Question

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 7% 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, 8, and 18 of the study period. 33 Retention Pond Channel Initial Cost, $ Annual Maintenance, S/Year 900,000 92,000 20 200,000 1,700,000 30,000 625,000 Reduced Flood Damage, $ The AB/C ratio is . The alternative that should be selected is the Click to select)

Answer 1

Answer:-

The present worth of cost retention pond:-

PW = 900,000 + 92,000 (P/A, 7%, 20)

        = 900,000 + 92,000 (10.594)

        = 900,000 + 974,648

        = 18,74,648

The present worth of Channel:-

PW = 1700,000 + 30,000 (P/A, 7%, 20)

        = 1700,000 + 30,000 (10.594)

        = 1700,000 + 3,17,820

        = 20,17,820

The present worth of benefit of retention pond at 7% annual interest will be:-

PW = 200,000 {(P/F, 7%, 3) + (P/F, 7%, 8) + (P/F, 7%, 18)}

        = 200,000 { 0.8163 + 0.5820 + 0.2959}

      = 200,000 * 1.6942

        = 3,38,840

The present worth of benefit of channel at 7% annual interest will be:-

PW = 625,000 {(P/F, 7%, 3) + (P/F, 7%, 8) + (P/F, 7%, 18)}

        = 625,000 { 0.8163 + 0.5820 + 0.2959}

      = 625,000 * 1.6942

        = 10,58,875

Now cost of channel is more, so to justify the cost, incremental cost will be calculated

ΔC = 20,17,820 - 18,74,648 = 1,43,172

Incremental benefit will be ΔB = 10,58,875 – 3,38,840 = 7,20,035

ΔB / C = 7,20,035 / 1,43,172 = 5.023

As the value of incremental B/C ratio is more than 1, The Alternative that should be selected is Pond