SallyJamesonValuingStockOptioninaCompensati.docx

SallyJamesonValuingStockOptioninaCompensati.docx

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SallyJamesonValuingStockOptioninaCompensati

FinancialEngineeringCaseStudy

SallyJameson:

ValuingStockOptioninaCompensationPackage

2012/5/31

CASEREVIEW

Ms.JamesonwasfacingachoicewhenshegotherfirstjobafterthegraduationofherMBAdegree.WhenshefoundawonderfuljobinthecompanyTelstar,shecangetbonusbesidestheregularsalary.Nowshehadthechoiceofeither$5,000incashor3,000optionsonTelstar’sstocks.

%

Thedetailedinformationcanbeasfollows:

EachoptiongrantedtheownertobuyoneshareofTelstarstockat$35ontheexact5yearslater.Thespotpriceofthatstockis$.

ButtheoptionwillberejectedifSallyleavesthecompanyduringthefirstfiveyears.

NowtheproblemSallyfacedwithiswhethersheshouldgetbonusincaseorbonusasoptions.Alsosomemarketdataaregiveninthecase.

—

QUESTIONANSWER

QUESTION1

WhatistheimpliedvolatilityoftheTelstarcallwithastrikepriceof$20andanexpirationdateofJanuary22,1994

ANSWER

UsingExcel,weformtheBlack-ScholesFormula,sothatwecanusethefunctionofsinglevariablesolutiontogettheimpliedvolatility.

Wehavealreadyknownstockprice,exercisepriceandoptionprice.

FromMay27,1992toJan22,1994,thereare604daysleft,soit’snearlyyears.

Inaddition,wehavegotthetableofTreasuryBonds’BEY（BondEquivalentYield）,soallweneedtodoistochangethemintocontinuouscompoundedrates.

∴

Andcc=ln（1+r）

BEY

r

cc

1year

…

%

%

%

2year

%

%

%

%

%

[

Thenwecaninputthesevariablestothespreadsheet,andgettheimpliedvolatilityofthiscalloptiontobe%

Currentpriceofunderlyingcommonstock

S=

Exerciseprice

K=

20

Risk-freerate（continuouslycompounded）

r=

%

》

Timetoexpiration

t=

Volatility（continuouslycompounded）

σ=

%

Callvalue

（

QUESTION2

）

IfweignoretaxconsiderationsandassumethatSallyJamesonisfreetosellheroptionsatanytimeaftershejoinsTelstar,whichcompensationpackageisworthmore

ANSWER

Firstofall,weshouldfindoutthecharacteristicsforthestockoptionsinthatcompensationpackage.

Fromthesentence“theoptionsrepresenttherighttobuyTelstarstockatasetprice,afterasetperiodoftime”,wecanknowthattheoptionsareEuropeanOptions.

Itsstrikepriceis$35,itsmaturityis5years.Thecurrentstockpriceis$.Andwealsocalculatethecontinuouslycompoundedinterestrateofafive-yeartreasurybondtobe%.

So,theonlythingunknownisthevolatility.Sincewehavegottheimpliedvolatilityoftheoptionssoldinthemarket,wecouldreasonablyguesstheimpliedvolatilityofSally’soptions.

Inthereality,thevolatilitysmileforequityoptionsshouldbelikethis:

So,withastrikepriceof$35,whichismuchhigherthanthecurrentpriceof$,weguesstheimpliedvolatilityshouldbelowerthan38%.

%

Currentpriceofunderlyingcommonstock

S=

Exerciseprice

K=

35

Risk-freerate（continuouslycompounded）

r=

%

Timetoexpiration

t=

|

5

Volatility（continuouslycompounded）

σ=

Callvalue

Fromdifferentscenariosassumingdifferentσ,wecancalculatedifferentoptionpricesandtotalvaluesasshowninthetablebelow.

σ

%

25%

'

30%

35%

38%

optionprice

cX3000

5000

~

5760

8160

10650

12180

Wedon’tthinkthevolatilitycanbelowerthan23%,so,wesuggestSallytoselectthestockoptions.

【

<

QUESTION3

HowshouldwefactorinthecomplicationsignoredintheabovequestionHowwouldtheyaffectthevalueoftheoptionstoMs.JamesonWhatshouldshedoWhy

ANSWER

AssumethatSallyacceptscash,investsitandreinveststheinterestwith5-yearT-bondrate%.Consideringthetax,thefuturevalueinyear5willbe$4357.

1

2

3

4

&

5

beginningbalance

3600

3740

3886

4037

4194

interest

195

202

210

；

218

227

tax

54

57

59

61

63

endingbalance

3740

3886

<

4037

4194

4357

WhataboutacceptingtheoptionsSincethey’reEuropeanoptions,thecurrentoptionpriceisthepresentvalueoftheexpectedfuturepayoff.Thus

E（π）＝c*erT=$

σ

%

25%

30%

35%

$

38%

optionprice

Expectedpayoff

'

Aftertaxincome

4683

5396

7644

9976

11409

So,evenifthevolatilityissolowas23%,theexpectedincomeisstillhigherthanthefuturevalueofcashcompensation.

However,SallyshouldalsoconsiderthelikelihoodthatshemightnotstayatTelstarthatlong.Tocalculatethebreakevenpoint,wethinkavolatilityof30%isreasonableandwesupposetheprobabilitysheleavesbeforeyear5isk.Let7724*（1-k）=4357,thesolutionisk=44%,whichmeansifSallyhasaprobabilityofleavingthecompanybeforeyear5largerthan44%,sheshouldselectcashcompensation.Otherwise,sheshouldselectstockoptions.

~

）

QUESTION4

WhatifMs.Jamesondecidedthattheoptionwasabetterdeal,butthatshedidn’twantallofherfinancialwealth（aswellasherhumancapital）tiedtothefortunesofTelstarAssumingsheworksatTelstarandacceptstheoptiongrant,isthereanythingshecandoto“untie”someofherwealthfromTelstar

ANSWER

Theideato“untie”thewealthisthatto“transfer”someorallofoptionvaluetoreinvestinotherassetsincludingcash.

a）Thoughusuallynotthecaseinreality,ifMs.Jamesoncanselltheoptions,tradingpartoftheoptionsinthemarketisonewaytountiethesigningbonusfromTheTelstar,shecanreinvestthemoneyshewillgetinotherassets.

b）Ms.JamesoncanalsoshortthestocksorstockfuturesofTelstar.Sincestockfuturesoftenhavehigherprices,wesuggestashortpositionofstockfutures.

Assuming30%volatility,Δ=,whichmeansifwechoosestockashedgingderivative,tocompletely“untie”thestockoption,Ms.Jamesononlyneeds*3000=1170sharesofstock.Topartlyuntie,shecanshortanamountlike500shares.

QUESTION5

DoesgrantingstockoptionscostcompaniesanythingIfso,whopaysWhatincentivesdoexecutivestockoptionplanscreatefortheirrecipients

ANSWER

AboutCost:

a）NowbothinAmericaandinChina,stockoptionstoemployeesarerequiredtobeexpensedincompany’sfinancialstatementsbyaccountingrules.Therefore,thoughnotaffectedfinancially,stockoptionsdrawdowntheincomenumbersinfinancialreportsofthecompany,which

b）Ifeventuallytheemployeesexercisetheoptions,sincethecompanyusuallyissuenewstockstotheemployeesinsteadofpurchasinginthemarket,therewillbedilutioneffect,resultinginlowerpriceofthestockinthewholemarket,whichmeanstheotherstockholdersarepayingfortheexercisingofstockoptions.

Incentives:

Stockoptionsconnectthebenefitsofthecompanyandtheexecutivesbydirectingthemtoworkforthegoalofthecompany:

iftheexecutiveswanttorealizethepossiblecapitalgainofexercisingthestockoptions,theyneedtoworkhardtoboostthevalueofthefirms.