A city council is planning to build a new bridge across a creek. This will require an immediate expenditure of $50 000, but will save citizens an estimated $5 000 in travel costs every year over the next twenty years. If the council's MARR is 5%, what is the BCR for the project?
A)0.1
B)1.25
C)1.44
D)1.64
E)2.00

Question

Quizplus · Accepted Answer

The Benefit-Cost Ratio (BCR) is calculated by dividing the present value of benefits by the present value of costs. The present value of benefits is the sum of the discounted values of annual savings ($5,000) over 20 years at a 5% discount rate. Using the formula for the present value of an annuity: PV = P * [(1 - (1 + r)^-n) / r], where P is the annual payment ($5,000), r is the annual interest rate (0.05), and n is the number of periods (20 years), we get: PV = $5,000 * [(1 - (1 + 0.05)^-20) / 0.05] ≈ $62,500. The cost is $50,000. Therefore, BCR = $62,500 / $50,000 = 1.25.

A City Council Is Planning to Build a New Bridge