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