Question

1. Zu car rental corporation is trying to determine whether to add 25 cars to its fleet. The company fully depreciates all its rental cars over 5 years using the straight line method. The new cars are expected to generate $140,000 per year in earnings before taxes and depreciation for 5 years. The company is entirely financed by equity and has a 35% tax rate. The required return on the company’s unlevered equity is 13% 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 firm?

b. Suppose the company can purchase the fleet of cars for $395,000. Additionally, assume the company can issue $260,000 for 5 year, 8% debt to finance the project. All principal will be repaid in one balloon payment at the end of the 5th year. What is the adjusted present value (APV) of the project?

Show all work.

Answer 1

a) Calculation of Maximum Price:-

Let Maximum price i.e., Present Value of Cash Outflow be denoted by A.

Net Present Value = Present Value of Cash inflows - Present Value of Cash Outflow

0 = [140000 * (1 - 0.35) * Cumulative Present Value Factors for 5 Years at the rate of 13 % + 0.20 A * 0.35 * Cumulative Present Value Factors for 5 Years at the rate of 13 %] - A

0 = [ 91000 * 3.517 + 0.07 A * 3.517] - A

A = 320047 + 0.24619 A

A - 0.24619 A = 320047

0.75381 A = 320047

A = 320047 / 0.75381

A = $ 424573 (approx)

Conclusion:- Maximum price that company is willing to pay for new fleets of car = $ 424573 (approx).

b) Adjusted Present Value (APV) of Project:-

(i) Net Present Value (Assuming Equity Financed):-

Present Value of Cash inflow - Present Value of Cash outflow

= [140000 * (1 - 0.35) * Cumulative Present Value Factors for 5 Years at the rate of 13 % + 0.20 * 395000 * 0.35 * Cumulative Present Value Factors for 5 Years at the rate of 13 %] - 395000

= [ 140000 * 0.65 * 3.517 + 27650 * 3.517 ] - 395000

= [ 320047 + 97245 (approx) ] - 395000

= 22292 (approx)

(ii) Present Value of financing project through debt = [ 260000 - { 260000 * Present Value Factor for Year 5 at the rate of 8 %} - { 260000 * (1 - 0.35) * (0.08) * Cumulative Present Value Factors for Five Years at the rate of 8 %} ]

= [ 260000 - {260000 * 0.681} - {13520 * 3.993} ]

= [ 260000 - 177060 - 53985 ]

= [ 260000 - 231045 ]

= $ 28955 (approx)

Adjusted Present Value (APV) of Project = Net Present Value (Assuming Equity Financed) + Present Value of finacing project through debt.

= 22292 + 28955

= $ 51247 (approx)

Conclusion:- Adjusted Present Value (APV) of Project = $ 51247 (approx)