Because of its age, your car costs $4,000 annually in maintenance expense.You could replace it with a newer vehicle costing $8,000.Both vehicles would be expected to last four more years.If your opportunity cost is 8 percent, by how much must maintenance expense decrease on the newer vehicle to justify its purchase?
A)$1,250
B)$1,585
C)$2,000
D)$2,415

Question

Quizplus · Accepted Answer

The cost of keeping the current car for four more years would be:
4 years x $4,000/year = $16,000

The cost of buying the newer car and keeping it for four years would be:
$8,000 + 4 years x (maintenance cost - depreciation) = $8,000 + 4 years x (maintenance cost - $8,000/4) = $8,000 + 4 years x (maintenance cost - $2,000) = $8,000 + 4(maintenance cost - $2,000)

In order to justify purchasing the newer car, the cost of owning it for four years must be less than the cost of keeping the current car for four years:
$8,000 + 4(maintenance cost - $2,000) < $16,000
4(maintenance cost - $2,000) < $8,000
maintenance cost - $2,000 < $2,000
maintenance cost < $4,000

Therefore, the maintenance expense on the newer vehicle must be less than $4,000 per year to justify its purchase. The decrease in maintenance expense required is:
$4,000 - maintenance cost = $4,000 - $2,415 = $1,585

So, the best choice is (B), a decrease in maintenance expense of $1,585.

Because of Its Age, Your Car Costs $4,000 Annually in Maintenance