One of two alternatives will be selected to reduce flood damage in a rural community in central Arizona. The estimates associated with each alternative are available. Use B/C analysis at a discount rate of 8% per year over a 20-year study period to determine which alternative should be selected. For analysis purposes only, assume that the benefits of reduced flood damage are available in years 3, 9, and 18 of the study period. Retention Pond Channel
Initial Cost, $880,000 1,500,000
Annual Maintenance, $/Year 92,000 30,000
Reduced Flood Damage, $ 200,000 625,000

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.

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