The cost of debt capital, rD, remains more or less constant up to a certain degree of leverage but rises thereafter at an increasing rate.
The cost of equity, rE remains more or less constant or rises only gradually up to a certain degree of leverage and rises sharply thereafter
The average cost of capital, rA, as a consequence of the above behaviour of rE and rD:
Decreases up to a certain point
Remains more or less unchanged for moderate increases in leverage thereafter
Rises beyond a certain point
The traditional approach is not as sharply defined as the net income approach or the net operating income approach. Several shapes of rD, rE and rA are consistent with this approach. The following figure graphically represents the above:
Behaviour of rA, rD and rE under traditional approach
In traditional approach average cost of capital is dependent on capital structure. There is an optimal capital structure which minimizes cost of capital.
MODIGLIANI AND MILLER THEORY
The Modigliani and Miller theory is based on the following assumptions:
Perfect Capital Market: Information is freely available and there is no problem of asymmetric information, transactions are costless, there are no bankruptcy costs, securities are infinitely divisible.
Rational Investors and Managers: Investors rationally choose a combination of risk and return that is most advantageous to them, Managers act in the interest of shareholders.
Homogenous Expectations: Investors hold identical expectations about future operating earnings.
Equivalent Risk Classes: Firms can be grouped into 'equivalent risk classes' on the basis of their business risk
Absence of Taxes: There is no tax to be paid by the company.
Proposition 1:
"The value of a firm is equal to its expected operating income divided by the discount rate appropriate to its risk class. It is independent of its capital structure."
This proposition is identical to the net operating income approach. MM invoked an arbitrage argument to prove this proposition. In equilibrium, identical assets must sell for the same price, irrespective of how they are financed.
Arbitrage Argument:
Consider 2 firms A and B, similar in all respects, except in their capital structure. Firm A is an unlevered firm financed by equity alone, whereas Firm B is a levered firm financed by a mix of equity and debt. The following are the financial details:
Particular
Firm A
Firm B
Operating Income (PBIT)
1,50,000
1,50,000
Interest
0
60,000
Equity Earnings
1,50,000
90,000
Cost of Equity
0.15
0.16
Market Value of Equity
10,00,000
5.62,500
Cost of debt
-
0.12
Market Value of Debt
0
5,00,000
Market Value of Firm
10,00,000
10,62,500
Average Cost of Capital
0.15
0.1412
As we can see, the value of the levered firm B is higher than that of the unlevered firm A even though both firms have same operating income and belong to the same risk.
Now, such a situation, as argued by MM, cannot persist because equity investors would do well to sell their equity in firm B (the firm which is valued more) and invest in firm A (which is valued less) with personal leverage.
It makes no difference whether investors love risk or abhor risk. All would agree that unlevered firm A and the levered firm B should have the same value. If investors can borrow and lend on their personal account on the same terms as the firm, they can mimic whatever a firm can do. Hence the value of the firm will be independent of the capital structure.
Proposition 2:
Implications of Proposition 1 for the expected return to the equity shareholders of company X:
Current capital structure
100% equity
Proposed capital structure
50% equity & 50% debt
Expected earnings per share
Rs 4
Rs 5
Price per share
Rs 20
Rs 20
Expected return to equity shareholders.
20%
25%
An increase in financial leverage increases the expected earnings per share but not the share price. This is because the change in the expected earnings s offset by a corresponding change in return required by the shareholders.
rE = rA + (rA-rD) (D/E)
The second proposition says:
"The expected return on equity is equal to the expected rate of return on assets, plus a premium. The premium is equal to the debt-equity ratio times the difference between the expected return on assets and expected return on debt."
Implications:
For low levels of debt, the firm's debt is considered risk free. This implies that rD is independent of D/E and hence rE increases linearly with D/E. As the debt of the firm crosses a threshold limit, the risk of default increases and the expected return on debt rD increases. To compensate for this, the rate of increase in rE decreases. That is, rE becomes less sensitive for further borrowings at higher levels of debt. This is because beyond the threshold level, a portion of the firm's risk is borne by the suppliers of debt capital. As the firm borrows more, more of its business risk is shifted from shareholders to creditors.
Criticisms of MM Theory:
The leverage irrelevance theorem of MM is valid if the perfect market assumptions underlying the analysis are satisfied. But, the real world is characterized by various imperfections:
Firms are liable to pay taxes on their income. In addition, investors who receive returns from their investments in firms are subject to taxes at a personal level.
Bankruptcy costs can be quite high
Agency costs exist because of the conflict of interest between managers and shareholders and between shareholders and creditors.
Managers seem to have a preference for a certain sequence of financing.
Information asymmetry exists because managers are better informed that investors.
Personal leverage and corporate leverage are not perfect substitutes.
Due to these imperfections, the capital structure of the firm has a bearing on valuation and firms regard capital structure decision as a major issue.
TAXATION AND CAPITAL STRUCTURE:
So far the methods assumed that no tax is levied which is impractical. There are corporate and personal taxes which affect the capital structure.
Corporate Taxes
Debt financing is advantageous when taxes are applicable to the corporate income due to the fact that the cost of debt i.e. interest is a tax deductible expense while dividends and retained earnings are not. This implies that the total income is greater for shareholders and debt holders when debt capital is used..
If debt employed by a levered firm is perpetual in nature, the present value of the tax shield associated with interest payment can be obtained by applying the formula for perpetuity.
Present value of tax shield = tcrDD = tcD rD
tC - corporate tax rate
D - market value of debt
rD - interest rate on Debt
The overall value of the firm increases by the above amount. Value of levered firm is given by sum of the value of unlevered firm and value of tax shield arising out of financial leverage. Thus greater the leverage greater is the value of the firm.
V = O (1 - tc) + tcD r
V - Value of the firm
O - Operating Income
r - capitalization rate
Corporate Taxes and Personal Taxes
When personal taxes are considered alongwith corporate taxes, if we assume that investors pay same rate of personal taxes on debt returns as well as equity returns, advantage of corporate tax in favour of debt capital remains in tact. If personal tax rate is tp then tax advantage of debt becomes:
tc D(1 - tp)
This formula is applicable when personal tax rate applicable to equity as well as debt income is same. Whereas in many countries including India it is not true. Equity income is taxed at a lower rate. When different tax rates apply tax advantage of debt is expressed as follows:
1 - (1 - tc)(1 - tpe) (1 - tpd)
