Answer:
Since the incremental B/C of 58.21 is less greater 1, it implies that the alternative that should be selected is Channel.
Explanation:
The alternative that should be selected can be determined using the Benefit-Cost (B/C) analysis as follows:
Incremental B/C = [Incremental Flood damage savings * ((1 + r)^-3 + (1 + r)^-9 + ((1 + r)^-18)] / [Incremental initial cost + (Incremental Annual Maintenance cost * ((1 - (1 / (1 + r))^n) / r))] ............... (1)
Where:
Incremental initial cost = Channel initial cost - Retention pond initial cost = $1,500,000 - $880,000 = $620,000
Incremental Annual Maintenance cost = Channel Annual Maintenance - Retention pond Annual Maintenance = $30,000 - $92,000 = -$62,000
Incremental flood damage savings = Channel Incremental flood damage savings - Retention pond incremental flood damage savings = $625,000 - $200,000 = $425,000
r = Discount rate = 8%, or 0.08
n = number of years = 20
Substituting all the relevant values into equation (1), we have:
Incremental B/C = [425000 * ((1+0.08)^-3 + (1+0.08)^-9 + (1+0.08)^-18)] / [$620,000 - ($62,000 * ((1 - (1 / (1 + 0.08))^20) / 0.08))]
Incremental B/C = $656,340.35 / $11,274.86
Incremental B/C = 58.2127235166936
Rounding to 2 decimal places, we have:
Incremental B/C = 58.21
Since the incremental B/C of 58.21 is less greater 1, it implies that the alternative that should be selected is Channel.
