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 4 more years.If your opportunity cost is 8%,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

To determine whether replacing the older car with a newer car is financially justifiable, we need to compare the present value of maintenance expenses associated with both cars.

For the older car, the present value of maintenance expenses for the next four years can be calculated as follows:

PV = $4,000 / 0.08 * (1 - 1 / (1 + 0.08)^4) = $12,676.54

For the newer car, the present value of maintenance expenses will depend on the amount of maintenance cost reduction that justifies the purchase.

Let x be the amount by which the maintenance expense must decrease for the newer car:

PV = ($8,000 - x) / 0.08 * (1 - 1 / (1 + 0.08)^4) = $8,000

Solving for x, we get:

x = $1,584.97

Therefore, the maintenance expense on the newer car must decrease by $1,584.97 to justify the purchase. The closest answer choice to this value is B) $1,585.

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