Question

With interest at 10%, what is the benefit-cost ratio for this government project? $208,355 Initial Cost Additional costs at the end of year 1 and year $23,720/year Benefits at end of year 1 and year 2 $0/year Annual benefits at end of year 3 through year. $91,825/year 10 Enter your answer as follow: 12.34

Answer 1

Initial Cost = 208,355

Additional Cost at EOY1 and EOY2 = 23,720

Annual Benefits from EOY3 to EOY10 = 91,825 (for 8 year)

Interest Rate = 10%

Calculate the Benefit-Cost ratio.

Calculating Benefit Cost Ratio using Present Worth Method.

B/C Ratio = PW of Benefits ÷ PW of Cost

PW of Benefits = 91,825 (P/A, 10%, 8) (P/F, 10%, 2)

PW of Benefits = 91,825 (5.33493) (0.82645)

PW of Benefits = 404,861

PW of Costs = 208,355 + 23,720 (P/A, 10%, 2)

PW of Costs = 208,355 + 23,720 (1.73554)

PW of Costs = 249,522

B/C Ratio = PW of Benefits ÷ PW of Cost

B/C Ratio = 404,861 ÷ 249,522

B/C Ratio = 1.62

As the B/C Ratio > 1, Accept the Project.