A library shelving system has a fi rst cost of $20,000 and a useful life of 10 years. The annual maintenance is expected to be $2,500. The annual benefi ts to the library staff are expected to be $9,000. If the effective annual interest rate is 10 percent, what is the benefi t-cost ratio of the shelving system?

The benefit cost ratio is 1.564

Explanation:

The benefit-cost ratio is the ratio of the present value of benefits to the present value of costs. It is thus calculated as follows.

Benefit-cost ratio = Present value of benefits / Present value of costs

Present value of costs = $20,000 + $2,500 (P/A, 10%, 10 years)

= $20,000 + $15,361

= $35,361

Present value of benefits = $9,000 (P/A, 10%, 10 years)

= $9,000 x 6.145

= $55,305

Benefit-cost ratio = $55,305 / $35,361

= 1.564