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.