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 $195,000 per year in earnings before taxes and depreciation for five years. The company is entirely financed by equity and has a 23 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 7 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? (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 $650,000. Additionally, assume the company can issue $420,000 of five-year debt to finance the project at the risk-free rate of 7 percent. All principal will be repaid in one balloon payment at the end of the fifth year. What is the APV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer - a

The maximum price that the company should be willing to pay for the new fleet of cars if it remains an all-equity company can be calculated using present value of the future cash flows which would be equal to the cost of new fleet of cars if the desired rate of return of the company of 12% is achieved. It also means that net present value from the project will be NIL at the desired rate of return of the company of 12%.

Let us assume the cost of new fleet of cars be x

Statement showing cash flows

Amount ($)

Particulars	Working	Year 1 to 5
Earnings from new cars	Given	195000
Depreciation on cost of new fleet of cars	x / 5	-0.20 x
Profit before tax		195000 - 0.20 x
Tax	23% of Profit before tax	-44850 + 0.046 x
Profit after tax		150150 - 0.154 x
Depreciation	Add back	0.20 x
Cash Flow		150150 + 0.046 x

If the present value of the future cash flows equals to the cost of new fleet of cars at the discount rate of 12%, then following equation will form to find the value of x -

Present value of the future cash flows = Cost of new fleet of cars

(150150 + 0.046 x) * Sum of Discount factors from year 1 to 5 = x

(150150 + 0.046 x) * 3.6048 = x

541260.72 + 0.1658 x = x

0.8342 x = 541260.72

x = 648838.07

Hence, the maximum price that the company should be willing to pay for the new fleet of cars is $648,838.07

Answer - b

If the company purchases the fleet of cars for $650,000 and issue $420,000 of five-year debt to finance the project, then the APV of the project can be calculated as below :

Statement showing cash flows

Amount ($)

Particulars	Working	Year 1 to 5
Earnings from new cars	Given	195000
Interest on Debt	($420,000 * 7%)	-29400
Depreciation on cost of new fleet of cars	($650,000 / 5)	-130000
Profit before tax		35600
Tax	23% of Profit before tax	-8188
Profit after tax		27412
Depreciation	Add back	130000
Cash Flow		157412

Note : It is assumed that Interest on debt is calculated on the principal amount of debt and interest is paid annually.

Statement showing APV

Amount ($)

Year	Particulars	Notes / Working	Amount (A)	Discount Factor @ 12% (B)	Present Value (A * B)
0	New fleet of cars cost paid	($650,000 - $420,000)	-230,000	1	-230,000
1 to 5	Cash Flows	Calculated above	157,412	3.6048	567,439
5	Balloon payment of principal of debt	Outflow at the end of year 5	-420,000	0.5674	-238,308
	Adjusted Present Value	99,131