Question

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, at which point they will be valueless. If your opportunity cost is 8%, by how much must maintenance expense decrease on the newer vehicle to justify its purchase?

Answer 1

Answer:

C $ 2,415.37

The newer vehicle should decrease maintenance cost by 2,415.37 or more to justify its purchase.

Explanation:

The annual maintenance expense will be for 4 years

we will compare the cost saving with the $8,000 cost for the new car.

So we need calculate the cuota of an annuity of 4 years at 8% discount with a present value of 8,000

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $8,000.00

time 4

rate 0.08

$8000 \div \frac{1-(1+0.08)^{-4} }{0.08} = C$

C $ 2,415.37

The cost savings should decrease for at least 2,415.37 to make it a  economic viable option