Question

As part of the rehabilitation of the downtown area of a southern U.S. city, the Parks and Recreation Department is planning to develop the space below several overpasses into basketball, handball, miniature golf, and tennis courts. The initial cost is expected to be $150,000 for improvements which are expected to have a 20-year life. Annual maintenance costs are projected to be $12,000. The department expects 24,000 people per year to use the facilities an average of 2 hours each. The value of the recreation has been conservatively set at $0.50 per hour. (a) At an interest rate of 3% per year, what is the conventional B/C ratio for the project? (15 points) (b) Is the project economically justified? (5 points)

Answer 1

Initial Cost = $150,000

Life = 20 years

Annual Maintenance Cost = $12,000 per years

Benefits = 24,000 people per years use for 2 hours each

Value = $0.50 per hour

Benefit per year = 24,000 * 2 * $0.50 = $24,000

a. Conventional B/C Ratio at interest rate of 3% (using Present Worth Method)

Conventional B/C Ratio = PW of Annual Benefits / (Initial Cost + PW of Annual Cost)

Conventional B/C Ratio = $24,000 (P/A, 3%, 20) / [$150,000 + $12,000 (P/A, 3%, 20)]

Conventional B/C Ratio = $24,000 (14.87747) / [$150,000 + $12,000 (14.87747)]

Conventional B/C Ratio = $357,059.28 / $328,529.64

Conventional B/C Ratio = 1.086

b. Is the project is econominally justified?

YES. As the B/C Ratio is greater than ONE, project is economically justified.