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 $220,000 per year in earnings before taxes and depreciation for five years. The company is entirely financed by equity and has a 21 percent tax rate. The required return on the company’s unlevered equity is 15 percent and the new fleet will not change the risk of the company. The risk-free rate is 6 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 $655,000. Additionally, assume the company can issue $430,000 of five-year debt to finance the project at the risk-free rate of 6 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

Answer 1

a)

The Maximum Price that a Company that a Company can afford is the Price that Makes the NPV of the transaction equal to 0.

NPV = - Purchase Price + PV ( 1-Tax ) ( EBDT) + PV of Depreciation tax shield

Let the Purchase price be X

0= -X + ( 1-0.21)( $ 220000) PVAF ( 15%,5) + (X/5 )PVAF ( 15%,5)*Tax rate

0 = -X + ( 0.79)( $ 220000)( 3.3522) + (X/5) *3.3522*0.21

0 = -X+ $ 582604.5560+0.6704X*0.21

0 = -X+$ 582604.5560+0.14079X

0=$ 582604.5560-0.85921X

0.85921X = $ 582604.5560

X = $ 582604.5560/0.85921

X = $ 678070.44

Hence Maximum Price we can afford is $ 678070.44

* Depreciation = (Cost of Asset - Salvage value)/Useful life

= ( X-0)/5

= X/5

b) Computation of Adjusted PV

Given Cost of the Asset = $ 655000

* Depreciation = (Cost of Asset - Salvage value)/Useful life

= ( $ 655000-0)/5

= $ 131000

Adjusted PV = NPV of a Unlevered firn+PV of Debt Financing advantages

Computation of NPV of a Unlevered firm

NPV = - Purchase Price + PV ( 1-Tax ) ( EBDT) + PV of Depreciation tax shield

NPV= -$ 655000+ ( 1-0.21)( $ 220000) PVAF ( 15%,5) + ($ 655000/5 )*Tax rate*PVAF ( 15%,5)

NPV= -$ 655000+( 0.79) ( $ 220000) ( 3.3522) +($ 131000)( 0.21)( 3.3522)

NPV= -$ 655000+ $ 582612.36+$ 92219.0220

NPV= -$ 655000+ $ 674831.3820

NPV = $ 19831.3820

Computation of PV of Tax advantage on interest

Interest per annum = Borrowed Amount * Cost of Debt

= $ 430000*0.06

= $ 25800

PV of Tax shield on Interest = Interest amount * Tax rate * PVAF ( 6%,5)

= $ 25800* 0.21* 4.2124

= $ 22822.78

Adjusted PV = NPV of a Unlevered firn+PV of Debt Financing advantages

= $ 19831.3820+$ 22822.78

= $ 42654.16

Hence APV of a Project is $ 42654.16

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