You are trying to pick the least-expensive car for your new delivery service. Yo

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 $15,500 to purchase and which will have OCF of –$1,500 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $22,000 to purchase and which will have OCF of –$800 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 12 percent, calculate the EAC. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

You are trying to pick the least-expensive car for your new delivery service. You have two choices: the Scion xA, which will cost $15,500 to purchase and which will have OCF of –$1,500 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $22,000 to purchase and which will have OCF of –$800 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.

Explanation / Answer

Present value of annuity factor (PVAF) = {1-(1+r)-n}/r

PVAF for 3 years = (1-1.12-3)/0.12 = 2.4018

PVAF for 4 years = (1-1.12-4)/0.12 = 3.0373

Present value of costs of Scion xA = $15,500 + ($1,500 * 2.4018) = $19,102.70

Present value of costs of Toyota prius = $22,000 + ($800 * 3.0373) = $24,429.84

Equivalent annual costs = Present value of costs/PVAF

EAC for Scion xA = $19,102.70/2.4018 = $7,953.49

EAC for Toyota prius = $24,429.84/3.0373 = $8,043.28

It is preferred to choose Scion xA because it has less EAC

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