Question

Your parents' car requires $4,000/yrto maintain when you leave for college. You could replace it with a newer car costing $12,000. Both vehicles will survive through college (i.e. 4 yrs) and will die when you graduate. If your opportunity cost is 8%, by how much would the maintenance cost decrease to justify the purchase?

Answer 1

If the PV of Maintenance cost equal > Purchase cost, we can buy the new car.

i.e till PV of Maintenance cost = Purchase Cost, We can use Old car.

Let x be the maintenance of Car

PV of Maintenance cost = Maintenance Cost per anum * PVAF (r%, n years)

= $ X * PVAF (8%, 4 years)

= $ X * 3.3121

Thus 3.3121X = $ 12000

= $ 3623.05

The Max Maintenance cost per anum is $ 3632.05

Decrease in maintenance cost to justify purchase = Present Maintenance cost - Max Maintenance cost

= $ 4000 - $ 36223.05

= $ 376.95