Question

ABC company has just purchased a life truck that has a useful life of 5 years. The engineer estimates that maintenance costs for the truck during the first year will be $2,000. As the truck ages, maintenance costs are expected to increase at a rate of $300 per year over the remaining life. Assume that the maintenance costs occur at the end of each year. The firm wants to set up a maintenance account that earns 8% interest per year. All future maintenance expenses will be paid out of this account. How much does the firm have to deposit in the account now?

Answer 1

$10,540

Step-by-step explanation:

To calculate, the formula for calculating the present value (PV) of a growing annuity is used as follows:

PVga = [P / (r - g)] * [1 - {(1 + g) / (1 + r)}^n] .................... (1)

Where;

P = maintenance costs for the first year = $2,000

r = interest per year = 8%, or 0.08

g = growth rate of maintenance costs = $300 / $2,000 = 0.15

n = useful life = 5

Substituting the values into equation (1), we have:

PVga = [2,000 / (0.08 - 0.15)] * [1 - {(1 + 0.15) / (1 + 0.08)}^5] = $10,539.88, or $10,540.

Therefore, the firm has to deposit $10,540 in the account now.