Sally-Jameson-Valuing-Stock-Option-in-a-Compensati

FinancialEngineeringCaseStudySallyJameson:ValuingStockOptioninaCompensationPackage2012/5/31CASEREVIEWMs.JamesonwasfacingachoicewhenshegotherfirstjobafterthegraduationofherMBAdegree.WhenshefoundawonderfuljobinthecompanyTelstar,shecangetbonusbesidestheregularsalary.Nowshehadthechoiceofeither$5,000incashor3,000optionsonTelstar’sstocks.Thedetailedinformationcanbeasfollows:EachoptiongrantedtheownertobuyoneshareofTelstarstockat$35ontheexact5yearslater.Thespotpriceofthatstockis$18.75.ButtheoptionwillberejectedifSallyleavesthecompanyduringthefirstfiveyears.NowtheproblemSallyfacedwithiswhethersheshouldgetbonusincaseorbonusasoptions.Alsosomemarketdataaregiveninthecase.QUESTIONANSWERQUESTION1WhatistheimpliedvolatilityoftheTelstarcallwithastrikepriceof$20andanexpirationdateofJanuary22,1994?ANSWERUsingExcel,weformtheBlack-ScholesFormula,sothatwecanusethefunctionofsinglevariablesolutiontogettheimpliedvolatility.Wehavealreadyknownstockprice,exercisepriceandoptionprice.FromMay27,1992toJan22,1994,thereare604daysleft,soit’snearly1.65years.Inaddition,wehavegotthetableofTreasuryBonds’BEY(BondEquivalentYield),soallweneedtodoistochangethemintocontinuouscompoundedrates.∵BEY=1000−PP×1T∴(1+r)T=1000P=BEY×T+1∴r=√BEY×T+1T−1Andcc=ln(1+r)BEYrcc1year4.02%4.02%3.94%2year5.25%5.12%4.99%1.65year4.74%4.63%Thenwecaninputthesevariablestothespreadsheet,andgettheimpliedvolatilityofthiscalloptiontobe38.4%CurrentpriceofunderlyingcommonstockS=18.75ExercisepriceK=20Risk-freerate(continuouslycompounded)r=4.63%Timetoexpirationt=1.65Volatility(continuouslycompounded)σ=38.40%Callvalue3.75QUESTION2IfweignoretaxconsiderationsandassumethatSallyJamesonisfreetosellheroptionsatanytimeaftershejoinsTelstar,whichcompensationpackageisworthmore?ANSWERFirstofall,weshouldfindoutthecharacteristicsforthestockoptionsinthatcompensationpackage.Fromthesentence“theoptionsrepresenttherighttobuyTelstarstockatasetprice,afterasetperiodoftime”,wecanknowthattheoptionsareEuropeanOptions.Itsstrikepriceis$35,itsmaturityis5years.Thecurrentstockpriceis$18.75.Andwealsocalculatethecontinuouslycompoundedinterestrateofafive-yeartreasurybondtobe5.26%.So,theonlythingunknownisthevolatility.Sincewehavegottheimpliedvolatilityoftheoptionssoldinthemarket,wecouldreasonablyguesstheimpliedvolatilityofSally’soptions.Inthereality,thevolatilitysmileforequityoptionsshouldbelikethis:So,withastrikepriceof$35,whichismuchhigherthanthecurrentpriceof$18.75,weguesstheimpliedvolatilityshouldbelowerthan38%.CurrentpriceofunderlyingcommonstockS=18.75ExercisepriceK=35Risk-freerate(continuouslycompounded)r=5.26%Timetoexpirationt=5Volatility(continuouslycompounded)σ=?Callvalue?Fromdifferentscenariosassumingdifferentσ,wecancalculatedifferentoptionpricesandtotalvaluesasshowninthetablebelow.σ23.34%25%30%35%38%optionprice1.671.922.723.554.06cX30005000576081601065012180Wedon’tthinkthevolatilitycanbelowerthan23%,so,wesuggestSallytoselectthestockoptions.QUESTION3Howshouldwefactorinthecomplicationsignoredintheabovequestion?HowwouldtheyaffectthevalueoftheoptionstoMs.Jameson?Whatshouldshedo?Why?ANSWERAssumethatSallyacceptscash,investsitandreinveststheinterestwith5-yearT-bondrate5.4%.Consideringthetax,thefuturevalueinyear5willbe$4357.12345beginningbalance36003740388640374194interest195202210218227tax5457596163endingbalance37403886403741944357Whataboutacceptingtheoptions?Sincethey’reEuropeanoptions,thecurrentoptionpriceisthepresentvalueoftheexpectedfuturepayoff.ThusE(π)＝c*erT=$3.57σ23.34%25%30%35%38%optionprice1.671.922.723.554.06Expectedpayoff2.172.503.544.625.28Aftertaxincome468353967644997611409So,evenifthevolatilityissolowas23%,theexpectedincomeisstillhigherthanthefuturevalueofcashcompensation.However,SallyshouldalsoconsiderthelikelihoodthatshemightnotstayatTelstarthatlong.Tocalculatethebreakevenpoint,wethinkavolatilityof30%isreasonableandwesupposetheprobabilitysheleavesbeforeyear5isk.Let7724*(1-k)=4357,thesolutionisk=44%,whichmeansifSallyhasaprobabilityofleavingthecompanybeforeyear5largerthan44%,sheshouldselectcashcompensation.Otherwise,sheshouldselectstockoptions.QUESTION4WhatifMs.Jamesondecidedthattheoptionwasabetterdeal,butthatshedidn’twantallofherfinancialwealth(aswellasherhumancapital)tiedtothefortunesofTelstar?AssumingsheworksatTelstarandacceptstheoptiongrant,isthereanythingshecandoto“untie”someofherwealthfromTelstar?ANSWERTheideato“untie”thewealthisthatto“transfer”someorallofoptionvaluetoreinvestinotherassetsincludingcash.a)Thoughusuallynotthecaseinreality,ifMs.Jamesoncanselltheoptions,tradingpartoftheoptionsinthemarketisonewaytountiethesigningbonusfromTheTelstar,shecanreinvestthemoneyshewillgetinotherassets.b)Ms.JamesoncanalsoshortthestocksorstockfuturesofTelstar.Sincestockfuturesoftenhavehigherprices,wesuggestashortpositionofstockfutures.Assuming30%volatility,Δ=0.39,whichmeansifwechoosestockashedgingderivative,tocompletely“untie”thestockoption,Ms.Jamesononlyneeds0.39*3000=1170sharesofstock.Topartlyuntie,shecanshortanamountlike500shares.QUESTION5Doesgrantingstockoptionscostcompaniesanything?Ifso,whopays?Whatincent