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

13-05-2019
Business

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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?

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Answer: The difference in the EAC of the two cars is $317,89; with an EAC of $6.612,54 for the Scion xA and $6.930,42 for the Toyota Prius, so the better option is the Scion xA.

Explanation: EAC means Equivalent annual cost and represents the cost per year of owning, operating, and maintaining an asset over its entire life. It is used to compare the cost-effectiveness of various assets that have unequal lifespans. The formula of EAC is the following:

EAC = NPV / A(t,r)

NPV: Net Present Value

A(t,r): Annuity factor

A(t,r) = (1 - 1/(1+r)^t) / r

t: Number of periods

r: Cost of capital

Therefore, we proceed to calculate the A(t,r) for each car:

1. Scion xA: (1 - 1/(1+12%)^3) / 12% = 2,401831268

2. Toyota Prius: (1 - 1/(1+12%)^5) / 12% = 3,604776202

Next, the initial costs must be divided by the annuity factor while adding in the OCF:

1. Scion xA: 13000/2,401831268 + 1200 = $6.612,54

2. Toyota Prius: 23000/3,604776202 + 550 = $6.930,42