Question

Leck my work Problem 09.013 Benefit/Cost Analysis of a Single Project As part of the rehabilitation of the downtown area of a southern U.S. city, the Parks and Recreation Department expects to develop the space below several overpasses into basketball, handball, miniature golf, and tennis courts. The estimates are initial cost of $185,000; life of 20 years and, annual M&O costs of $16,000. The department expects 26,000 people per year to use the facilities an average of 2 hours each. The value of the recreation has been conservatively set at $1.2 per hour. At a discount rate of 5% per year, what is the B/C ratio for the project? The B/C ratio is

Answer 1

Initial cost = $185,000

Annual M&O cost = $16,000

Interest rate = 5%

Time period = 20 years

Calculate the present worth of annual M&O cost -

PW = Annual M&O cost(P/A, i, n)

PW = $16,000(P/A, 5%, 20)

PW = $16,000 * 12.4622

PW = $199,395.2

The present worth of annual M&O cost is $199,395.2

It has been stated that 26,000 people will use the facility for an average of 2 hours each every year.

So, the facilities will be used for 52,000 hours in a year.

The vaule of recreation is $1.2 per hour.

Annual benefit from recreation = Number of hours in a year used for recreation at facilities * Value of recreation per hour

Annual benefit from recreation = 52,000 * $1.2 = $62,400

Calculate the present worth of the annual benefit from recreation -

PW = Annual benefit from recreation(P/A, i, n)

PW = $62,400(P/A, 5%, 20)

PW = $62,400 * 12.4622 = $777,641.28

The present worth of the annual benefit from recreation is $777,641.28

Calculate the B/C ratio -

B/C ratio = [Present worth of annual benefit from recreation]/[Initial cost + Present worth of annual M&O cost]

B/C ratio = $777,641.28/[$185,000 + $199,395.2]

B/C ratio = $777,641.28/$384,395.2

B/C ratio = 2.02

Thus,

The B/C ratio is 2.02