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. At a discount rate of 3% per year, what is the conventional B/C ratio for the project?

Here B / C ratio means the benefit by cost ratio, so here we will first individually calculate the benefit and cost which the parks and recreation department will receive.

BENEFIT RECEIVED =

$24,000(people that will come) x 2 (average hour ) x $.50 ( rate per hour )

= $24,000

calculating present value, where i = interest and n = number of years

$24,000 / (1+i)^1 + $24,000 / (1+i)^2 + _ __ _ + $24,000 / (1+i)^20

= $24,000 x [ 1 - 1 / (1+.03)^20 ] / .03 ( given i = 3% )

= $357,060

PRESENT VALUE OF COST INCURRED =

$150,000 + $12,000 / (1+i)^1 + $12,000 / (1+i)^2 + _ _ + $12,000 / (1+i)^20

= $150,000 + $12,000 x [ 1 - 1 / (1+.03)^20 ] / .03

= $328,530

B / C RATIO = $357,060 / $328,530

= 1.0868