AEM 2500 Fall 2009
HW #5 Solutions
1.
CostBenefit Analysis
a.
Using the given formula, the construction costs over three years, including
interest, expressed in year 3 are:
[$500 m * (1+r)
2
] + [$500 m * (1+r)
1
] + [$500 m * (1+r)
0
]
Thus, using each discount rate, the present value of construction costs are:
Construction costs at 10% = $500 m * [1.1
2
+1.1+1] = $1,655 m
Construction costs at
5% = $500 m * [1.05
2
+1.05+1] = $1,576 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
$1,655 m
$1,576 m
Operating costs
$500 m
$1,000 m
Agricultural products costs
$450 m
$900 m
Forest products costs
$200 m
$400 m
Total Costs
$2,805 m
$3,876 m
Hydropower benefits
$1,500 m
$3,000 m
Irrigation benefits
$750 m
$1,500 m
Total Benefits
$2,250 m
$4,500 m
Net Benefits
$555 m
$624 m
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View Full DocumentBased on quantifiable costs and benefits, the project offers net benefits at a 5%
discount rate but not at a 10% discount rate – hence, the selection of the discount
rate is extremely important in benefit cost analyses!
Consideration of
unquantified costs (relocation costs, watershed damage, and habitat damage) will
only make the project less appealing at a 10% discount rate so the project is
definitely not recommended.
Inclusion of the unquantified costs at a 5% discount
rate means that the results of the costbenefit analysis are uncertain.
Depending
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 Fall '07
 POE,G.
 Net Present Value

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