Zoso is a rental car company that is trying to determine whether to add 25 cars
ID: 2756827 • 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 $150,000 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 14 percent, and the new fleet will not change the risk of the company. The risk-free rate is 5 percent.
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?
Suppose the company can purchase the fleet of cars for $365,000. Additionally, assume the company can issue $295,000 of four-year, 5 percent debt 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?
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 $150,000 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 14 percent, and the new fleet will not change the risk of the company. The risk-free rate is 5 percent.
Explanation / Answer
The maximum price that Zoso 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 + (1-0.35)($150,000)*(1-[1/1.14^4])/0.14 + (0.35)(P/5)(1-[1/1.14^4])/0.14
Set the NPV equal to zero.
Solving for P we get $236,739.12
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
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)
=-365,000+(1-.35)*($150,000)*(1-[1/1.14^4])/0.14+ 0.35*(365,000/4)(1-[1/1.14^4])/0.14
=$12,143.64
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), 5%.
=295,000-(1 – 0.35)(0.05)($295,000)(1-[1/1.05^4])/0.05 – [$295,000/(1.05)4
=$86,300
APV=12,143.64+86,300=$98,443.64
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