Question

You are trying to pick the least-expensive car for your new delivery service. You have two choices: the Scion xA, which will cost $24,000 to purchase and which will have OCF of –$3,200 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $32,500 to purchase and which will have OCF of –$1,650 annually throughout that vehicle’s expected 4-year life. Both cars will be worthless at the end of their life. You intend to replace whichever type of car you choose with the same thing when its life runs out, again and again out into the foreseeable future.

    

If the business has a cost of capital of 13 percent, calculate the EAC. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

     

Scion's EAC	$
Toyota's EAC	$

  

Which one should you choose?

	Toyota
	Scion

Answer 1

Scion's Net Present Value = 24000 + 3200 / 1.13 + 3200 / (1.13)² + 3200 /(1.13) ³

= 31555. 68

Net Present Value = EAC * [ 1 - (1+r) ^-n ​] / r

31555.68= EAC * [ 1 - (1+0.13) ^-3 ​] / 0.13

EAC = 13364. 52

Prius = 32500 + 1650 / 1.13 + 1650 / (1.13)² + 1650 /(1.13) ³ ​+ 1650 /(1.13)⁴

= 37407.88

Net Present Value = EAC * [ 1 - (1+r) ^-n ​] / r

37407.88= EAC * [ 1 - (1+0.13) ^-4 ​] / 0.13

EAC = 12576.31

Since Toyota's EAC is lower than Scion it should be chosen.

The answer is Toyota.