Table 176

Modigliani and Miller Summary

I. The no-tax case

A. Proposition I: The value of the firm levered (VL) is equal to the value of the firm unlevered (VU):

Implications of Proposition I:

1. A firm's capital structure is irrelevant.

2. A firm's weighted average cost of capital (WACC) is the same no matter what mixture of debt and equity is used to finance the firm.

B. Proposition II: The cost of equity, RE, is:

Re = Ra + (Ra - Rd) x (D/E) where RA is the WACC, RD is the cost of debt, and D/E is the debt-equity ratio. Implications of Proposition II:

1. The cost of equity rises as the firm increases its use of debt financing.

2. The risk of the equity depends on two things: the riskiness of the firm's operations (business risk) and the degree of financial leverage (financial risk). Business risk determines RA; financial risk is determined by D/E.

II. The tax case

A. Proposition I with taxes: The value of the firm levered (VL) is equal to the value of the firm unlevered (VU) plus the present value of the interest tax shield:

VL = VU + TC x D where TC is the corporate tax rate and D is the amount of debt. Implications of Proposition I:

1. Debt financing is highly advantageous, and, in the extreme, a firm's optimal capital structure is 100 percent debt.

2. A firm's weighted average cost of capital (WACC) decreases as the firm relies more heavily on debt financing.

B. Proposition II with taxes: The cost of equity, RE, is:

where RU is the unlevered cost of capital, that is, the cost of capital for the firm if it has no debt. Unlike the case with Proposition I, the general implications of Proposition II are the same whether there are taxes or not.

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