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RelevantcashflowsWorkingcapitaltreatmentInflationRiskAnalysis:SensitivityAnalysis,ScenarioAnalysis,andSimulationAnalysisTopic11(Chapter8)CashFlowEstimationandRiskAnalysisTopic11KeytermsRelevantcashflow相关现金流量Incrementalcashflow增量现金流量Sunkcost沉没成本Opportunitycost机会成本Changeinnetoperatingworkingcapital净经营营业资本的变化Newexpansionprojects新扩张项目Replacementproject重置项目Sensitivityanalysis敏感性分析Base-caseNPV基础净现值Scenarioanalysis情景分析Worst-casescenario最差情景事件Best-casescenario最佳情景事件Basecase基础事件Montecarlosimulation蒙特卡罗模拟Risk-adjusteddiscountrate风险调整贴现率Whateffectdidtheexpansionhaveonnetoperatingworkingcapital(NOWC)?NOWC08 =($7,282+$632,160+$1,287,360) -($524,160+$489,600) =$913,042.NOWC07 =$793,800.=-OperatingCAOperatingCLNOWCWhateffectdidtheexpansionhaveoncapitalusedinoperations? =NOWC+Netfixedassets.

=$913,042+$939,790 =$1,852,832.

=$1,138,600.Operatingcapital08Operatingcapital07OperatingcapitalDidtheexpansioncreateadditionalnetoperatingprofitaftertaxes(NOPAT)?NOPAT=EBIT(1-Taxrate)NOPAT08 =-$690,560(1-0.4) =-$690,560(0.6) =-$414,336.NOPAT07 =$125,460.Whatisyourinitialassessmentoftheexpansion’seffectonoperations? 2008 2007Sales $5,834,400 $3,432,000NOPAT ($414,336) $125,460NOWC $913,042 $793,800Operatingcapital $1,852,832 $1,138,600

Whateffectdidthecompany’sexpansionhaveonitsnetcashflowandoperatingcashflow?NCF08 =NI+DEP =-$519,936+$116,960 =-$402,976.NCF07 =$87,960+$18,900=$106,860.OCF08 =NOPAT+DEP =-$414,336+$116,960 =-$297,376.OCF07 =$125,460+$18,900 =$144,360.Whatwasthefreecashflow(FCF)

for2008?FCF=NOPAT-Netcapitalinvestment=-$414,336-($1,852,832-$1,138,600)=-$414,336-$714,232=-$1,128,568.Howdoyousupposeinvestorsreacted?Cost:$200,000+$10,000shipping+$30,000installation.Depreciablecost$240,000.Inventorieswillriseby$25,000andpayableswillriseby$5,000.Economiclife=4years.Salvagevalue=$25,000.MACRS3-yearclass.ProposedProjectIncrementalgrosssales=$250,000.Incrementalcashoperatingcosts=$125,000.Taxrate=40%.Overallcostofcapital=10%.01234InitialOutlayOCF1OCF2OCF3OCF4+TerminalCFNCF0NCF1NCF2NCF3NCF4SetupwithoutnumbersatimelinefortheprojectCFs.=Corporatecashflow

with

project

minusCorporatecashflow

withoutprojectIncrementalCashFlowNO. Thecostsofcapitalarealreadyincorporatedintheanalysissinceweusethemindiscounting.Ifweincludedthemascashflows,wewouldbedoublecountingcapitalcosts.ShouldCFsincludeinterestexpense?Dividends?NO.Thisisasunkcost.Focusonincrementalinvestmentandoperatingcashflows.Suppose$100,000hadbeenspentlastyeartoimprovetheproductionlinesite.Shouldthiscostbeincludedintheanalysis?Yes.Acceptingtheprojectmeanswewillnotreceivethe$25,000.Thisisanopportunitycostanditshouldbechargedtotheproject.A.T.opportunitycost=$25,000(1-T)=$15,000annualcost.Supposetheplantspacecouldbeleasedoutfor$25,000ayear.Wouldthisaffecttheanalysis?Yes.Theeffectsontheotherprojects’CFsare“externalities”.NetCFlossperyearonotherlineswouldbeacosttothisproject.Externalitieswillbepositiveifnewprojectsarecomplementstoexistingassets,negativeifsubstitutes.Ifthenewproductlinewoulddecreasesalesofthefirm’sotherproductsby$50,000peryear,wouldthisaffecttheanalysis?NetInvestmentOutlayatt=0(000s)

NWC =$25,000-$5,000 =$20,000.Equipment($200)Freight+Inst.(40)ChangeinNWC(20)NetCF0($260)Basis=Cost+Shipping+Installation

$240,000DepreciationBasicsAnnualDepreciationExpense(000s)Year%xBasis=Depr.10.33$240$7920.4510830.153640.0717Year1OperatingCashFlows(000s)Year1Netrevenue$125Depreciation

(79)Before-taxe$46Taxes(40%)

(18)Nete$28Depreciation79NetoperatingCF$107Year4OperatingCashFlows(000s)Year1Year4Netrevenue$125$125Depreciation(79)(17)Before-taxe$46$108Taxes(40%)(18)(43)Nete$28$65Depreciation7917NetoperatingCF$107$82NetTerminalCashFlowatt=4(000s)Salvagevalue$25TaxonSV(10)RecoveryonNWC20

NetterminalCF$35

Whatifyouterminateaprojectbeforetheassetisfullydepreciated?Cashflowfromsale=Saleproceeds -taxespaid.Taxesarebasedondifferencebetweensalespriceandtaxbasis,where:Basis=Originalbasis-Accum.deprec.Originalbasis =$240.After3years =$17remaining.Salesprice =$25.Taxonsale =0.4($25-$17)

=$3.2.Cashflow =$25-$3.2=$21.7.Example:IfSoldAfter3Years(000s)ProjectNetCFsonaTimeLineEnterCFsinCFLOregisterandI=10. NPV=$81,573. IRR=23.8%.*Inthousands.01234(260)*10711889117Whatistheproject’sMIRR?(000s)(260)MIRR=?01234(260)*10711889

117.0 97.9 142.8

142.4 500.11. EnterpositiveCFsinCFLO:

I=10;SolveforNPV=$341.60.2. UseTVMkeys:PV=341.60,N=4

I=10;PMT=0;SolveforFV=500.10.(TVofinflows)3. UseTVMkeys:N=4;FV=500.10;

PV=-260;PMT=0;SolveforI=17.8. MIRR=17.8%.CalculatorSolutionWhatistheproject’spayback?(000s)Cumulative:Payback=2+35/89=2.4years.01234(260)*(260)107(153)118(35)8954117171No.Netrevenuesareassumedtobeconstantoverthe4-yearprojectlife,soinflationeffectshavenotbeenincorporatedintothecashflows.If5%inflationisexpectedoverthenext5years,arethefirm’scashflowestimatesaccurate?InDCFanalysis,kincludesanestimateofinflation.Ifcashflowestimatesarenotadjustedforinflation(i.e.,areintoday’sdollars),thiswillbiastheNPVdownward.Thisbiasmayoffsettheoptimisticbiasofmanagement.Realvs.NominalCashflowsWhatdoes“risk”meanin

capitalbudgeting?Uncertaintyaboutaproject’sfutureprofitability.Measuredby

NPV,

IRR,beta.Willtakingontheprojectincreasethefirm’sandstockholders’risk?Isriskanalysisbasedonhistoricaldataorsubjectivejudgment?Cansometimesusehistoricaldata,butgenerallycannot.Soriskanalysisincapitalbudgetingisusuallybasedonsubjectivejudgments.Whatthreetypesofriskarerelevantincapitalbudgeting?Stand-aloneriskCorporateriskMarket(orbeta)riskHowiseachtypeofriskmeasured,andhowdotheyrelatetooneanother?1.Stand-AloneRisk:Theproject’sriskifitwerethefirm’sonlyassetandtherewerenoshareholders.Ignoresbothfirmandshareholderdiversification.Measuredbythe

orCVofNPV,IRR,orMIRR.0 E(NPV)ProbabilityDensityFlatterdistribution,larger

,largerstand-alonerisk.Suchgraphicsareincreasinglyusedbycorporations.NPV2.CorporateRisk:Reflectstheproject’seffectoncorporateearningsstability.Considersfirm’sotherassets(diversificationwithinfirm).Dependson:project’s

,anditscorrelationwithreturnson firm’sotherassets.Measuredbytheproject’scorporatebeta.Profitability0YearsProjectXTotalFirmRestofFirm1. ProjectXisnegativelycorrelatedtofirm’sotherassets.2. Ifr<1.0,somediversificationbenefits.3. Ifr=1.0,nodiversificationeffects.3.MarketRisk:Reflectstheproject’seffectonawell-diversifiedstockportfolio.Takesaccountofstockholders’otherassets.Dependsonproject’s

andcorrelationwiththestockmarket.Measuredbytheproject’smarketbeta.Howiseachtypeofriskused?Marketriskistheoreticallybestinmostsituations.However,creditors,customers,suppliers,andemployeesaremoreaffectedbycorporaterisk.Therefore,corporateriskisalsorelevant.Stand-aloneriskiseasiesttomeasure,moreintuitive.Coreprojectsarehighlycorrelatedwithotherassets,sostand-aloneriskgenerallyreflectscorporaterisk.Iftheprojectishighlycorrelatedwiththeeconomy,stand-aloneriskalsoreflectsmarketrisk.Whatissensitivityanalysis?ShowshowchangesinavariablesuchasunitsalesaffectNPVorIRR.Eachvariableisfixedexceptone.ChangethisonevariabletoseetheeffectonNPVorIRR.Answers“whatif”questions,e.g.“Whatifsalesdeclineby30%?”IllustrationChangefromBaseLevelResultingNPV(000s)UnitSalesSalvagek-30%$10$78$105-20358097-105881890828282+101058374+201298467+301538561

-30-20-10Base102030 Value

82

NPV(000s)UnitSalesSalvagekSteepersensitivitylinesshowgreaterrisk.SmallchangesresultinlargedeclinesinNPV.Unitsaleslineissteeperthansalvagevalueork,soforthisproject,shouldworrymostaboutaccuracyofsalesforecast.ResultsofSensitivityAnalysisWhataretheweaknessesof

sensitivityanalysis?Doesnotreflectdiversification.Saysnothingaboutthelikelihoodofchangeinavariable,i.e.asteepsaleslineisnotaproblemifsaleswon’tfall.Ignoresrelationshipsamongvariables.Whyissensitivityanalysisuseful?Givessomeideaofstand-alonerisk.Identifiesdangerousvariables.Givessomebreakeveninformation.Whatisscenarioanalysis?Examinesseveralpossiblesituations,usuallyworstcase,mostlikelycase,andbestcase.Providesarangeofpossiblees.Assumeweknowwithcertaintyallvariablesexceptunitsales,whichcouldrangefrom900to1,600.

E(NPV)=$82

(NPV)=47 CV(NPV)=

(NPV)/E(NPV)= 0.57ScenarioProbabilityNPV(000)Worst0.25$15Base0.5082Best0.25148Ifthefirm’saverageprojecthasaCVof0.2to0.4,isthisahigh-riskproject?Whattypeofriskisbeingmeasured?SinceCV=0.57>0.4,thisprojecthashighrisk.CVmeasuresaproject’sstand-alonerisk.Itdoesnotreflectfirmorstockholderdiversification.Wouldaprojectinafirm’score

businesslikelybehighlycorrelatedwiththefirm’sotherassets?Yes.Economyandcustomerdemandwouldaffectallcoreproducts.Buteachproductwouldbemoreorlesssuccessful,socorrelation<+1.0.Coreprojectsprobablyhavecorre-lationswithinarangeof+0.5to+0.9.Howdocorrelationand

affect

aproject’scontributionto

corporaterisk?If

Pisrelativelyhigh,thenproject’scorporateriskwillbehighunlessdiversificationbenefitsaresignificant.Ifprojectcashflowsarehighlycor-relatedwiththefirm’saggregatecashflows,thentheproject’scorporateriskwillbehighif

Pishigh.Wouldacoreprojectinthefurniturebusinessbehighlycorrelatedwiththegeneraleconomyandthuswiththe“market”?Probably.Furnitureisadeferrableluxurygood,sosalesareprobablycorrelatedwithbutmorevolatilethanthegeneraleconomy.Wouldcorrelationwiththe

economyaffectmarketrisk?Yes.Highcorrelationincreasesmarketrisk(beta).Lowcorrelationlowersit.Witha3%riskadjustment,should

ourprojectbeaccepted?Projectk=10%+3%=13%.That’s30%abovebasek.NPV=$60,541.Projectremainsacceptableafteraccountingfordifferential(higher)risk.Shouldsubjectiveriskfactorsbeconsidered?Yes.Anumericalanalysismaynotcapturealloftheriskfactorsinherentintheproject.Forexample,iftheprojecthasthepotentialforbringingonharmfullawsuits,thenitmightberiskierthanastandardanalysiswouldindicate.Arethereanyproblemswithscenarioanalysis?Onlyconsidersafewpossiblees.Assumesthatinputsareperfectlycorrelated--all“bad”valuesoccurtogetherandall“good”valuesoccurtogether.Focusesonstand-alonerisk,althoughsubjectiveadjustmentscanbemade.Whatisasimulationanalysis?Acomputerizedversionofscenarioanalysiswhichusescontinuousprobabilitydistributions.Computerselectsvaluesforeachvariablebasedongivenprobabilitydistributions.

(More...)NPVandIRRarecalculated.Processisrepeatedmanytimes(1,000ormore).Endresult:ProbabilitydistributionofNPVandIRRbasedonsampleofsimulatedvalues.Generallyshowngr