SallyJamesonValuingStockOptioninaCompensatiWord文件下载.docx
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SallyJamesonValuingStockOptioninaCompensatiWord文件下载.docx
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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
Firstofall,weshouldfindoutthecharacteristicsforthestockoptionsinthatcompensationpackage.
Fromthesentence“theoptionsrepresenttherighttobuyTelstarstockatasetprice,afterasetperiodoftime”,wecanknowthattheoptionsareEuropeanOptions.
Itsstrikepriceis$35,itsmaturityis5years.Thecurrentstockpriceis$.Andwealsocalculatethecontinuouslycompoundedinterestrateofafive-yeartreasurybondtobe%.
So,theonlythingunknownisthevolatility.Sincewehavegottheimpliedvolatilityoftheoptionssoldinthemarket,wecouldreasonablyguesstheimpliedvolatilityofSally’soptions.
Inthereality,thevolatilitysmileforequityoptionsshouldbelikethis:
So,withastrikepriceof$35,whichismuchhigherthanthecurrentpriceof$,weguesstheimpliedvolatilityshouldbelowerthan38%.
35
|
5
Fromdifferentscenariosassumingdifferentσ,wecancalculatedifferentoptionpricesandtotalvaluesasshowninthetablebelow.
σ
25%
'
30%
35%
38%
optionprice
cX3000
5000
~
5760
8160
10650
12180
Wedon’tthinkthevolatilitycanbelowerthan23%,so,wesuggestSallytoselectthestockoptions.
【
<
QUESTION3
HowshouldwefactorinthecomplicationsignoredintheabovequestionHowwouldtheyaffectthevalueoftheoptionstoMs.JamesonWhatshouldshedoWhy
AssumethatSallyacceptscash,investsitandreinveststheinterestwith5-yearT-bondrate%.Consideringthetax,thefuturevalueinyear5willbe$4357.
1
2
3
4
&
beginningbalance
3600
3740
3886
4037
4194
interest
195
202
210
;
218
227
tax
54
57
59
61
63
endingbalance
4357
WhataboutacceptingtheoptionsSincethey’reEuropeanoptions,thecurrentoptionpriceisthepresentvalueoftheexpectedfuturepayoff.Thus
E(π)=c*erT=$
$
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
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
AboutCost:
a)NowbothinAmericaandinChina,stockoptionstoemployeesarerequiredtobeexpensedincompany’sfinancialstatementsbyaccountingrules.Therefore,thoughnotaffectedfinancially,stockoptionsdrawdowntheincomenumbersinfinancialreportsofthecompany,which
b)Ifeventuallytheemployeesexercisetheoptions,sincethecompanyusuallyissuenewstockstotheemployeesinsteadofpurchasinginthemarket,therewillbedilutioneffect,resultinginlowerpriceofthestockinthewholemarket,whichmeanstheotherstockholdersarepayingfortheexercisingofstockoptions.
Incentives:
Stockoptionsconnectthebenefitsofthecompanyandtheexecutivesbydirectingthemtoworkforthegoalofthecompany:
iftheexecutiveswanttorealizethepossiblecapitalgainofexercisingthestockoptions,theyneedtoworkhardtoboostthevalueofthefirms.
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