Question

Benton is a rental car company that is trying to determine whether to add 25 cars to its fleet. The company fully depreciates all its rental cars over five years using the straight-line method. The new cars are expected to generate $220,000 per year in earnings before taxes and depreciation for five years. The company is entirely financed by equity and has a 21 percent tax rate. The required return on the company’s unlevered equity is 15 percent and the new fleet will not change the risk of the company.

a. What is the maximum price that the company should be willing to pay for the new fleet of cars if it remains an all-equity company? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b. Suppose the company can purchase the fleet of cars for $655,000. Additionally, assume the company can issue $430,000 of five-year debt to finance the project at the risk-free rate of 6 precent. All principal will be repaid in one balloon payment at the end of the fifth year. What is the APV of the project?

Answer 1

a). The maximum price which they should pay is the price at which NPV of buying the cars equals zero.

NPV    = -purchase price + PV of after-tax EBITDA + PV of depreciation tax shield

0 = -P + 220,000*(1-21%)*PVIFA(15%,5) + (21%*P/5)*PVIFA(15%,5)

P = 220,000*(1-21%)*3.3522 + (0.042*P*3.3522)

0.8592P = 58,260.46

P = 678,070.44 (Maximum price which can be paid)

b). APV = All-equity NPV + PV of financing side effects

All-equity NPV = - purchase price + PV of after-tax EBITDA + PV of depreciation tax shield

= -655,000 + 220,000*(1-21%)*PVIFA(15%,5) + (21%*(655,000/5)*PVIFA(15%,5)

= -655,000 + 173,800*3.3522 + 27,510*3.3522 = 19,822.34

PV of financing side effects = proceeds - PV of after-tax interest payments - PV of principal paid off

Since debt level is known, these cash flows will be discounted at the pre-tax cost of debt of 6%.

= 430,000 - (6%*430,000*(1-21%)*PVIFA(6%,5)) - (430,000*PVIF(6%,5))

= 430,000 - (20,382*4.2124) - (430,000*0.7473) = 22,822.59

APV = 19,822.34 + 22,822.59 = 42,644.93