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

C $ 2,415.37

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

Step-by-step 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 / (1-(1+r)^(-time) )/(rate) = C\\`

PV $8,000.00

time 4

rate 0.08

`8000 / (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