西南财大课件金融经济学lecture6realoptions1.docx
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西南财大课件金融经济学lecture6realoptions1.docx
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西南财大课件金融经济学lecture6realoptions1
西南财大课件金融经济学】lecture6-realoptions_1
RealOptions
October102005
CorporateFinance
2
DCFsfailures
StandardDCFassumesastaticviewoftheworld
Eitheryouinvestoryoudont
Ifyoudoyouknowwhattheexpectedcashflowsare
Howeverinmanyinvestments
Thereisleewayaboutthetimingoftheinvestment
Therearechoicesonecanmakeinthefuture
Thequestionhowtointroducetheseincapitalbudgeting
CorporateFinance
3
TheValuetoWait
Optionpricingisausefulmethodtoaccountfortimingandirreversibility
Example
Aninvestmentproject
IfthenextgovernmentisliberalNPV100
IfconservativeNPV-100
Thenextgovisgoingtobeliberalwithprobability50
NPVoftheprojectis5x100-5x1000
CorporateFinance
4
Uncertainty
Supposetherearelocalelectionsbetweennowandthegeneralelections
Ifthelocalelectionsarewonbyliberalstheprobthattheywillalsowinthenextgeneralelectionis8
NPV-100x20100x8060
Ifnottheprobis20
NPV-100x80100x20–60
CorporateFinance
5
Valueofwaiting
Supposeyoucanpostponethedecisiontoinvestatacostof5
Thenifliberalsloseyoudontinvest
Iftheprobofliberalswinningthelocalelectionis50NPV5x605x0–525
Sothevalueoftheprojectis25whentheoptiontowaitisconsidered
AstraightforwardDCFanalysiswouldvegotitwrong
CorporateFinance
6
Options
StarttheprojectexerciseanAmericanoption
Delayingtheprojectlosedividends
Butgaininformation
Theoptimalexercisemomenttradesthesetwooff
CorporateFinance
7
ATaxonomy
DeferralOptionAmericancall
OptiontoAbandonAmericanput
OptiontoExpandAmericancall
SwitchingOptionsputcalloptions
CompoundOptions
RainbowOptionsaffectedbyseveraluncertaintysourcesegpriceandquantity
8
Set-up
Initialoutlayatt0104
Discountrate20[]
Riskfreerate8[]
Projectspayoffatt1
V180prob
V–60prob
CorporateFinance
9
Set-up
Suppose
Thereexistsatwinsecurityasfollows
Notethat5ofthesereplicatetheinvestmentspayoff
QHowwouldyouthencalculatethevalueoftheinvestmentonthebasisofthissecurity
CorporateFinance
10
Set-up
Fromthetwinsecuritywecanderivetheriskneutralprobability
whichcanbeusedtovaluethedifferentoptions
CorporateFinance
11
Set-up
Alternativelysupposenotwinsecurityexists
Wecanthoughvaluetheproject
V180prob
V–60prob
Thususingdiscountrateof20[]
Fromwhichrisk-neutralprobabilitiescanbecalculated
Thereforewecanusetheprojectitselfasunderlyingasset
wedoassumethoughthatwecancalculatediscountrate
CorporateFinance
12
InGeneral
Anyinvestmentcanbeanalysedasanoption
Strikepricecashoutlaytostarttheproject
StockpricePVoffuturecashflowsexcInv
Maturity
Timewheninvestmentismade
Timewhenuncertaintyresolves
Dividendsforgonecashflows
CorporateFinance
13
OptiontoDefer
Supposeyoucanpostponetheinvestmentfornextyear
SothatyouknowatthetimeoftheinvestmentwhetheritisV–orV
Thecostofdoingsoisthatthecostoftheinvestmentrisesto11232
ThevalueEoftheinvestmentopportunityisasfollows
E1V–I10180–1123206768
E1–V––I1060–1123200
CorporateFinance
14
OptiontoDefer
Valueoftheinvestmenttodayis
Andthevalueoftheoptiontodeferistherefore
2507--42907
CorporateFinance
15
OptiontoExpand
AnadditionalinvestmentofI180doublesthescaleoftheproject
E1V12V1-I1180360–80280
Expand
E1–V1–2V1–-I160120–8060
Donotexpand
Thevalueoftheprojecttodayis
CorporateFinance
16
OptiontoContractdownsize
Suppose
I050
I1H5832
I1
I1L25
WhereI1HleadstothesamepayoffsasbeforeandI1Lhalvesthescaleoftheproject
CorporateFinance
17
OptiontoContractdownsize
E1V1–I1H05V1-I1L180–583290–2512168
Donotcontract
E1–V1––I1H05V1–-I1L60–583230–255
Contract
Thevalueoftheprojecttodayis
CorporateFinance
18
OptiontoSwitch
Alternativeuseoftheprojectsalvagevalue
A11275
A1–68
Howmuchisitworthtobeabletoswitch
E1V1A11801275180
Donotswitch
E1–V1–A1–606868
CorporateFinance
19
OptiontoSwitch
Projectvalue
Acquiringorbuildingthepossibilitytoswitchisworth444
CorporateFinance
20
ConcludingRemarks
YoucanvaluearealoptionwithBS
butBSisnotflexible
notimingissues
nocomplexoptions
Thebinomialvaluationismoreflexible
NotebinomialvaluationisNOTjustadecisiontree
Youmustvalueiediscountthingsproperly
CorporateFinance
21
Literature
Ch9browseatwill
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