7) (25 points) Maintenance costs for a flood control project follow a cyclical p

Question

7) (25 points) Maintenance costs for a flood control project follow a cyclical pattern with the following costs occurring over a 6-year period. End of Year1 Maintenance $10,000 Cost 4 $10,000 6 $35,000 2 $10,000 S10,000 $10,000 a) (15 points) Compute an equivalent annual cost over a single 6-year maintenance cycle. MARR is 10% per year compounded annually b) (10 points) It is anticipated that the sequence of costs will repeat itself every 6 years forever. the capitalized cost (worth) of the maintenance costs. Determine

Explanation / Answer

a) Present worth of the cost = 10000(P/F, 10%, 1) + 10000(P/F, 10%, 2) + 10000(P/F, 10%, 3) + 10000(P/F, 10%, 4) + 10000(P/F, 10%, 5) + 35000(P/F, 10%, 6)

= 10000(0.9091) + 10000(0.8264) + 10000(0.7513) + 10000(0.6830) + 10000(0.6209) + 35000(0.5645)

= 9091 + 8264 + 7513 + 6830 + 6209 + 19757.5

= 57,664.5

Equivalent Annual Cost = 57664.5(A/P, 10%, 6)

                                      = 57664.5(0.2296)

                                      = $13,239.77

b) Capitalized cost = 13,239.77 / 0.10 = $132,397.7

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