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AsilluswatedinTable4-12,thefuturevalueoftheafter-taxpositivecashflowsis$41,542. Thediscount rate, which equates this to the original $10,000 investment over the 5-year period, is 33%. Again, given the example, the MIRR should actually be labeled as a nominal MIRR of 33% because the after-tax cash flows were in current dollars, If the dollars were constant, the interim cash flows would be reinvested at the real rate of 8.74%, and the resulting MIRR of 29.2% would be a real rate. Asstatedearlier,MIRRcanbeusedtoevaluateprojectshavingdifferentscalesorlives. Asanexample, assume two alternative projects, X and Y , each costing $15,000, which will be invested at the beginning of year one. Project X returns $7,000 at the end of years one, two, and three;and Project Y returns $3,000 at the end of years one through ten. Assume a discount rate of 10%. In this example, the NPVs of each cash flow stream is $2,408 for Project X and $3,434 for Project Y. On the other hand, the IRR is 18.9% for Project X and 15.1% for Project Y. Thus, Project Y is the best alternative when using an NFV analysis and Project X is the best alternative when using IRR analysis. This result ignores the fact that cash inflows fkom Project X can be reinvested over the remaining 7 years of the analysis period. Giventhedifferentprojectlives,theanalystshouldcalculateanMIRR. Thiscanbedonebyassuming a reinvestment rate of 10% for Project X. The first step is to calculate terminal values for Project X under alternative reinvestment rates. For Project X, the future value of the $7,000 annuity for 3 years is calculated. This is then reinvested at the discount rate of 10% for the remaining 7 years of the analysis to arrive at a terminal value (future value) of $45,152. In the case of Project Y , the future value of the $3,000 annuity for 10 years is calculated to arriveataterminalvalueof$47,813. Next,calculatethediscountrate,whichwillequatetheterminal values, when discounted back to the base year, with the investment. Project X:$45,152/(1 + d)N- $15,000 = 0 (4-17) MIRR = 11.7% Project Y: $47,813/(1 + d)N- $15,000 = 0 (4- 18) MIRR = 12.3%. The MIRR in this example reveals that given a reinvestment rate of 10%for Project X, Project Y should beundertaken,notProjectX. ThisresultmatchestheresultsofthepreviousexampleofNPVanalysis. Sometimes a project will require investment near the middle or end of an analysis period after positive cash inflow has occurred, or there may simply be negative cash flows near the middle and end of the analysis period. This situation can lead to multiple positive solutions for ordinary IRR calculations. MIRR should be used in these situations. Simple Payback Period Introduciion Simple payback (SPB) is a quick, simple way to compare alternative projects. It is relatively easy to utilizeandassuchisaverypopularfinancialtool. Simplepaybackisthenumberofyearsnecessaryto recover the project cost of an investment under consideration. SPB is commonly used and recommended when risk is an issue (i.e., significant uncertainties are present) because SPB allows for a quick assessment of the duration during which an investor’s capital is at risk. SPB is not recommended when evaluating alternatives involving financing and tax features because their 56PDF Image | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
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