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anannuity. Foranannuity,motherformulacanbeusedforcdculathgpresentvalue. Theformulafor cdculating the present value of an annuity is as folIowsll: Where: PV = present value F = cash flow in each of N future years d = annual discount rate. For example, assume a cash inflow of $100 per year at the end of each year for the next 5 years at a discount rate of 10%. The following calc'ulation is obtained by applying the formula in Eq. (2-12): 0'10)5 - = $100 x 3.7908 = $379.08 (2-13) PV = $100 x ~o.io(i+ 0.10)51 In this example, the present value of the annuity is $379.08. In these examples, the issue of real or nominal discount rates and dollars was not addressed. As was pointed out in the Discount Rates subsection in Section 2, a real discount rate excludes inflation, whereas anominalvalueincludesinflation. Theimportantthingtorememberwhencalculatingpresentvalueis to use real discount rates if cash flows are in constant dollars and to use nominal discount rates if cash flows are in current dollars. Taxes Introduction Taxesrepresentadditionalcoststhatarenodifferentfrom,forexample,laborandmaterialscosts. As such, dl relevant taxes should be included in an economic analysis. The most complete analysis of an investment in a technology or a project requires the analysis of each year of the life of the investment, taking into account relevant costs, including taxes. Inmostcircumstances,cashflowwillbethebasisforanalyzingalternativeinvestments. Anafter-taxcash flow should account for federal and state income taxes (if state income taxes are applicable). In most cases,analysesshouldbebasedonafter-taxcashflows. AsStermolepointsout,theeffectsofincome tax can vary widely from one alternative to another, so it is generally imperative to compare the relative economics of investment alternatives on an after-tax basis to have a valid economic analysis (Stermole 1984). Anillustrationoftheimportanceofafter-taxanalysisisnoteworthyhere. Supposeafossilfuelplantwith relatively low capita1 costs and high fuel costs is being compared to a solar plant with relatively high capital costs and no fuel costs. Depreciation for tax purposes will be a major factor in this analysis. The "The present value interest factor, [(l +d)N- l]/[d(l +d)N],used in the calculation of net present value, is the reciprocal of the uniform capital recovery factor (UCRF). (2- 12)PDF Image | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
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