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It is proposed to install a geothermal heat pump to provide space heating to a four-bedroom home that requires 23,300 kWh of space heating per year. The heat pump and vertical well loop system needed for geothermal heating costs $18,400 to install. The geothermal heat pump has a coefficient of performance (COP) of 3.5 and is powered by electricity purchased at 8.5¢/kWh. Alternatively, a gas furnace can be installed to deliver space heating. The gas furnace costs $2650 and has a fuel efficiency of 90%. Natural gas costs $25 per 106 Btu. The geothermal heat pump and the gas furnace both have a projected lifetime of 25 years.

a. What is the simple payback period (yr) for installation of the geothermal system rather than the gas furnace?

b. For a discount rate of 7%, what is the net present value ($) of the geothermal heat pump system, assuming no escalation in the costs of electricity and natural gas?

c. What is the internal rate of return (IRR) with no fuel cost escalation? Determine the IRR to the nearest tenth of a percent.

d. Which option – geothermal heat pump or gas furnace – provides less expensive space heating over the system lifetime, if the cost of electricity increases at 1% per year (due to coal emissions control requirements), whereas the cost of natural gas decreases at 1% per year (due to increased supply from shale gas development)? Provide calculations in support of your answer.

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