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 $18,000 to purchase and which will have OCF of –$2,000 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $27,000 to purchase and which will have OCF of –$1,050 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.

If the business has a cost of capital of 13 percent, calculate the EAC.

Explanation / Answer

One iteration of each delivery car will consist of the following cash flows:

The NPV of one Scion xA will be:

Treating this as the present value of a 3-period annuity, setting i to 12 percent, and solving for payment will yield a payment of -$7,028.89, which is the Scion’s EAC.

Treating this as the present value of a 3-period annuity, setting i to 13 percent, and solving for payment will yield a payment of -$5,623.40, which is the Scion’s EAC.

The NPV of one Toyota Prius will be:

Treating this as the present value of a 3-period annuity, setting i to 13 percent, and solving for payment will yield a payment of -$10,112.35, which is the Toyota’s EAC.

Based on the EACs, we should choose the Scion

Year 0 1 2 3 4 Scion xA CFs -18,000 -2,000 -2,000 -2,000 Toyota Prius CFs - -27,000 -1,050 -1,050 -1,050 -1,050

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