《金融学》（第二版） 课件 （英文） -Chapter17 Real Options

Chapter17:

RealOptionsObjectiveRealOptionsDeferralOptionBlack-ScholesFormulaRealOptions1Chapter17Contents17.1InvestinginRealOptions17.2DeferralOptions:TheCaseofUncertaintyandIrreversibility17.3ApplyingtheBlack-ScholesFormulatoValueRealOptions2IntroductionWeshowhowtoapplyfinancialeconomictheorytostrategicdecisionmaking.Weshowhowoptiontheorymaybeappliedtoevaluatemanagement’sabilitytotimethestartofaninvestmentproject,toexpandit,ortoabandonit,afterithasbegun317.1InvestinginRealOptionsTodatewehaveignoredmanagement’sabilitytodelaythestartofaprojectexpandaprojectabandontheprojectFailuretotaketheseoptionsintoaccountwillresultinanunderstatedNPV4TheMovieIndustry(Example)WewillexamineadecisioninthemovieindustryinordertounderstandtheimportanceofoptionsinevaluatingprojectsWeaddsomehypotheticalnumbers,andtokeepthecentralideasclearlyinfocus,theexamplewillthesimplestpossible5DerwynProductions:TimeA,RightsPurchaseDecisionDerwynProductions,isconsideringpurchasingtheexclusivemovierightsto“UnfinishedBusiness.”(Anunpublishedbook,authoredbyLouGrymshewwhohasseveralmovie‘hits’,andacoupleof‘bombs’)Cost$1MillionifpurchasedCost$0Millionifnotpurchased6DerwynProductions:TimeB,Book’sDebut(Event)CriticsandthepublicprovideinformationvaluableindeterminingtheultimatesuccessofthemovieManagementhasnoinfluenceoverthisnode7DerwynProductions:TimeC,ProductionDecisionContingency:Successfulbook(Prob=0.5) Makethemovie,NPVofmovie=$4millionDon’tmakethemovie,NPVmovie=$0millionContingency:Unsuccessfulbook(Prob=0.5)Makethemovie,NPVofmovie=-$4millionDon’tmakethemovie,NPVmovie=$0million8DerwynProductions:DecisionTree(yes,no)Buythemovierightstobook?(Cost$1Million)(Probability=0.5)MaketheMovie?(NPV-$4Million)(Probability=0.5)Makethemovie?(NPV$4Million)BookaSuccess?9DecisiontoAcquireRightsIfthedecisiontoundertaketheprojectismadeundertheassumptionofasingleup-frontdecisionthentheprojectmustalwaysberejectedBut…IfDerwynmakesthelogicalmanagerialdecisionateachstage,then(aslongasthecostofcapitalfortheprojectislessthan100%)theprojectshouldbeundertaken10VolatilityandProjectEvaluationThereisacommonnotionthatriskininvestmentdecisionsissomethingthatneedstobepenalized:RiskycashflowsareoftendiscountedatahigherrateBut…wehavejustseenaninvestmentdecisioncontaininganoption-likefeature,andweknowthatoptionsalwaysbecomemorevaluablewithhighervolatility11“UnfinishedBusiness”Thepublisheralsohasanotherbook,“RiskyBusiness,”andDerwynbelievesthatit’sidenticalto“UnfinishedBusiness”inalleconomicrespectsotherthanthepayoff,whichis(-$8million,8million)Runningthenumbersshows:themorevolatileprojectincreasesshareholders’wealthmorethanthelessvolatileone12SummarySomeprojectsarenaturallyrichinvaluablemanagerialoptions(R&D),whileotherprojectshaveoptionsthatarerelativelyhardtofind,andthendiscovered,arenotparticularlyvaluable(fast-foodfranchisee)Sometimes,management’sabilitytorecognizetheoptionsinabusinesssituationisthekeythatdistinguishesawinningbusinessfromitslesssuccessfulsiblings1317.2DeferralOption:TheCaseofUncertaintyandIrreversibilityInvestmentsinprojectscanbeundertakennoworpostponedPostponingordeferringaprojectallowsmanagerstoobtaininformationaboutfuturepayoffs14TheDecisiontoInvestDecision:Buildafactorytoday,oneyearlater,ornotatallCosttobuild,I,zerosalvagevalue,zerooperatingcosts(zeromarginalcosts)Oneunitofoutputproducedperyear,currentpriceofoutputPo.Pricenextyearandeveryyearthereafter:P1=P2=P3=...=P∞

15DecisiontoInvest(continued)Futurepriceuncertain:itcangoupbyuwithaprobabilityofq;itcangodownbydwithaprobabilityof1-q.Valueofproject(assumeperpetualcashflows),NPVo(I,Po,q,u,d,r)whereristhediscountrateNPVo=-I+Po+Po[q(1+u)/r+(1-q)(1-d)/r]16DecisiontoInvest(Continued)

I=$1,600,Po=$200,u=$100,d=$100q=.5,1-q=.5.Expectedvalueofperpetualcashflowswhenpriceis$300:.5($300)/.10=$1500Expectedvalueofperpetualcashflowswhenpriceis$100:.5($100)/.10=$500ExpectedNPVo= −$1600+$200+$1500+$500=$60017DecisiontoInvest(Continued)Att=1weknowwhatthepricewillbe,either$100or$300.IfP1=$100,NPV1=−$1600+$100+$100/.10=-$500andwerejecttheproject.IfP1=$300,NPV1=−$1600+$300+$300/.10=$1700andweaccepttheproject.18DecisiontoInvest(Continued)TheexpectedNPVoftheprojectatt=ois:[.5(1700)+.5(0)]/.10=$772.73Noteattime1ifP1=$100wedonotundertaketheprojectandNPV1=0Conclusion:Optiontodeferinvestmentisvaluable,NPVatt=oincreasesby$172.73=$772.73-$600.0019NPVProfilesforCurrentandDeferredDecisions20NPVSensitivitiestoInitialPriceParameter(P0)21NPVSensitivitiestoInitialInvestmentCost(I)22ValueoftheDeferralOptionUsingtheBinominalOptionPricingModelConsiderthedeferraloptionasacalloptiononastreamoffactoryoutputoneperiodfromnowandthattheexercisepriceoftheoptionistheinvestmentcostofthefactory,soE=I.Valueofcallatmaturity:C1(P1)=P1+P1/r–IifP1+P1/r>I 0otherwise23DeferralOptionUsingBinomialOptionPricingModelCon’tValueofcontingentclaims:C1(100)=0,C1(300)=$1700Valueofhedgeratioh:h=[C1(300)-C1(100)]/($300-$100)=8.524DeferralOptionUsingBinomialOptionPricingModelCon’tCashflowsassociatedwithhedgedportfolio:CFo=CFo–8.5($200),CF1=8.5P1+(0.10)8.5(200)–C1(P1)Ifthepricefallsthepayoffis:8.5($100)+$170-0=$1020Ifthepricerisesthepayoffis:8.5($300)+$170-$1700=$102025DeferralOptionUsingBinomialOptionPricingModelCon’tNowfindCFo,theinitialoutlayneededtolockin$1020onperiodlater:CFo=-Co+8.5($200)=$1,020/1.10=$927.27Solveforthecurrentvalueofthedeferraloption:Co=8.5($200)-$927.27=$1700-$927.27=$772.73Conclusion:Donotexercisetheoptiontoinvesttoday,investoneyearlaterwhenpriceuncertaintyisresolved.

2617.3ApplyingtheBlack-ScholesFormulatovalueRealOptionsThissectionshowshowtoapplytheBlack-Scholesoptionpricingformulaincapitalbudgetingbyusingtwoexamples27Raider’sTakeoverofTargetusinganoptionSupposethatRaiderInc.isconsideringacquiringTargetInc.Assume:thatbothcompaniesare100%financedbyequitydividedinto1-millionsharesthatTargetisworth$100,000,000TargetoffersRaidertheoptiontopurchase100%ofTarget’ssharesoneyearfromnowRf=6%,costofoption$6million,sTarget=0.2028Raider’sTakeoverofTargetUsingOptions:ComputationObservethattheTargetsFutureisequaltotheoption’sstrike,sothesimplifiedBSequationmaybeusedTheNPVoftheinvestmentistherefore$(8-6)millions=$2millions(doit)Thepremiumdistributedtotheshareholders29ImplicitOptions:ElectroUtilityElectroUtilityhastheopportunitytoinvestinaprojecttobuildapower-generatingplantPhase1:invest$6millionnowforthebuildingPhase2:purchaseequipmentcosting$106millioninoneyear30ImplicitOptions:ElectroUtilitySupposethat,viewedfromtoday’sperspective,thevalueofthecompletedplantis$112thestandarddeviationofthecapitalreturnfromtheprojectis0.2031ImplicitOptions:ElectroUtilityTheexpectedvalue