Suppose rD  12%,  10%, Tc  33%, TD 

20%.

a. What is the marginal tax rate on stock income TE which would make an investor indifferent in terms of after-tax returns between holding stock or bonds? Assume all betas are zero.

b. What is the probability that a firm will not utilize its tax shield if, on the margin, the firm is indifferent between issuing a little more debt or equity?

rE 14.2. Consider a single period binomial setting where the riskless interest rate is zero, and there are no taxes. A firm consists of a machine that will produce cash flows of $210 if the economy is good and $80 if the economy is bad. The good and bad states occur with equal risk-neutral probability.

Initially, the firm has 100 shares outstanding and debt with a face value of $50 due at the end of the period. What is the share price of the firm?

total value of the firm unaltered by this type of capital structure change.

Result 14.4: Assume that the pretax cash flows of the firm are unaffected by a change in a firm’s capital structure, and that there are no transaction costs or opportunities for arbitrage. With corporate taxes at the rate Tc, but no personal taxes, the value of a levered firm with static risk-free perpetual debt is the value of an otherwise equivalent unlevered firm plus the product of the corporate tax rate and the market value of the firm’s debt; that is VL  VU
TcD Result 14.5: Assume that the pretax cash flows of the firm are unaffected by a change in a firm’s capital structure, and that there are no transaction costs or opportunities for arbitrage. With corporate taxes but no personal taxes, a firm’s optimal capital structure will include enough debt to completely eliminate the firm’s tax liabilities.

Result 14.6: Assume that the pretax cash flows of the firm are unaffected by a change in a firm’s capital structure, and that there are no transaction costs of opportunities for arbitrage. If investors all have personal tax rates on debt and equity income of TD and TE, respectively, and if the corporate tax rate is Tc, then the value of a levered firm exceeds the value of an otherwise equivalent unlevered firm by TgD; that is VL  VU
TgD, where Result 14.7: Assume there is a tax gain from leverage, but the taxable earnings of firms are low relative to their present values.

• With riskless future cash flows, firms will want to use debt financing up to the point where they eliminate their entire corporate tax liabilities, but they will not want to borrow beyond that point.

• With uncertainty, firms will pick the debt ratio that weighs the benefits associated with the debt tax shield when it can be used against the higher cost of debt in cases where the debt tax shield cannot be used.

• Firms with more nondebt tax shields are likely to use less debt financing.

Result 14.8: For low tax bracket investors, it is often cheaper to lease an asset than to buy it.

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