Question

Question 3 1 pts A bridge design firm is performing an economic analysis of two mutually exclusive designs for a highway overpass. The steel girder option has an initial cost of $2.03 million, and the concrete option has an initial cost of $2.43 million. Every 25 years, the steel bridge must be painted at a cost of $420,000, and all other maintenance costs are the same for both options. The steel bridge is expected to last 50 years, and concrete bridge is expected to last 75 years. Both are assumed to be identically replaced indefinitely. Based on the shortest acceptable analysis period for each option, determine the equivalent uniform annual cost (EUAC) for the best option using an interest rate of 8%. Express your answer in $ to the nearest $1,000.

Answer 1

Option 1: Steel bridge

EUAC of option=[2030000+420000*(P/F,0.08,25)+420000*(P/F,0.08,25)]*(A/P,0.08,50)

Let us calculate the interest factors

(P/F,0.08,25)=1/(1+0.08)^25=0.146017905

(P/F,0.08,50)=1/(1+0.08)^50=0.021321229

(A/P,1,n) = 1 -

0.08 (A/P,000,00) = 0.081742858 1- (0.05)60

EUAC of option=(2030000+420000*0.146017905+420000*0.021321229)*0.081742858=$171683.09

Option 2: Concrete bridge

EUAC of option=2430000*(A/P,0.08,75)

0.08 (A/P,0.08,75) = 7 = 0.080249840

EUAC of option=2430000*0.080249840=$195,00711

We find that EUAC is lower in case of steel bridge. So, it is better.

EUAC of best option=$171683.09 or say $172,000