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 $1,000. 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 12% 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

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Business

Renee

30 March, 05:06

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 $1,000. 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 12% 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

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Arely · Answer 1

Total amount to be invested today = $1,706.432

Explanation:

The first maintenance cost would occur a year from now, then the Present value will be equal to:

PV = 1,000 * 1.12^ (-1)

PV = 892.857

The rest of the maintenance cost represents an annuity.

We will determine the PV of the annuity of $300 discounted at 12% per annum starting in year 2

PV = A * 1 - (1+r) ^ (-n)

A - 300, r = 12%, n = 4

PV in year 1 = 300 * 1 - (1.12) ^ (-4) = 911.204804

PV in year 0 = F * (1+r) ^ (-n)

= 911.204804 * 1.12^ (-1) = 813.57

Total amount to be invested today = 813.57 + 892.85=1706.43

Total amount to be invested today = $1,706.432