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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 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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BEYONDINPUTS:CHOOSINGANDUSINGTHERIGHTMODEL

Choosingtherightmodel

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SummarizingtheInputs

¨ Insummary,atthisstageintheprocess,weshouldhaveanestimateofthe¤ thecurrentcashflowsontheinvestment,eithertoequityinvestors(dividendsorfreecashflowstoequity)ortothefirm(cashflowtothefirm)

¤ thecurrentcostofequityand/orcapitalontheinvestment¤ theexpectedgrowthrateinearnings,baseduponhistoricalgrowth,analystsforecastsand/orfundamentals

¨ Thenextstepintheprocessisdeciding¤ whichcashflowtodiscount,whichshouldindicate¤ whichdiscountrateneedstobeestimatedand¤ whatpatternwewillassumegrowthtofollow

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WhichcashflowshouldIdiscount?

¨ UseEquityValuation(a)forfirmswhichhavestableleverage,whetherhighornot,and(b)ifequity(stock)isbeingvalued

¨ UseFirmValuation(a)forfirmswhichhaveleveragewhichistoohighortoolow,andexpecttochangetheleverageovertime,becausedebtpaymentsandissuesdonothavetobefactoredinthecashflowsandthediscountrate(costofcapital)doesnotchangedramaticallyovertime.(b)forfirmsforwhichyouhavepartialinformationonleverage(eg:interestexpensesaremissing..)(c)inallothercases,whereyouaremoreinterestedinvaluingthefirmthantheequity.(ValueConsulting?)

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Givencashflowstoequity,shouldIdiscountdividendsorFCFE?

¨ UsetheDividendDiscountModel(a)Forfirmswhichpaydividends(andrepurchasestock)whichareclosetotheFreeCashFlowtoEquity(overaextendedperiod)(b)ForfirmswhereFCFEaredifficulttoestimate(Example:BanksandFinancialServicecompanies)

¨ UsetheFCFEModel(a)ForfirmswhichpaydividendswhicharesignificantlyhigherorlowerthantheFreeCashFlowtoEquity.(Whatissignificant?...Asaruleofthumb,ifdividendsarelessthan80%ofFCFEordividendsaregreaterthan110%ofFCFEovera5-yearperiod,usetheFCFEmodel)(b)Forfirmswheredividendsarenotavailable(Example:PrivateCompanies,IPOs)

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WhatdiscountrateshouldIuse?

¨ CostofEquityversusCostofCapital¤ Ifdiscountingcashflowstoequity ->CostofEquity¤ Ifdiscountingcashflowstothefirm ->CostofCapital

¨ Whatcurrencyshouldthediscountrate(riskfreerate)bein?¤ Matchthecurrencyinwhichyouestimatetheriskfreeratetothecurrencyofyourcashflows

¨ ShouldIuserealornominalcashflows?¤ Ifdiscountingrealcashflows ->realcostofcapital¤ Ifnominalcashflows ->nominalcostofcapital¤ Ifinflationislow(<10%),stickwithnominalcashflowssincetaxesarebaseduponnominalincome

¤ Ifinflationishigh(>10%)switchtorealcashflows

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WhichGrowthPatternShouldIuse?

¨ Ifyourfirmis¤ largeandgrowingatarateclosetoorlessthangrowthrateoftheeconomy,or¤ constrainedbyregulationfromgrowingatratefasterthantheeconomy¤ hasthecharacteristicsofastablefirm(averagerisk&reinvestmentrates)

UseaStableGrowthModel¨ Ifyourfirm

¤ islarge&growingatamoderaterate(≤Overallgrowthrate+10%)or¤ hasasingleproduct&barrierstoentrywithafinitelife(e.g.patents)

Usea2-StageGrowthModel¨ Ifyourfirm

¤ issmallandgrowingataveryhighrate(>Overallgrowthrate+10%)or¤ hassignificantbarrierstoentryintothebusiness¤ hasfirmcharacteristicsthatareverydifferentfromthenorm

Usea3-Stageorn-stageModel

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TheBuildingBlocksofValuation

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Choose aCash Flow Dividends

Expected Dividends toStockholders

Cashflows to Equity

Net Income- (1- δ) (Capital Exp. - Deprec’n)

- (1- δ) Change in Work. Capital= Free Cash flow to Equity (FCFE)[δ = Debt Ratio]

Cashflows to Firm

EBIT (1- tax rate)- (Capital Exp. - Deprec’n)- Change in Work. Capital= Free Cash flow to Firm (FCFF)

& A Discount Rate Cost of Equity• Basis: The riskier the investment, the greater is the cost of equity.• Models:

CAPM: Riskfree Rate + Beta (Risk Premium)APM: Riskfree Rate + Σ Betaj (Risk Premiumj): n factors

Cost of CapitalWACC = ke ( E/ (D+E))

+ kd ( D/(D+E))

kd = Current Borrowing Rate (1-t)E,D: Mkt Val of Equity and Debt

& a growth pattern

t

gStable Growth

gTwo-Stage Growth

|High Growth Stable

gThree-Stage Growth

|High Growth StableTransition

TYINGUPLOOSEENDS

Thetroublestartsafteryoutellmeyouaredone..

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Butwhatcomesnext?

Value of Operating Assets

+ Cash and Marketable Securities

+ Value of Cross Holdings

+ Value of Other Assets

Value of Firm

- Value of Debt

= Value of Equity

- Value of Equity Options

= Value of Common Stock

/ Number of shares

= Value per share

Operating versus Non-opeating cashShould cash be discounted for earning a low return?

How do you value cross holdings in other companies?What if the cross holdings are in private businesses?

What about other valuable assets?How do you consider under utlilized assets?

What should be counted in debt?Should you subtract book or market value of debt?What about other obligations (pension fund and health care?What about contingent liabilities?What about minority interests?

What equity options should be valued here (vested versus non-vested)?How do you value equity options?

Should you divide by primary or diluted shares?

Should you discount this value for opacity or complexity?How about a premium for synergy?What about a premium for intangibles (brand name)?

Should there be a premium/discount for control?Should there be a discount for distress

Should there be a discount for illiquidity/ marketability?Should there be a discount for minority interests?

Since this is a discounted cashflow valuation, should there be a real option premium?

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1.TheValueofCash

¨ Thesimplestandmostdirectwayofdealingwithcashandmarketablesecuritiesistokeepitoutofthevaluation- thecashflowsshouldbebeforeinterestincomefromcashandsecurities,andthediscountrateshouldnotbecontaminatedbytheinclusionofcash.(Usebetasoftheoperatingassetsalonetoestimatethecostofequity).

¨ Oncetheoperatingassetshavebeenvalued,youshouldaddbackthevalueofcashandmarketablesecurities.

¨ Inmanyequityvaluations,theinterestincomefromcashisincludedinthecashflows.Thediscountratehastobeadjustedthenforthepresenceofcash.(Thebetausedwillbeweighteddownbythecashholdings).Unlesscashremainsafixedpercentageofoverallvalueovertime,thesevaluationswilltendtobreakdown.

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AnExerciseinCashValuation

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CompanyA CompanyB CompanyC

EnterpriseValue $1,000.0 $1,000.0 $1,000.0

Cash $100.0 $100.0 $100.0

Returnoninvestedcapital 10% 5% 22%

Costofcapital 10% 10% 12%

Tradesin US US Argentina

In which of these companies is cash most likely to bea) A Neutral Asset (worth $100 million)b) A Wasting Asset (worth less than $100 million)c) A Potential Value Creator (worth >$100 million)

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Shouldyoueverdiscountcashforitslowreturns?

¨ Therearesomeanalystswhoarguethatcompanieswithalotofcashontheirbalancesheetsshouldbepenalizedbyhavingtheexcesscashdiscountedtoreflectthefactthatitearnsalowreturn.¤ Excesscashisusuallydefinedasholdingcashthatisgreaterthanwhatthe

firmneedsforoperations.¤ Alowreturnisdefinedasareturnlowerthanwhatthefirmearnsonits

non-cashinvestments.¨ Thisisthewrongreasonfordiscountingcash.Ifthecashisinvested

inrisklesssecurities,itshouldearnalowrateofreturn.Aslongasthereturnishighenough,giventherisklessnatureoftheinvestment,cashdoesnotdestroyvalue.

¨ Thereisarightreason,though,thatmayapplytosomecompanies…Managerscandostupidthingswithcash(overpricedacquisitions,pie-in-the-skyprojects….)andyouhavetodiscountforthispossibility.

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Cash:DiscountorPremium?

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ADetour:ClosedEndMutualFunds

¨ Assumethatyouhaveaclosed-endfundthatinvestsin‘averagerisk” stocks.Assumealsothatyouexpectthemarket(averageriskinvestments)tomake11.5%annuallyoverthelongterm.Iftheclosedendfundunderperformsthemarketby0.50%,estimatethediscountonthefund.

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TheMostFamousClosedEndFundinHistory?

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1.84

2.272.42

1.90

2.62

1.91

1.33

1.62

1.87

1.57

1.82

1.611.52 1.52

1.80

1.07

1.54

1.37

1.211.34 1.29

1.51

1.30

0.00

0.50

1.00

1.50

2.00

2.50

3.00

$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

$400,000

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

BerkshireHathaway:TheFadingBuffettPremium

P/BVRatio MarketCap BVofEquity

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2.DealingwithHoldingsinOtherfirms

¨ Holdingsinotherfirmscanbecategorizedinto¤ Minoritypassiveholdings,inwhichcaseonlythedividendfromtheholdingsisshowninthebalancesheet

¤ Minorityactiveholdings,inwhichcasetheshareofequityincomeisshownintheincomestatements

¤ Majorityactiveholdings,inwhichcasethefinancialstatementsareconsolidated.

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