Question

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 $2.04 million, and the concrete option has an initial cost of $2.5 million. Every 25 years, the steel bridge must be painted at a cost of $450,000, 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. Based on the shortest acceptable analysis period, determine the present worth of costs for the best option using an interest rate of 9%. Express your answer in $ to the nearest $10,000.

Answer: 2120701.0

Answer #1

Analysis period chosen = 150 years (LCM of lives of both types of bridges)

i = 9%

Steel bridge:

It would be replaced at the same cost after 50 years and 100 years (cost of painting is incurred in years 25, 75 and 125)

PW (cost) = 2040000 + 450000/1.09^{25}
+ 2040000/1.09^{50} + 450000/1.09^{75}
+ 2040000/1.09^{100}+
450000/1.09^{125}

PW = $ 2120701

Concrete bridge:

It would be replaced at the same cost after 75 years

PW (cost) = 2500000 + 2500000/1.09^{75}

PW = $ 2503899

Best option: Steel girder bridge

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