The World Bank is considering an application from the country of Equatoria for a
ID: 2612933 • Letter: T
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.
an alternative project: a number of smaller dams constructed so as not to flood significant agricultural or forest lands. For this project, total construction costs are exactly half the costs of the big dam project, and power/irrigation benefits are also half as much. But there is no damage to farmland or forest, and there are no ecological or resettlement costs.
a. Do a complete cost-benefit analysis of the alternative project if the interest rate is 10%.
b. Do a complete cost-benefit analysis of the alternative project if the interest rate is 5%.
For each scenario (a. to b.), indicate a definite “yes”, definite “no,” or uncertain result (25 points
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.
Cost- Benefit analysis for 5% Interest
Costs
PV
Benefits
PV
Construction
47.25 Billion
Hydro Power
4.73 Billion
Operation
1.58 Billion
Irrigation Water
3.15 Billion
Flooded Ag
1.42 Billion
Total PV of Benefits
7.88 Billion
Flooded Forests
630 Million
Total PV of Costs
50.87 Billion
Net Benefits (NPV)
NB=PVB - PVC
-43 Billion
Discount Rate
5%
n
30
useful life time of the dam (after construction)
Current Value
CV(annual)
Costs
Construction
1.50 Billion
Operation
50 Million
Flooded Ag
45 Million
Flooded Forests
20 Million
Benefits
Hydro Power
150 Million
Irrigation Water
100 Million
in both 10% and 5% cost benefit analysis both the project should be recomended
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 $100millionRelated Questions
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