Zoso is a rental car company that is trying to determine whether to add 25 cars
ID: 2807211 • Letter: Z
Question
Zoso 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 four years using the straight-line method. The new cars are expected to generate $165,000 per year in earnings before taxes and depreciation for four years. The company is entirely financed by equity and has a 35 percent tax rate. The required return on the company’s unlevered equity is 12 percent, and the new fleet will not change the risk of the company. The risk-free rate is 8 percent. 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? b. Suppose the company can purchase the fleet of cars for $380,000. Additionally, assume the company can issue $265,000 of four-year debt at the risk-free rate of 8 percent to finance the project. All principal will be repaid in one balloon payment at the end of the fourth year. What is the adjusted present value (APV) of the project?
Explanation / Answer
Solution:
a. The maximum price that the company 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. Discounting the depreciation tax shield at the risk-free rate, the NPV equation for the project is:
NPV = –Purchase Price + PV[(1 –tC)(EBTD)] +PV(Depreciation Tax Shield)
If we let P equal the purchase price of the fleet, then the NPV is:
NPV = –P + (1 – .35)($165,000)PVIFA12%,4+ (.35)(P/4)PVIFA12%,4
Set the NPV equal to zero.
0 = –P + (1 – .35)($165,000)PVIFA12%,4+ (.35)(P/4)PVIFA12%,4
P = $325,755.72 + 0.2658P
0.7342P = $325,755.72
P = $443,668.69
Therefore, the most that Zoso should be willing to pay for the fleet of cars with all-equity funding is $443,669.
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 Zoso’s case, the NPV of financing side effects equals the after-tax present value of the cash flows resulting from the firm’s debt.
APV = NPV(All-Equity) + NPV(Financing Side Effects)
NPV(All-Equity)
NPV = -Purchase Price + PV[(1- TC )(Earnings Before Taxes and Depreciation)] +
PV(Depreciation Tax Shield)
Zoso paid $380,000 for the fleet of cars. Because this fleet will be fully depreciated over five years using the straight-line method, annual depreciation expense equals $95,000 (= $380,000/4).
NPV = -$380,000 + (1-0.35)($165,000) (PVIFA @ 12%, 4) + (0.35)($95,000)(PVIFA @ 12%, 4)
= $46,748
NPV(Financing Side Effects)
The net present value of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt.
NPV(Financing Side Effects) = Proceeds – After-Tax PV(Interest Payments) – PV(Principal Payments)
Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt (rB), 8%.
NPV(Financing Side Effects) = $265,000 – (1 – 0.35)(0.08)($265,000) (PVIFA @ 8%, 4) – [$265,000/(1.08)4]
= $45,641
APV
APV = NPV(All-Equity) + NPV(Financing Side Effects)
= $46,748 + $45,641
= $92,389
Therefore, if Zoso uses $265,000 of four-year, 8% debt to fund the $380,000 purchase, the Adjusted Present Value (APV) of the project is $92,389.
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