16.12 The general expression for the value of a leveraged firm in a world in which TS = 0 is

where V_U = Value of an unlevered firm T_C = Effective corporate tax rate for the firm T_B = Personal tax rate of the marginal bondholder B = Debt level of the firm C(B) = Present value of the costs of financial distress for the firm as a function of its debt level. [Note: C(B) encompasses all non–tax-related effects of leverage on the firm’s value.]

Assume all investors are risk-neutral.

a. In their no-tax model, what do Modigliani and Miller assume about TC, TB, and C(B)?
What do these assumptions imply about a firm’s optimal debt-equity ratio?

b. In their model that includes corporate taxes, what do Modigliani and Miller assume about TC, TB, and C(B)? What do these assumptions imply about a firm’s optimal debt-equity ratio?

c. Assume that IBM is certain to be able to use its interest deductions to reduce its corporate tax bill. What would the change in the value of IBM be if the company issued $1 billion in debt and used the proceeds to repurchase equity? Assume that the personal tax rate on bond income is 20 percent, the corporate tax rate is 34 percent, and the costs of financial distress are zero.

d. Assume that USX is virtually certain not to be able to use interest deductions. What would the change in the value of the company be from adding $1 of perpetual debt rather than $1 of equity? Assume that the personal tax rate on bond income is 20 percent, the corporate tax rate is 35 percent, and the costs of financial distress are zero.

e. For companies that may or may not be able to use the interest deduction, what would the change in the value of the company be from adding $1 of perpetual debt rather than $1 of equity? Assume that the personal tax rate on bond income is 20 percent, the corporate tax rate is 35 percent, and the costs of financial distress are zero. Also assume the probability of using the incremental deduction is 65 percent.

Transcribed Image Text:

V = + [ 1 ( -(1-T) (1 - TB) XB-C(B)