the same rate of 6% at which A has raised the debt). Now he has Rs. 1680 shares of B. On these shares he will get the dividend of Rs. 201.60 out of which he may pay Rs. 36 as interest on borrowing, he shall be left with net annual income of Rs. 165.60 which is an increase of Rs. 21.60 over his income when he held the share of A. The action of a number of investors on these lines will tend to drive up the price of shares of B and drive down the price of shares of A. The process will continue till equilibrium is achieved i.e. total value of the 2 firms is the same. Suppose market price of shares of A remain unchanged i.e. value of firm A continues to be Rs. 1,68,000 i.e. Rs. 60,000 debt + Rs. 1,08,000 value of shares (90,000 XI.20), the arbitrage process will continue till the market price of all shares of B is Rs. 1,68,000 i.e. price per share of B is 1,68,000 / 1,50,000 = 1.12 ARBITRAGE PROCESS (From levered to unlevered) (1) Sell the shares of levered firm. (2) Raise proportionate loan to create home – made leverage. (3) Invest in the shares of unlevered firm. Arbitrage Process – (From unlevered firm to levered firm). (1) Sell the shares of unlevered firm. (2) Invest proportionate amount in debentures to undo the firm leverage (firm as borrowed money, investors has lent money. To his MM call as unwinding of the leverage.) (3) Invest in the shares of levered firm. The process continues till market value of both the firms is the same. CORPORATE TAX (NI APPROACH & TRADITIONAL APPROACH) If tax is considered, we calculate value of equity by dividing EAT by Ke. Value of firm is equal to value of equity plus value of debt.
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Corporate Tax (NOI approach & MM Approach) The advocates of both these approach agree that their conclusion (i.e. overall cost of capital and valuation of firm are not affected by financial leverage) holds goods only if tax is ignored. The overall cost of capital will decreases and value of firm will increases with financial leverage if tax is considered. As interest is allowed as deduction for computing taxable income, it reduces overall cost of capital and increases value of firm. We find value of firm in two steps: Step I – Value of unlevered firm = EBIT (I – T) Ke Even if the firm is a levered one, we assume for this step that it is unlevered. Step II – Value of levered firm = Value of unlevered firm + Borrowing x Tax rate. Ques. 1: A company presents you the following figures: Profits (before interest and Taxes) Less: Interest on debentures @ 2,00,000 Less: Interest on long term loan @ 10% 2,00,000
24,00,000
4,00,000 20,00,000 Less: Income tax @ 50% 10,00,000 Profit after tax 10,00,000 No. of equity shares(of RS. 10 each) 4,00,000 Earning per share 2.5 Ruling market price 20 Price earning Ratio 8 The company has undistributed reserve and profit of Rs. 65,00,000. The company needs to raise Rs. 45,00,000 for repayment of debentures and modernisation of its plants and seeks your opinion on the advisability of taking recourse to which of the following modes of raising the needful funds of the consideration of the probable price of the share to rule on implementation. (1) Raising the entire amt. by term loans from Banks. Interest @ 10% (2) Raising partly by issue of 1,00,000 equity shares. Estimated price to fetch Rs. 18 per share and rest by term loans from Bank @ 10%. The company expects that the rate of return i.e. profit before Tax & Interest on funds employed will improve by 4% because of modernisation and that if the debt equity ratio (i.e. debt / debt plus share holders fund) exceeds 35% the price earning ratio is to go down to 6. [Ans. Rate of Return 20%, IInd Plan] Ques. 2: Company X and Company Y are in the same risk class, and are identical in every fashion except that company X uses debt while company Y does not. The levered firm has Rs. 9,00,000 debentures, carrying 10% rate of interest. Both the firms earn 20% before interest and taxes on their total assets of Rs. 15 lakhs. Assume perfect capital markets, rational investors and so on, a tax rate of 50% and Capitalisation rate of 15% for an all equity company. (i) Compute the value of rims X and Y using the net income (NI) approach. (ii) Compute the value of each firm using the net operating income (NOI) approach. (iii) Using the NOI approach, calculate the overall cost of capital (Ke) for firms X and Y.
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Which of these two firms has an optimal capital structure according to the NOI approach? Why? [Ans. (i) X-16,00,000, Y-10,00,000; (ii) X-14,50,000, Y-10,00,000; (iii) 10.34%] Ques. 3: Companies U and L are identical in every respect, except that U is unlevered while L is levered. Company L has Rs. 20 lakhs of 8% debentures outstanding. Assume (1) That all the MM assumptions are met. (2) That the tax rate is 50%. (3) That EBIT is Rs. 6 lakhs; and (4) That equity capitalisation rate for company U is 10%. What would be the value for each firm according to MM’s approach? [Ans. Vu = 30,00,000, Ve = 40,00,000] Ques. 4: Compute the equilibrium values and Capitalisation rates of equity (Ke) of the companies A and B on the basis of the following data. Assume that (i) there is no income tax (ii) the equilibrium value of average cost of capital is 8.5%. INITIAL DISEQUILIBRIUM Company A. Company B. Total Market Value Rs. 250 Rs. 300 Debt 0 150 Equity 250 150 Expected net operating Income 25 25 Interest 0 9 Net Income 25 16 Cost of equity (Ke) 10% 10.7% Leverage (Debt / Value) 0 0.5 Average cost of capital 10% 8.33% [Ans. - Equilibrium Values – 294.12; Capitalisation rate of equity 8.5%, 11.1%]
- Sapna Bhupendra jain; 98112-55704
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