Aswath Damodaran
CLOSUREINVALUATION
TheBigEnchilada
191
GettingClosureinValuation
192
¨
Apubliclytradedfirmpotentiallyhasaninfinitelife.Thevalueistherefore
thepresentvalueofcashflowsforever.
t=∞ CF
t
Value = ∑
t
t=1 (1+r)
¨
Sincewecannotestimatecashflowsforever,weestimatecashflowsfora
“growthperiod” andthenestimateaterminalvalue,tocapturethevalue
attheendoftheperiod:
t=N CF
t + Terminal Value
Value = ∑
N
t
(1+r)
(1+r)
t=1
Aswath Damodaran
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WaysofEstimatingTerminalValue
193
Terminal Value
Liquidation
Value
Most useful
when assets
are separable
and
marketable
Aswath Damodaran
Multiple Approach
Easiest approach but
makes the valuation
a relative valuation
Stable Growth
Model
Technically soundest,
but requires that you
make judgments about
when the firm will grow
at a stable rate which it
can sustain forever,
and the excess returns
(if any) that it will earn
during the period.
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1.Obeythegrowthcap
194
¨
Whenafirm’scashflowsgrowata“constant” rateforever,thepresent
valueofthosecashflowscanbewrittenas:
Value=ExpectedCashFlowNextPeriod/(r- g)
where,
r=Discountrate(CostofEquityorCostofCapital)
g=Expectedgrowthrate
¨
Thestablegrowthratecannotexceedthegrowthrateoftheeconomybut
itcanbesetlower.
•
•
•
¨
Ifyouassumethattheeconomyiscomposedofhighgrowthandstablegrowthfirms,
thegrowthrateofthelatterwillprobablybelowerthanthegrowthrateofthe
economy.
Thestablegrowthratecanbenegative.Theterminalvaluewillbelowerandyouare
assumingthatyourfirmwilldisappearovertime.
Ifyouusenominalcashflows anddiscountrates,thegrowthrateshouldbenominalin
thecurrencyinwhichthevaluationisdenominated.
Onesimpleproxyforthenominalgrowthrateoftheeconomyisthe
riskfree rate.
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194
RiskfreeRatesandNominalGDPGrowth
¨
¨
RiskfreeRate=ExpectedInflation+
ExpectedRealInterestRate
Therealinterestrateiswhatborrowers
agreetoreturntolendersinreal
goods/services.
¨
¨
NominalGDPGrowth=ExpectedInflation
+ExpectedRealGrowth
Therealgrowthrateintheeconomy
measurestheexpectedgrowthinthe
productionofgoodsandservices.
The argument for Risk free rate = Nominal GDP growth
1.
In the long term, the real growth rate cannot be lower than the real interest rate,
since you have the growth in goods/services has to be enough to cover the promised
rate.
2.
In the long term, the real growth rate can be higher than the real interest rate, to
compensate risk taking. However, as economies mature, the difference should get
smaller and since there will be growth companies in the economy, it is prudent to
assume that the extra growth comes from these companies.
Period
1954-2015
1954-1980
1981-2008
2009-2015
10-YearT.Bond
Rate
5.93%
5.83%
6.88%
2.57%
InflationRate RealGDPGrowth
3.61%
3.06%
4.49%
3.50%
3.26%
3.04%
1.66%
1.47%
NominalGDP
growthrate
6.67%
7.98%
6.30%
3.14%
NominalGDP- T.Bond
Rate
0.74%
2.15%
-0.58%
0.57%
APracticalReasonforusingtheRiskfree
RateCap– PreserveConsistency
196
¨
¨
You are implicitly making assumptions about nominal growth
in the economy, with your risk free rate. Thus, with a low risk
free rate, you are assuming low nominal growth in the
economy (with low inflation and low real growth) and with a
high risk free rate, a high nominal growth rate in the
economy.
If you make an explicit assumption about nominal growth in
cash flows that is at odds with your implicit growth
assumption in the denominator, you are being inconsistent
and bias your valuations:
¤
¤
If you assume high nominal growth in the economy, with a low risk
free rate, you will over value businesses.
If you assume low nominal growth rate in the economy, with a high
risk free rate, you will under value businesses.
Aswath Damodaran
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2.Don’twaittoolong…
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¨
Assumethatyouarevaluingayoung,highgrowthfirmwith
greatpotential,justafteritsinitialpublicoffering.Howlong
wouldyousetyourhighgrowthperiod?
a.
b.
c.
d.
¨
<5years
5years
10years
>10years
Whileanalystsroutinelyassumeverylonghighgrowth
periods(withsubstantialexcessreturnsduringtheperiods),
theevidencesuggeststhattheyaremuchtoooptimistic.
Mostgrowthfirmshavedifficultysustainingtheirgrowthfor
longperiods,especiallywhileearningexcessreturns.
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Andtietocompetitiveadvantages
198
¨
¨
¨
Recappingakeylessonaboutgrowth,itisnot
growthpersethatcreatesvaluebutgrowthwith
excessreturns.Forgrowthfirmstocontinueto
generatevaluecreatinggrowth,theyhavetobeable
tokeepthecompetitionatbay.
Proposition1:Thestrongerandmoresustainable
thecompetitiveadvantages,thelongeragrowth
companycansustain“valuecreating”growth.
Proposition2:Growthcompanieswithstrongand
sustainablecompetitiveadvantagesarerare.
Aswath Damodaran
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3.Don’tforgetthatgrowthhastobeearned..
199
¨
Inthesectiononexpectedgrowth,welaidoutthefundamental
equationforgrowth:
Growthrate=ReinvestmentRate*Returnoninvestedcapital
+Growthratefromimprovedefficiency
¨
¨
Instablegrowth,youcannotcountonefficiencydeliveringgrowth
andyouhavetoreinvesttodeliverthegrowthratethatyouhave
forecast.
Consequently,yourreinvestmentrateinstablegrowthwillbea
functionofyourstablegrowthrateandwhatyoubelievethefirm
willearnasareturnoncapitalinperpetuity:
¤
¨
ReinvestmentRate=Stablegrowthrate/StableperiodROC=g/ROC
Yourterminalvalueequationcanthenberewrittenas:
TerminalValueinyearn = Aswath Damodaran
./01 234 567 (56
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(>?@7?A>BCD7BE6F)
199
TheBigAssumption
200
Growthrateforever
Returnoncapitalinperpetuity
6%
8%
10%
12%
14%
0.0%
$1,000
$1,000
$1,000
$1,000
$1,000
0.5%
$965
$987
$1,000
$1,009
$1,015
1.0%
$926
$972
$1,000
$1,019
$1,032
1.5%
$882
$956
$1,000
$1,029
$1,050
2.0%
$833
$938
$1,000
$1,042
$1,071
2.5%
$778
$917
$1,000
$1,056
$1,095
3.0%
$714
$893
$1,000
$1,071
$1,122
Terminal value for a firm with expected after-tax operating income of
$100 million in year n+1 and a cost of capital of 10%.
Aswath Damodaran
200
ExcessReturnstoZero?
201
¨
¨
Therearesome(McKinsey,forinstance)whoarguethatthereturnon
capitalshouldalwaysbeequaltocostofcapitalinstablegrowth.
Butexcessreturnsseemtopersistforverylongtimeperiods.
Aswath Damodaran
201
Anddon’tfallforsleightofhand…
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¨
¨
AtypicalassumptioninmanyDCFvaluations,whenit
comestostablegrowth,isthatcapitalexpenditures
offsetdepreciationandtherearenoworkingcapital
needs.Stablegrowthfirms,wearetold,justhaveto
makemaintenancecapex(replacingexistingassets)to
delivergrowth.Ifyoumakethisassumption,what
expectedgrowthratecanyouuseinyourterminalvalue
computation?
Whatifthestablegrowthrate=inflationrate?Isitokay
tomakethisassumptionthen?
Aswath Damodaran
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4.Beinternallyconsistent
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¨
Riskandcostsofequityandcapital:Stablegrowthfirmstend
to
¤
¤
¤
¨
¨
Havebetasclosertoone
Havedebtratiosclosertoindustryaverages(ormaturecompany
averages)
Countryriskpremiums(especiallyinemergingmarketsshouldevolve
overtime)
Theexcessreturnsatstablegrowthfirmsshouldapproach(or
become)zero.ROC->CostofcapitalandROE->Costof
equity
Thereinvestmentneedsanddividendpayoutratiosshould
reflectthelowergrowthandexcessreturns:
¤
¤
Stableperiodpayoutratio=1- g/ROE
Stableperiodreinvestmentrate=g/ROC
Aswath Damodaran
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