Three alternatives are being considered for improving a street intersection.The annual dollar savings on account of the improvement is shown below.  Assume that the intersection will last for 25 years and the interest rate is 5%.  Each of the three improvements is mutually exclusive but provides similar benefits. The alternative that is the most economical is: 

Alternative                         Total cost         Annual Benefit

A                                       $10,000           $  800

B                                       $12,000           1,000

C                                       $19,000           1,400

Solution:

Estimate the Net Present Worth (NPW) for each alternative and identify the most economical alternative for construction. 

Net Present Worth (NPW) = PW of benefits - PW of costs

Use the present worth factor for uniform series: 

  (P/A, i =5%, 25 yrs) = 14.094 (from the Factor Tables)

  NPW(A)  = ($800 x 14.094) - $10,000     = $1,275.20

  NPW(B)  = ($1000 x 14.094) - $12,000   = $2,094.00   

  NPW(C)  = ($1400 x 14.094) - $19,000   =   $731.60

Therefore, select Alternate B because it has the highest net present worth.