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# A dam is proposed on a stretch ofi1jer a river that is currently used

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A dam is proposed on a stretch ofi1jer a river that is
currently used for recreation. The dam will generate
electricity. The dam will have a useful life of 50 years,
after which its reservoir will be full of sediment and the
dam will need to be removed. The following are the
characteristics of the dam: Initial cost: \$100,000,000
Electricity produced: 100.000Mwh per year, @ \$100/Mwh
Cost of decommissioning dam: \$10,000,000 Value of
recreation lost: \$5,000,000 per year a) If the social
discount rate is 3% per year, is the dam a good idea? b) If
the social discount rate is 10% per year, is the dam a good
idea?
Solution
given:
initial cost = 100,000,000
cash flow per year from electricity produced = 100,000 *
100 = 10,000,000
cash flow from recreation lost = -5,000,000
net cash flow per year C = 10,000,000 -5,000,000 =
5,000,000
terminal cash flow = cost of decommsiing dam = -
10,000,000

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step1:
find present value of cash flow per year
PV = C * [1-(1+i)^-n]/i
= 5,000,000 * [1-(1+0.03)^-50]/0.03
= 128,648,820
step2:
find net present value
NPV = - intial cost + PV of net cash flows per year +
present value ofterminal cash flow
= -100,000,000 + 128,648,820 - 10,000,000/(1+0.03)^50
= 26,367,749.24
Since NPV is positive, dam is a good idea
b)
discount rate i =10%
PV = C * [1-(1+i)^-n]/i
= 5,000,000 * [1-(1+0.1)^-50]/0.1
= 49,574,072.44
NPV = - intial cost + PV of net cash flows per year +
present value ofterminal cash flow
= -100,000,000 + 49,574,072.44 - 10,000,000/(1+0.1)^50
= -50,511,113.08
Since NPV is negative, dam is not a good idea

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A dam is proposed on a stretch ofi1jer a river that is currently used for recreation. The dam will generate electricity. The dam will have a useful life of 50 years, after which its reservoir will be full of sediment and the dam will need to be removed. The following are the characteristics of the dam: Initial cost: \$100,000,000 Electricity produced: 100.000Mwh per year, @ \$100/Mwh Cost of decommissioning dam: \$10,000,000 Value of recreation lost: \$5,000,000 per year a) If the social discount rate is 3% per year, is the dam a good idea? b) If the social discount rate is 10% per year, is the dam a good idea? Solution given: initial cost = 100,000,000 cash flow per year from electricity produced = 100,000 * 100 = 10,000,000 cash flow from recreation lost = -5,000,000 net cash flow per year C = 10,000,000 -5,000,000 = 5,000,000 terminal cash flow = cost of decommsiing dam = 10,000,000 s ...
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