eduardo schwartz kbl 12 slides
TRANSCRIPT
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ChallengesandOpportunities
UCLA
Anderson
SchoolKarlBorch Lecture:May2012
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MinesandOilDeposits
ForestryResources
ExpropriationRisk
in
Natural
Resources
Internet
Companies InformationTechnology
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BasicideasaboutRealOptionsValuation
Naturalresourceinvestmentsandthe
stoc astic
e avioro
commo ity
prices
ResearchandDevelo mentInvestments
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BasicIdeasaboutRealOptions
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financialoptionstheorytooptionsonreal(non
financial
assets
Optionsarecontingentdecisions Give the o ortunit to make a decision after ou see
howevents
unfold
Payoffisusuallynotlinear
RealOptionvaluationsarealignedwithfinancial
marketvaluations
Ifpossibleusefinancialmarketinputandconcepts
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respondtoit(flexibility)arethesourceof
Whennottouserealoptions:
en
t ere
are
no
opt ons
at
aWhenthereislittleuncertainty
Whenconsequencesofuncertaintycanbe
ignored Mostprojectsaresubjecttooptions
valuation
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1.Optiontoexpandaproject:
theoptiontodevelopanewproject.
2.
Optionto
postpone
investment:
,
mightnotbeoptimaltoexercisetheoption
,
informationinthefuture(valuationof
mines).
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3. Optiontoabandon:
,
alwayshavetheoptiontoabandonitifweare
.4. Optiontotemporarilysuspendproduction:
openandclosefacility.
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Tra t ona
Va uat onToo s
D F
Requireforecasts
generallyused
rate
when
options
(e.g.,
exit
option)
are
Futuredecisionsarefixedattheoutset
no ex y or a ng ec s ons ur ng ecourseoftheinvestmentproject
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Letsfirstlookatoneaspectofthenew
a roach Traditionalvs.CertaintyEquivalentapproach
Optionsalittlelater
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Riskadjusteddiscountrate
N
tCCNPV
t k1 )1(
expected
cash
flow
in
period
ttCk riskadjusteddiscountrate
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N tCEQ
tt
fr10
)1(
exchanged
for
risky
cash
flow
(market
based)
t
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ConsiderasimplifiedvaluationofaMineor
OilDe osit
Themainuncertaintyisinthecommodity
exist(copper,gold,oil)
BrennanandSchwartz(1985)
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.
TraditionalValuation:
N
t
tttN
t
tt CostSqCCostv
CNPV 00Re
N CostF
tt
fr10
)1(
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CoxandRoss(1976),HarrisonandKreps(1979)and
Harrisonand
Pliska
(1981)
show
that
the
absence
ofarbitrageimplytheexistenceofaprobability
distributionsuchthatsecuritiesarepricedattheir
discounted(at
the
risk
free
rate)
expected
cash
flows
underthisriskneutralorriskadjustedprobabilities
(Equivalent
Martingale
Measure).
Adjustmentfor
risk
is
in
the
probability
distribution
of
cashflowsinsteadofthediscountrate(Certainty
EquivalentApproach).
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hedged)theseprobabilitiesareunique.
mar etsarenotcomp etet eyarenot
necessarilyunique
(any
of
them
will
eterminet esamemar etva ue .
Futures ricesareex ectedfutures ot
pricesunder
this
risk
neutral
distribution.
.
T
][ 00 T
ttrQ
XeEVf
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OptionPricingTheoryintroducedthe
conceptof
pricing
by
arbitrage
methods.
Forthepurposeofvaluingoptionsitcanbe
assumedthatthe
ex ected
rate
of
return
on
thestockistheriskfreerateofinterest. Then,
(underthe
new
distribution)
can
be
.
the
market
is
complete
and
the
EMM
is
unique.
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UsingtheRiskNeutralFrameworktovalue
projectsallows
us
to
Usealltheinformationcontainedinfutures
riceswhen
these
rices
exist
Takeintoaccountalltheflexibilities(options)
Usethepowerfulanalyticaltoolsdevelopedin
contingentclaimsanalysis
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BlackScholesworld
, ,ofthisworld
F =S 1+r T,
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Trueandriskneutralstochastic
processfor
Gold
prices
dS
0 dtNdz
zS
~
~zdrdtS
,
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Ris neutra istri utioncan eo taine rom
futuresprices
or
other
traded
assets
Coppermine,oildeposits
Futureprices
are
available
only
for
short
time
Copperminescanlast50years!
Themodelsfitpricesanddynamicsverywell
formaturitiesofavailablefutures rices
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Nee anequi i riummo e CAPM too tain
riskneutral
distribution
because
there
are
no
futuresprices
R&Dprojects
Internetcompanies
Informationtechnolo
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ummary:
ea
p ons
a ua on Formanyprojects,flexibilitycanbeanimportant
componentof
value
Theoptionpricingframeworkgivesusapowerfultooltoanalyzethoseflexibilities
Thereal
options
approach
to
valuation
is
being
appliedinpractice
Theapproachisbeingextendedtotakeintoaccountcompetitiveinteractions(impactofcompe on
on
exerc se
s ra eg es
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SolutionProcedures
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DynamicProgrammingapproach
aysoutposs e utureoutcomesan o s
backthevalueoftheoptimalfuturestrategy
binomialmethod
widelyusedofpricingsimpleoptions
goodforpricingAmericantypeoptions
notso
good
when
there
are
many
state
variables
or
therearepathdependencies
Needtousetheriskneutraldistribution
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Partia i erentia equation PDE
hasclosed
form
solution
in
very
few
cases
BSequationforEuropeancalls
generallysolvedbynumericalmethods
veryflexible
goodforAmericanoptions
forpathdependenciesneedtoaddvariables
notgoodforproblemswithmorethanthreefactors
technicallymoresophisticated(needtoapproximateboundaryconditions)
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mu a onapproac averagesthevalueoftheoptimalstrategyatthe
decision date for thousands of ossible outcomes
verypowerfulapproach easilyappliedtomultifactormodels
rec yapp ca e opa epen en pro ems
canbe
used
with
general
stochastic
processes
intuitive,transparent,flexibleandeasilyimplemented
Butitisforwardlooking,whereasoptimalexerciseof
Americano tions
has
features
of
d namic
programming
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ValuingAmericanOptionsbySimulation:A
simpleleast
squares
approach
Thisconditionalexpectationisthekeytobeingable
tomake
o timal
exercise
decisions.
Mainideaoftheapproachisthattheconditionalex ectedvalueofcontinuationcanbeestimated
fromthe
cross
sectional
information
from
the
simulationbyleastsquares.
30
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ValuingAmericanOptionsbySimulation:A
simpleleast
squares
approach
eest matet econ t ona expectat on unct on yregressingdiscountedexpostcashflowsfrom
valuesofthestatevariables.
isan
efficient
estimator
of
the
conditional
.estimatetheoptimalstoppingrulefortheoption,
andhence
its
current
value.
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NaturalResourceInvestments
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Firstpaperoncommodities1982:ThePricingof
Commodity
Linked
Bonds,
bonds
in
which
the
payout(couponand/orprincipal)islinkedtothe
priceofacommodity(oil,copper,gold)
In1985,
Evaluating
Natural
Resource
Investments
(withM.Brennan),mineandoildepositscouldbe
interpretedandvaluedascomplexoptionsonthe
underlying
commodities.
One
of
the
first
papers
on
RealOptions.
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Assumedstochasticprocessforcommodityprices
.
forgoldbutnotforothercommodities.
Assumptionnotsatis actory ecausesupp yan
demandadjustmentsinducemeanreversionincommo ty
pr ces
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Inthenext30yearsIwrote(aloneandwith
coauthors)
many
articles
trying
to
make
more
realisticassumptionsabouttheprocessfollowedby
commodityprices.Includingaboutelectricityprices
where
seasonality
is
important PresidentialaddresstotheAFA(1997)onThe
StochasticBehaviorofCommodityPrices:
Implications
for
Valuation
and
Hedging
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ThreeFactorModel:Actual
(Cortazarand
Schwartz
(2003))
SdzSdtdS
33 za
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111
222 z
*
333 zta
We need to make assumptions about the functional
orm o e mar e pr ces o r s s
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Oil Futures 01/08/99
Three-Factor Model30.00
25.00
15.00
20.00
e(US$)
Observed
Model
10.00
Pri
0.00
5.00
0 1 2 3 4 5 6 7 8 9 10
Maturity (Years)
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Oil Futures 10/12/00
Three-Factor Model
35
25
30
)
Observed
Model
15
20
Price
(US
10
0
0 1 2 3 4 5 6 7 8 9 10
a ur y ears
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Acceptthemodelpredictionsformaturities
wherethere
are
no
futures
rices?
Maybeafewyearsonly?
Assume at uturesprices
Assumefutures ricesincreaseatafixedrate
(inflation?)?
nce
ere
smore
uncer a n y
n
sarea,
whatdiscountratetouse(riskfreerate?)?
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TworecentpaperswithAndersTrolle
Unspanned stochasticvolatilityandthepricingof
commodit derivatives 2009
Pricingexpropriation
risk
in
natural
resource
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Extenttowhichvolatilityisspannedbyfutures
Arecommodityoptionsredundantsecurities?
Critical
for
pricing,
hedging
and
risk
management
of
commodityoptionsandrealoptions
Weanalyzetheseissuesinthecrudeoilmarketand
develop
a
new
model
for
pricing
commodity
derivativesinthepresenceofunspannedstochastic
volatility
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marketintheworld
arges rangeo ma ur esan s r epr ces,w c varysignificantlyduringthesampleperiod
DailydatafromJan2,1990toMay18,2006
Wechoosethe12mostliquidcontractsforthe
analysis M1,M2,M3,M4,M5,M6(first6monthly
contracts)
Q1,
Q2
(next
two
quarterly
contracts
expiringinMar,Jun,SeporDec) Y1,Y2,Y3,Y4(next
fouryearlycontractsexpiringinDec)
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Ifweregresschangesinvolatilityonthereturnsof
futures
contracts
(or
its
PC),
the
R2
will
indicate
the
extenttowhichvolatilityisspanned
Butvolatilityisnotdirectlyobservable
Returnon
Straddles:
Call
+Put
with
the
same
strike
closesttoATM lowdeltasandhi hve as.
Modelindependent
expectedvolatilityoverthelifeoftheoption
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Wefactoranalyzethecovariancematrixofthe
futuresreturnsandretainthefirstthreeprincipal
components
(PCs) Regressstraddlereturns(changesinimplied
volatilities onPCsandPCss uared
WefindthattheR2aretypicallyverylow,especiallyfortheimpliedvolatilityregressions(between0and
21%)
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Thus,factorsthatexplainfuturesreturnscannot
explain
changes
in
volatility Wethenfactoranalyzethecovariancematrixofthe
residualsfromtheseregressions.Ifthereis
unspanned
stochastic
volatility
in
the
data
we
should
seelargecommonvariationintheresiduals
WefindthattypicallythefirsttwoPCexplainover
80%of
the
variation
in
the
residuals
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Pricing expropriation risk in natural
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Pricingexpropriationriskinnatural
resourcecontracts
ConferenceonTheNaturalResourcesTrap,Private
InvestmentwithoutPublicCommitment(Kennedy
School,Harvard)
Therearemanydimensionstothestudyof
expropriation
risk
in
natural
resource
investments:
political,environmental,sociological,economic
Inourapproachweabstractfrommanyofthese
issuesand
we
concentrate
on
some
of
the
im ortant
economictradeoffsthatarisefromagovernment
havin ano tiontoex ro riatetheresource
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xpropr a on
p on Wevalueanaturalresourceproject,inparticularan
oilfield
ex osed
to
ex ro riation
risk
Weviewthegovernmentasholdinganoptionto
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Weabstract
from
the
various
o erational
o tions
thataretypicallyembeddedinnaturalresource
ro ectsandconcentrateontheex ro riationo tion
Spotprices,
futures
prices
and
volatilities
are
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Expropriationoptioncanbeexercisedatanytimeduringthe
lifeoftheoption:Americanstyle(LSM)
everypo n
n
me
egovernmen
mus
compare
e
valueofimmediateexercisewiththeconditionalexpected
Outcomeis
the
optimal
exercise
time
for
each
simulated
path
whichcanbeusedtovaluetheex ro riationo tion
Wecanalsoestimatethevalueoftheoilfieldtothe
governmentandthefirmbothinthepresenceandabsenceof
expropriationrisk
Main Results
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MainResults For
agiven
contractual
arrangement
the
value
of
the
expropriationoptionincreaseswith
Thespotprice
Theslope
of
the
futures
curve
(contango,
backwardation)
Thevolatilityofthespot(futures)price
Foragivensetofstatevariablesthevalueofthe
expropriationoptiondecreaseswiththe
Taxrate
Variousexpropriationcosts
Theincreaseinthefieldsvaluetothegovernmentdueto
expropriationriskisalwayssmallerthanthedecreaseinthefieldvaluetothefirms,sincetherearedeadweightlosses
assoc a e w expropr a on pro uc on ne c encyan
reputationalcosts)
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ep armaceut ca n ustry as ecomearesearc orientedsectorthatmakesamajorcontributionto
.
Thesuccessoftheindustryingeneratingastreamof
createdan
intense
public
policy
debate
over
issues
thefinancingofthecostofresearch
the
rices
char ed
for
its
roducts
thesociallyoptimaldegreeofpatentprotection
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Thereis
atrade
off
between
promoting
marketoutcomes.
duringthelifeofthepatentcompensatetheinnovatorforitsrisk investment.
Theonset
of
competition
after
the
expiration
of
the atentlimitsthedeadwei htlossestosociet thatarisefrommonopolypricingunderthepatent.
Regulationhashadimportanteffectsonthecostofinnovationinthepharmaceuticalindustry.
AnalysisofR&Dprojectsisaverydifficult
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investmentproblem
a esa ongt metocomp ete
Uncertaintyaboutcostsofdevelopmentandtimetocomp et on
Highprobabilityoffailure(fortechnicaloreconomicreasons
Drugrequires
approval
by
the
FDA
Uncertaintyaboutlevelanddurationoffuturecashflows
Abandonmentoption
is
very
valuable
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Research Spending Per New Drug
Total R&D
-Company Ticker
drugs approved
Per Drug ($Mil)
2011 ($Mil)
AstraZeneca AZN 5 11,790.93 58,955
GlaxoSmithKline GSK 10 8,170.81 81,708
Sano i SNY 8 7,909.26 63,274
RocheHoldingAG RHHBY 11 7,803.77 85,841
Pfizer Inc. PFE 14 7,727.03 108,178
Johnson &
Johnson JNJ 15 5,885.65 88,285Eli Lilly & Co. LLY 11 4,577.04 50,347
oLaboratories ABT 8 4,496.21 35,970
Merck & Co Inc MRK 16 4,209.99 67,360
Bristol-MyersSquibb Co. BMY 11 4,152.26 45,675
Novartis AG NVS 21 3,983.13 83,646
Amgen Inc. AMGN 9 3,692.14 33,229
ources: nno n en er or esearc n ome ca nnova on; omsonReuters Fundamentals via FactSet Research Systems
PfizerYouthPillAteUp$71MillionBefore
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ItFlopped
: ay ,
Theexperimentaldrugaimedtoreversethephysicalec ne
t at
comes
w t
ag ng.
Nearlyadecadeofresearch.
Patientstakingthefrailtydrughadgainedsomemuscle
mass
but
less
than
3%
more
than
the
p ace ogroup w c a soexper ence musc eincrease.
rugappeare
ne ect ve.
Medivation,Pfizerendworkon
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AlzheimersDrug
WSJ January18,2012
upfront andupto$500millionifsuccessful
.
Some5.4
million
in
the
US
and
18
million
worldwideareestimatedtohaveAlzheimers
reach$25billionperyear
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MostprescribednamebrandintheUSwith
3.5
million
eo le
takin
it
ever
da Enterthemarketin1997andlosspatent
.
salesof
$81
billion
But(WSJMay2,2112),Pfizer'sfirstquarter
rofit declined 19% as sales of its to roduct
Lipitor,tumbled71%intheU.S.amid
.
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1. EvaluationofResearchandDevelopment
Investments(withM.Moon,2000)
2. PatentsandR&DasRealOptions(2004)
3. R&D Investments with Com etitive Interactions
(withK.
Miltersen,
2004)
.
ResearchIncentives(withJ.Hsu,2008)
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Patentsand
R&D
as
Real
Options
MethodologyforthevaluationofasingleR&D
Orequivalently,fordeterminingthevalueofapatent
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TreatthepatentprotectedR&Dprojectorthepatentasacomplexoptiononthevariablesunderlyingthevalueoftheproject
expectedcoststocompletion
anticipatedcashflows
Uncertainty
is
introduced
in
the
analysis
by
allowing
thesevariablestofollowstochasticprocessesthroughtime
Theriskadjustedprocessforthecashflowsisobtained
using
the
beta
of
traded
pharmaceutical
companies
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pro ec a es me ocomp e e
Maximumrateofinvestment
Totalcosttocompletionisrandomvariable
Probabilit of failure catastro hic events
Optionto
abandon
the
project
en,an ,pro ec scomp e e cas ows
starttobegenerated
Cashflows
are
uncertain
(level
and
duration)
ProjectispatentprotecteduntiltimeT
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-
Receive C
Invest K at rate ITerminal value
0 T
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Expectedcosttocompletionfollows(technicaluncertainty):
dzIKIdtdK 2)(
Varianceof
cost
to
completion:
2
22
2
)~
(
K
KVar
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CashflowratefollowsGeometricBrownianmotionwhich
CdwCdtdC
Riskadjustedprocessusedforvaluation:
CdwCdtCdwCdtdC *
ValueofProjectonceInvestmenthas
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beenCompleted:
V(C,t)
0*
1 22
CrVVCVVC
CTCV
Hassolution:
**C
*,
r
oc as c process or e rue re urn on e
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oc as cprocess or e rue re urnon e
projectonce
investment
is
completed
dwdtrV
)(
Volatilityand
risk
premium
are
the
same
as
for
cash
flows.
m
ValueoftheInvestment
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Opportunity:F(C,K,t)
*)()(
11
[
2
1
222 CFFIKCFIKFCMax
CCKKKCCI 0])( IFrFIF tK
Subjectto
boundary
condition
at
completion
of
investment:
),(),0,( CVCF
Problem with this is that time of com letion is random.
Simulated Paths of Cost to Completion and Quarterly Cash Flow
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Simulated Paths of Cost to Completion and Quarterly Cash Flow
120 9
1007
8
Investment is completed
and Cash Flows start
Ant icipated Cash Flows
80
5
6
40 3
4
Realized Cash Flows
201
2Cost to Completion
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
Cost to Completion Distribut ion
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Cost to Completion Distribut ion
9000
7000
8000
5000
6000
3000
40002.3% reach
patent expiration
1000
2000
35 55 75 95 115 135 155 175 195
Cost to Completion
Figure 4:
Critical Values for Investment
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18.00
16.00
17.00
13.00
14.00
.
FlowR
ate Invest at Maximum Rate
11.00
12.00
C
ash
Do not Invest
Pro ect Value E ual 0
9.00
10.00
.80.00 85.00 90.00 95.00 100.00 105.00 110.00 115.00 120.00
Cost to Completion
R&DInvestmentswithCompetitiveInteractions
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(joint
with
K.
Miltersen) oncen ra esoncompe ve n erac onsan e
effectithasonvaluationandoptimalinvestment
Realoptionsframeworkisextendedtoincorporategametheoreticalconcepts
TwofirmsinvestinginR&Dfordifferentdrugsbothtargeted
to
cure
the
same
disease
Ifbothfirmssuccessful:Duopolyprofitsinmarketingphase. Butitcanaffectdecisionsindevelopment
.outcomeinmarketingphase
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Competition ringsa out
Higherproductionatlowerprices
Higherprobabilityofsuccess
Shorteravera edevelo menttime
Butwith
higher
total
development
costs
and
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Whats new in this paper?
QualityoftheR&Doutputismodeledexplicitly
thequality
thefirmspricing(andquantity)strategy
Marketdemand
Firmspriceandquantitystrategycoulddependon
Monopolypower
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us on rac s:
Fulldiscretionaryresearchgrant
Sponsorcopayment
Pull Contracts:
Extendedpatent
protection
xe pr cepurc asecomm men
Variablepricepurchasecommitment
on rac pec cs
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Developerretainsright,suppliesmonopolyquantity
Fulldiscretionaryresearchgrant
Sponsorcopayment
Patentextension
Sponsor
can
contract
the
socially
optimal
quantity
tobe roduced
Purchasecommitmentcontracts
asymmetricinformationbetweenvaccinedevelo erands onsor andfromcontractin issues
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at st erequ re eve o monetary ncent vetoinducethefirmtoundertakethevaccineR&D?
atare
t e
expecte
pr ce,
quant ty
supp e
an
efficacyofthedevelopedvaccine?
at st epro a tyt atav a evacc new e
developed? at st econsumersurp usgenerate
Whatistheexpectedcostperindividualsuccessfully
vacc nate