17-1 a. MM Proposition I states the relationship between leverage and firm value. Proposition I without taxes is V = EBIT/rsU. Since both EBIT and rsU are constant, firm value is also constant and capital structure is irrelevant. With corporate taxes, Proposition I becomes V = Vu + TD. Thus, firm value increases with leverage and the optimal capital structure is virtually all debt. b. MM Proposition II states the relationship between leverage and cost of equity. Without taxes, Proposition II is rsL = rsU + (rsU – rd)(1 – T)(D/S). Thus, rs increases in a precise way as leverage increases. In fact, this increase is just sufficient to offset the increased use of lower cost debt. When corporate taxes are added, Proposition II becomes Here the increase in equity costs is less than the zero-tax case, and the increasing use of lower cost debt causes the firm’s cost of capital to decrease, and again, the optimal capital structure is virtually all debt. c. The Miller model introduces personal taxes. The effect of personal taxes is, essentially, to reduce the advantage of corporate debt financing.

d. Financial distress costs are incurred when a leveraged firm facing a decline in earnings is forced to take actions to avoid bankruptcy. These costs may be the result of delays in the liquidation of assets, legal fees, the effects on product quality from cutting costs, and evasive actions by suppliers and customers.

e. Agency costs arise from lost efficiency and the expense of monitoring management to ensure that debtholders’ rights are protected.

f. The addition of financial distress and agency costs to either the MM tax model or the Miller model results in a trade-off model of capital structure. In this model, the optimal capital structure can be visualized as a trade-off between the benefit of debt (the interest tax shelter) and the costs of debt