公司理财（英文版·第5版）课件 第22章　实物期权

CorporateFinanceFifthEditionChapter22RealOptionsCopyright©2020,2017,2014PearsonEducation,Inc.

AllRightsReservedChapterOutline(1of2)22.1RealVersusFinancialOptions22.2DecisionTreeAnalysis22.3

TheOptiontoDelay:InvestmentasaCallOption22.4GrowthandAbandonmentOptionsChapterOutline(2of2)22.5InvestmentswithDifferentLives22.6OptimallyStagingInvestments22.7RulesofThumb22.8KeyInsightsfromRealOptionsLearningObjectives(1of3)Definetheterm“realoption.”Drawdecisiontreestorepresentalternativedecisionsandpotentialoutcomesinanuncertaineconomy.Describethreetypesofrealoptions—timing,growth,andabandonment—andexplainwhyitisimportanttoconsiderthoseoptionswhenevaluatingprojects.Illustratehow,giventheoptiontowait,aninvestmentthatcurrentlyhasanegativeN

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Vcanhaveapositivevalue.LearningObjectives(2of3)Describesituationsinwhichtheoptiontowaitismostvaluable.Choosebetweeninvestmentsofdifferentlivesbyevaluatingtheoptiontoreplaceorextendtheshorterlivedprojectattheendofitsoriginallife.Discussthesituationinwhichequivalentannualbenefitmethodresultsinoptimaldecisionmaking.LearningObjectives(3of3)Describethetypesofinvestmentsthatshouldbedonefirstinamulti-stageinvestmentdecision,andcalculateprojectrankingsaccordingtoEq.22.3.Defineandusetheprofitabilityindexandthehurdleraterulesofthumb.22.1RealVersusFinancialOptionsRealOptionTherighttomakeaparticularbusinessdecision,suchasacapitalinvestmentAkeydistinctionbetweenrealoptionsandfinancialoptionsisthatrealoptions,andtheunderlyingassetsonwhichtheyarebased,areoftennottradedincompetitivemarkets.22.2DecisionTreeAnalysis(1of3)DecisionTreeAgraphicalrepresentationoffuturedecisionsanduncertaintyresolution22.2DecisionTreeAnalysis(2of3)AssumeUnitedStudiosholdsthemovierightsforanationalbest-sellerandanoptiontoproduceasequelbasedonthesamebook.Itbelievesthatshootingbothmoviessimultaneouslycouldbeproducedforatotalbudgetof$525million.Ifinsteadthemoviesareproducedsequentially,thetotalexpectedcostwillbe$575million.22.2DecisionTreeAnalysis(3of3)ThedecisiontreeshowingUnited’soptionslooksliketheoneonthefollowingslideBecausetheN

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Vofshootingbothmoviessimultaneouslyis$125million,theoptimaldecision(showninblue)wouldbetosetupthebooth

Figure22.1United’sInvestmentwithoutRealOptionsRepresentingUncertainty(1of4)Unitedisawarethatthevalueoftheprojectisdependentonwhetherornotthefirstmovieisablockbuster.Ifthefirstmovieisablockbuster,thestudioexpectstoearnatotalof$900millionbetweenbothmovies.Ifthefirstmovieisonlyamoderatehit,thestudioexpectstoearnatotalof$400betweenthetwomovies.Thereisa50%chanceofthefirstmoviebeingablockbuster.Figure22.2RepresentingUncertaintyRepresentingUncertainty(2of4)DecisionNodesAnodeonadecisiontreeatwhichadecisionismadeCorrespondstoarealoptionInformationNodesAtypeofnodeonadecisiontreeindicatinguncertaintythatisoutofthecontrolofthedecisionmakerRepresentingUncertainty(3of4)InUnited’scaseThesquarenoderepresentsthedecisiontoinvestordonothing.Theroundnoderepresentstheuncertainstateofnature,blockbusterversusmoderatehit.RepresentingUncertainty(4of4)Inreality,Uniteddoesnothavetocommittomakingthesequelbeforetheyknowifthefirstmovieisamoderatehitorblockbuster.Figure22.3United’sInvestmentwiththeRealOptiontoProduceSequentiallyRealOptionsFigure22.3showsthatitisnotoptimalforUnitedtoproducethesequelunlessthefirstfilmisablockbuster.SolvingDecisionTreesManycorporateinvestmentdecisionscontainrealoptions.Theycanbeanalyzedbycreatingadecisiontreethatidentifiesthefollowing:DecisionnodesshowingthechoicesavailableateachstageInformationnodesshowingthepayoffrelevantinformationtobelearnedInvestmentsmadeandpayoffsearnedovertimeOncethedecisiontreeiscreated,wecanvaluetheinvestmentopportunity.22.3TheOptiontoDelay:InvestmentasaCallOptionThereisoftenacosttodelayinganinvestmentdecision.However,bydelaying,youwillgainadditionalinformationregardingthevalueoftheinvestment.Thedecisiontowaitthereforeinvolvesatrade-offbetweenthesecostsandthebenefitofremainingflexible.AnInvestmentOption(1of9)Assumeyouhavenegotiatedadealwithaelectriccarmanufacturertoopenoneofitsdealershipsinyourhometown.Thetermsofthecontractspecifythatyoumustopenthedealershipeitherimmediatelyorinexactlyoneyear.Ifyoudoneither,youlosetherighttoopenthedealershipatall.Figure22.4ElectricCarDealershipInvestmentOpportunityAnInvestmentOption(2of9)Howmuchyoushouldpayforthisopportunity?Itwillcost$5milliontoopenthedealership,whetheryouopenitnoworinoneyear.Ifyouopenthedealershipimmediately,youexpectittogenerate$600,000infreecashflowthefirstyear.Futurecashflowsareexpectedtogrowatarateof2%peryear.Thecostofcapitalforthisinvestmentis12%.AnInvestmentOption(3of9)Ifthedealershipweretoopentoday,itsvaluewouldbeThiswouldgiveanN

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Vof$1million

Giventheflexibilityyouhavetodelayopeningforoneyear,whatshouldyoubewillingtopay?Whenshouldyouopenthedealership?AnInvestmentOption(4of9)Thepayoffifyoudelayisequivalenttothepayoffofaone-yearEuropeancalloptiononthedealershipwithastrikepriceof$5million.AssumeTherisk-freeinterestrateis5%.Thevolatilityis40%.Ifyouwaittoopenthedealershipyouhaveanopportunitycostof$600,000.Intermsofafinancialoption,thefreecashflowisequivalenttoadividendpaidbyastock.Theholderofacalloptiondoesnotreceivethedividenduntiltheoptionisexercised.Table22.1Black-ScholesOptionValueParametersforEvaluatingaRealOptiontoInvestFinancialOptionBlankRealOptionExampleStockPriceSCurrentMarketValueofAsset$6millionStrikePriceKUpfrontInvestmentRequired$5millionExpirationDateTFinalDecisionDate1yearRisk-FreeRatersubfRisk-FreeRate5%VolatilityofStockSigma.VolatilityofAssetValue40%DividendDivFCFLostfromDelay$0.6millionAnInvestmentOption(5of9)Thecurrentvalueoftheassetwithoutthe“dividends”thatwillbemissedisThepresentvalueofthecosttoopenthedealershipinoneyearisAnInvestmentOption(6of9)ThecurrentvalueofthecalloptiontoopenthedealershipisAnInvestmentOption(7of9)Thevaluetodayfromwaitingtoinvestinthedealershipnextyear(andonlyopeningitifitisprofitabletodoso)is$1.20million.ThisexceedstheN

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Vof$1millionfromopeningthedealershiptoday.Thus,youarebetteroffwaitingtoinvest,andthevalueofthecontractis$1.20million.AnInvestmentOption(8of9)Whatistheadvantageofwaitinginthiscase?Ifyouwait,youwilllearnmoreaboutthelikelysuccessofthebusiness.Becausetheinvestmentinthedealershipisnotyetcommitted,youcancancelyourplansifthepopularityofthedealershipshoulddecline.Byopeningthedealershiptoday,yougiveupthisoptionto“walkaway”.AnInvestmentOption(9of9)Whetheritisoptimaltoinvesttodayorinoneyearwilldependonthemagnitudeofanylostprofitsfromthefirstyearcomparedtothebenefitofpreservingyourrighttochangeyourdecision.Figure22.5TheDecisiontoInvestintheDealershipFactorsAffectingtheTimingofInvestment(1of2)Whenyouhavetheoptionofdecidingwhentoinvest,itisusuallyoptimaltoinvestonlywhentheN

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Vissubstantiallygreaterthanzero.YoushouldinvesttodayonlyiftheN

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Vofinvestingtodayexceedsthevalueoftheoptionofwaiting.Giventheoptiontowait,aninvestmentthatcurrentlyhasanegativeN

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Vcanhaveapositiveone.FactorsAffectingtheTimingofInvestment(2of2)OtherFactorsAffectingtheDecisiontoWaitVolatilityTheoptiontowaitismostvaluablewhenthereisagreatdealofuncertainty.DividendsAbsentdividends,itisnotoptimaltoexerciseacalloptionearly.Intherealoptioncontext,itisalwaysbettertowaitunlessthereisacosttodoingso.Thegreaterthecost,thelessattractivetheoptiontodelaybecomes.TextbookExample22.1(1of5)EvaluatingtheDecisiontoWaitProblemSupposeyourcurrentestimateoftheelectriccardealership’svalueis$6million.Whatwouldbethevalueofthedealershipcontractifthevolatilityofthedealership’svaluewere25%ratherthan40%?Alternatively,supposethevolatilityis40%,butwaitingwouldleadcompetitorstoexpandandreducethefuturefreecashflowsofthedealershipby10%.Whatisthevalueofthecontractinthiscase?TextbookExample22.1(2of5)SolutionWithalowervolatilityof25%,wehaveThevalueofthecalloptionisTextbookExample22.1(3of5)Therefore,itisbettertoinvestimmediatelyandgetanN

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Vof$1million,ratherthanwait.Withthelowervolatility,notenoughinformationwillbelearnedoverthenextyeartojustifythecostofwaiting.Nowlet’ssupposethevolatilityis40%,butwaitingleadstoincreasedcompetition.Inthiscase,weshoulddeductthelossfromincreasedcompetitionasanadditional“dividend”thatweforegobywaiting.Thus,TextbookExample22.1(4of5)ThevalueofthecalloptioninthiscaseisTextbookExample22.1(5of5)Again,itwouldnotbeoptimaltowait.Inthiscase,despitetheinformationtobegained,thecostsassociatedwithwaitingaretoohigh.AlternativeExample22.1(1of6)ProblemAssumeYourcompanyisconsideringanewprojectatacostof$12million.Theprojectmaybegintodayorinexactlyoneyear.Youexpecttheprojecttogenerate$1,500,000infreecashflowthefirstyearifyoubegintheprojecttoday.Freecashflowisexpectedtogrowatarateof3%peryear.AlternativeExample22.1(2of6)ProblemAssumeTherisk-freerateis4%.Theappropriatecostofcapitalforthisinvestmentis11%.Thestandarddeviationoftheproject’svalueis30%.Shouldyoubegintheprojecttodayorwaitoneyear?AlternativeExample22.1(3of6)SolutionThus,theN

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Voftheprojecttodayis

Thecurrentvalueoftheprojectwithoutthe“dividend”thatwillbemissedisAlternativeExample22.1(4of6)SolutionThepresentvalueofthecosttobegintheprojectinoneyearisAlternativeExample22.1(5of6)SolutionAlternativeExample22.1(6of6)SolutionThevalueofwaitingoneyeartostarttheprojectis$5,927,619.TheN

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Vofstartingtheprojectis$6,750,000.Thus,itisoptimaltobegintheprojecttodayratherthanwait.InvestmentOptionsandFirmRiskIntheelectriccardealershipexample,thebetaofthefirmwillequalthebetaoftheoptiononadealership.Thebetaofafirmwiththeoptiontoopenadealershipwillbeconsiderablylargerthanthebetaofadealershipitself.Allelseequal,firmsforwhichahigherfractionoftheirvaluedependsonfuturegrowthwilltendtohavehigherbetas.22.4GrowthandAbandonmentOptionsGrowthOptionArealoptiontoinvestinthefutureAbandonmentOptionTheoptiontodisinvestBecausetheseoptionshavevalue,theycontributetothevalueofanyfirmthathasfuturepossibleinvestmentopportunities.ValuingGrowthPotential(1of11)Futuregrowthopportunitiescanbethoughtofasacollectionofrealcalloptionsonpotentialprojects.Thiscanexplainwhyyoungfirmstendtohavehigherreturnsthanolder,establishedfirms.ValuingGrowthPotential(2of11)AssumeStartUpIncorporatedisanewcompanywhoseonlyassetisapatentonanewdrug.Ifproduced,thedrugwillgeneratecertainprofitsof$1millionperyearfor17years(afterthen,competitionwilldriveprofitstozero).Itwillcost$10milliontodaytoproducethedrug.Theyieldona17-yearrisk-freeannuityiscurrently8%peryear.ValuingGrowthPotential(3of11)Whatisthevalueofthepatent?TheN

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VofinvestinginthedrugtodayisGiventoday’sinterestrates,itdoesnotmakesensetoinvestinthedrugtoday.Whatifinterestratespermanentlyfall(rise)to5%(10%)inoneyear?ValuingGrowthPotential(4of11)Ifratesriseto10%,theN

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Visstillnegative,anditdoesnotmakesensetoinvestinthedrugtoday.Ifratesfallto5%,theN

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VofinvestinginthedrugtodayisIfratesfallto5%,theN

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Vispositive,anditmakessensetoinvestinthedrugtoday.Figure22.6StartUp’sDecisiontoInvestintheDrugValuingGrowthPotential(5of11)Recallthattofindrisk-neutralprobabilities,theprobabilitiesthatsetthevalueofafinancialassettodayequaltothepresentvalueofitsfuturecashflowsmustbesolvedforInthiscase,a17-yearrisk-freeannuitythatpays$1000peryearisused.ValuingGrowthPotential(6of11)ThevalueoftheannuitytodayisValuingGrowthPotential(7of11)Ifinterestratesriseto10%inoneyear,thevalueoftheannuitywillbeValuingGrowthPotential(8of11)Ifinterestratesfallto5%inoneyear,thevalueoftheannuitywillbeValuingGrowthPotential(9of11)Recallthattherisk-neutralprobabilityofinterestratesisincreasingto10%,istheprobabilitysuchthattheexpectedreturnoftheannuityisequaltotherisk-freerateof6%ValuingGrowthPotential(10of11)Thevaluetodayoftheinvestmentopportunityisthepresentvalueoftheexpectedcashflows(usingrisk-neutralprobabilities)discountedattherisk-freerate:ValuingGrowthPotential(11of11)Inthisexample,eventhoughthecashflowsoftheprojectareknownwithcertainty,theuncertaintyregardingfutureinterestratescreatessubstantialoptionvalueforthefirm.Thefirm’sabilitytousethepatentandgrowshouldinterestratesfallisworth$221,693.TheOptiontoExpand(1of7)Consideraninvestmentopportunitywithanoptiontogrowthatrequiresa$10millioninvestmenttoday.Inoneyearyouwillfindoutwhethertheprojectissuccessful.Theriskneutralprobabilitythattheprojectwillgenerate$1millionperyearinperpetuityis50%;otherwise,theprojectwillgeneratenothing.Atanytimewecandoublethesizeoftheprojectontheoriginalterms.Figure22.7StagedInvestmentOpportunityTheOptiontoExpand(2of7)Byinvestingtoday,theexpectedannualcashflowsare$500,000(ignoringtheoptiontodoublethesizeoftheproject)TheOptiontoExpand(3of7)ComputingtheN

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VgivesThenegativeN

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Vsuggeststhatyoushouldnottakeontheprojecttoday.However,thismeansyouwillneverfindoutwhethertheprojectissuccessful.TheOptiontoExpand(4of7)Nowconsiderundertakingtheprojectandexercisingthegrowthoptiontodoublethesizeinayeariftheproducttakesoff.TheN

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VofdoublingthesizeoftheprojectinayearinthisstateisTheOptiontoExpand(5of7)Therisk-neutralprobabilitythatthisstatewilloccuris50%,sotheexpectedvalueofthisgrowthoptionis$3.333million.ThepresentvalueofthisamounttodayisTheOptiontoExpand(6of7)Youhavethisoptiononlyifyouchoosetoinvesttoday,sotheN

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VofundertakingthisinvestmentistheN

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Vcalculatedaboveplusthevalueofthegrowthoptionweobtainbyundertakingtheproject:TheOptiontoExpand(7of7)ThisanalysisshowsthattheN

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Voftheinvestmentopportunityispositiveandthefirmshouldundertakeit.Itisoptimaltoundertaketheinvestmenttodayonlybecauseoftheexistenceofthefutureexpansionoption.TheOptiontoAbandon(1of10)AssumeyouaretheC

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OofachainofgourmetfoodstoresandareconsideringopeninganewstoreintherecentlyrenovatedFerryBuildinginBoston.Ifyoudonotsigntheleaseonthestoretoday,someoneelsewill,soyouwillnothavetheopportunitytoopenastorelater.Thereisaclauseintheleasethatallowsyoutobreaktheleaseatnocostintwoyears.Includingtheleasepayments,thenewstorewillcost$10,000permonthtooperate.TheOptiontoAbandon(2of10)Becausethebuildinghasjustreopened,youdonotknowwhatthepedestriantrafficwillbe.Ifyourcustomersaremainlylimitedtomorningandeveningcommuters,youexpecttogenerate$8,000permonthinrevenueinperpetuity.If,however,thebuildingbecomesatouristattraction,youexpecttogenerate$16,000permonthinrevenueinperpetuity.TheOptiontoAbandon(3of10)Thereisa50%probabilitythattheFerryBuildingwillbecomeatouristattraction.Thecoststosetupthestorewillbe$400,000.Therisk-freeinterestrateisconstantat7%peryear(or0.565%permonth).TheOptiontoAbandon(4of10)ThenumberoftouristsvisitingtheBostonFerryBuildingrepresentsidiosyncraticuncertainty.Becausethisisthekindofuncertaintyinvestorsinyourcompanycancostlesslydiversifyaway,theappropriatecostofcapitalistherisk-freerate.TheOptiontoAbandon(5of10)Ifyouwereforcedtooperatethestoreunderallcircumstances,theexpectedrevenuewillbe$12,000TheN

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VoftheinvestmentisGiventhenegativeN

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V,itwouldnotmakesensetoopenthestore.TheOptiontoAbandon(6of10)Inreality,youwouldnothavetokeepoperatingthestoreYouhaveanoptiontogetoutoftheleaseaftertwoyearsatnocostAfterthestoreisopen,itwillbeimmediatelyobviouswhethertheFerryBuildingisatouristattraction.Thedecisiontreeisshownonthenextslide.Figure22.8DecisiontoOpenaStoreintheBostonFerryBuildingTheOptiontoAbandon(7of10)IftheFerryBuildingisatouristattraction,theN

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VoftheinvestmentopportunityisTheOptiontoAbandon(8of10)IftheFerryBuildingdoesnotbecomeatouristattraction,youwillclosethestoreaftertwoyears,andtheN

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VoftheinvestmentopportunityisTheOptiontoAbandon(9of10)Thereisanequalprobabilityofeachstate.TheN

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VofopeningthestoreisByexercisingtheoptiontoabandontheventure,youlimityourlossesandtheN

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Vofundertakingtheinvestmentbecomespositive.Thevalueoftheoptiontoabandonis$154,607;thedifferencebetweentheN

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VwithandwithouttheoptionTheOptiontoAbandon(10of10)Itiseasytoignoreorunderstatetheimportanceoftheoptiontoabandon.Manytimes,abandoninganeconomicallyunsuccessfulventurecanaddmorevaluethanstartinganewone.Managersoftende-emphasizethisalternative.22.5InvestmentswithDifferentLives

(1of2)ComparingMutuallyExclusiveInvestmentswithDifferentLivesConsiderCanadianMotorsLastyear,anengineeringfirmwasaskedtodesignanewmachineforuseinproduction.22.5InvestmentswithDifferentLives

(2of2)Thefirmhasproducedtwodesigns.Thecheaperdesignwillcost$10milliontoimplementandlastfiveyears.Themoreexpensivedesignwillcost$16millionandlast10years.Inbothcases,themachinesareexpectedtosaveCanadianMotors$3millionperyear.Ifthecostofcapitalis10%,whichdesignshouldCanadianMotorsapprove?StandaloneNPVofEachDesign(1of2)TheN

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Vofadoptingtheshorter-liveddesignisTheN

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Vofadoptingtheshorter-liveddesignisTheN

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Vrulewouldsuggestchoosingthelonger-livedproject,however,N

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Vignoresthedifferenceintheprojects’lifespans.StandaloneNPVofEachDesign(2of2)Totrulycomparethetwooptions,wemustconsiderwhatwillhappenoncetheshorter-livedequipmentwearsout.Considerthreepossibilities:ThetechnologyisnotreplacedItisreplacedatthesametermsTechnologicaladvancesallowsittobereplacedatimprovedterms.NoReplacementIftheshorter-livedtechnologyisnotreplacedandthefirmrevertstoitsoldproductionprocess,therewillbenobenefitoncethefive-yearlifeends.Inthatcase,theoriginalcomparisoniscorrect,andthe10-yearmachinewillincreasefirmvaluebymorethanthefive-yearmachine.Onereasonfornotreplacingthemachineisifthecostisexpectedtoincrease.Ifthecostinfiveyearsisexpectedtobe$11.37millionorhigher,theN

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Voftheadditionalinvestmentwillbezeroorless,soreplacementwillnotbeoptimal.ReplacementattheSameTermsSupposeweexpectthecostsandbenefitsoftheshorter-liveddesigntobethesameinfiveyears.Inthatcase,thetotalN

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Voverthe10-yearhorizonwillbeBecausethisN

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Visstillinferiortothe$2.43millionforthe10-yeardesign,wewillstillchoosethelonger-livedmachine.ReplacementatImprovedTerms(1of2)Inreality,thefuturecostofamachineisuncertain.Ifweexpecttechnologicaladvancestohavecausedthecostofthenewtechnologytofallby$3millionattheendoffiveyears,theN

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Voftheshorter-liveddesignwillhaveincreasedto3+1.37=$4.37million.ReplacementatImprovedTerms(2of2)TheN

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Vofthefive-yeardesignovera10-yearhorizonwillbeThisimprovementresultsinahigherN

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Vfortheshorter-liveddesign,comparedto$2.43millionforthe10-yearmachine.ValuingtheReplacementOptionInordertocomparethetwodesignscorrectly,wemustdeterminethevalueofthereplacementoption,whichwilldependonthelikelihoodthatthecostofthemachinewillincreaseordecrease.EquivalentAnnualBenefitMethodEquivalentAnnualBenefitMethodAmethodofchoosingbetweenprojectswithdifferentlivesbyselectingtheprojectwiththehigherequivalentannualbenefitItignoresthevalueofanyrealoptionsbecauseitassumesthatbothprojectswillbereplacedontheiroriginalterms.TextbookExample22.2(1of2)ValuingtheReplacementOptionProblemSupposethecostoftheshorter-livedmachineisequallylikelytoriseto$13million,stayequalto$10million,orfallto$7million,andsupposethisriskisidiosyncraticanddoesnotchangetheproject’scostofcapital.Whichmachineshouldthefirmchoose?TextbookExample22.2(2of2)SolutionIfthecostrisesto$13million,thefirmwillchoosenottoreplacethemachineandgetanN

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Vof0.Ifthecoststaysthesameorfalls,thefirmwillreplacethemachineandgetanN

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Vof$1.37millionor$4.37million,respectively.Giventheprobabilities,theN

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Vofthefive-yearmachineoverthe10-yearhorizonisThus,giventhisuncertainty,theshorter-livedmachineoffersahigherN

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Vover10yearsthanthe$2.43millionN

P.Vofthelonger-livedmachine.Bycommittingtothelonger-livedproject,thefirmwouldgiveupitsrealoptiontoreacttotechnologicalandmarketchanges.22.6OptimallyStagingInvestmentsInsomesituations,wecanchoosetheorderofdevelopmentstages.Ifso,howcanwemaximizethevalueoftherealoptionswecreate?AnExample:EclecticMotors(1of2)EclecticMotorsisconsideringdevelopinganelectriccarthatwouldcompetedirectlywithgasoline-poweredcars.Theymustovercomethreetechnologicalhurdles:Developmaterialstosignificantlyreducethecar’sbodyweight.Developamethodtorapidlyrechargethebatteries.Advancebatterytechnologytoreduceweightandincreasestoragecapacity.AsshowninTable22.2(nextslide),eachtaskrequiresfurtherresearchandsubstantialrisk.Table22.2RequiredTime,Cost,andLikelihoodofSuccessforEclectic’sProjectTechnologyCostTimeProbabilityofSuccessMaterials$100million1year50%Recharger$400million1year50%Battery$100million4years25%AnExample:EclecticMotors(2of2)SupposeAllthreerisksareidiosyncratic,andtherisk-freerateis6%.Givenresources,thecompanycanonlyworkononetechnologyatatime.Byappropriatelystagingtheseinvestments,theycanenhancefirmvalue.Assumingitmakessensetoproceed,inwhichordershouldtheydevelopthetechnologies?MutuallyDependentInvestmentsThisprojectrepresentsasituationwithmutuallydependentinvestments,inwhichthevalueofoneprojectdependsontheoutcomeoftheothers.Inthiscase,weassumeallthreechallengesmustbeovercome,ortherewillbenobenefit.InvestmentScale(1of2)Considerfirstthematerialsandrechargertechnologies.Ifwebeginwiththematerialstechnology,theexpectedcosttocompletebothisInvestmentScale(2of2)Ifwebeginwiththerechargertechnology,theexpectedcosttocompletebothisThus,Eclecticshouldbeginwiththematerialstechnology.Ifitisunsuccessful,theywillnotwastemoneyontherechargertechnology.InvestmentTimeandRisk(1of2)Nowcomparethematerialsandbatterytechnologies.Thesetwohavethesamecost,butthebatterytechnologyhasagreaterchanceoffailureandtakeslongertodevelop.Ifwebeginwiththematerialstechnology,itcostsasfollows:InvestmentTimeandRisk(2of2)Ifwebeginwiththebatterytechnology,theexpectedcosttocompletebothisasfollows:Thus,Eclecticshouldworkonthebatterytechnologybeforeworkingonthematerials.AGeneralRule(1of2)Givenitsgreaterrisk,thebatterytechnology’ssuccesswilltellthefirmmoreabouttheoverallviabilityoftheprojectthantheothertwo.Givenitslongertimerequirement,theinvestmentinthesecondtechnologycanbepostponed,sothecompanybenefitsfromthetimevalueoftheinvestment.Ingeneral,itisbeneficialtoinvestinriskierandlengthierprojectsfirst.AGeneralRule(2of2)Ingeneral,wecanfindtheoptimalordertostagemutuallydependentprojectsbyrankingeach,fromhighesttolowest,accordingtoWherePV(success)isthevalueatthestartoftheprojectofreceiving$1iftheprojectsucceeds,whichistherisk-neutralprobabilityofsuccess.TextbookExample22.3(1of2)DecidingtheOrderofInvestmentwithMultipleStagesProblemUsethefailurecostindextodeterminetheoptimalinvestmentorderforEclectic’selectriccarproject.TextbookExample22.3(2of2)SolutionEvaluatingthefailurecostindexforeachstage,wehaveMaterials:Recharger:Battery:So,Eclecticshoulddevelopthebatteriesfirst,thenthebodymaterials,andfinallythecharger,matchingourearlieranalysis.AlternativeExample22.3(1of3)ProblemMatthewsCompanyisconsideringthedev