You are trying to pick the least-expensive car for your new delivery service. You have two choices: the Scion xA, which will cost $14,500 to purchase and which will have OCF of −$1,300 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $20,500 to purchase and which will have OCF of −$700 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 11 percent, calculate the EAC. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
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| Steps to calculate the EAC i.e. Equivalent annual cost is as under | |||||||||
| Step 1 | |||||||||
| Calculation of annuity factor for both option | |||||||||
| Annuity factor = [1-(1+r)^-n]/r | |||||||||
| r = cost of capital | |||||||||
| n = life of car in years | |||||||||
| Scion xA Annuity factor = [1-(1+0.11)^-3]/0.11 = 2.443715 | |||||||||
| Toyota Prius Annuity Factor = [1-(1+0.11)^-4]/0.11 = 3.102446 | |||||||||
| Step 2 | |||||||||
| The initial cost must be divided by the annuity factor and the annual maintenance cost added in. | |||||||||
| The resulting calculation is the EAC. | |||||||||
| EAC Scion Xa = [$14500 / 2.443715] + $1300 = $7,233.59 | |||||||||
| EAC Toyoto Prius = [$20500 / 3.102446] + $700 = $7,307.69 | |||||||||
| You should choose Scion Xa as it has lower EAC compared to Toyoto Prius. | |||||||||
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