A contractor purchased a Caterpillar D-13 dozer for $100,000 and owned it for five years. The annual cost for maintenance and repair is provided in the Table. With annual interest rate at 7% and end-of-year disbursements, the uniform annual cost for maintenance and repair for the dozer is most nearly:
Year Maintenance and Repair Costs
1 $4,500
2 $9,000
3 $11,800
4 $13,500
5 $22,500
Solution: The Equivalent Uniform Annual Cost (EUAC) can be computed for this irregular series of payments in two steps:
Step 1: Compute the Present Worth for five years using the single payment present worth factors.
PW of cost = 4500(P/F, 7%, 1) + 9000(P/F, 7%, 2) + 11800(P/F, 7%, 3) + 13500(P/F, 7%, 4) + 22500(P/F, 7%, 5)
= 4500(.9346) + 9000(.8734) + 11800(.8163) + 13500(.7629) + 22500(.7130)
= $48,040.29
Step 2: With the PW of cost known, compute the EUAC using the capital recovery factor.
EUAC = 48,040(A/P, 7%, 5)
= 48,040(.2439)
= $11,717.03