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 12 percent, what is the difference in the EAC of the two cars?

Question

Quizplus · Accepted Answer

The EAC of the Scion xA is $3,517.88 and the EAC of the Toyota Prius is $3,207.50. The difference is $310.38.The EAC is calculated as follows:EAC = (PV of initial investment + PV of future OCF) / (PV of annuity factor)The PV of the initial investment is simply the initial investment. The PV of the future OCF is the sum of the present values of each year's OCF. The PV of the annuity factor is the present value of an annuity of $1 per year for the number of years in the project.For the Scion xA, the PV of the initial investment is $13,000. The PV of the future OCF is -$1,200 * (PVIFA(12%,3)) = -$3,063.60. The PV of the annuity factor is (PVIFA(12%,3)) = 2.40183. Therefore, the EAC is ($13,000 - $3,063.60) / 2.40183 = $3,517.88.For the Toyota Prius, the PV of the initial investment is $23,000. The PV of the future OCF is -$550 * (PVIFA(12%,5)) = -$2,475.00. The PV of the annuity factor is (PVIFA(12%,5)) = 3.60478. Therefore, the EAC is ($23,000 - $2,475.00) / 3.60478 = $3,207.50.The difference in the EAC of the two cars is $3,517.88 - $3,207.50 = $310.38.

You Are Trying to Pick the Least Expensive Car for Your