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UnitedTechnologies:DCFpartsvaluationCostofcapital,bybusiness

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Division Unlevered Beta

Debt/Equity Ratio

Levered beta

Cost of equity

After-tax cost of debt

Debt to Capital

Cost of capital

Carrier 0.83 30.44% 0.97 9.32% 2.95% 23.33% 7.84% Pratt & Whitney 0.81 30.44% 0.95 9.17% 2.95% 23.33% 7.72% Otis 1.19 30.44% 1.39 12.07% 2.95% 23.33% 9.94% UTC Fire & Security 0.65 30.44% 0.76 7.95% 2.95% 23.33% 6.78% Hamilton Sundstrand 1.04 30.44% 1.22 10.93% 2.95% 23.33% 9.06% Sikorsky 1.17 30.44% 1.37 11.92% 2.95% 23.33% 9.82%

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UnitedTechnologies:DCFvaluationFundamentals,bybusiness

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Division Total Assets

Capital Invested Cap Ex

Allocated Reinvestment

Operating income after taxes

Return on capital

Reinvestment Rate

Carrier $10,810 $6,014 $191 $353 $816 13.57% 43.28% Pratt & Whitney $9,650 $5,369 $412 $762 $1,316 24.51% 57.90% Otis $7,731 $4,301 $150 $277 $1,536 35.71% 18.06% UTC Fire & Security $10,022 $5,575 $95 $176 $336 6.03% 52.27% Hamilton Sundstrand $8,648 $4,811 $141 $261 $681 14.16% 38.26% Sikorsky $3,985 $2,217 $165 $305 $296 13.37% 102.95%

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UnitedTechnologies,DCFvaluationGrowthChoices

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Division Cost of capital

Return on capital

Reinvestment Rate

Expected growth

Length of growth period

Stable growth rate

Stable ROC

Carrier 7.84% 13.57% 43.28% 5.87% 5 3% 7.84% Pratt & Whitney 7.72% 24.51% 57.90% 14.19% 5 3% 12.00% Otis 9.94% 35.71% 18.06% 6.45% 5 3% 14.00% UTC Fire & Security 6.78% 6.03% 52.27% 3.15% 0 3% 6.78% Hamilton Sundstrand 9.06% 14.16% 38.26% 5.42% 5 3% 9.06% Sikorsky 9.82% 13.37% 102.95% 13.76% 5 3% 9.82%

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UnitedTechnologies,DCFvaluationValuesoftheparts

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Business Cost of capital

PV of FCFF

PV of Terminal Value

Value of Operating Assets

Carrier 7.84% $2,190 $9,498 $11,688 Pratt & Whitney 7.72% $3,310 $27,989 $31,299 Otis 9.94% $5,717 $14,798 $20,515 UTC Fire & Security 6.78% $0 $4,953 $4,953 Hamilton Sundstrand 9.06% $1,902 $6,343 $8,245 Sikorsky 9.82% -$49 $3,598 $3,550 Sum $80,250

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UnitedTechnologies,DCFvaluationSumoftheParts

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Valueoftheparts =$80,250Valueofcorporateexpenses

=$4,587

Valueofoperatingassets(sumofpartsDCF)=$75,663Valueofoperatingassets(sumofpartsRV) =$74,230Valueofoperatingassets(companyDCF) =$71,410Enterprisevalue(basedonmarketprices) =$52,261

=Corporate ExpensesCurrent (1− t)(1+ g)

(Cost of capitalCompany − g)=408(1−.38)(1.03)(.0868−.03)

PRIVATECOMPANYVALUATION

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ProcessofValuingPrivateCompanies

¨ Theprocessofvaluingprivatecompaniesisnotdifferentfromtheprocessofvaluingpubliccompanies.Youestimatecashflows,attachadiscountratebasedupontheriskinessofthecashflowsandcomputeapresentvalue.Aswithpubliccompanies,youcaneithervalue¤ Theentirebusiness,bydiscountingcashflowstothefirmatthecostof

capital.¤ Theequityinthebusiness,bydiscountingcashflowstoequityatthe

costofequity.¨ Whenvaluingprivatecompanies,youfacetwostandard

problems:¤ Thereisnotmarketvalueforeitherdebtorequity¤ Thefinancialstatementsforprivatefirmsarelikelytogobackfewer

years,havelessdetailandhavemoreholesinthem.

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1.NoMarketValue?

¨ Marketvaluesasinputs:Sinceneitherthedebtnorequityofaprivatebusinessistraded,anyinputsthatrequirethemcannotbeestimated.1. Debtratiosforgoingfromunleveredtoleveredbetasandfor

computingcostofcapital.2. Marketpricestocomputethevalueofoptionsandwarrants

grantedtoemployees.¨ Marketvalueasoutput:Whenvaluingpubliclytradedfirms,themarketvalueoperatesasameasureofreasonableness.Inprivatecompanyvaluation,thevaluestandsalone.

¨ Marketpricebasedriskmeasures,suchasbetaandbondratings,willnotbeavailableforprivatebusinesses.

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2.CashFlowEstimationIssues

¨ Shorterhistory:Privatefirmsoftenhavebeenaroundformuchshortertimeperiodsthanmostpubliclytradedfirms.Thereisthereforelesshistoricalinformationavailableonthem.

¨ DifferentAccountingStandards:Theaccountingstatementsforprivatefirmsareoftenbasedupondifferentaccountingstandardsthanpublicfirms,whichoperateundermuchtighterconstraintsonwhattoreportandwhentoreport.

¨ Interminglingofpersonalandbusinessexpenses:Inthecaseofprivatefirms,somepersonalexpensesmaybereportedasbusinessexpenses.

¨ Separating“Salaries” from“Dividends”:Itisdifficulttotellwheresalariesendanddividendsbegininaprivatefirm,sincetheybothendupwiththeowner.

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PrivateCompanyValuation:Motivematters

¨ Youcanvalueaprivatecompanyfor¤ ‘Show’ valuations

n Curiosity:Howmuchismybusinessreallyworth?n Legalpurposes:Estatetaxanddivorcecourt

¤ Transactionvaluationsn Saleorprospectivesaletoanotherindividualorprivateentity.n Saleofonepartner’sinteresttoanothern Saletoapubliclytradedfirm

¤ Aspreludetosettingtheofferingpriceinaninitialpublicoffering¨ Youcanvalueadivisionordivisionsofapubliclytradedfirm

¤ Aspreludetoaspinoff¤ Forsaletoanotherentity¤ Todoasum-of-the-partsvaluationtodeterminewhetherafirmwillbe

worthmorebrokenuporifitisbeingefficientlyrun.

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Privatecompanyvaluations:Fourbroadscenarios

¨ Privatetoprivatetransactions:Youcanvalueaprivatebusinessforsalebyoneindividualtoanother.

¨ Privatetopublictransactions:Youcanvalueaprivatefirmforsaletoapubliclytradedfirm.

¨ PrivatetoIPO:Youcanvalueaprivatefirmforaninitialpublicoffering.

¨ PrivatetoVCtoPublic:Youcanvalueaprivatefirmthatisexpectedtoraiseventurecapitalalongthewayonitspathtogoingpublic.

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I.PrivatetoPrivatetransaction

¨ Inprivatetoprivatetransactions,aprivatebusinessissoldbyoneindividualtoanother.Therearethreekeyissuesthatweneedtoconfrontinsuchtransactions:¨ Neitherthebuyernorthesellerisdiversified.Consequently,risk

andreturnmodelsthatfocusonjusttheriskthatcannotbediversifiedawaywillseriouslyunderestimatethediscountrates.

¨ Theinvestmentisilliquid.Consequently,thebuyerofthebusinesswillhavetofactorinan“illiquiditydiscount” toestimatethevalueofthebusiness.

¨ Keypersonvalue:Theremaybeasignificantpersonalcomponenttothevalue.Inotherwords,therevenuesandoperatingprofitofthebusinessreflectnotjustthepotentialofthebusinessbutthepresenceofthecurrentowner.

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Anexample:Valuingarestaurant

¨ AssumethatyouhavebeenaskedtovalueaupscaleFrenchrestaurantforsalebytheowner(whoalsohappenstobethechef).Boththerestaurantandthechefarewellregarded,andbusinesshasbeengoodforthelast3years.

¨ Thepotentialbuyerisaformerinvestmentbanker,whotiredoftheratrace,hasdecidetocashoutallofhissavingsandusetheentireamounttoinvestintherestaurant.

¨ Youhaveaccesstothefinancialstatementsforthelast3yearsfortherestaurant.Inthemostrecentyear,therestaurantreported$1.2millioninrevenuesand$400,000inpre-taxoperatingprofit.Whilethefirmhasnoconventionaldebtoutstanding,ithasaleasecommitmentof$120,000eachyearforthenext12years.

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Pastincomestatements…

3 years ago

2 years ago Last year

Revenues $800 $1,100 $1,200 Operating at full capacity- Operating lease expense $120 $120 $120 (12 years left on the lease)

- Wages $180 $200 $200(Owner/chef does not draw salary)

- Material $200 $275 $300 (25% of revenues)- Other operating expenses $120 $165 $180 (15% of revenues)Operating income $180 $340 $400- Taxes $72 $136 $160 (40% tax rate)Net Income $108 $204 $240

All numbers are in thousands

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Step1:Estimatingdiscountrates

¨ Conventionalriskandreturnmodelsinfinancearebuiltonthepresumptionthatthemarginalinvestorsinthecompanyarediversifiedandthattheythereforecareonlyabouttheriskthatcannotbediversified.Thatriskismeasuredwithabetaorbetas,usuallyestimatedbylookingatpastpricesorreturns.

¨ Inthisvaluation,bothassumptionsarelikelytobeviolated:¤ Asaprivatebusiness,thisrestauranthasnomarketpricesorreturnstouseinestimation.

¤ Thebuyerisnotdiversified.Infact,hewillhavehisentirewealthtiedupintherestaurantafterthepurchase.

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Nomarketprice,noproblem…Usebottom-upbetastogettheunleveredbeta

¨ Theaverageunleveredbetaacross75publiclytradedrestaurantsintheUSis0.86.

¨ Acaveat:Mostofthepubliclytradedrestaurantsonthislistarefast-foodchains(McDonald’s,BurgerKing)ormassrestaurants(Applebee’s,TGIF…)Thereisanargumenttobemadethatthebetaforanupscalerestaurantismorelikelytobereflecthigh-endspecialtyretailersthanitisrestaurants.Theunleveredbetafor45high-endretailersis1.18.

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80 unitsof firm specificrisk

20 units of market risk

Private owner of businesswith 100% of your weatlthinvested in the business

Publicly traded companywith investors who are diversified

Is exposedto all the riskin the firm

Demands acost of equitythat reflects thisrisk

Eliminates firm-specific risk in portfolio

Demands acost of equitythat reflects only market risk

Market Beta measures justmarket risk

Total Beta measures all risk= Market Beta/ (Portion of the total risk that is market risk)

Private Owner versus Publicly Traded Company Perceptions of Risk in an Investment

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Estimatingatotalbeta

¨ Togetfromthemarketbetatothetotalbeta,weneedameasureofhowmuchoftheriskinthefirmcomesfromthemarketandhowmuchisfirm-specific.

¨ Lookingattheregressionsofpubliclytradedfirmsthatyieldthebottom-upbetashouldprovideananswer.¤ TheaverageR-squaredacrossthehigh-endretailerregressionsis25%.¤ Sincebetasarebasedonstandarddeviations(ratherthanvariances),

wewilltakethecorrelationcoefficient(thesquarerootoftheR-squared)asourmeasureoftheproportionoftheriskthatismarketrisk.

¨ TotalUnleveredBeta=MarketBeta/Correlationwiththemarket=1.18/0.5=2.36

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Thefinalstepinthebetacomputation:EstimateaDebttoequityratioandcostofequity

¨ Withpubliclytradedfirms,were-leverthebetausingthemarketD/Eratioforthefirm.Withprivatefirms,thisoptionisnotfeasible.Wehavetwoalternatives:¤ Assumethatthedebttoequityratioforthefirmissimilartotheaverage

marketdebttoequityratioforpubliclytradedfirmsinthesector.¤ Useyourestimatesofthevalueofdebtandequityastheweightsinthe

computation.(Therewillbeacircularreasoningproblem:youneedthecostofcapitaltogetthevaluesandthevaluestogetthecostofcapital.)

¨ Wewillassumethatthisprivatelyownedrestaurantwillhaveadebttoequityratio(14.33%)similartotheaveragepubliclytradedrestaurant(eventhoughweusedretailerstotheunleveredbeta).¤ Leveredbeta=2.36(1+(1-.4)(.1433))=2.56¤ Costofequity=4.25%+2.56(4%)=14.50%(TBondratewas4.25%atthetime;4%istheequityriskpremium)

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Estimatingacostofdebtandcapital

¨ Whilethefirmdoesnothavearatingoranyrecentbankloanstouseasreference,itdoeshaveareportedoperatingincomeandleaseexpenses(treatedasinterestexpenses)CoverageRatio=OperatingIncome/Interest(Lease)Expense

=400,000/120,000=3.33Ratingbasedoncoverageratio=BB+ Defaultspread=3.25%After-taxCostofdebt=(Riskfree rate+Defaultspread)(1– taxrate)

=(4.25%+3.25%)(1- .40)=4.50%¨ Tocomputethecostofcapital,wewillusethesameindustry

averagedebtratiothatweusedtoleverthebetas.¤Costofcapital=14.50%(100/114.33)+4.50%(14.33/114.33)=13.25%¤(Thedebttoequityratiois14.33%;thecostofcapitalisbasedonthedebttocapitalratio)

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Step2:Cleanupthefinancialstatements

Stated AdjustedRevenues $1,200 $1,200- Operating lease expenses $120 Leases are financial expenses- Wages $200 $350 ! Hire a chef for $150,000/year- Material $300 $300- Other operating expenses $180 $180Operating income $400 $370- Interest expnses $0 $69.62 7.5% of $928.23 (see below)Taxable income $400 $300.38- Taxes $160 $120.15Net Income $240 $180.23

Debt 0 $928.23 ! PV of $120 million for 12 years @7.5%

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Step3:Assesstheimpactofthe“key” person

¨ Partofthedrawoftherestaurantcomesfromthecurrentchef.Itispossible(andprobable)thatifhesellsandmoveson,therewillbeadropoffinrevenues.Ifyouarebuyingtherestaurant,youshouldconsiderthisdropoffwhenvaluingtherestaurant.Thus,if20%ofthepatronsaredrawntotherestaurantbecauseofthechef’sreputation,theexpectedoperatingincomewillbelowerifthechefleaves.¤ Adjustedoperatingincome(existingchef)=$370,000¤ Operatingincome(adjustedforchefdeparture)=$296,000

¨ Astheowner/chefoftherestaurant,whatmightyoubeabletodotomitigatethislossinvalue?

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Step4:Don’tforgetvaluationfundamentals

¨ Tocompletethevaluation,youneedtoassumeanexpectedgrowthrate.Aswithanybusiness,assumptionsaboutgrowthhavetobeconsistentwithreinvestmentassumptions.Inthelongterm,Reinvestmentrate=Expectedgrowthrate/Returnoncapital

¨ Inthiscase,wewillassumea2%growthrateinperpetuityanda20%returnoncapital.

Reinvestmentrate=g/ROC=2%/20%=10%¨ Eveniftherestaurantdoesnotgrowinsize,thisreinvestment

iswhatyouneedtomaketokeeptherestaurantbothlookinggood(remodeling)andworkingwell(newovensandappliances).

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Step5:Completethevaluation

¨ Inputstovaluation¤ AdjustedEBIT=$296,000¤ Taxrate=40%¤ Costofcapital=13.25%¤ Expectedgrowthrate=2%¤ Reinvestmentrate(RIR)=10%

¨ ValuationValueoftherestaurant=ExpectedFCFFnextyear/(Costofcapital–g)=ExpectedEBITnextyear(1- taxrate)(1- RIR)/(Costofcapital–g)

=296,000(1.02)(1-.4)(1-.10)/(.1325- .02)=$1.449million

Valueofequityinrestaurant=$1.449million- $0.928million(PVofleases)b=$0.521million

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Step6:Considertheeffectofilliquidity

¨ Inprivatecompanyvaluation,illiquidityisaconstanttheme.Allthetalk,though,seemstoleadtoaruleofthumb.Theilliquiditydiscountforaprivatefirmisbetween20-30%anddoesnotvaryacrossprivatefirms.

¨ Butilliquidityshouldvaryacross:¤ Companies:Healthierandlargercompanies,withmoreliquidassets,shouldhavesmallerdiscountsthanmoney-losingsmallerbusinesseswithmoreilliquidassets.

¤ Time:Liquidityisworthmorewhentheeconomyisdoingbadlyandcreditistoughtocomebythanwhenmarketsarebooming.

¤ Buyers:Liquidityisworthmoretobuyerswhohaveshortertimehorizonsandgreatercashneedsthanforlongerterminvestorswhodon’tneedthecashandarewillingtoholdtheinvestment.

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TheStandardApproach:Illiquiditydiscountbasedonilliquidpubliclytradedassets

¨ Restrictedstock:ThesearestockissuedbypubliclytradedcompaniestothemarketthatbypasstheSECregistrationprocessbutthestockcannotbetradedforoneyearaftertheissue.

¨ Pre-IPOtransactions:Thesearetransactionspriortoinitialpublicofferingswhereequityinvestorsintheprivatefirmbuy(sell)eachother’sstakes.

¨ Inbothcases,thediscountisestimatedthebethedifferencebetweenthemarketpriceoftheliquidassetandtheobservedtransactionpriceoftheilliquidasset.¤ DiscountRestrictedstock=Stockprice– Priceonrestrictedstockoffering

¤ DiscountIPO =IPOofferingprice– Priceonpre-IPOtransaction

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TheRestrictedStockDiscount

¨ Aggregatediscountstudies¤ Maherexaminedrestrictedstockpurchasesmadebyfourmutualfundsinthe

period1969-73andconcludedthattheytradedanaveragediscountof35.43%onpubliclytradedstockinthesamecompanies.

¤ Moroney reportedameandiscountof35%foracquisitionsof146restrictedstockissuesby10investmentcompanies,usingdatafrom1970.

¤ Inastudyofrestrictedstockofferingsfromthe1980s,Silber(1991)findsthatthemediandiscountforrestrictedstockis33.75%.

¨ Silberrelatedthesizeofthediscounttocharacteristicsoftheoffering:LN(RPRS)=4.33+0.036LN(REV)- 0.142LN(RBRT)+0.174DERN+0.332DCUST¤ RPRS=Relativepriceofrestrictedstock(topubliclytradedstock)¤ REV=Revenuesoftheprivatefirm(inmillionsofdollars)¤ RBRT=RestrictedBlockrelativetoTotalCommonStockin%¤ DERN=1ifearningsarepositive;0ifearningsarenegative;¤ DCUST=1ifthereisacustomerrelationshipwiththeinvestor;0otherwise;

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CrosssectionaldifferencesinIlliquidity:ExtendingtheSilberregression

Figure 24.1: Illiquidity Discounts: Base Discount of 25% for profitable firm with $ 10 million in revenues

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

5 10 15 20 25 30 35 40 45 50 100 200 300 400 500 1000Revenues

Dis

coun

t as %

of V

alue

Profitable firm Unprofitable firm

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TheIPOdiscount:Pricingonpre-IPOtransactions(in5monthspriortoIPO)

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The“sampling” problem

¨ WithbothrestrictedstockandtheIPOstudies,thereisasignificantsamplingbiasproblem.¤ Thecompaniesthatmakerestrictedstockofferingsarelikelytobe

small,troubledfirmsthathaverunoutofconventionalfinancingoptions.

¤ ThetypesofIPOswhereequityinvestorsselltheirstakeinthefivemonthspriortotheIPOatahugediscountarelikelytobeIPOsthathavesignificantpricinguncertaintyassociatedwiththem.

¨ Withrestrictedstock,themagnitudeofthesamplingbiaswasestimatedbycomparingthediscountonallprivateplacementstothediscountonrestrictedstockofferings.Onestudyconcludedthatthe“illiquidity” aloneaccountedforadiscountoflessthan10%(leavingthebalanceof20-25%tobeexplainedbysamplingproblems).

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Analternativeapproach:Usethewholesample¨ Alltradedassetsareilliquid.Thebidaskspread,measuringthe

differencebetweenthepriceatwhichyoucanbuyandselltheassetatthesamepointintimeistheilliquiditymeasure.

¨ Wecanregressthebid-askspread(asapercentoftheprice)againstvariablesthatcanbemeasuredforaprivatefirm(suchasrevenues,cashflowgeneratingcapacity,typeofassets,varianceinoperatingincome)andarealsoavailableforpubliclytradedfirms.

¨ Usingdatafromtheendof2000,forinstance,weregressedthebid-askspreadagainstannualrevenues,adummyvariableforpositiveearnings(DERN:0ifnegativeand1ifpositive),cashasapercentoffirmvalueandtradingvolume.Spread=0.145– 0.0022ln(AnnualRevenues)-0.015(DERN)– 0.016(Cash/FirmValue)– 0.11($Monthlytradingvolume/FirmValue)Youcouldpluginthevaluesforaprivatefirmintothisregression(withzerotradingvolume)andestimatethespreadforthefirm.

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EstimatingtheilliquiditydiscountfortherestaurantApproach used Estimated discount Value of restaurantBludgeon (Fixed discount) 25% $0.521 (1- .25) = $0.391

millionRefined Bludgeon (Fixed discount with adjustment for revenue size/ profitability)

28.75% (Silber adjustment for small revenues and positive profits to a base discount of 25%)

$0.521 (1-.2875) = $0.371 million

Bid-ask spread regression = 0.145 – 0.0022 ln (1.2) -0.015 (1) –0.016 (.05) – 0.11 (0)= 12.88%

$0.521 (1-.1288) = $0.454 million

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II.Privatecompanysoldtopubliclytradedcompany

¨ Thekeydifferencebetweenthisscenarioandthepreviousscenarioisthatthesellerofthebusinessisnotdiversifiedbutthebuyeris(oratleasttheinvestorsinthebuyerare).Consequently,theycanlookatthesamefirmandseeverydifferentamountsofriskinthebusinesswiththesellerseeingmoreriskthanthebuyer.

¨ Thecashflowsmayalsobeaffectedbythefactthatthetaxratesforpubliclytradedcompaniescandivergefromthoseofprivateowners.

¨ Finally,thereshouldbenoilliquiditydiscounttoapublicbuyer,sinceinvestorsinthebuyercanselltheirholdingsinamarket.

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Revisitingthecostofequityandcapital:RestaurantValuation

Private Public

Unlevred beta 2.36 1.18

Debt to equity ratio 14.33% 14.33%

Tax rate 40% 40%

Pre-tax cost of debt 7.50% 7.50%

Levered beta 2.56 1.28

Riskfree rate 4.25% 4.25%

Equity risk premium 4% 4%

Cost of equity 14.5% 9.38%

After-tax cost of debt 4.50% 4.50%

Cost of capital 13.25% 8.76%

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Revaluingtherestauranttoa“public”buyer

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So,whatpriceshouldyouaskfor?

¨ Assumethatyourepresentthechef/owneroftherestaurantandthatyouwereaskingfora“reasonable” pricefortherestaurant.Whatwouldyouaskfor?

a. $454,000b. $1.484millionc. Somenumberinthemiddle¨ Ifitis“somenumberinthemiddle”,whatwilldetermine

whatyouwillultimatelygetforyourbusiness?

¨ Howwouldyoualtertheanalysis,ifyourbestpotentialbidderisaprivateequityorVCfundratherthanapubliclytradedfirm?

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