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HW_5_Solutions_Problem_Set

# HW_5_Solutions_Problem_Set - AEM 250 Spring 2008 HW#5...

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AEM 250 Spring 2008 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 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 \$1,821 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 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 -\$721 m \$545 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 selectionof the discount rate is extremely important in benefit cost analyses! Consideration of unquantified costs (relocation costs, watershed damage, and habitat damage) will
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HW_5_Solutions_Problem_Set - AEM 250 Spring 2008 HW#5...

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