Question

The fire chief of a medium-sized city has estimated that the initial cost of a new fire station will be $4 million. Annual upkeep costs are estimated at $300,000. Benefits to citizens of $550,000 per year and disbenefits of $90,000 per year have also been identified. Use a discount rate of 4% per year to determine if the station is economically justified by the conventional B/C ratio.

Answer 1

Answer: So B/C ratio = PW(B)/PW(C) = $\frac{11500000}{11500000}$= 1

So economically there is no befit and no loss of new fire station.

Explanation:

Net annual benefit B = Benefit-Disbenefit = 550000-90000 = 460000  

I = 4000000

O&M(Annual keep up cost) = 300000

i = 0.04  

As n is not given so assuming this project to be perceptual.

P.V of perpetuity = $\frac{A}{i}$

Now;

PW(B)=tex]\frac{460000}{0.04}[/tex] = $11500000

PW (C) = I +PW$\times$(O&M) = $4000000+\frac{300000}{0.04}$ = $11500000

So B/C ratio =$\frac{PW(B)}{PW(C)}$=$\frac{11500000}{11500000}$ = 1

So economically there is no befit and no loss of new fire station.