The city of Mersey is planning to construct a bridge across the Cavendashim rive
ID: 1173798 • Letter: T
Question
The city of Mersey is planning to construct a bridge across the Cavendashim river. The first cost of the bridge will be $6149275. Annual maintenance and repairs will be $28398 for the first 5 years, and then will increase to $35992 for each of the next 10 years. For the final 5 years, the annual maintenance and repairs will increase again to $53173 per year. A major overhaul of $448663 will be performed at the end of year 8. Using an interest rate of 7%, what is the equivalent uniform annual cost for the 20-year period?
Explanation / Answer
we need to calculate Present Worth of Cost first
PW of Cost=First Cost+PW of other costs
PW of Other Costs=$28398(1/1.07+1/1.07^2+1/1.07^3+1/1.07^4+1/1.07^5)+$35992/1.07^5(1/1.07+1/1.07^2+1/1.07^3+1/1.07^4+1/1.07^5)+$53173/1.07^10(1/1.07+1/1.07^2+1/1.07^3+1/1.07^4+1/1.07^5)+448663/1.07^8
=$593612.008
First Cost=$6149275
PW of Costs=$6,742,887
Equivalent annual uniform cost=PW of Cost/Sum of PV discount factor
=6742887/10.5940=$636481.68
SUM of PV discount factor=(1/1.07+1/1.07^2+...+1/1.07^20)=10.5940
ANswer is $636481.68
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