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 $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

Answer 1

Total amount to be invested today =$1,706.432

Step-by-step 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