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OnewaytopumpupROE:Usemoredebt

ROE=ROC+D/E(ROC- i (1-t))where,

ROC=EBITt (1- taxrate)/BookvalueofCapitalt-1D/E=BVofDebt/BVofEquityi =InterestExpenseonDebt/BVofDebtt=Taxrateonordinaryincome

¨ NotethatBookvalueofcapital=BookValueofDebt+BookvalueofEquity- Cash.

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DecomposingROE:Brahmain1998

¨ Brahma(nowAmbev)hadanextremelyhighreturnonequity,partlybecauseitborrowedmoneyataratewellbelowitsreturnoncapital¤ ReturnonCapital=19.91%¤ Debt/EquityRatio=77%¤ After-taxCostofDebt=5.61%¤ ReturnonEquity=ROC+D/E(ROC- i(1-t))

=19.91%+0.77(19.91%- 5.61%)=30.92%

¨ Thisseemslikeaneasywaytodeliverhighergrowthinearningspershare.What(ifany)isthedownside?

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DecomposingROE:TitanWatches(India)in2000

¨ ReturnonCapital=9.54%¨ Debt/EquityRatio=191%(bookvalueterms)¨ After-taxCostofDebt=10.125%¨ ReturnonEquity=ROC+D/E(ROC- i(1-t))

=9.54%+1.91(9.54%- 10.125%)=8.42%

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II.ExpectedGrowthinNetIncomefromnon-cashassets

¨ ThelimitationoftheEPSfundamentalgrowthequationisthatitfocusesonpershareearningsandassumesthatreinvestedearningsareinvestedinprojectsearningthereturnonequity.Totheextentthatcompaniesretainmoneyincashbalances,theeffectonnetincomecanbemuted.

¨ Amoregeneralversionofexpectedgrowthinearningscanbeobtainedbysubstitutingintheequityreinvestmentintorealinvestments(netcapitalexpendituresandworkingcapital)andmodifyingthereturnonequitydefinitiontoexcludecash:¤ NetIncomefromnon-cashassets=Netincome– Interestincomefrom

cash(1- t)¤ EquityReinvestmentRate=(NetCapitalExpenditures+ChangeinWorking

Capital)(1- DebtRatio)/NetIncomefromnon-cashassets¤ Non-cashROE=NetIncomefromnon-cashassets/(BVofEquity– Cash)¤ ExpectedGrowthNetIncome =EquityReinvestmentRate*Non-cashROE

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Estimatingexpectedgrowthinnetincomefromnon-cashassets:CocaColain2010

¨ In2010,CocaColareportednetincomeof$11,809million.Ithadatotalbookvalueofequityof$25,346millionattheendof2009.

¨ CocaColahadacashbalanceof$7,021millionattheendof2009,onwhichitearnedincomeof$105millionin2010.

¨ CocaColahadcapitalexpendituresof$2,215million,depreciationof$1,443millionandreportedanincreaseinworkingcapitalof$335million.CocaCola’stotaldebtincreasedby$150millionduring2010.¤ EquityReinvestment=2215- 1443+335-150=$957million¤ Non-cashNetIncome=$11,809- $105=$11,704million¤ Non-cashbookequity=$25,346- $7021=$18,325million¤ ReinvestmentRate=$957million/$11,704million=8.18%¤ Non-cashROE=$11,704million/$18,325million=63.87%¤ Expectedgrowthrate=8.18%*63.87%=5.22%

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III.ExpectedGrowthinEBITAndFundamentals:StableROCandReinvestmentRate

¨ Whenlookingatgrowthinoperatingincome,thedefinitionsare¤ ReinvestmentRate=(NetCapitalExpenditures+ChangeinWC)/EBIT(1-t)

¤ ReturnonInvestment=ROC=EBIT(1-t)/(BVofDebt+BVofEquity-Cash)

¨ ReinvestmentRateandReturnonCapitalExpectedGrowthrateinOperatingIncome=(NetCapitalExpenditures+ChangeinWC)/EBIT(1-t)*ROC=ReinvestmentRate*ROC

¨ Proposition:Thenetcapitalexpenditureneedsofafirm,foragivengrowthrate,shouldbeinverselyproportionaltothequalityofitsinvestments.

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EstimatingGrowthinOperatingIncome,iffundamentalsstayunchanged¨ Cisco’sFundamentals

¤ ReinvestmentRate=106.81%¤ ReturnonCapital=34.07%¤ ExpectedGrowthinEBIT=(1.0681)(.3407)=36.39%

¨ Motorola’sFundamentals¤ ReinvestmentRate=52.99%¤ ReturnonCapital=12.18%¤ ExpectedGrowthinEBIT=(.5299)(.1218)=6.45%

¨ Cisco’sexpectedgrowthrateisclearlymuchhigherthanMotorola’ssustainablegrowthrate.AsapotentialinvestorinCisco,whatwouldworryyouthemostaboutthisforecast?a. ThatCisco’sreturnoncapitalmaybeoverstated(why?)b. ThatCisco’sreinvestmentcomesmostlyfromacquisitions(why?)c. ThatCiscoisgettingbiggerasafirm(why?)d. ThatCiscoisviewedasastar(why?)e. Alloftheabove

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TheMagicalNumber:ROIC(oranyaccountingreturn)anditslimits

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IV.OperatingIncomeGrowthwhenReturnonCapitalisChanging

¨ Whenthereturnoncapitalischanging,therewillbeasecondcomponenttogrowth,positiveifthereturnoncapitalisincreasingandnegativeifthereturnoncapitalisdecreasing.

¨ IfROCt isthereturnoncapitalinperiodtandROCt+1 isthereturnoncapitalinperiodt+1,theexpectedgrowthrateinoperatingincomewillbe:

ExpectedGrowthRate=ROCt+1 *Reinvestmentrate+(ROCt+1 – ROCt)/ROCt

¨ Ifthechangeisovermultipleperiods,thesecondcomponentshouldbespreadoutovereachperiod.

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Motorola’sGrowthRate

¨ Motorola’scurrentreturnoncapitalis12.18%anditsreinvestmentrateis52.99%.

¨ WeexpectMotorola’sreturnoncapitaltoriseto17.22%overthenext5years(whichishalfwaytowardstheindustryaverage)ExpectedGrowthRate=ROCNewInvestments*ReinvestmentRateCurrent+{[1+(ROCIn5years-ROCCurrent)/ROCCurrent]1/5-1}=.1722*.5299+{[1+(.1722-.1218)/.1218]1/5-1}=.1629or16.29%

¨ OnewaytothinkaboutthisistodecomposeMotorola’sexpectedgrowthinto¤Growthfromnewinvestments:.1722*5299=9.12%¤Growthfrommoreefficientlyusingexistinginvestments:16.29%-9.12%=7.17%

NotethatIamassumingthatthenewinvestmentsstartmaking17.22%immediately,whileallowingforexistingassetstoimprovereturnsgradually

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TheValueofGrowth

Expected growth = Growth from new investments + Efficiency growth= Reinv Rate * ROC + (ROCt-ROCt-1)/ROCt-1

Assume that your cost of capital is 10%. As an investor, rank these firms in the order of most value growth to least value growth.

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TopDownGrowth

GrowthIV186

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EstimatingGrowthwhenOperatingIncomeisNegativeorMarginsarechanging

¨ Allofthefundamentalgrowthequationsassumethatthefirmhasareturnonequityorreturnoncapitalitcansustaininthelongterm.

¨ Whenoperatingincomeisnegativeormarginsareexpectedtochangeovertime,weuseathreestepprocesstoestimategrowth:¤ Estimategrowthratesinrevenuesovertime

n Determinethetotalmarket(givenyourbusinessmodel)andestimatethemarketsharethatyouthinkyourcompanywillearn.

n Decreasethegrowthrateasthefirmbecomeslargern Keeptrackofabsoluterevenuestomakesurethatthegrowthisfeasible

¤ Estimateexpectedoperatingmarginseachyearn Setatargetmarginthatthefirmwillmovetowardsn Adjustthecurrentmargintowardsthetargetmargin

¤ Estimatethecapitalthatneedstobeinvestedtogeneraterevenuegrowthandexpectedmarginsn Estimateasalestocapitalratiothatyouwillusetogeneratereinvestmentneeds

eachyear.

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TeslainJuly2015:GrowthandProfitability

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Tesla:ReinvestmentandProfitability

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Expected Growth Rate

Equity Earnings Operating Income

HistoricalFundamentalsAnalysts HistoricalFundamentals

Stable ROE Changing ROE

ROE * Retention RatioROEt+1*Retention Ratio+ (ROEt+1-ROEt)/ROEt

Stable ROC

ROC * Reinvestment Rate

Changing ROC

ROCt+1*Reinvestment Rate+ (ROCt+1-ROCt)/ROCt

Negative Earnings

1. Revenue Growth2. Operating Margins3. Reinvestment NeedsEarnings per share Net Income

Stable ROE Changing ROE

ROE * Equity Reinvestment Ratio

ROEt+1*Eq. Reinv Ratio+ (ROEt+1-ROEt)/ROEt

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CLOSUREINVALUATION

TheBigEnchilada

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GettingClosureinValuation

¨ Apubliclytradedfirmpotentiallyhasaninfinitelife.Thevalueisthereforethepresentvalueofcashflowsforever.

¨ Sincewecannotestimatecashflowsforever,weestimatecashflowsfora“growthperiod” andthenestimateaterminalvalue,tocapturethevalueattheendoftheperiod:

Value = CFt

(1+r)tt=1

t=∞∑

Value = CFt

(1+r)t+

Terminal Value(1+r)N

t=1

t=N∑

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WaysofEstimatingTerminalValue

Terminal Value

Liquidation Value

Multiple Approach Stable Growth Model

Most useful when assets are separable and marketable

Easiest approach but makes the valuation a relative valuation

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

¨ Whenafirm’scashflowsgrowata“constant” rateforever,thepresentvalueofthosecashflowscanbewrittenas:Value=ExpectedCashFlowNextPeriod/(r- g)where,

r=Discountrate(CostofEquityorCostofCapital)g=Expectedgrowthrate

¨ Thestablegrowthratecannotexceedthegrowthrateoftheeconomybutitcanbesetlower.• Ifyouassumethattheeconomyiscomposedofhighgrowthandstablegrowthfirms,

thegrowthrateofthelatterwillprobablybelowerthanthegrowthrateoftheeconomy.

• Thestablegrowthratecanbenegative.Theterminalvaluewillbelowerandyouareassumingthatyourfirmwilldisappearovertime.

• Ifyouusenominalcashflows anddiscountrates,thegrowthrateshouldbenominalinthecurrencyinwhichthevaluationisdenominated.

¨ Onesimpleproxyforthenominalgrowthrateoftheeconomyistheriskfree rate.

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RiskfreeRatesandNominalGDPGrowth

¨ RiskfreeRate=ExpectedInflation+ExpectedRealInterestRate

¨ Therealinterestrateiswhatborrowersagreetoreturntolendersinrealgoods/services.

¨ NominalGDPGrowth=ExpectedInflation+ExpectedRealGrowth

¨ Therealgrowthrateintheeconomymeasurestheexpectedgrowthintheproductionofgoodsandservices.

The argument for Risk free rate = Nominal GDP growth1. 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.

Period10-YearT.Bond

Rate InflationRate RealGDPGrowthNominalGDPgrowthrate

NominalGDP- T.BondRate

1954-2015 5.93% 3.61% 3.06% 6.67% 0.74%1954-1980 5.83% 4.49% 3.50% 7.98% 2.15%1981-2008 6.88% 3.26% 3.04% 6.30% -0.58%2009-2015 2.57% 1.66% 1.47% 3.14% 0.57%

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APracticalReasonforusingtheRiskfreeRateCap– PreserveConsistency¨ You are implicitly making assumptions about nominal growth

in the economy, with your risk free rate. Thus, with a low riskfree rate, you are assuming low nominal growth in theeconomy (with low inflation and low real growth) and with ahigh risk free rate, a high nominal growth rate in theeconomy.

¨ If you make an explicit assumption about nominal growth incash flows that is at odds with your implicit growthassumption in the denominator, you are being inconsistentand 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.

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2.Don’twaittoolong…

¨ Assumethatyouarevaluingayoung,highgrowthfirmwithgreatpotential,justafteritsinitialpublicoffering.Howlongwouldyousetyourhighgrowthperiod?a. <5yearsb. 5yearsc. 10yearsd. >10years

¨ Whileanalystsroutinelyassumeverylonghighgrowthperiods(withsubstantialexcessreturnsduringtheperiods),theevidencesuggeststhattheyaremuchtoooptimistic.Mostgrowthfirmshavedifficultysustainingtheirgrowthforlongperiods,especiallywhileearningexcessreturns.

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Andtietocompetitiveadvantages

¨ Recappingakeylessonaboutgrowth,itisnotgrowthpersethatcreatesvaluebutgrowthwithexcessreturns.Forgrowthfirmstocontinuetogeneratevaluecreatinggrowth,theyhavetobeabletokeepthecompetitionatbay.

¨ Proposition1:Thestrongerandmoresustainablethecompetitiveadvantages,thelongeragrowthcompanycansustain“valuecreating”growth.

¨ Proposition2:Growthcompanieswithstrongandsustainablecompetitiveadvantagesarerare.

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3.Don’tforgetthatgrowthhastobeearned..

¨ Inthesectiononexpectedgrowth,welaidoutthefundamentalequationforgrowth:Growthrate=ReinvestmentRate*Returnoninvestedcapital

+Growthratefromimprovedefficiency¨ Instablegrowth,youcannotcountonefficiencydeliveringgrowth

andyouhavetoreinvesttodeliverthegrowthratethatyouhaveforecast.

¨ Consequently,yourreinvestmentrateinstablegrowthwillbeafunctionofyourstablegrowthrateandwhatyoubelievethefirmwillearnasareturnoncapitalinperpetuity:¤ ReinvestmentRate=Stablegrowthrate/StableperiodROC=g/ROC

¨ Yourterminalvalueequationcanthenberewrittenas:TerminalValueinyearn =

./01234 567 (569

:;<)

(>?@7?A>BCD7BE6F)

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TheBigAssumption

Returnoncapitalinperpetuity6% 8% 10% 12% 14%

Grow

thra

tefo

rever 0.0% $1,000 $1,000 $1,000 $1,000 $1,000

0.5% $965 $987 $1,000 $1,009 $1,0151.0% $926 $972 $1,000 $1,019 $1,0321.5% $882 $956 $1,000 $1,029 $1,0502.0% $833 $938 $1,000 $1,042 $1,0712.5% $778 $917 $1,000 $1,056 $1,0953.0% $714 $893 $1,000 $1,071 $1,122

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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%.

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ExcessReturnstoZero?

¨ Therearesome(McKinsey,forinstance)whoarguethatthereturnoncapitalshouldalwaysbeequaltocostofcapitalinstablegrowth.

¨ Butexcessreturnsseemtopersistforverylongtimeperiods.

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Anddon’tfallforsleightofhand…

¨ AtypicalassumptioninmanyDCFvaluations,whenitcomestostablegrowth,isthatcapitalexpendituresoffsetdepreciationandtherearenoworkingcapitalneeds.Stablegrowthfirms,wearetold,justhavetomakemaintenancecapex(replacingexistingassets)todelivergrowth.Ifyoumakethisassumption,whatexpectedgrowthratecanyouuseinyourterminalvaluecomputation?

¨ Whatifthestablegrowthrate=inflationrate?Isitokaytomakethisassumptionthen?

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4.Beinternallyconsistent

¨ Riskandcostsofequityandcapital:Stablegrowthfirmstendto¤ Havebetasclosertoone¤ Havedebtratiosclosertoindustryaverages(ormaturecompany

averages)¤ Countryriskpremiums(especiallyinemergingmarketsshouldevolve

overtime)¨ Theexcessreturnsatstablegrowthfirmsshouldapproach(or

become)zero.ROC->CostofcapitalandROE->Costofequity

¨ Thereinvestmentneedsanddividendpayoutratiosshouldreflectthelowergrowthandexcessreturns:¤ Stableperiodpayoutratio=1- g/ROE¤ Stableperiodreinvestmentrate=g/ROC

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