The World Bank is considering an application from the country of Equatoria for a

Question

The World Bank is considering an application from the country of Equatoria for a large dam project. Some costs and benefits of the project (dollar values) are as follows:

• Construction costs: $500 million/year for three years

• Operating costs: $50 million/year

• Hydropower to be generated: 3 billion Kilowatt hours/year

• Price of electricity: $0.05/Kilowatt hour

• Irrigation water available from the dam: 5 billion gallons/year

• Price of water: $0.02/gallon

• Agricultural product lost from flooded lands: $45 million/year

• Forest products lost from flooded lands: $20 million/year

There are also additional, less easily quantifiable, losses: human costs to villagers who will be forced to move, watershed damage, and ecological costs of habitat destruction. It is also possible that the new lake are may contribute to the spread of water-borne diseases.

Do a formal cost-benefit analysis using the quantifiable factors listed. Assume that the lifespan of the dam is 30 years; assume that construction begin now (in Year 0). All other impacts start once the dam is completed (in Year 3) and continue for 30 years (until Year 32).

For each scenario (a. and b.), indicate a definite “yes”, definite “no,” or uncertain result

Scenarios to analyze:

A. Do a complete cost-benefit analysis if the interest rate is 10%.

B. Do a complete cost-benefit analysis if the interest rate is 5%.

Complete the Data summary (for each scenario analyzed)

Costs PV Benefits PV Construction $? Hydro Power $? Operation $? Irrigation Water $? Flooded Ag $? Total PV of Benefits $? Flooded Forests $? Total PV of Costs $? Net Benefits (NPV) NB=PVB - PVC ? Discount Rate ?% n ? useful life time of the dam (after construction) Current Value CV(annual) Costs Construction $? Operation $? Flooded Ag $? Flooded Forests $? Benefits Hydro Power $? Irrigation Water $?

Explanation / Answer

A) initial condition: cost benefit analysis if interest rate is 10%

first step is to find out PVs of different and benefits

PV of construction= 500/(1+.10)^1+ 500/(1+.10)^2+500/(1+.10)^3   = $1243.426 million

as all other impact starts when construction is done in 3 rd year

so

PV of operating cost = 50/(1+.10)^3+............50/(1+.10)^32 = 50/(1+.10)^3 {1+1/(1+.10)^1+........1/(1+.10)^29 }

                                   = 50/(1+.10)^3 { 1- ((1/(1+.10))^30)}/ {1-(1/(1+.10))}= $ 389.541 million

PV of flooded agricultural products = 45/(1+.10)^3+............45/(1+.10)^32 =45/(1+.10)^3 {1+1/(1+.10)^1+........1/(1+.10)^29 }
                                   = 45/(1+.10)^3 { 1- ((1/(1+.10))^30)}/ {1-(1/(1+.10))}= $ 350.58 million

PV of flooded forests=20/(1+.10)^3+............20/(1+.10)^32 =20/(1+.10)^3 {1+1/(1+.10)^1+........1/(1+.10)^29 }
                                   = 20/(1+.10)^3 { 1- ((1/(1+.10))^30)}/ {1-(1/(1+.10))}= $ 155.81 million

( note: this calcuation is based on sumof GP series: a, ar, ar^2...ar^n and sum is given by a(1-r^n)/(1-r) )

now we will find PV OF BENEFITS:

value of electricity produced per year= 3 000million*.05=$150 million/ per year
PV OF electricity=150/(1+.10)^3+............150/(1+.10)^32 =150/(1+.10)^3 {1+1/(1+.10)^1+........1/(1+.10)^29 }
                                   = 150/(1+.10)^3 { 1- ((1/(1+.10))^30)}/ {1-(1/(1+.10))}= $ 1168.62 million

value of water produced per year= 5000million*.02=$100 million/ per year
PV OF water =100/(1+.10)^3+............100/(1+.10)^32 =100/(1+.10)^3 {1+1/(1+.10)^1+........1/(1+.10)^29 }
                                   = 100/(1+.10)^3 { 1- ((1/(1+.10))^30)}/ {1-(1/(1+.10))}= $ 779.08 million

according to cost benefit analysis as this project is earning net loss at r=10% there will be complete' NO 'for this project. because addition to this economic loss , there are other cost which this project is inferring on economy.

B) similar cost benefit analysis can be done for R= 5% following the same steps

if in that case net gain come out to be positive, then project can be initiated at r=5%

if net loss persists then project will not be started at r=5%

Costs PV Benefits PV Construction $1243.426 million Hydro Power $ 1168.62 million Operation $ 389.541 million Irrigation Water $ 779.08 million Flooded Ag $ 350.58 million Total PV of Benefits $1947.70 million Flooded Forests $ 155.81 million Total PV of Costs $2139.37 million Net Benefits (NPV) NB=PVB - PVC $-191.66 million that means net loss of 191 million Discount Rate 10% n 32( from 3 to 32 time period dam is useful for 30 years useful life time of the dam (after construction) Current Value CV(annual) Costs Construction $ 500 million Operation $50 million Flooded Ag $45million Flooded Forests $20million Benefits Hydro Power $150million Irrigation Water $100million

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