chapter 18 homework

18.24 : You must assume that both kinds of kinds of investments are taxed at the same marginal rate

18.26: With debt financing , income tax per year = [ $500,000 - (1,300,000*8%]* 40%= $396,000*40%= $158400 and Net Income is $237,600[$500,000-$104,000-$158400] If all cash financing, income tax per year = $500,000 *40%= $200,000 and Net income is $300,000 Annual tax savings = $200,000-$158,400=$41,600 each year for two years, so PV=$41,600/1.10+41,600/1.1^2 aprox. $72,198

18.28

a.) The overall cost of capital for the firm is constant at 15%. The net per tax return is $500 million, so after-tax return is $500*(1-0.25)= $375 million. If the firm is fully equity financed, its value  is $375/1.15 aprox. 326.087 million

b.) As shown in previous calculation, the firm has a value of $375/1.15 approx. 326.087 million. Now we look at interest tax shield. If 50% had been financed with debt the debt would have been 0.5*(326.087) approx. 163.04 million. The expected return on the debt at 50% debt = 5%+10%(0.5)^2=7.5%. The interest expense tax savings of 0.25*$12.23 approx. $3.06 Using APV, the value of the firm $375/1.15+$3.075/1.15 approx. $328.75 million. This is higher than the $326.087 million, so $163.04 would just be a little less than 50% debt. Iterating will get more accurate value, but it would be almost the same.

c) The WACC = 15%-0.25(7.5%)(0.5)=14.0625%. The value of the firm is found by discounting the cash as if all equity financed by this rate $375/1.140625 approx. $328.77

d.) If we assume that the overall cost of capital of the firm will remain of the firm will remain unchanged regardless of the amount of debt financing and the tax is the only item of relevance, then the optimal capital structure is 100% debt. At 100% debt the overall cost of capital for the firm is still 15%. The interest expense is 0.15*(326.087)=$48.91305, so the expected tax savings is 0.25($48.913)=$12.2283. The bondholders are now the owners of the firm and the APV=$375/1.15+$12.2283/1.15 approx $336.72. Because there is no equity, the WACC = W Debt* E rDebt* 1- taxrate)= 100%*15%* (1-0.25) = 11.25%

18.30 The manager does not have to do a thing. Investors sort themselves automatically according to their personal income tax rate and assets expected pre-tax rates of return

18.32 High tax firms should use debt financing that is held by low-tax investors. Low-tax growth firms should use equity financing (i.e., retained earnings), which is held by high tax investors