ERE HW 5 Solution

# ERE HW 5 Solution - AEM 2500 Fall 2009 HW#5 Solutions 1...

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AEM 2500 Fall 2009 HW #5 Solutions 1. Cost-Benefit 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 kW-hours times \$0.05 per kW-hour). 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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Based 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 cost-benefit analysis are uncertain. Depending
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ERE HW 5 Solution - AEM 2500 Fall 2009 HW#5 Solutions 1...

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