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 four years using the straightline method. The new cars are expected to generate $255,000 per year in earnings before taxes and depreciation for four years. The company is entirely financed by equity and has a 25 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.

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 $625,000. Additionally, assume the company can issue $370,000 of four-year debt to finance the project at the risk-free rate of 5 percent. All principal will be repaid in one balloon payment at the end of the fourth 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

To determine the maximum price that Benton should be willing to pay for the new fleet of cars, we need to calculate the present value of the earnings before taxes and depreciation for four years.

Step-by-step explanation:

To determine the maximum price that Benton should be willing to pay for the new fleet of cars, we need to calculate the present value of the earnings before taxes and depreciation for four years. First, we calculate the present value factor using the required return on unlevered equity, which is 14%. The present value factor can be calculated as (1 + required return)^(-time period). In this case, since the earnings are expected for four years, the present value factor is (1 + 0.14)^(-4).

Once we have the present value factor, we can calculate the present value of the earnings before taxes and depreciation for each year by multiplying the earnings by the present value factor. The present value for each year is $255,000 multiplied by the present value factor.

Finally, we add up the present values for all four years to get the maximum price that Benton should be willing to pay for the new fleet of cars.

Answer 2

The maximum price Benton should pay is $893,250, while with debt financing, the APV of the project is $154,866.98.

How to solve

Benton Rental Car Expansion Analysis

a. Maximum Price under All-Equity Financing:

Annual pre-tax earnings: $255,000

Depreciation: $255,000 / 4 years = $63,750 per year

Taxable income: $255,000 - $63,750 = $191,250

Taxes: $191,250 * 25% = $47,812.50

After-tax earnings: $191,250 - $47,812.50 = $143,437.50

Required return: 14%

PV of perpetuity: After-tax earnings / Required return = $143,437.50 / 0.14 = $1,024,550

Maximum price: PV of perpetuity - Depreciation over 4 years = $1,024,550 - ($63,750 * 4) = $893,250

b. APV with Debt Financing:

Investment: $625,000 (equipment) + $370,000 (debt) = $995,000

Interest expense: $370,000 * 5% = $18,500 per year

Tax shield: $18,500 * 25% = $4,625 per year

Year 1-3:

After-tax operating income**: Same as all-equity case ($143,437.50)

Free cash flow**: After-tax income + Tax shield - Interest expense = $143,437.50 + $4,625 - $18,500 = $129,562.50

Year 4:

After-tax operating income**: Same as all-equity case

Free cash flow**: After-tax income + Tax shield - Debt repayment + Interest expense = $143,437.50 + $4,625 - $370,000 + $18,500 = -$203,437.50

Discount factor: (1 + 5%)^-1 = 0.952381

APV:

Sum of present values of cash flows:

Year 1-3: ($129,562.50 * 0.952381) * 3 = $348,249.71

Year 4: -$203,437.50 * 0.952381 = -$193,382.73

APV = $348,249.71 - $193,382.73 = $154,866.98

Therefore, under all-equity financing, the maximum price Benton should pay is $893,250, while with debt financing, the APV of the project is $154,866.98. This suggests debt financing can increase project value despite the initial investment being higher.