lecture capbud risk
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Chapter 7
Risk and Real
Options inCapitalBudgeting
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Project Analysis &
Evaluation• Evaluating NPV Estiates – !o" relia#le is our NPV estiate$ –
%orecasting Risk Bad decisions'ro errors in projected cash (o"s)• *e ight accept a “#ad” project)• *e ight reject a “good” project)
– Projected vs) Actual cash (o"s – +,+O -gar#age in gar#age out. – Capital #udgeting is NO/ an entirely
echanical process)
2
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WACC & Project RiskExpected
Ret
urn (%)
Beta
SML
WACC
= !%
= "%#ncorrect
acceptance
#ncorrect
rejection
B
A$!
R f=
A = '$
ir* = '
B = '+
If a firm uses its WACC to make accept/reject decisions for all types ofprojects, it will hae a tendency toward incorrectly acceptin! riskyprojects and incorrectly rejectin! less risky projects"
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/ypes o' Risk
• 0tand alone risk1 0tand alone risk iseasured #y the varia#ility o' the project#se2pected return)
• Corporate or "ithin34r risk1 Corporate riskis easured #y the project#s ipact onuncertainty a#out the 4r#s 'utureearnings)
• 5arket6 or #eta6 risk1 5arket risk iseasured #y the project#s eect on the4r#s #eta)
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8uanti'ying Risk and itsAppraisal
• Risk is the varia#ility o' possi#le outcoes• Assuption o' independence
– No causative relationship #et"een cash (o"s 'ro periodto period
– Risk3'ree rate 'or discounting• ,solate the tie value o' oney
– 0tandard deviation o' the pro#a#ility distri#ution o' NPVs
• 9:
( )∑= +
=n
t t
f
t
R
A NPV
0 1
( )∑= +
n
t t
f
t
R
σ
02
2
1
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0tandardi;ing the<ispersion
• Assess the pro#a#ility o' adversity
• <eterining pro#a#ilities o' adverseevents
– Consult the noral pro#a#ility distri#utionta#le
– E2press dierences 'ro the ean inters o' standard deviations to deterine
the pro#a#ility
• %undaental 'or a realistic assessent
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,n'oration +enerated
• Pro#a#ility distri#ution o' ,RR – Copute the ean and standard deviation
• Nonnoral distri#ution
• Biases in o#taining in'oration – Adjustent 'or #iases
• Pro#les – Over3adjustent
– Accounta#ility – Results depends on #ehavioral considerations
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<ependence o' Cash %lo"s-C%s. over /ie
• Conse=uence o' C%s #eing correlated overtie – Per'ect correlation
• C%s deviate in e2actly the sae relative anner• >inear 'unction
– 5oderate correlation• ?se a series o' conditional pro#a#ility distri#utions
• /ake account o' the correlation o' C%s over tie
σ = σ
t
1+Rf ( ) t
t =0
n
∑
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/otal Risk 'or 5ultiple,nvestents
• /otal risk
– /he su o' systeatic and unsysteatic
risk
• 0tandard deviation -0<.
• Correlation #et"een projects
• %easi#le co#inations and doinance
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0tandard <eviation
• <epends on – <egree o' correlation #et"een various
projects
• !igher the degree o' positive correlation thegreater the 0< o' the port'olio
– 0< o' possi#le NPVs o' each project
• +reater the 0< o' individual projects the
greater the 0< o' the port'olio
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Correlation Bet"eenProjects
• Range o' correlation
– Bet"een @ and )@@
– >ack o' negatively correlated projects
• ?nrelated lines o' #usiness tend tohave lo" degrees o' correlation
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%easi#le Co#ination and<oinance
• Evaluating 'easi#le co#inations
– <eterine "hich co#inationsdoinate in NPV andor 0<
– <eterines the ecient 'rontier
• Relation to e2isting port'olio
– ,nvestent proposals can #eeliinated #ecause they are doinated
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Real Options in Capital,nvestents
• Valuation in general
• /ypes o' option – Option to vary output
– Option to a#andon
– Option to postpone
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Valuation in +eneral• Real options
– Enhance the "orth o' a project – <icult to value
• <ecision trees• 0iulations• Ad hoc approaches
• Project "orth NPV D option value• As the nu#er o' options increases – ?ncertainty increases – Option value increases – Project#s "orth increases
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/he Option to E2pand
• ?sing a decision tree – E2pected NPVs 'or the various #ranches
– 0e=uence o' decisions and chance events
– Optial set o' decisions• Rolling #ack the tree
• Back"ard induction
– Coparing NPVs• Optial decision at the 4rst decision point
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/he Option to A#andon
• Provides a sa'ety net
• Consists o' – 0elling the asset
or
– Eploying the asset in another area
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Econoic Rationale 'orA#andonent
• 0ae as capital #udgeting
• Project "orth NPV "ithout a#andonent D Value o' a#andonent option
• A#andon a project – ,' the PV o' possi#le 'uture #ene4ts
current a#andonent value – Appears #etter no" than in the 'uture
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• Abandonment Option MakesSituation Better
– A signi4cant iproveent occurs• A portion o' the do"nside is eliinated
"hen events turn un'avora#le
– A#andonent is ore valua#le
• /he greater the volatility o' C%s – A#andonent itigates the eects o'
#ad outcoes
• Ongoing Abandonment
Evaluations – Optial tie to a#andon
– Continual assessent o' projects
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/he Option to Postpone or /ie
• O#tain ne" in'oration – 5arket – Prices
– Cost• +ive up
– ,nteri C%s – %irst over advantage
• Coodity situation• Noncoodity situation
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%inal O#servations on RealOptions
• Real options are dierent 'ro 4nancialoptions – Cannot use risk neutrality
–E2ercise price can change over tie – Volatility is dicult to easure
– ,precise opportunity cost
– 5ore dicult to value
• Recognition o' anageent (e2i#ility
• 5ore uncertainty is a positive "ith real options
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/echni=ues 'or easuringstand alone risk
1. Sensitivity Analysis
2. Scenario Analysis
3. Monte Carlo Simulation Analysis
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“*hat ,' ”1 0ensitivityAnalysis
• 0ho"s ho" changes in one input varia#le aect NPV or ,RR)
• All varia#les6 e2cept the one o' interest6 are 42ed) Change onevaria#le to see eect on NPV or ,RR)
• Ans"ers “"hat i' ” =uestions6 e)g)6 “"hat i' sales decline #y :FG$”
• Advantages
– Provides rough easure o' stand3alone risk)
– ,denti4es “dangerous” varia#les)
• <isadvantages
– <oes not re(ect diversi4cation)
– 0ays nothing a#out the likelihood o' the change in the
varia#le) – ,gnores relationships aong varia#les)
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“*hat ,' ”1 0cenario
Analysis• E2aines several discrete scenarios6 usually a"orst case6 #est case6 and ost likely case)
• Brackets the range o' likely outcoes)
• Advantages – Provides use'ul in'oration on a project#s stand alone
risk #y sho"ing the range o' likely outcoes)
• <isadvantages
– Only a 'e" discrete outcoes are considered)
– Assues input varia#les are per'ectly correlated -e)g)6all the #est or "orst things "ill happen at the saetie.) /his leads to overstateent o' the e2trees)
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“*hat ,'”1 0iulation
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“*hat ,' ”1 0iulationAnalysis
• /echni=ue in "hich pro#a#le 'uture events are siulated on a
coputer)• 5odel the project that sho"s the relationship #et"een NPV
and paraeters and e2ogenous varia#le)
• 0peci'y the values o' the paraeter and the pro#a#ilitydistri#ution o' the e2ogenous varia#le)
• Pro#a#ility distri#utions are selected 'or the input varia#les) /he coputer dra"s rando nu#ers 'ro the speci4eddistri#utions to siulate 'uture levels o' sales6 e2penses6 etc)
• /he process is repeated a large nu#er o' ties -6@@@D. andthe average NPV and standard deviation are deterined)
• Advantages
– Re(ects pro#a#ilities o' 'uture inputs) – Provides e2pected NPV and standard deviation #ased on
input pro#a#ilities and relationships aong inputs)
• <isadvantages1Pro#a#ility distri#utions are su#jective)No true decision rule)
5ay look ore accurate than it really is)24
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<ecision /ree Analysis• ?se'ul in evaluating projects "ith capital outlays ade
over several years)
– At t@H Conduct a Rs)F@6@@@ 'easi#ility study on theuse o' ne" underground natural gas storage technology)
– At tH 0pend Rs))F illion 'or a pilot projectdeonstrating the ne" technology)
– At tIH ,nvest Rs)7F illion in a 'ull scale undergroundstorage 'acility)
– At t7H 0pend Rs)I@ illion to e2pand the e2isting'acility)
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,easi-i.it/
Stud/
(! 0)
Pi.otProject
('! M)
,u..1Sca.e
,aci.it/
(! M)
Expansion
( M)
Stop
Stop
Stop
s n ap a
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s n ap aBudgeting
• *hat does “risk” ean in capital #udgeting$ – ?ncertainty a#out a project#s 'uture
pro4ta#ility) – 5ay #e easured #y σNPV6 σ,RR6 or the
project#s #eta) – *ill the project increase the 4r#s and
shareholder#s risk$ – Risk analysis ay soeties
incorporate historical data #ut're=uently is #ased on su#jective
judgeents)• /ypes o' risk
– 0tand3alone risk – Corporate risk – 5arket risk
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,ncorporat ng R s nto
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,ncorporat ng R s ntoCapital Budgeting
• /he Certainty E=uivalent 5ethod – Estiate the certainty e=uivalent cash
(o"s 'or each period) – <iscount at the risk3'ree rate to get NPV)
• /he Risk3Adjusted <iscount Rate5ethod -RA<R. – Estiate a discount rate that re(ects the
riskiness o' the project#s cash (o"s)
– <iscount the estiated cash (o"s at therisk3adjusted rate to get NPV) – <eterining risk3adjusted rates1
• . /he “pure play” ethod• :. 0u#jective approach• J. <ivisional cost o' capital
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ore on e ure ay
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ore on e ure ay5ethod
• %ind one or ore nonintegrated6 single3product 4rs "hose line o' #usiness is thesae as that o' the project #eing evaluated)
• Estiate the #eta 'or the other 4r)
• ?nlever the #eta o' the other 4r)
• Copute leveraged the #eta to re(ect thecapital structure o' project)
• ?se the 05>CAP5 to deterine the project#scost o' e=uity 3 then 4nd the project#s *ACC)
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)/()1(1 S DT
LU
×−+
= β β
[ ])/()1(1 S DT U L ×−+= β β
)( RF M i RF si k k k k −+= β
)1(Project T wk wk k d d s sii −+=
/he !oe <epot1 A 0ensitivity Analysis
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/he !oe <epot1 A 0ensitivity Analysis
/he 'ollo"ing is an analysis o' ane" store #eingconsidered #y the !oe <epot6 "ith the 'ollo"ing
assuption governing the #ase case1• ,nitial ,nvestent in the store Rs) :)F illion
• E2pected li'e o' the store @ years
• 0alvage Value o' the store preises at the end o' @years Rs) F)F illion
• E2pected Revenues s=uare 'oot in the 4rst year Rs)J@@ s=uare 'ootH +ro"th rate FGH
• Pre ta2 operating argin -EB,/0ales. @G
• *orking capital as a percentage o' Revenue @GH
investent is at the #eginning o' each period andcopletely salvagea#le at the end o' the project li'e)
• /he depreciation each year is coputed using 5ARC0depreciation rates)
•/he corporate ta2 rate is JKGH the cost o' capital is: FG