HW 5a - AEM 250 Spring 2007 HW#5 Solutions 1 are a The...

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AEM 250 Spring 2007 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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