Question

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 $190,000, life of 20 years, and annual M&O costs of $21,000. The department expects 20,000 people per year to use the facilities an average of 2 hours each. The value of the recreation has been conservatively set at $1.00 per hour. At a discount rate of 6% per year, what is the B/C ratio for the project?

Answer 1

Benefit Cost Ratio=1.28

Step-by-step explanation:

Benefit-Cost ratio is the benefit by cost ratio.

To determine this, we first calculate the (i)benefit and (ii)cost which the parks and recreation department will receive and incur respectively.

BENEFIT RECEIVED =

$24,000(people that will come) x 2 (average hour ) x $1( rate per hour )

= $48,000

We determine the present value, where i = interest and n = number of years.

Present Value= [TeX]P\cdot\frac{1-\frac{1}{(1+r)^t}}{r}[/TeX]

[TeX]=48000\cdot\frac{1-\frac{1}{(1+0.06)^{20}}}{0.06}[/TeX]

=$550,556.22

PRESENT VALUE OF COST INCURRED

Initial Cost=$190000

Annual M&O Cost=$21000

Present Value= [TeX]P\cdot\frac{1-\frac{1}{(1+r)^t}}{r}[/TeX]

[TeX]=190000+ 21000\cdot\frac{1-\frac{1}{(1+0.06)^{20}}}{0.06}[/TeX]

=190000+240868.35

=$430868.35

B / C RATIO = $550,556.22/$430868.35

= 1.28