# Hertz: Depreciation and Present Value

17.1Honda and GM are competing to sell a fleet of 25 cars to Hertz. Hertz fully depreciates all of its rental cars over five years using the straight-line method. The firm expects the fleet of 25 cars to generate $100,000 per year in earnings before taxes and depreciation for five years. Hertz is an all-equity firm in the 34-percent tax bracket. The required return on the firm’s unlevered equity is 10 percent, and the new fleet will not add to the risk of the firm.

a. What is the maximum price that Hertz should be willing to pay for the new fleet of cars if it remains an all-equity firm? b. Suppose Hertz purchases the fleet from GM for $325,000, and Hertz is able to issue $200,000 of five year, 8% debt in order to finance the project. All principal will be repaid in one balloon payment at the end of the fifth year. What is the Adjusted Present Value (APV) of the project?

17.1a.The maximum price that Hertz should be willing to pay for the fleet of cars with all-equity funding is the price that makes the NPV of the transaction equal to zero.

NPV = -Purchase Price + PV[(1- TC )(Earnings Before Taxes and Depreciation)] +

PV(Depreciation Tax Shield)

Let P equal the purchase price of the fleet.

NPV = -P + (1-0.34)($100,000)A50.10 + (0.34)(P/5)A50.10

Set the NPV equal to zero.

0 = -P + (1-0.34)($100,000)A50.10 + (0.34)(P/5)A50.10

P= $250,191.93 + (P)(0.34/5)A50.10

P = $250,191.93 + 0.2578P

0.7422P = $250,191.93

P = $337,095

Therefore, the most that Hertz should be willing to pay for the fleet of cars with all-equity funding is $337,095.

b.The adjusted present value (APV) of a project equals the net present value of the project if it were funded completely by equity plus the net present value of any financing side effects. In Hertz’s case, the NPV of financing side effects equals the after-tax present value of the cash...

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