# Risk analysis and real options in capital budgeting

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Risk analysis and real options in capital budgeting4.293. Equivalent Annual Annuities (EAA) approach>Involves calculating the annual cash flow of an annuity that has the same life asthe project and whose present value (PV) equals the NPV of the project.>Effectively represents the annual payments a project would provide if it were anannuity.>EAA is calculated as inverse of NPV function:>where:NPV = the net present value of the original project chainPVIFAt,r%= the present value of annuity factor for t years at r%nrtrtrrrPVIFAPVIFANPVEAA)1(1...)1(1)1(1where,;21%,%,
Risk analysis and real options in capital budgeting4.30
Risk analysis and real options in capital budgeting4.31Which Method to Use to Adjust for Unequal Lives?>Decision rule with adjustment methods:Select project with the highest NPV over the lowest common life period or theproject with the highest NPVor EAA1.Withidenticalrequired rates of return:Lowest common life, NPVand EAA will give the same accept or rejectdecision2.Withdifferentrequired rates of return:Lowest common life and NPVmay give different signalsEAA is not appropriatewhen required rates of return differ across projects>.NPV(Constant Chain of Replacement, NPV in Perpetuity) is thepreferred methodNote, however, that the Brigham and Houston (2013) textbook only outlinesthe replacement chain and EAA methods, with no reference to the NPVmethod
Risk analysis and real options in capital budgeting4.32Example of Mutually Exclusive Projects with UnequalLives>Evaluation of two projects:>Project A:Cost=\$500,000 and Annual cash flow=\$200,000Life =5years and required return =18%>Project B:Cost=\$800,000 and Annual cash flow=\$180,000Life =10years and required return =14%>Method 1:Calculation of normal projectNPVs:Project A = \$200,000(3.1272) - \$500,000 = \$125,440Project B = \$180,000(5.2161) - \$800,000 = \$138,898Prefer Project B as it has a higher NPV
Risk analysis and real options in capital budgeting4.33Example of Mutually Exclusive Projects with UnequalLives continued>Method 2:Equivalent Annual Annuity (EAA):Project A = \$125,440 / 3.1272 = \$40,112.56Project B = \$138,898 / 5.2161 = \$26,628.71>Method 3:NPV in Perpetuity (NPV)A = \$125,440(2.2878/1.2878) = \$222,849.63B = \$138,898(3.7072/2.7072) = \$190,204.48>Comparison of results:Standard NPV suggests selecting Project BEAA and NPVsuggest selecting Project AShould rely on EAA and NPVand select Project A
Risk analysis and real options in capital budgeting4.34Estimating Project Risk>So far we have focused mainly on measuring firm-specific risk, suchas through the traditional WACC process, and applications to project-specific risk measures. There is, however, some contention as towhat the most appropriate type of risk to consider is:>Stand-alone riskThe level of risk based on this project only (or the risk level if this was the onlyproject of the firm). This is normally measured as the variability of the project’sexpected cash flows (returns),and disregards how it relates to other projectsthat the firm has and the investment portfolio of firm stockholders>Corporate (Within-firm) risk

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Term
Three
Professor
DUSA
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