A public utility in a medium-size city is consider­ing two cash rebate programs to achieve water con­servation. Program 1, which is expected to cost an average of $60 per household, provides a rebate of 75% of the purchase and installation costs of an ultra-low-flush toilet ($100 max). This program is projected to achieve a 5% reduction in overall household water use over a 5-year evaluation pe­riod. This will benefit the citizenry to the extent of $1.25 per household per month. Program 2 in­volves turf replacement with xeric (low water need) landscaping. The program is expected to cost $500 per household, but it will result in re­duced water cost estimated at $8 per household per month (on the average). Use the B/C method at a discount rate of 0.5% per month to determine which

Question

program, if any, the utility should under­take. The programs may be (a) mutually exclusive, or (b) independent.

What will be an ideal response?

Answer 1

Compare on a per household basis
(a) Program 1 vs. DN
B = $1.25 per month
C = 60(A/P,0.5%,60)
= 60(0.01933)
= $1.16

B/C = 1.25/1.16
= 1.08 eliminate DN
Program 2 vs. 1
?B = 8.00 – 1.25 = $6.75
?C = (500 – 60)(A/P,0.5%,60)
= 440(0.01933)
= $8.51
?B/C = 6.75/8.51
= 0.79
Select program 1

(b) Program 1: B/C = 1.08 (from above) Acceptable

Program 2:
B = 8.00 per month
C = 500(A/P,0.5%,60)
= 500(0.01933)
= $9.67

B/C = 8.00/9.67
= 0.83 Not acceptable