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 $2.03 million, and the concrete option has an initial cost of $2.42 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

We have the following information

	Steel Girder Bridge	Concrete Bridge
Initial Cost	$2,030,000	$2,420,000
Painting Cost (every 25 years)	$420,000	0
Life	50 years	75 years
Interest Rate	8%	8%

Steel Girder Bridge

Equivalent annual worth = 2,030,000(A/P, i, n) + 420,000(A/P, i, n) + 420,000(A/P, i, n)

Equivalent annual worth = 2,030,000(A/P, 8%, 50) + 420,000(A/P, 8%, 25) + 420,000(A/P, 8%, 50)

Equivalent annual worth = 2,030,000[0.08(1 + 0.08)⁵⁰/((1 + 0.08)⁵⁰ – 1)] + 420,000[0.08(1 + 0.08)²⁵/((1 + 0.08)²⁵ – 1)] + 420,000[0.08(1 + 0.08)⁵⁰/((1 + 0.08)⁵⁰ – 1)]

Equivalent annual worth = (2,030,000 × 0.0817) + (420,000 × 0.0937) + (420,000 × 0.0817)

Equivalent annual worth of Steel Girder Bridge = $239,519

Concrete Bridge

Equivalent annual worth = 2,420,000(A/P, i, n)

Equivalent annual worth = 2,420,000(A/P, 8%, 75)

Equivalent annual worth = 2,420,000[0.08(1 + 0.08)⁷⁵/((1 + 0.08)⁷⁵ – 1)]

Equivalent annual worth = 2,420,000 × 0.0802

Equivalent annual worth of Concrete Bridge = $194,084

Since, the equivalent annual worth of Concrete Bridge is lower, so Concrete Bridge should be selected.