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 $13,000 to purchase and which will have OCF of −$1,200 annually throughout the vehicle's expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $23,000 to purchase and which will have OCF of −$550 annually throughout that vehicle's expected five-year life. Both cars will be worthless at the end of their life. If 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, and if your business has a cost of capital of 16 percent, what is the difference in the EAC of the two cars?

a. $317.88
b. $310.38
c. $413.25
d. $361.13

Answer 1

Answer:$584.40

Explanation: to calculate the EAC (Equivalent Annual Cost) of the two cars:

Scion xA

Annuity factor = (1 - 1/(1+r)^t)/r

=(1 - 1/(1+0.16)^3)/0.16

=2.246

EAC for Scion xA

= (13,000/2.246) + 1200

=5,790.65+1200

=$6,990.65

Toyota Prius

Annuity factor = (1 - 1/(1+r)^t)/r

=(1 - 1/(1+0.16)^5)/0.16

=3.274

EAC for Toyota Prius

= (23,000/3.274) + 550

=7025.05+550

=$7,575.05

Difference in the EAC of the above cars = $7,575.05-$6,990.65

=$584.40