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:

a. Construction costs: $500 million/year for three years

b. operating costs: $50 million/year

c. Hydropower to be generated: 3 billion Kilowatt hours/year

d. Price of electricity: $0.05/Kilowatt hour

e. Irrigation water available from dam: 5 billion gallons/year

f. Price of water: $0.02/gallon

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

h. 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 area may contribute to the spread of water-borne diseases.

Do a formal cost-benefit analysis using the quantifiable factors previously listed. Assume that the lifespan of the dam is 30 years. Assume that construction begins now (in Year 0). All other impacts start once the dam is completed (in Year 3) and continue for 30 years (until Year 32). Do a complete cost/benefit analysis for two possible interest rates: 10 percent and 5 percent. Do your figures indicate a definite “yes,” definite “no,” or uncertain result in each case?

Now consider 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. Evaluate this project, and compare it to the larger project at the two interest rates

Explanation / Answer

Ans a)

Cost for 30 years = (operating cost + agricultural product lost + forest product lost) / year = $115 m/year

Benefit per year = (earning by electricity + earning by water)/ year = 3000*0.05 + 5000*0.0 = $250m/year

So net benefit = 250-115=$135m/year

So we see that project is viable if interest is 5% and not viable if interest is 10 %

b)

Cost for 30 years = (operating cost ) / year = $50 m/year

Benefit per year = (earning by electricity + earning by water)/ year = 3000*0.05/2 + 5000*0.0/2 = $125m/year

So net benefit = 125-50=$75m/year

So we see that project is viable if interest is 5% and not viable if interest is 10 %

Comparing it to the larger project we see that both projects are not viable if i=10% and larger project yields greater benefits if i=5%

Year n Benefits i=0.10 PV=benefit/(1+i)^n i=0.05 PV=benefit/(1+i)^n 0 -500 0.1 -500.0 0.05 -500.0 1 -500 0.1 -454.5 0.05 -476.2 2 -500 0.1 -413.2 0.05 -453.5 3 135 0.1 101.4 0.05 116.6 4 135 0.1 92.2 0.05 111.1 5 135 0.1 83.8 0.05 105.8 6 135 0.1 76.2 0.05 100.7 7 135 0.1 69.3 0.05 95.9 8 135 0.1 63.0 0.05 91.4 9 135 0.1 57.3 0.05 87.0 10 135 0.1 52.0 0.05 82.9 11 135 0.1 47.3 0.05 78.9 12 135 0.1 43.0 0.05 75.2 13 135 0.1 39.1 0.05 71.6 14 135 0.1 35.5 0.05 68.2 15 135 0.1 32.3 0.05 64.9 16 135 0.1 29.4 0.05 61.8 17 135 0.1 26.7 0.05 58.9 18 135 0.1 24.3 0.05 56.1 19 135 0.1 22.1 0.05 53.4 20 135 0.1 20.1 0.05 50.9 21 135 0.1 18.2 0.05 48.5 22 135 0.1 16.6 0.05 46.1 23 135 0.1 15.1 0.05 44.0 24 135 0.1 13.7 0.05 41.9 25 135 0.1 12.5 0.05 39.9 26 135 0.1 11.3 0.05 38.0 27 135 0.1 10.3 0.05 36.2 28 135 0.1 9.4 0.05 34.4 29 135 0.1 8.5 0.05 32.8 30 135 0.1 7.7 0.05 31.2 31 135 0.1 7.0 0.05 29.7 32 135 0.1 6.4 0.05 28.3 Total benefit -316.0 452.6

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