Question

With interest at 10%, what is the benefit-cost ratio for this government project?

Initial Cost	$244,793
Additional costs at the end of year 1 and year 2	$22,478/year
Benefits at end of year 1 and year 2	$0/year
Annual benefits at end of year 3 through year 10	$96,236/year

Enter your answer as follow: 12.34

Answer 1

Calculating the B/C Ratio using Present Worth Method.

Step – 1 Calculate the PW of the Costs

PW of the Costs = Initial Cost + PW of additional Cost at 1^st and 2^nd year

PW of the Costs = $244,793 + $22,478 (P/A, 10%, 2)

PW of the Costs = $244,793 + $22,478 (1.73554) = 283,804

Step – 2 Calculate the PW of Benefits

PW of Benefits = $96,236 (P/A, 10%, 8) (P/F, 10%, 2)

PW of Benefits = $96,236 (5.33493) (0.82645) = 424,310

Step – 3 Calculate the Benefit-Cost Ratio

B/C ratio = PW of Benefits ÷ PW of Costs

B/C ratio = 424,310 ÷ 283,804

B/C Ratio = 1.495 or rounded to two decimal value it will be 1.50

The benefit cost ratio will be 1.50.

As the B/C Ratio is greater than ONE, accept the project.