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AV =UCRFxNPV AV = UCWxF&k(l-kn)/(1-k)] Where: = cash flow to be annualized k = [(l+0)i(1+d)]. Note that if there is no escalation in price (i.e., hp = 0), then AV = Fo. Also note that the formula for annualized cost assumes that the price escalation is measured in the same type of dollars (either constant or current) as is used for the discount rate, d. Internal Rate of Return Introduction The internal rate of return (IRR) for aninvestment that has a series of future cash flows (IF,, F,, ...F,) is theratethatsetstheNPVofthecashflowsequaltozero. TheIRRanalysisallowsforthecomparison of a wide variety of investment activities. However, IRR is not recommended when evduathg investments in which further investment after return is required because downstream investments are improperly discounted and multiple positive PRR values can occur. IRR is commonly used for acceptheject decisions, allowing a quick comparison with a minimum acceptable rate of return (hurdle rate). IRRisnotrecommendedwhenselectingamongmutuallyexclusivealternativesbecausethevalues of differing investment sizes are not considered (an investor will choose to invest more in an alternative with more favorable returns). This shortcoming may be corrected by applying IRR on an incremental basis. IRRisalsonotrecommendedwhenrankingprojectsbecauseIRRimplicitlyassumesreinvestment of returns at the IRR. The viability of a project is usualIly assessed with IRR by comparing the IRR of the project with a "hurdle rate" that represents the IRR of the next best alternative (the opportunity cost of capital). IRR also has the advantage that it can be used to directly compare the after-tax return on readily available financial instruments, such as bonds, thereby providing the investor with a quick qualitative assessment of the project. FO Discussion IRR equals the rate for which: Where: 0=NPV=EN,=[,F,4 (1 +d)n] NPV = net present value of the capital investment (4-15) = cash flows received at time n d = rate that equates the present value of positive and negative cash flows when used as a discount rate. Table 4-10 illustrates the after-tax cash flows resulting from the use of the same example as was used in the Net Present Value subsection. This example involved the following assumptions: an investment of $10,000 made at the beginning of the year; no salvage value; O&M costs of $1,300 in year zero, inflating Fn 52PDF Image | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
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