财务管理-第二十五章-PPT课件

Chapter25OptionValuation McGraw Hill Irwin Copyright 2013byTheMcGraw HillCompanies Inc Allrightsreserved KeyConceptsandSkills UnderstandandbeabletousePut CallParityBeabletousetheBlack ScholesOptionPricingModelUnderstandtherelationshipsbetweenoptionpremiumsandstockprice exerciseprice timetoexpiration standarddeviation andtherisk freerateUnderstandhowtheoptionpricingmodelcanbeusedtoevaluatecorporatedecisions 25 2 ChapterOutline Put CallParityTheBlack ScholesOptionPricingModelMoreaboutBlack ScholesValuationofEquityandDebtinaLeveragedFirmOptionsandCorporateDecisions SomeApplications 25 3 ProtectivePut BuytheunderlyingassetandaputoptiontoprotectagainstadeclineinthevalueoftheunderlyingassetPaytheputpremiumtolimitthedownsideriskSimilartopayinganinsurancepremiumtoprotectagainstpotentiallossTrade offbetweentheamountofprotectionandthepricethatyoupayfortheoption 25 4 AnAlternativeStrategy Youcouldbuyacalloptionandinvestthepresentvalueoftheexercisepriceinarisk freeassetIfthevalueoftheassetincreases youcanbuyitusingthecalloptionandyourinvestmentIfthevalueoftheassetdecreases youletyouroptionexpireandyoustillhaveyourinvestmentintherisk freeasset 25 5 ComparingtheStrategies Stock PutIfS E exerciseputandreceiveEIfS E letputexpireandhaveSCall PV E PV E willbeworthEatexpirationoftheoptionIfS E letcallexpireandhaveinvestment EIfS E exercisecallusingtheinvestmentandhaveS 25 6 Put CallParity Ifthetwopositionsareworththesameattheend theymustcostthesameatthebeginningThisleadstotheput callparityconditionS P C PV E Ifthisconditiondoesnothold thereisanarbitrageopportunityBuythe low sideandsellthe high sideYoucanalsousethisconditiontofindthevalueofanyofthevariables giventheotherthree 25 7 Example FindingtheCallPrice Youhavelookedinthefinancialpressandfoundthefollowinginformation Currentstockprice 50Putprice 1 15Exerciseprice 45Risk freerate 5 Expirationin1yearWhatisthecallprice 50 1 15 C 45 1 05 C 8 29 25 8 ContinuousCompounding ContinuouscompoundingisgenerallyusedforoptionvaluationTimevalueofmoneyequationswithcontinuouscompoundingEAR eq 1PV FVe RtFV PVeRtPut callparitywithcontinuouscompoundingS P C Ee Rt 25 9 Example ContinuousCompounding Whatisthepresentvalueof 100tobereceivedinthreemonthsiftherequiredreturnis8 withcontinuouscompounding PV 100e 08 3 12 98 02Whatisthefuturevalueof 500tobereceivedinninemonthsiftherequiredreturnis4 withcontinuouscompounding FV 500e 04 9 12 515 23 25 10 Example PCPwithContinuousCompounding Youhavefoundthefollowinginformation Stockprice 60Exerciseprice 65Callprice 3Putprice 7Expirationisin6monthsWhatistherisk freerateimpliedbytheseprices S P C Ee Rt60 7 3 65e R 6 12 9846 e 5RR 1 5 ln 9846 031or3 1 25 11 Black ScholesOptionPricingModel TheBlack ScholesmodelwasoriginallydevelopedtopricecalloptionsN d1 andN d2 arefoundusingthecumulativestandardnormaldistributiontables 25 12 Example OPM Youarelookingatacalloptionwith6monthstoexpirationandanexercisepriceof 35 Thecurrentstockpriceis 45 andtherisk freerateis4 Thestandarddeviationofunderlyingassetreturnsis20 Whatisthevalueofthecalloption LookupN d1 andN d2 inTable25 3N d1 9761 9772 2 9767N d2 9671 9686 2 9679 C 45 9767 35e 04 5 9679 C 10 75 25 13 Example OPMinaSpreadsheet ConsiderthepreviousexampleClickontheexcelicontoseehowthisproblemcanbeworkedinaspreadsheet 25 14 PutValues Thevalueofaputcanbefoundbyfindingthevalueofthecallandthenusingput callparityWhatisthevalueoftheputinthepreviousexample P C Ee Rt SP 10 75 35e 04 5 45 06Notethataputmaybeworthmoreifexercisedthanifsold whileacallisworthmore alivethandead unlessthereisalargeexpectedcashflowfromtheunderlyingasset 25 15 Europeanvs AmericanOptions TheBlack ScholesmodelisstrictlyforEuropeanoptionsItdoesnotcapturetheearlyexercisevaluethatsometimesoccurswithaputIfthestockpricefallslowenough wewouldbebetteroffexercisingnowratherthanlaterAEuropeanoptionwillnotallowforearlyexercise therefore thepricecomputedusingthemodelwillbetoolowrelativetothatofanAmericanoptionthatdoesallowforearlyexercise 25 16 Table25 4 25 17 VaryingStockPriceandDelta Whathappenstothevalueofacall put optionifthestockpricechanges allelseequal TakethefirstderivativeoftheOPMwithrespecttothestockpriceandyougetdelta Forcalls Delta N d1 Forputs Delta N d1 1Deltaisoftenusedasthehedgeratiotodeterminehowmanyoptionsweneedtohedgeaportfolio 25 18 WorktheWebExample ThereareseveralgoodoptionscalculatorsontheInternetCandclickontheBasicCalculatorunderAnalysisServicesPricethecalloptionfromtheearlierexampleS 45 E 35 R 4 t 5 2Youcanalsochooseastockandvalueoptionsonaparticularstock 25 19 Figure25 1 InsertFigure25 1here 25 20 Example Delta Considerthepreviousexample Whatisthedeltaforthecalloption Whatdoesittellus N d1 9767ThechangeinoptionvalueisapproximatelyequaltodeltatimesthechangeinstockpriceWhatisthedeltafortheputoption N d1 1 9767 1 0233Whichoptionismoresensitivetochangesinthestockprice Why 25 21 VaryingTimetoExpirationandTheta Whathappenstothevalueofacall put aswechangethetimetoexpiration allelseequal TakethefirstderivativeoftheOPMwithrespecttotimeandyougetthetaOptionsareoftencalled wasting assets becausethevaluedecreasesasexpirationapproaches evenifallelseremainsthesameOptionvalue intrinsicvalue timepremium 25 22 Figure25 2 Insertfigure25 2here 25 23 Example TimePremiums Whatwasthetimepremiumforthecallandtheputinthepreviousexample CallC 10 75 S 45 E 35Intrinsicvalue max 0 45 35 10Timepremium 10 75 10 0 75PutP 06 S 45 E 35Intrinsicvalue max 0 35 45 0Timepremium 06 0 0 06 25 24 VaryingStandardDeviationandVega Whathappenstothevalueofacall put whenwevarythestandarddeviationofreturns allelseequal TakethefirstderivativeoftheOPMwithrespecttosigmaandyougetvegaOptionvaluesareverysensitivetochangesinthestandarddeviationofreturnThegreaterthestandarddeviation themorethecallandtheputareworthYourlossislimitedtothepremiumpaid whilemorevolatilityincreasesyourpotentialgain 25 25 Figure25 3 Insertfigure25 3here 25 26 VaryingtheRisk FreeRateandRho Whathappenstothevalueofacall put aswevarytherisk freerate allelseequal ThevalueofacallincreasesThevalueofaputdecreasesTakethefirstderivativeoftheOPMwithrespecttotherisk freerateandyougetrhoChangesintherisk freeratehaveverylittleimpactonoptionsvaluesoveranynormalrangeofinterestrates 25 27 Figure25 4 Insertfigure25 4here 25 28 ImpliedStandardDeviations AlloftheinputsintotheOPMaredirectlyobservable exceptfortheexpectedstandarddeviationofreturnsTheOPMcanbeusedtocomputethemarket sestimateoffuturevolatilitybysolvingforthestandarddeviationThisiscalledtheimpliedstandarddeviationOnlineoptionscalculatorsareusefulforthiscomputationsincethereisnotaclosedformsolution 25 29 WorktheWebExample UtofindtheimpliedvolatilityofastockofyourchoiceCtogettherequiredinformationClickonthewebsurfertogotoNuma entertheinformationandfindtheimpliedvolatility 25 30 EquityasaCallOption Equitycanbeviewedasacalloptiononthefirm sassetswheneverthefirmcarriesdebtThestrikepriceisthecostofmakingthedebtpaymentsTheunderlyingassetpriceisthemarketvalueofthefirm sassetsIftheintrinsicvalueispositive thefirmcanexercisetheoptionbypayingoffthedebtIftheintrinsicvalueisnegative thefirmcanlettheoptionexpireandturnthefirmovertothebondholdersThisconceptisusefulinvaluingcertaintypesofcorporatedecisions 25 31 ValuingEquityandChangesinAssets Considerafirmthathasazero couponbondthatmaturesin4years Thefacevalueis 30million andtherisk freerateis6 Thecurrentmarketvalueofthefirm sassetsis 40million andthefirm sequityiscurrentlyworth 18million SupposethefirmisconsideringaprojectwithanNPV 500 000 Whatistheimpliedstandarddeviationofreturns Whatisthedelta Whatisthechangeinstockholdervalue 25 32 PCPandtheBalanceSheetIdentity Riskydebtcanbeviewedasarisk freebondminusthecostofaputoptionValueofriskybond Ee Rt PConsidertheput callparityequationandrearrangeS C Ee Rt PValueofassets valueofequity valueofariskybondThisisjustthesameasthetraditionalbalancesheetidentityAssets liabilities equity 25 33 MergersandDiversification DiversificationisafrequentlymentionedreasonformergersDiversificationreducesriskand therefore volatilityDecreasingvolatilitydecreasesthevalueofanoptionAssumediversificationistheonlybenefittoamergerSinceequitycanbeviewedasacalloption shouldthemergerincreaseordecreasethevalueoftheequity Sinceriskydebtcanbeviewedasrisk freedebtminusaputoption whathappenstothevalueoftheriskydebt Overall whathashappenedwiththemergerandisitagooddecisioninviewofthegoalofstockholderwealthmaximization 25 34 ExtendedExample PartI ConsiderthefollowingtwomergercandidatesThemergerisfordiversificationpurposesonlywithnosynergiesinvolvedRisk freerateis4 25 35 ExtendedExample PartII UsetheOPM oranoptionscalculator tocomputethevalueoftheequityValueofthedebt valueofassets valueofequity 25 36 ExtendedExample PartIII Theassetreturnstandarddeviationforthecombinedfirmis30 Marketvalueassets combined 40 15 55Facevaluedebt combined 18 7 25 TotalMVofequityofseparatefirms 25 681 9 867 35 548Wealthtransferfromstockholderstobondholders 35 548 34 120 1 428 exactincreaseinMVofdebt 25 37 M AConclusions MergersfordiversificationonlytransferwealthfromthestockholderstothebondholdersThestandarddeviationofreturnsontheassetsisreduced therebyreducingtheoptionvalueoftheequityIfmanagement sgoalistomaximizestockholderwealth thenmergersforreasonsofdiversificationshouldnotoccur 25 38 ExtendedExample LowNPV PartI StockholdersmaypreferlowNPVprojectstohighNPVprojectsifthefirmishighlyleveragedandthelowNPVprojectincreasesvolatilityConsideracompanywiththefollowingcharacteristicsMVassets 40millionFaceValuedebt 25millionDebtmaturity 5yearsAssetreturnstandarddeviation 40 Risk freerate 4 25 39 ExtendedExample LowNPV PartII Currentmarketvalueofequity 22 657millionCurrentmarketvalueofdebt 17 343million 25 40 ExtendedExample LowNPV PartIII Whichprojectshouldmanagementtake EventhoughprojectBhasalowerNPV itisbetterforstockholdersThefirmhasarelativelyhighamountofleverageWithprojectA thebondholdersshareintheNPVbecauseitreducestheriskofbankruptcyWithprojectB thestockholdersactuallyappropriateadditionalwealthfromthebondholdersforalargergaininvalue 25 41 ExtendedExample NegativeNPV PartI We veseenthatstockholdersmightpreferalowNPVtoahighone butwouldtheyeverpreferanegativeNPV Undercertaincircumstances theymightIfthefirmishighlyleveraged stockholdershavenothingtoloseifaprojectfailsandeverythingtogainifitsucceedsConsequently theymaypreferaveryriskyprojectwithanegativeNPVbuthighpotentialrewards 25 42 ExtendedExample NegativeNPV PartII ConsiderthepreviousfirmTheyhaveoneadditionalprojecttheyareconsideringwiththefollowingcharacteristicsProjectNPV 2millionMVofassets 38millionAssetreturnstandarddeviation 65 EstimatethevalueofthedebtandequityMVequity 25 423millionMVdebt 12 577million 25 43 ExtendedExample NegativeNPV PartIII Inthiscase stockholderswouldactuallypreferthenegativeNPVprojecttoeitherofthepositiveNPVprojectsThestockholdersbenefitfromtheincreasedvolatilityassociatedwiththeprojecteveniftheexpectedNPVisnegativeThishappensbecauseofthelargelevelsofleverage 25 44 Conclusions Asageneralrule managersshouldn