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2) The World Bank is considering an application from the country of Equatoria (not a real country) for a large dam project. S
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Answer #1

Total Costs = Construction Costs + Operating Costs

Where, C = $500 million/year,

And, O = $50/year

Total Revenue = Revenue from Hydro-Power Electricity + Revenue from Irrigational Water + No Agricultural Product Loss from Floods + No Forest Product Loss from Floods

Revenue from Hydro-Power Electricity for one year = $(0.05*3) billion = $0.15 billion = $150million

Revenue from Irrigational Water for one year = $(0.02*5) billion = $0.1 billion = $100million

No Agricultural Product Loss from Floods = $45 million/year

No Forest Product Loss from Floods = $20 million/year

Now, we can produce two cases:

  • Assuming Social Discount Rate of 5%,

COSTS:

Construction Costs (C) = 1500 + 1500/(1.05) + 1500/(1.05)2 = $4289.1156

Operating Costs (O) = 50/(1.05)2 + 50/(1.05)3 + ….. + 50/(1.05)32 =

                                 = 50/(1.05)32 [(1.05)+ (1.05)2 + ….. + (1.05)30] = $69.71          

BENEFITS:
Revenue from Hydro-Power Electricity (HPE) = 150/(1.05)2 + 150/(1.05)3 + ….. + 150/(1.05)32 = 150/(1.05)32 [(1.05)+ (1.05)2 + ….. + (1.05)30] = $209.148

Revenue from Irrigational Water (IW) = 100/(1.05)2 + 100/(1.05)3 + ….. + 100/(1.05)32 = 100/(1.05)32 [(1.05)+ (1.05)2 + ….. + (1.05)30] = $139.4326

No Agricultural Product Loss from Floods = 45/(1.05)2 + 45/(1.05)3 + ….. + 45/(1.05)32 = 45/(1.05)32 [(1.05)+ (1.05)2 + ….. + (1.05)30] = $62.7446

No Forest Product Loss from Floods = 20/(1.05)2 + 20/(1.05)3 + ….. + 20/(1.05)32 = 20/(1.05)32 [(1.05)+ (1.05)2 + ….. + (1.05)30] = $27.8865

Thus, Benefit-Cost Ratio = (Total Benefits)/(Total Cost) = (432.2117)/(4358.8256) = 0.0991

  • Assuming Social Discount Rate of 10%,

COSTS:

Construction Costs (C) = 1500 + 1500/(1.1) + 1500/(1.1)2 = $4103.3057

Operating Costs (O) = 50/(1.1)2 + 50/(1.1)3 + ….. + 50/(1.1)32 =

                                 = 50/(1.1)32 [(1.1)+ (1.1)2 + ….. + (1.1)30] = $155.8167

BENEFITS:
Revenue from Hydro-Power Electricity (HPE) = 150/(1.1)2 + 150/(1.1)3 + ….. + 150/(1.1)32 = 150/(1.1)32 [(1.1)+ (1.1)2 + ….. + (1.1)30] = $233.7251

Revenue from Irrigational Water (IW) = 100/(1.1)2 + 100/(1.1)3 + ….. + 100/(1.1)32 = 100/(1.1)32 [(1.1)+ (1.1)2 + ….. + (1.1)30] = $155.8167

No Agricultural Product Loss from Floods = 45/(1.1)2 + 45/(1.1)3 + ….. + 45/(1.1)32 = 45/(1.1)32 [(1.1)+ (1.1)2 + ….. + (1.1)30] = $70.1175

No Forest Product Loss from Floods = 20/(1.1)2 + 20/(1.1)3 + ….. + 20/(1.1)32 = 20/(1.1)32 [(1.1)+ (1.1)2 + ….. + (1.1)30] = $31.1633

Thus, Benefit-Cost Ratio = (Total Benefits)/(Total Cost) = (490.8226)/(4259.1224) = 0.1152

My recommendation would be to keep the SDR above 5% and below 10%.

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