高级公司金融Options and Corporate Finance.ppt

DRAFT CONFIDENTIAL CHAPTER5 OptionsandCorporateFinance 5 1StocksandBondsasOptions Althoughoptionsarepublictradedderivativesecurities theconceptitselfisubiquitousincorporatefinance Oneofthemostimportantandnovelapplicationincorporatefinanceistheoptioninterpretationofstocksandbonds Assumethevalueofafirm sassetsisA ThefirmissuedazerocouponbonddueattimeTwithfacevalueF ThevaluesofthestockandbondofthefirmattimeTisshowninthenextfigures ValueofStockAtT StocksandBondsasCallOptions AtthematurityTofthebond IfA F shareholderspaybackbondandreceiveA F IfA F Shareholdersdefaultandstockhasnovalue Thestockofafirmisacalloptiononthefirm TheassetsofthefirmistheunderlyingassetsThefacevalueofthebondisthestrikeprice Thematurityofthebondisthematurityofthecall F ValueofBondAtT StocksandBondsasCallOptions AtmaturityT IfA F shareholderspaybackbondandbondholdersreceivethefixedamount F IfA F shareholdersdefaultandbondholderstakeoverthefirmandgetA Holdingabondisequivalentto OwningtheassetsofthefirmWritingacalloptiontotheshareholders StocksandBondsasPutOptions Owningassets Owingbond Owningaput StocksandBondsasPutOptions Theshareholders positioncanbeexpressedbythreeclaims Theyownthefirm A TheyoweFininterestandprincipaltothebondholders Ifthedebtwereriskfree thesetwoclaimswouldfullydescribethestockholders situation However becauseofthepossibilityofdefault weneedathirdclaim TheshareholdersownaputoptiononthefirmwithanexercisepriceofF Thegroupofbondholdersistheselleroftheput StocksandBondsasPutOptions AtmaturityT whenAFPutoptionisoutofmoney Shareholdersdonotexercise TheypaybackdebtandstillowntheresidualvalueofthefirmA F StocksandBondsasPutOptions StocksandBondsasPutOptions Bondholderspositioncanbedescribedbytwoclaims ThebondholdersareownedFamountofmoney ThehavesoldaputoptiononthefirmtotheshareholderswithanexercisepriceofF AtmaturityT whenAFShareholdersdonotexercisetheput bondholdersreceiveF Valueofriskybond Valueofdefault freebond Valueofputoption PositionsofShareholdersandBondholders AResolutionoftheTwoViews Theput callparityshowsthefollowingequation 1 AResolutionoftheTwoViews Theput callparityshowsthefollowingequation 2 LoanGuarantees Ifafirmexperiencefinancialdistress itwillbedifficultorimpossibleforthefirmtoraisedebtbecauseinvestorswillgenerallyrequirehigherinterestrateorevencutthecredit Largefirmswillseekloanguaranteesfromgovernment Iftheborrowingfirmdefaultontheguaranteedloan thegovernmentwillmakeupthedifference Whatisthevalueoftheguarantee Doesithurttaxpayers LoanGuarantee Therighthandsideofequation 2 impliesthatThevalueofguaranteeisthevalueofaputoptionontheassetsofthefirm 5 2OptionsandCorporateDecisions OptionsandCapitalBudgetingForleveragedfirmtheshareholdersmightpreferalowerNPVprojecttoahigheronejustbecausetheloweroneisriskier TheymightevenpreferanegativeNPVprojecttoapositiveNPVproject AhypotheticalfirmHisasthefollows riskfreerateis4percent OptionsandCapitalBudgeting Thestockofthefirmisacalloptionontheassetsofthefirm Black Scholesformulacanbeusedtoobtainthevalueofthestock Thestrikepriceis 40m Thecurrentpriceoftheassetsis 20m Thematurityis5years Thevolatilityoftheassetsis50 peryear Thevalueoftheequityis 5 744m Thevalueofthedebtis 20m 5 744m 14 256m Theleverageis14 265 5 744 248 Thedeltais0 5469 OptionsandCapitalBudgeting Thefirmhastwomutuallyexclusiveinvestments whichaffectboththemarketvalueofthefirm sassetsandthefirm sassetreturnstandarddeviationasfollows Whichprojectisbetter Whichprojectwillthefirmchoose OptionsandCapitalBudgeting UsingBlack ScholesformulaitiseasytoobtaintheequityvaluesanddebtvaluesiffirmHundertakeprojectAorprojectB ProjectAbenefitsboththeshareholdersandthebondholders butmostofthegaingoestothebondholders ProjectBhasahugeimpactonthevalueoftheequity plusitreducesthevalueofthedebt OptionsandCapitalBudgeting ImplicationsoftheanalysisWhentheequityhasadeltasignificantlysmallerthan1 anyvaluecreatedwillgopartiallytobondholders Shareholdershaveastrongincentivetoincreasethevarianceofthereturnonthefirm sasset Shareholderswillhaveastrongpreferenceforvariance increasingprojectsasopposedtovariance decreasingones evenifthatmeansalowerNPV AnExtremeCaseforFirmH IfthecharacteristicsoffirmHareasthefollows Theequityanddebtvaluesare 2 012mand 17 988m Thedebt equityratiois893 Deltais0 2415 Thecalloptionisdeepoutofthemoney Thevaluecreatedwillmostgotodebtholders AnExtremeCaseforFirmH FirmHhasaninvestmentprojectunderconsiderationthatmustbetakennowornever IffirmHtakestheproject equityvaluebecomes 4 834anddebtvaluebecomes 16 166 AnExtremeCaseforFirmH Theequityvaluemorethandoubles Inthiscaseshareholdershaveastrongpreferenceforhugevolatilitybecausebankruptcyisalikelyoutcome Thisislikeusingthelastdollaronalotteryticket It sabadinvestment buttherearen talotofotheroptions OptionsandCorporateDecisions MergersanddiversificationInvestmenttheoriesshowthatdiversificationisvaluablewheninvestorsformtheirpersonalportfolios Diversificationisoftencitedasareasonfortwofirmstomerge Isdiversificationreallyagoodreasonformerge Let sconsidertwocompanies SunshineSwimwear SS andPolarWinterwear PW Bothcompanieshavehighlyseasonalcashflows Ifthecompaniesweretomerge thecombinedcompanywouldhaveamuchmorestablecashflowsandislesslikelytobebankrupt Mergersanddiversification Theoperationsofthetwofirmsareverydifferent sotheproposedmergerisapurely financial merger whichresultsno synergies orothervaluecreatingpossibilities Thefollowingsarethepremergerinformation Theriskfreerateis5percent Mergersanddiversification AccordingtotheBlack ScholesformulatheequityvaluesanddebtvaluesforSunshineSwimwearandPolarWinterwearareasfollows Afterthemerger thecombinedfirm sassetswillsimplybethesumofthepremergervalues 30 10 40 Thetotalvalueofthedebtis 16 Assumethecombinedfirm sassetreturnstandarddeviationis40percent whichislowerthanforeitherofthetwoindividualfirmsduotodiversification Mergersanddiversification Theequityanddebtvaluesforthecombinedfirmareasfollows Theequityvalueofthecombinedfirm 26 464 islessthanthesumoftheequityvaluesoftwoseparatefirms 20 424 7 001 Thedebtvalueofthecombinedfirm 13 354 islargerthanthesumofthedebtvaluesofthetwoseparatefirms 9 576 2 999 Mergersanddiversification Implications Diversificationworksinthesensethatitreducesthevolatilityofthefirm sreturnonassets Thisriskreductionbenefitsthebondholdersbymakingdefaultlesslikely Bymerging thefirmsinsureeachother sbonds Areductioninreturnvarianceontheunderlyingassetreducesthevalueofequityasacalloption Defaultisvaluabletoshareholders Apurelyfinancialmergerreducesthelikelihoodofbankruptcyandinturnthevalueofdefault Financialmergercreatesvalueonlyifthecombinedfirmbearsmoredebtaftermergertotakeadvantageofmoretaxshield 5 3OptionsandRealInvestments ConventionalDCFanalysisdiscounts riskadjusted futureexpectedcashflowsfrominvestmentprojecttoobtainNPVatdatecurrentperiodtojudgeaninvestmentproject Themethodimplicitlyassumesthatonceaninvestmenthasbeenundertakenfirmsarereadytoacceptwhateveroutcomesinthefutureandnofurthercontingentactionswillbetaken Thismethodalsoassumesthataninvestmentprojectbeingevaluatedcurrentlyshouldbeeitheracceptedimmediatelyorrejectedforever Actuallyfirmshavetheoptiontotakeactionsaftertheinitiationofinvestmentprojectsandevenhavetheoptiontochoosewhentostartaproject TheOptiontoAbandon Valuingaminewithoutabandonmentoption Thevalueofacoppermineislargelydeterminedbythepriceofcopper SupposesomeofthecopperQ1intheminewillbeextractedatdate1andtheremainderQ2atdate2 TheextractioncostsareK1andK2respectively Thepricesofcopperindate1anddate2arep1andp2 Thepricesaretheonlyunknownvariablesatthebeginning Whatisthevalueofthemine TheOptiontoAbandon Thecashflowsatdate1anddate2ofthemineareasthefollowing C1 p1Q1 K1C2 p2Q2 K2Thevalueofthemineis Thevalueofaminecanbeviewedasaderivativewiththecopperastheunderlyingassets Iftheforwardcontractoncopperexists thecashflowsofacopperminearepossibletobeperfectlytrackedandthenvaluedbythenoarbitragerule TheOptiontoAbandon Thetrackingportfoliosareasthefollows AforwardcontracttopurchaseQ1unitsofcopperatdate1atthecurrentforwardpriceofF1perunit andasecondforwardcontracttopurchaseQ2unitsofcopperatdate2atthecurrentforwardpriceofF2perunit Arisk freezero couponbondpayingF1Q1 K1inyear1 andasecondriskfreezero couponbondpayingF2Q2 K2atdate2 Thevalueofthemineisthen TheOptiontoAbandon ValuingaminewithabandonmentoptionTheconventionalvaluationtechniqueimplicitlyassumethattheamountQtobeextractedatdate1anddate2arepredeterminedandfixedatdate0 Whateverhappenstothecopperprice loworhigh theseamountswillbeextracted whichmakesthemineequivalenttoaforwardcontracttobuyQ1copperwithstrikepriceK1atdate1 andaforwardcontracttobuyQ2copperwithstrikepriceK2atdate2 TheOptiontoAbandon Theownersoftheminecanchoosenottoextractthecopperwhenpriceofcopperislowerandthecostofextractionisnotabletobecovered Inthiscasethepayoffatdate1anddate2areMax p1Q1 K1 0 andMax p2Q2 K2 0 ThecashflowsfromamineareequivalenttothecashflowsofanoptiontopurchaseQ1unitsofcopperatanexercisepriceofK1 ASimpleBinomialExample ValuingtheminewithabandonmentoptionPennyCopperMining sBrazilianminewillproduce75millionpoundsofcopperoneyearfromnowifeconomicconditionsarefavorable Penny smanagersforecasttwopossibleoutcomesforcopperpricesthen 0 5perpoundifdemandislowand 0 9perpoundifdemandishigh Theyear1forwardpriceiscurrently 0 6perpound Theriskfree1yearinterestrateis5percent Theextractioncostsare 0 8perpound soifdemandturnsouttobelow thefirmwillshutdownthemine Whatisthevalueofthemine TheBinomialTree Trackingportfolio XpoundsofcopperpurchasedforwardYdollarsinvestedinzero couponbondstoday X 18 750 000poundsofcopperforwardY 1 785 714investedinzero couponbonds TheOptiontoDelaytheStartofaProject ConventionalDCFanalysisimplicitlyassumethatanyinvestmentprojectisantake it or leave itdecision Theprojectcanandonlycanbeundertakenatdate0 Firmshavetheoptiontodelaythestartoftheproject UndertakingaprojectisequivalenttoexercisinganAmericancalloption Theinitialcostisthestrikeprice Thepresentvalueoffuturecashflowscanbeviewedasthevalueofunderlyingasset Aslongastheunderlyingeconomyisuncertain thegenericlessonofAmericancalloptionsappliestotherealinvestment delayexercisingisvaluable AnExample CreatingValuebyRejectinga PositiveNPVProject AcmeIndustriesisconsideringbuildingaplantwhichcosts 100initialinvestment Thefirm smanagementcanimmediatelyinvestthe 100million orwaituntilnextyear Iftheprojectisundertakenimmediately thecashflowinthenextyearwillbe 10million andaperpetualannualcashflowstreamofeither 15millionor 2 5millionfollowsthereafter dependingonwhethertheeconomicconditionisgoodorbad Iftheprojectisdelayed the 10millioncashflowatthenextyearwillbelost Onlytheperpetualcashflowstreamwillbecaptured Assumingthattherisk freeinterestrateis5percentperyearandthat 1investedinthemarketportfoliotodaywillbewortheither 1 3or 0 8 WhatistheNPVoftheproject TheBinomialTrees Donotwait TheBinomialTrees Wait NPV 100 15 0 05 200 NPV 100 2 5 0 05 50 Thefirmwillnottaketheprojectifbadstateoccuratyear1 CreatingValuebyRejectinga PositiveNPVProject Iftheprojectisundertakenimmediately theNPVispositive IfthefirmwaituntilnextperiodIftheeconomicconditionisgood takingtheprojectgenerateapositiveNPV 200matyear1 Iftheeconomicconditionisbad takingtheprojectgenerateanegativeNPV 50matyear1 Thefirmwillnottaketheproject Atyear0 theNPVoftheprojectis CreatingValuebyRejectinga PositiveNPVProject Mostprojectscanbeviewedasasetofmutuallyexclusiveprojects Takingtheprojectstodayisoneproject waitingtotaketheprojectnextyearisanotherproject andwaitingthreeyearsisyetanotherproject AssumingimmediateinvestmentmayignoresthepotentialalternativehigherNPVproject TakingtheprojectimmediatelyisequivalenttoreceivetheaverageNPVsfromtwoprojects 100 10 15 0 05 1 05 195 24 atgoodstate and 100 10 2 5 0 05 1 05 42 86 atbadstate BywaitingandtakingcontingentactionsthefirmavoidsnegativeNPVexante ThisisessentiallythesameintuitiontounderstandthelateexercisingofAmericancalloption TheValueofVacantLand Vacantlandhasvaluebecauseitrepresentsanoptiontoturnthevacantlandintodevelopedland Theownerpaystheconstructioncosts strikeprice toobtainthevalueofadevelopedland underlyingasset Thelandmaybedevelopedintocondominiums anofficebuilding orashoppingmall dependingonwhichchoicegeneratesthemaximumvalue Waitinghasvalueintworegards Similartothepreviousexample theeconomicconditionisrevealedinfuturewhentheownercanmakestatecontingentactions Therelativeattractivenessofthealternativewaystodevelopthelandmaychangeduetotheeconomicuncertainty AnExample Aninvestorownsalotthatissuitableforeithersixorninecondominiumunits Theperunitconstructioncostsofthebuildingwithsixunitsare 80 000andwithnineunits 90 000 Constructioncostsarethesamewhetherconstructiontakesplacethisyearornext Thecurrentmarketpriceofexistingcomparablecondominiumsis 100 000perunit Theperyearrentrateis 8 000perunit andtherisk freerateis12percent Ifmarketconditionsarefavorablenextyear eachcondominiumwillsellfor 120 000 ifconditionsareunfavorable eachwillsellforonly 90 000 Whatisthevalueofthelot DevelopingtheLandImmediately Theownerofthelandcandevelopthelandimmediately Buildingsixcondominiumsearns6 100 000 80 000 120 000Buildingninecondominiumsearns9 100 000 90 000 90 000Buildingsixcondominiumsismoreattractive TheNPVofdevelopingimmediatelyis 120 000 Iftheownerchoosetowaitforonemoreyear thebinomialtreeisasthefollowing TheBinomialTreesforWaiting 1 128 000 1 98 000 10 000 1 12 7 15 NPVofdevelopingoneyearlater 270 000 7 15 60 000 8 15 1 12 141 071 Ifthefavorablestateoccurs 9 unitcondominium 9 120 000 90 000 270 0006 unitcondominium 6 120 000 80 000 240 000Ifthebadstateoccurs 9 unitcondominium 9 90 000 90 000 06 unitcondominium 6 90 000 80 000 60 000Delaytheprojectismorevaluablethanundertakingitimmediately TheOptiontoExpandCapacity Inadditiontotheoptiontoabandonandtheoptiontodelay theoptiontoexpandcapacityalsoaddvaluetoafirm Forexample AcmeIndustriesisconsideringbuildingaplant Theplantwillgeneratecashflowstwoyearsfromnow Thecashflowsfromtheplantwillbe 200millionfollowingtwogoodyears 150millionfollowingonegoodandonbadyear and 100millionfollowingtwobadyears Theinitialcostoftheplantis 140million Afteroneyear however ifthestateoftheeconomylooksgood thefirmhastheoptiontodoubletheplant scapacitybyinvestinganother 140 Riskfreerateis5percentandthat 1investedinthemarketportfoliotodayyieldsfuturevalues dependingonthestateoftheeconomy showninthenextfigure CashFlowsIfThereIsNoCapacityChange Year0 Year1 Year2 CashFlowsIfThereIsCapacityChange 140 TheProcessForMarketPortfolio 1 3 0 8 ValuingtheProject ValueofplantwithouttheoptiontoexpandcapacityAtthegoodstateofyear2 thevalueoftheplantwithouttheoptiontoexpandcapacityis 0 53 200 0 47 150 1 05 168 10Atthebadstateofyear2 thevalueoftheplantwithouttheoptiontoexpandcapacityis 0 35 150 0 65 100 111 90TheNPVofplantatyear0is 0 5 168 10 0 5 111 90 140 6 67ValueofplantwiththeoptiontoexpandcapacityThevalueoftheplantatgoodstateofyear2is 0 53 400 0 47 300 140 196 19TheNPVatyear0is 0 5 196 19 0 5 111 90 140 6 71Theoptiontoexpandingoodstateenhancesthevalueofbuildingaplant ValueofFlexibilityinProductionTechnology Flexibility suchastheoptiontoabandon theoptiontodelayortheoptiontoexpandcapacity isvaluabletoafirm Thissubsectionshowsthatafirmwithsuchflexibilitymaywanttochooseamethodofproductionthatdiffersfromthatoftheircompetitors Althoughbydoingsofirmincreasestherisk italsoincreasesthevalueofitsflexibility TheProductionDecisionofASugarProducer BackgroundAfirmthatproducesandsellsrefinedsugarmustdecidewhethertopurchaseequipmentthatallowsittoproducethesugarfromsugarcaneorfromsugarbeets Theothersugarproducersinthemarketusesugarcaneastheirinputforrefinedsugarproduction Asaresult thepriceofrefinedsugarimmediatelyreflectsanyincreasesinthepriceofsugarcane Howeverfluctuationsinthepriceofsugarbeetsarenotastiedtothepriceofrefinedsugarasinthepriceofsugarcanebecausethecompetingfirmscurrentlydonotusesugarbeetsasaninput TheProductionDecisionofASugarProducer ThenumericalexampleInagoodeconomy thecostofproducingrefinedsugarwithsugarcaneis 0 6perpoundandthecostofusingsugarbeetsis 0 54perpound Inabadeconomy thecostofproducingrefinedsugarwithsugarcanefallsto 0 4perpound Thecostofproducingwithsugarbeetsfallsto 0 5perpound Thepriceofrefinedsugarisalways 0 03perpoundgreaterthanthecostofproductionusingsugarcane Theriskneutralprobabilitiesassociatedwitheachofthesetwostatesoftheeconomyareassumedtobe0 5 Assumingthatthefixedcostofbuildingasugarcaneandsugarbeetplantarethesame whichmethodofproducingrefinedsugarisbetterwhen a capacityisfixed or b capacityisflexibleinthatthefirmiscommittedtoproducingatleast1millionpoundsofrefinedsugarintheplantbut atacostof 40 000thefirmcandoublecapacityto2millionpoundondiscoveringthestateoftheeconomy TheBinomialTrees Sugarbeetsasinput Sugarcaneasinput SugarcaneorSugarBeets IfthecapacityisfixedSugarcane 1m 0 63 0 6 0 5 1m 0 43 0 4 0 5 30mSugarbeets 1m 0 63 0 54 0 5 1m 0 43 0 50 0 5 10mThecostofproducingthesugarusingsugarbeetsishigher IfthecapacitycanbeexpandedSugarcane 1m 0 63 0 6 0 5 1m 0 43 0 4 0 5 30mSugarbeets 2m 0 63 0 54 40 000 0 5 1m 0 43 0 50 0 5 35mThoughusingsugarbeetsismorecostly itintroducesmorevariabilitywhichenhancesthevalueoftheflexibility optiontoexpandthecapacity 5 4Warrants Warrantsarecalloptionsthatgivetheholdertheright butnottheobligation tobuysharesofcommonstockdirectlyfromacompanyatafixedpriceforagivenperiodoftime Warrantstendtohavelongermaturityperiodsthanexchangetradedoptions Warrantsaregenerallyissuedwithprivatelyplacedbonds Warrantsarealsocombinedwithnewissuesofcommonstockandpreferredstock giventoinvestmentbankersascompensationforunderwritingservices Inthiscase theyareoftenreferredtoasaGreenShoeOption Warrants Thesamefactorsthataffectcalloptionvalueaffectwarrantvalueinthesameways Stockprice Exerciseprice Riskfreerate Volatilityinthestockprice Expirationdate Dividends TheDifferenceBetweenWarrantsandCallOptions Calloptionsareissuedbyindividualinvestorsorinstitutions whilewarrantsareissuedbythefirms Whenawarrantisexercised afirmmustissuenewsharesofstock Butwhentheoptionsareexercisedthereisnochangeinthetotalnumberoftheshares Onlytheownershipoftheshareschanges Thee