Apply incremental BC analysis at an interest rate of 12 per

Apply incremental B/C analysis at an interest rate of 12% per year to determine which alternative should be selected. Use a 20-year study period, and assume the damage costs might occur in year 6 of the study period.

Solution

Alt A has a lower initial cost, so we do an incremental analysis of (B - A).

Incremental first cost ($) = 800,000 - 600,000 = 200,000

Incremental M&O cost ($) = 70,000 - 50,000 = 20,000

Incremental damage cost ($) = 250,000 - 950,000 = - 70,000 (A negative damage is a benefit).

Present value (PV) of incremental benefit ($) = 70,000 x PVIF(12%, 6) = 70,000 x 0.5066 = 35,462

PV of incremental cost ($) = 200,000 + 20,000 x PVIFA(12%, 20) = 200,000 + 20,000 x 7.4694

= 200,000 + 149,388 = 349,388

Incremental B/C Ratio = PV of incremental benefits / PV of incremental costs

= $35,462 / $349,388 = 0.10

Since incremental BCR for alternative B over alternative A is less than 1, Alternative A should be selected.