HW #5 Solutions
1.
a. The construction costs over three years, including interest, expressed in year 4
are:
[$500 m * (1+r)
3
] + [$500 m * (1+r)
2
] + [$500 m * (1+r)
1
]
Thus, using each discount rate, the present value of construction costs are:
Construction costs at 10% = $500 m * [(1.1
3
)+(1.1
2
)+1.1]
= $1,821 m
Construction costs at
5% = $500 m * [(1.05
3
)+(1.05
2
)+1.05] = $1,655 m
The present values of operating costs evaluated at each discount rate are:
Operating costs at 10% = $50 m / 0.1
=
$500 m
Operating costs at
5% = $50 m / 0.05 = $1,000 m
The annual costs of flooding agricultural and forest land can be converted to
present values using the formula
PV = C
i
/r.
At a 10% discount rate, PV is 10* C
i
and with a 5% discount rate, PV is 20* C
i
.
The annual benefits of hydropower are $150 million (3 billion kWhours times
$0.05 per kWhour).
The annual benefits of irrigation water are $75 million (5
billion gallons times $0.015 per gallon).
These benefits can be converted to
present values using the formula PV = B
i
/r.
At a 10% discount rate, PV is 10* B
i
and with a 5% discount rate, PV is 20* B
i
.
We can now express all quantifiable
costs and benefits in the table below.
Cost/Benefit
10% discount rate
5% discount rate
Construction costs
$1,821 m
$1,655 m
Operating costs
$500 m
$1,000 m
Agricultural products costs
$450 m
$900 m
Forest products costs
$200 m
$400 m
Total Costs
$2,971 m
$3,955 m
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 Spring '07
 POE,G.
 Net Present Value

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