Question

The city of Mersey is planning to construct a bridge across the Cavendashim river. The first cost of the bridge will be $6263631. Annual maintenance and repairs will be $28885 for the first 5 years, and then will increase to $42554 for each of the next 10 years. For the final 5 years, the annual maintenance and repairs will increase again to $54929 per year. A major overhaul of $484947 will be performed at the end of year 9. Using an interest rate of 8%, 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? See example 6-3 and 6-4 in the book.

Enter your answer as 1234

Answer 1

In this question, first calculate the PW of all the cost.

Since in this question all are cost, there is no need to indicate the cost as negative.

Life = 20 years

Rate of interest = 8%

PW = $6263631 + $28885 (P/A, 8%, 5) + $42554 (P/A, 5%, 10) (P/F, 8%, 5) +

         $54929 (P/A, 8%, 5) (P/F, 8%, 15) + $484947 (P/F, 8%, 9)

PW = $6263631 + $28885 (3.9927) + $42554 (6.7101) (0.6806) +

         $54929 (3.9927) (0.3152) + $484947 (0.5002)

PW = $6,263,631 + $115,329 + $194,340 + $69,128 + $242,570

PW = $6,884,998

Equivalent uniform annual cost = PW (A/P, 8%, 20)

Equivalent uniform annual cost = $6,884,998 (0.1019)

Equivalent uniform annual cost = $701,581

Equivalent uniform annual cost for 20 years $701,581.