Question

Two bride designs have been proposed for the new interstate highway to cross Rio de Lubbock. A bridge constructed from wood will cost $6,000 and will last for 8 years. A bridge constructed from steel will cost $11,000 and will last for 20 years. Either bridge will have a 0 salvage value. at the end of its life. Use an interest rate of 8% and determine which material will be more economical for the construction of the bridge.

Uniform annual cost of wood design:Uniform annual cost of steel design:

Answer 1

Uniform annual cost A = $1,044.088

Uniform annual cost B= $1,120.374

Option A is cheaper because it has a lower equivalent annual cost

Step-by-step explanation:

To determine the better of the two options, we would compare the equivalent annual cost of each options using a discount rate of 8% per annum

Uniform annual cost = PV/Annuity factor

Annuity factor = (1- (1+r)^(-n))/r

r- rate , n- years

Option A-

r- 8% , n- 8, PV - 6000

(1- (1.08)^(-8))/0.08= 4.62287

Equivalent Annual cost

= 6000/5.74663

Uniform annual cost=$1,044.088

Option B

Annuity factor = 1 -1.08^(-20)/0.08 =9.8181

Equivalent annual cost

= 11,000/9.8181

Uniform annual cost=$1,120.374

Option A is cheaper because it has a lower equivalent annual cost