Question

The city of Mersey is planning to construct a bridge across the Cavendashim river. The first cost of the bridge will be $6,209,348. Annual maintenance and repairs will be $29,658 for the first 5 years, and then will increase to $39,654 for each of the next 10 years. For the final 5 years, the annual maintenance and repairs will increase again to $52,045 per year. A major overhaul of $539,772 will be performed at the end of year 9. Using an interest rate of 1%, what is the equivalent uniform annual cost for the 20-year period?

Hint: Since this is an equivalent uniform annual cost, do you need to indicate that as negative?

Answer 1

ANSWER:

I = 1%

PW = FIRST COST + AMR FOR 1ST FIVE YEARS(P/A,I,N) + AMR FOR THE NEXT 10 YEARS(P/A,I,N)(P/F,I,N) + AMR FOR THE LAST 5 YEARS(P/A,I,N)(P/F,I,N) + OVERHAUL COST IN YEAR 9(P/F,I,N)

PW = 6,209,348 + 29,658(P/A,1%,5) + 39,654(P/A,1%,10)(P/F,1%,5) + 52,045(P/A,1%,5)(P/F,1%,15) + 539,772(P/F,1%,9)

PW = 6,209,348 + 29,658 * 4.853 + 39,654 * 9.471 * 0.9515 + 52,045 * 4.853 * 0.8613 + 539,772 * 0.9143

PW = 6,209,348 + 143,930.274 + 357,348.227 + 217,542.318 + 493,513.54

PW = 7,421,682.36

AW = PW(A/P,I,N)

AW = 7,421,682.36(A/P,1%,20)

AW = 7,421,682.36 * 0.0554

AW = 411,161.203

SO THE ANNUAL EQUIVALENT COST IS $411,161.203