Adjusted Present Value Astudyontheproperties,functioningandapplicabilityof theadjustedpresentvaluecompanymodel

Author: SebastianOotjersBSc Studentnumber: 0041823 Master: IndustrialEngineering&Management Track: FinancialEngineering&Management Date: September26,2007 Supervisors(UniversityofTwente) ir.H.Kroon prof.dr.J.Bilderbeek Supervisors(KPMG) dr.J.Weimer drs.F.Siblesz Educationalinstitution: UniversityofTwente Department: FMBE Company: KPMGCorporateFinance

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Foreword

Thisresearchreportistheresultoffivemonthsofresearchintotheadjustedpresentvalue companyvaluationmodel.Thismasterthesisservesasafinalassignmenttocompletethe MasterIndustrialEngineering&Management(FinancialEngineering&ManagementTrack). TheresearchprojectwasperformedatKPMGCorporateFinance,locatedinAmstelveen, fromMay21,2007upuntilSeptember28,2007,undersupervisionofJeroenWeimer (PartnerKPMGCorporateFinance),FrankSiblesz(ManagerKPMGCorporateFinance),Jan Bilderbeek(UniversityofTwente)andHenkKroon(UniversityofTwente). Thesubjectofthismasterassignmentwaschosenafterdeliberationwiththesupervisorsat KPMGCorporateFinanceontheresearchneedsofKPMGCorporateFinance. Itisimplicitlyassumedinthisresearchreportthatthereaderhasbeeneducatedorisactive inthefieldofcorporatefinance.Itisalsoassumedthatthereaderisawareofexistenceof (company)valuationaspartofthecorporatefinanceworkingfield. Anycomments,questionsorremarksthatcomeforthfromreadingthisresearchreportcanbe directedtomethroughthecontactinformationgivenbelow. Theonlythingremainingistowishthereaderapleasanttimereadingthisreportandtohope thatthisreportprovidesthereaderwithaclearinsightintheadjustedpresentvaluemodel. SebastianOotjers StudentIndustrialEngineering&Management [email protected]

MasterThesisSebastianOotjers 3 s0041823 IEMFEM

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Executive summary

Theresearchobjectiveofthisresearchprojectistoformulateatheoryonthedifferences betweentheenterpriseDCFmodelandtheAPVmodel,andtheeffectsofthesedifferences onthevaluationoutcome. ThereareanumberofdifferencesbetweentheenterpriseDCFmodelandtheAPVmodel. Thesedifferencesareasshowninthetablebelow. Enterprise DCF model APV model

Cashflow FCFF FCFF

Discountrate WACC KuorKd

Costofequity Levered Unlevered

Costofdebt Creditratingbased Creditratingbased

Constantleverageratio Capitalstructure Constantleverageratio orfixeddebt Notexplicitlytakeninto Separateterminthe Probabilityofdefault account valuation Notexplicitlytakeninto Separateterminthe Costsoffinancialdistress account valuation TherearefivescenariosinwhichtheAPVmodelcanbeusedtodeterminethecorrectvalue ofthecompany,ifthecapitalstructureand/ortheprobabilityofdefaultassumptionofthe enterpriseDCFmodelareviolated.Thevalidateddifferencesinvaluationoutcomesare showninthetablebelow. Scenario Model Compare to Effect on valuation outcome Constantleverageratio& DCForAPV(ME) n.a. V(APV)=V(DCF) no significantPoD

Constantleverageratio& APV(ME) DCF V(APV)<V(DCF) significantPoD V(APV)>V(DCF)or Fixedamountofdebt APV(MM) DCF V(APV)=V(DCF)or V(APV)<V(DCF) V(APV)>V(DCF)or Finitelife&debtknown APV(general) DCF V(APV)=V(DCF)or V(APV)<V(DCF) Combinationofscenario4and Debtknownuptot,then APV(general)+ DCF 1oracombinationofscenario4 constantleverageratio APV(ME) and2 TheAPVmodelistheoreticallymorecorrectandalsogivesasignificantlydifferentvaluation outcomethantheenterpriseDCFmodelincaseswherethecompanyundervaluationsuffers fromfinancialdistress. Inothercases,theAPVmodelistheoreticallymorecorrectbutthedifferenceinvaluation outcomewithregardtotheenterpriseDCFmodelisnegligible.Thepracticalsituationsthat relatetothecasesinwhichthedifferencebecomesinsignificantarethoseofamanagement orleverageandprojectfinance.Asaresultofthenonsignificantdifference,theAPV modelandtheenterpriseDCFmodelcanbothbeusedtovaluethecompanyeventhough theAPVmodelgivesatheoreticallymorecorrectcompanyvalue. Intheremainingcases,eitherboththeenterpriseDCFmodelandtheAPVmodelcanbe usedtodeterminethecompanyvalueornoneofthetwomodelsisfitforthedeterminationof thecompanyvalue.

MasterThesisSebastianOotjers 5 s0041823 IEMFEM ABCD Table of contents

Chapter1:Researchdesign...... 9 1.1Researchcontext ...... 9 1.2Researchobjective,researchframeworkandresearchissues...... 10 1.3Researchstrategy...... 11 1.3.1Deskresearch ...... 11 1.3.2Justification...... 11 1.4Structureoftheresearchreport...... 12 Chapter2:Theoreticalbackground ...... 13 Introduction ...... 13 2.1Introductiontovaluationtheory...... 13 2.1.1Definitionsinandrationaleofvaluation ...... 13 2.1.2Valuationapproaches...... 14 2.1.3Parametersnormallyusedinvaluationmodels ...... 15 2.1.4Fivediscountedcashflowvaluationmodels...... 18 2.1.5Subjectsofanalysisregardingthegeneralassumptionsofavaluationmodel ...... 20 2.2Probabilityofdefault ...... 20 2.2.1Ratings ...... 21 2.2.1Altman’sZscore ...... 23 2.2.3Ohlson’sOscore...... 25 2.2.4Contingentclaimsmodels...... 26 2.2.5Subjectsofanalysisregardingtheprobabilityofdefault...... 28 2.3Capitalstructure...... 29 2.3.1Definitionofcapitalstructure...... 29 2.3.2Financialdeficit...... 30 2.3.3Effectsofcapitalstructure...... 30 2.3.4Capitalstructuredevelopmenttheories...... 31 2.3.5Factorsthatinfluencecapitalstructure ...... 31 2.3.6Supportforthedifferenttheoriesbythefourteenfactors...... 32 2.3.7Debtcapacity...... 33 2.3.8Viewsofotherauthors...... 35 2.3.9Subjectsofanalysisregardingcapitalstructure...... 35 2.4Costsoffinancialdistress ...... 36 2.4.1Definitionoffinancialdistress...... 36 2.4.2Costeffectsoffinancialdistress...... 37 2.4.3Estimationofthecostsoffinancialdistress ...... 38 2.4.4Commentsonthecostsoffinancialdistress...... 39 2.4.5Subjectsofanalysisregardingthecostsoffinancialdistress...... 39 Conclusion ...... 40 Generalsubjectsofanalysis ...... 40 Subjectsofanalysisregardingtheprobabilityofdefault...... 40 Subjectsofanalysisregardingthecapitalstructure...... 40 Subjectsofanalysisregardingthecostsoffinancialdistress...... 41 Applicationofthesubjectsofanalysis ...... 41 Chapter3:Thetwomodelscompared ...... 42 Introduction ...... 42 3.1BasicassumptionsoftheenterpriseDCFmodel...... 42 3.1.1DefinitionoftheenterpriseDCFmodel...... 42 3.1.2StepsintheenterpriseDCFmodel ...... 43 3.1.3Modelingofthecashflows...... 43 3.1.4StructureoftheenterpriseDCFmodel ...... 43 3.1.5Terminalvalue...... 44 3.1.6Theweightedaveragecostofcapital...... 46 3.1.7Nonoperatingassetsandnonequityclaims ...... 51 3.1.8Conclusion...... 52 3.2BasicassumptionsoftheAPVmodel...... 54 3.2.1DefinitionoftheAPVmodel ...... 54 3.2.2Valueoftheunleveredcompany...... 54

MasterThesisSebastianOotjers 6 s0041823 IEMFEM ABCD 3.2.3Theexpectedbankruptcycost ...... 55 3.2.4Interesttaxshields ...... 55 3.2.5CommentsontheMillerModiglianiandtheMilesEzzellframework ...... 60 3.2.6Whichauthor,whichbeta?...... 62 3.2.7CommentsonthecorrectnessoftheMillerModiglianiframework ...... 63 3.2.8Conclusion...... 63 3.2.9Commentonthisparagraph...... 64 3.3TheenterpriseDCFmodelassessedatthenongeneralsubjectsofanalysis...... 66 3.3.1Capitalstructure ...... 66 3.3.2Probabilityofdefault...... 67 3.3.3Costsoffinancialdistress...... 68 3.3.4Conclusion...... 68 3.4TheAPVmodelassessedatthenongeneralsubjectsofanalysis...... 68 3.4.1CapitalStructure...... 69 3.4.2Probabilityofdefault...... 70 3.4.3Costoffinancialdistress ...... 71 3.4.4Conclusion...... 72 3.5TheoreticaldifferencesbetweentheenterpriseDCFmodelandtheAPVmodel ...... 72 3.5.1Thedifferencesandsimilaritiesinbasicassumptions ...... 72 3.5.2Thedifferencesregardingcapitalstructure,theprobabilityofdefaultandthecosts offinancialdistress...... 72 3.5.3Overview ...... 73 3.5.4Methodchoice ...... 73 3.5.5AdjustmenttotheenterpriseDCFtoincludedistress...... 74 3.5.6Conclusion...... 76 3.6Impactofthedifferencesonthevaluationoutcome ...... 77 3.6.1Scenario1:Constantleverageratio&nosignificantprobabilityofdefault...... 77 3.6.2Scenario2:Constantleverageratio&significantprobabilityofdefault...... 77 3.6.3Scenario3:Fixedamountofdebt ...... 78 3.6.4Scenario4:Finitelifeandaknownamountofdebtateachpointintime...... 79 3.6.5Scenario5:Debtknownuptotimet,followedbyaconstantleverageratio ...... 79 3.6.6Conclusion...... 80 Conclusion ...... 80 BasicassumptionsoftheenterpriseDCFmodel...... 80 BasicassumptionsoftheAPVmodel ...... 80 TheenterpriseDCFmodelassessedatthenongeneralsubjectsofanalysis ...... 81 TheAPVmodelassessedatthenongeneralsubjectsofanalysis ...... 81 DifferencesbetweentheenterpriseDCFmodelandtheAPVmodel...... 82 Impactofthedifferencesonthevaluationoutcome ...... 82 Practice...... 82 Chapter4:Validation ...... 83 Introduction ...... 83 4.1Validationapproach ...... 83 4.2Basicscenarios...... 83 4.2.1Scenario1:Constantleverageratio&nosignificantprobabilityofdefault...... 84 4.2.2Scenario2:Constantleverageratio&significantprobabilityofdefault...... 91 4.2.3Scenario3:Fixedamountofdebt ...... 91 4.2.4Scenario4:Finitelife&knownamountofdebt...... 93 4.2.5Scenario5:Debtknownuptotimet,thenaconstantleverageratio ...... 93 4.3Sensitivityanalysis...... 96 4.3.1Leveredbeta ...... 96 4.3.2Costofdebt ...... 97 4.3.3Taxrate ...... 97 4.3.4Marketleverageratio...... 97 4.3.5Amountofsalesin2003...... 98 Conclusion ...... 98 Chapter5:Conclusion ...... 101 Introduction ...... 101 5.1Overviewof(valid)differences...... 101 5.2Situationalconditionsofvaluationoutcomedifferences...... 103

MasterThesisSebastianOotjers 7 s0041823 IEMFEM ABCD 5.3Implicationsofthedifferencesbetweenthetwovaluationmodels...... 104 5.4Furtherresearchsuggestions ...... 105 5.4.1Costsoffinancialdistress...... 105 5.4.2Exactdifferencesinvaluationoutcomes...... 105 Literature...... 106 AppendixI:Decisiontree...... 109 AppendixII:Valuationtool...... 110 Introduction ...... 110 II.1Modelassumptions ...... 110 II.1.1Generalguidelines ...... 110 II.1.2Theinputsheets...... 110 II.1.3Theprocessingsheets ...... 111 II.1.4Theoutputsheets...... 111 II.2Commentsonthemodel...... 112 II.3Example ...... 112 Conclusion ...... 120 AppendixIII:Relationsbetweentoolworksheets...... 121 AppendixIV:Commentsonvaluationtool ...... 122

MasterThesisSebastianOotjers 8 s0041823 IEMFEM ABCD Chapter 1: Research design

1.1 Research context Valuation,forthepurposeofthisresearchproject,isdefinedastheprocessofdetermining thecurrentworthofanassetorcompany.Overtheyears,severalvaluationmodelshave beendeveloped.Oneofthesemodelsistheenterprisediscountedcashflow(DCF)model. Forthepurposeofthisresearchproject,theenterpriseDCFmodelisdefinedasavaluation modelthatisusedtoestimatethevalueofanassetoracompanybyusingfreecashflow projectionsanddiscountingthemusingtheweightedaveragecostofcapital(WACC)toarrive atapresentvalue.Anothervaluationmodelistheadjustedpresentvalue(APV)model.For thepurposeofthisresearchproject,APVisdefinedasthenetpresentvalueofanassetor companyiffinancedsolelybyequityplusthepresentvalueofanyfinancingbenefitsminus theexpectedcostsoffinancialdistress.Netpresentvalueisthedifferencebetweenthe presentvalueofcashinflowsandthepresentvalueofcashoutflows.Presentvalueisthe amountthatafuturesumofmoneyisworthtodaygivenaspecifiedrateofreturn. TheenterpriseDCFmodelisamainvaluationmodelofpractitioners.TheenterpriseDCF modelcomprisestwoassumptions,namelythatthecapitalstructureofcompanyremains constantovertimeandthatthecostsoffinancialdistressarezero.Therearescenariosin whichtheactualcapitalstructuredevelopmentsandthecostsoffinancialdistressdifferfrom theassumptionsmadebytheenterpriseDCFmodel,whichcausesanerrorinthevaluation. Insuchscenarios,theAPVmodelisamoreappropriatevaluationmodelsinceitdoesnot containthetwoenterpriseDCFmodelassumptions. TheAPVmodelisthusasubstitutefortheenterpriseDCFmodelinscenarioswherethe enterpriseDCFmodelassumptionsareviolated.Inordertodecidewhentousewhichmodel anumberofaspectshavetobeanalyzed.First,therearecircumstancesunderwhicheither theAPVmodelortheenterpriseDCFmodelshouldbeused.Second,thedifferences betweenthevaluationoutcomesofthetwomodelsunderthedifferentcircumstanceshaveto beanalyzedtodeterminethevaluationerrorasaresultofthechoicefortheinappropriate model.Third,theeffectofthenonconstantcapitalstructureandthenonzerocostsoffinancial distressontheAPVmodelvaluationoutcomeneedtobeanalyzedsincethesearethetwo aspectsonwhichtheAPVmodeldiffersfromtheenterpriseDCFmodel.Andasalastpointof analysis,thesetwofactorsneedtobemodeledinordertoobtainthemostaccuratevaluation outcomeunderdifferentcircumstances. TheAPVmodeland,especially,theenterpriseDCFmodelareextensivelydiscussedinthe corporatefinanceliterature.However,theamountofcorporatefinanceliteraturethatfocuses onthefouraspectsdiscussedintheprevioussubsectionisnotthatsubstantial.Indifferent textbooksandarticles 1isdefinedthattheAPVmodelismoreappropriateincaseofanon constantcapitalstructure.However,theterm‘nonconstant’hasnotbeenspecified.Itisalso leftunclearwhetherthenonconstantleverageratioistheonlyreasonforswitchingtotheAPV model.Thereisalsoalackofstudiesthatcomparethevaluationoutcomesofthetwomodels forspecificscenarios.Therefore,therearenoclearstatementsonthedifferentoutcomes consideringcertaincircumstances.Therearealsoveryfewauthorsthatdiscusstheeffectsof thecostsoffinancialdistressonthevaluationoutcomeundertheAPVmodel.Atlast,there aremultipletheoriesforboththemodelingofthedevelopmentofcapitalstructureaswellas forthemodelingoftheprobabilityofdefault.Thereis,however,noclearembedmentofthese modelingapproachesintotheapplicationoftheAPVmodel. So,theAPVmodelisanalternativefortheenterpriseDCFmodelwhentheassumptions underlyingtheenterpriseDCFmodelareviolatedbythevaluationsituationathand.There are,however,anumberofaspectsoftheAPVmodelthatneedtobestudiedandspecifiedto supportafoundedchoiceforeithertheenterpriseDCFmodelortheAPVmodelunder particularcircumstances.

1 ForinstanceinKolleret al.(2005)orKruschwitz&Löffler(1998)

MasterThesisSebastianOotjers 9 s0041823 IEMFEM ABCD 1.2 Research objective, research framework and research issues Theobjectiveofthisresearchprojectisbasedontheresearchcontextdescribedinthe previousparagraphandfunctionsasaguidefortheformulationoftheresearchframework. Theresearchobjectiveis to formulate a theory onthedifferencesbetweentheenterprise DCFmodelandtheAPVmodel,andtheeffectsofthesedifferencesonthevaluationoutcome by analyzing thebasicassumptionsofbothmodels,thecircumstancesinwhicheitherone shouldbeused,theimpactofthenonconstantcapitalstructureandthenonzerocostsof financialdistressonthevaluationoutcomeundertheAPVmodel,andthewayinwhichthese twofactorscanbemodeledtoobtainthemostaccuratevaluationoutcome. Inordertoarriveattheintendedresult,atheoryonthedifferencesbetweenthetwovaluation models,twoobjectshavetobestudied.Thesetwo research objects aretheenterpriseDCF modelandtheAPVmodelitself.Thetheoryonthedifferencesbetweenthetwovaluation modelswillbebasedontheanalysisofeachvaluationmodel.Toensurethattheanalysesof thevaluationmodelscanbecompared,eachmodelisstudiedthroughthe research perspective .Thisresearchperspectiveconsistsofanumberof subjects of analysis .The subjectsofanalysisarechosenbasedontheirabilitytoclearlyanddistinctivelystudythetwo valuationmodelsandareretrievedfromrelevantliterature.Therearefourkeyconceptsthat arerelevantforstudyingthevaluationmodels: 1. Basicassumptionsofvaluationmodels 2. Probabilityofdefault 3. Costsoffinancialdistress 4. Influenceofcapitalstructure Therelationsintheresearchframeworkcanbeillustratedasfollows. Adjustedpresentvalue Theoryonvaluation models Resultsof analysis Theoryon(modeling) probabilityofdefault Subjectsofanalysis Theoryondifferences Theoryon(modeling) capitalstructure Resultsof analysis Theoryoncostsof financialdistress Discountedcashflow

(a) (b) (c) (d) Tosummarizetheresearchapproach,thestepstobetakeninthecourseoftheresearch projectareasfollows: a)Ananalysisofthevariousaspectsofvaluationmethodsthatarerelevantfortheenterprise DCFmodelandtheAPVmodelprovidesthesubjectsofanalysisb)usedtoevaluatethe enterpriseDCFandtheAPVvaluationmodels.c)Acomparisonofbothevaluationsresultsin d)atheoryonthedifferencesbetweentheenterpriseDCFmodelandtheAPVmodelandthe effectofthesedifferencesonthevaluationoutcome. Theresearchobjectiveisaformulationoftheintendedresultoftheresearchproject;the researchframeworkprovidesthestepstobetakentoarriveattheintendedresult.The researchissuesserveasameanstodeterminetheknowledgerequiredforrealizingthe objective.Theresearchissuesaredividedintocentralquestionsandsubquestions.The threecentralquestionsare: 1. WhatsubjectsarerelevantforanalyzingtheenterpriseDCFandtheAPVvaluation model? 2. HowaretheenterpriseDCFmodelandtheAPVmodelspecifiedinthelightofthese subjects? 3. Whatarethedifferencesbetweenthetwomodelsandwhatistheeffectofthese differencesonthevaluationoutcomeunderwhichcircumstances?

MasterThesisSebastianOotjers 10 s0041823 IEMFEM ABCD Thesubquestionsforthefirstcentralquestionareformulatedsothattheyprovidetheanswer tothecentralquestionbycombiningtheanswersofthesubquestions.Thesubquestionsare asfollows: 1.1 Whatsubjectscanbederivedfromtheoriesonvaluationmodels? 1.2 Whatsubjectscanbederivedfromprobabilityofdefaulttheories? 1.3 Whatsubjectscanbederivedfromtheoriesoncapitalstructure? 1.4 Whatsubjectscanbederivedfromfinancialdistresscoststheories? Thesubquestionsofthesecondcentralquestionareasfollows: 2.1 WhatarethebasicassumptionsunderlyingtheenterpriseDCFmodel? 2.2 WhatarethebasicassumptionsunderlyingtheAPVmodel? 2.3 WhatarethespecificationsoftheenterpriseDCFmodelstudiedinthelightofthe subjectsofanalysis? 2.4 WhatarethespecificationsoftheAPVmodelstudiedinthelightofthesubjectsof analysis? Ananswertothesecondcentralquestionisprovidedbythecombinedanswersofthesub questions.Subquestions2.1and2.2describethebasicsofeachvaluationmodel.This informationismainlyrelevantasbackgroundinformationforansweringsubquestions2.3and 2.4.Theresultofthisprocessisanoverviewofeachvaluationmodel. Thethirdcentralquestioncanbesubdividedintothefollowingsubquestions: 3.1 WhatarethedifferencesbetweentheenterpriseDCFmodelandtheAPVmodel? 3.2 Whatistheeffectofthedifferencesonthevaluationoutcomeunderwhich circumstances? 1.3 Research strategy Thisparagraphfocusesontheresearchstrategyfollowedtoarriveattheresearchobjective. First,theliteraturesurveyresearchstrategyisdescribed.Second,thedecisiontousethe literaturesurveyresearchstrategyisjustified. 1.3.1 Desk research Deskresearchisaresearchstrategywherebytheresearchersusematerialproducedby others. Adeskresearchprojectischaracterizedby: 1. Theuseof existing material 2. The absence of direct contact withtheresearchobject 3. Lookingatthematerialbeingusedfrom a different perspectivethanatthetimeofits production Indeskresearchbyfarthemaincharacteristicisthatthematerialusedhasbeenproduced entirelybyothers.Threecategoriesofexistingmaterialcanbeusedforcarryingoutadesk researchproject:literature,secondarydataandofficialstatisticalmaterial.Literatureis understoodtomeanbooks,articles,conferenceproceedingsandsuchthatcontainthe knowledgeproductsofscientists.Secondarydataisempiricaldatacompiledbyother researchersortheresearcherselfduringpreviousresearchprojects.Officialstatistical materialisunderstoodtobedatagatheredperiodicallyorcontinuouslyforabroaderpublic. Twomainvariantsofdeskresearchcanbedistinguished,namelyliteraturesurveyand secondaryresearch.Paralleltothisdistinctionbetweenknowledgesourcesanddatasources, inthefirsttypeofresearchonewoulduseknowledgeproducedbyothers,andinthesecond typeofresearchempiricaldataproducedbyothers. 1.3.2 Justification Theobjectiveoftheresearchprojectistoformulateatheoryonthedifferencesbetweenthe enterpriseDCFmodelandtheAPVmodelandtheeffectsofthosedifferencesonthe valuationoutcome.Todeterminethesedifferences,thefocusoftheresearchwillbeondepth ratherthanonbreadth(whichwouldbethecasewhentheresearchobjectivewouldbeto giveacompleteoverviewofallexistingvaluationmodels). Inordertoacquireanindepthcomparisonofthetwovaluationmodels,aqualitative approachinwhichmultipleaspectsofthetwomodelsareanalyzedisrequired.Theresearch

MasterThesisSebastianOotjers 11 s0041823 IEMFEM ABCD projecthasanonempiricalnature,sincethetworesearchobjectsaretheories,whichare studiedonqualitativeaspects. Theabovegivesaclearindicationthattheappropriateresearchstrategyisthatofadesk research.Theresearchconsistsofusingexistingmaterialtocomparetwotheoriesinanin depthmannerwithouthavingdirectcontactwiththeresearchobject. Aliteraturesurveyischaracterizedbythefactthatknowledgeproducedbyothersisused, comparedtothesecondarysearchthatusesempiricaldataproducedbyothers.Sincethe researchprojectcomparesdifferenttheories,aliteraturesurveyisthemostappropriateform ofdeskresearch. 1.4 Structure of the research report Theremainderofthisreportisdividedinchaptersthatarelinkedtotheresearchissues. Chapter2focusesonthetheoreticalbackgroundoftheresearchproject,whichistheanswer tocentralquestionone.Inchapter2,thesubjectsofanalysisareidentifiedthroughan analysisofavailableliteratureonthefouraspects.Chapter3focusesonthesecondandthird researchissueandisthemostimportantchapterofthisresearchprojectasitcontainsthe analysiswhichleadstotheformulationofthetheoryonthedifferencesbetweenthetwo valuationmodelsandtheeffectofthesedifferencesonthevaluationoutcome,theresearch objective. Chapter4,thevalidationchapter,aimstovalidatetheresultsfromchapter3.Thetheory statedinchapter3istestedthroughtheimplementationofdifferentscenariosintothe valuationmodeldescribedinappendixII.Thisleadstoanoverviewofresultsonthevalidityof thestatementsfromchapter3. Chapter5,thefinalchapterofthisreport,concludesonthevaliddifferencesbetweenthetwo valuationmodelsandgivesanoverviewofthecircumstancesunderwhichcertaineffectson thevaluationoutcomesofeachvaluationmodelarerealized.Asalastcontribution,chapter5 discussesfurtherresearchsuggestionsthatcomeforthfromthisresearchproject. InappendixIIthetheoreticalresultsoftheanalysisinchapter3aretranslatedtoavaluation modelintheshapeofaMicrosoftExcelworkbook.Thisworkbookcanbeusedtodetermine thevalueofacompanyunderdifferentcircumstances.AppendixIIalsocontainsanexample ofavaluationthroughtheAPVmodel.

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Chapter 2: Theoretical background

Introduction TheobjectiveofthisresearchprojectistoidentifythedifferencesbetweentheenterpriseDCF modelandtheAPVmodel.Inordertocomparethetwomodelsinadistinctivemanner,they bothneedtobecomparedonthesamesetofsubjects. Thischapterdiscussestheareasofresearchthatarerelatedtotheaspectsofthetwo valuationmodels,asdiscussedintheresearchcontextsectionofchapter1.Thefour researchareasaregeneralvaluationtheory,probabilityofdefaultestimation,capitalstructure theory,andthecostsoffinancialdistress. Ineachparagraph,dedicatedtoaparticularresearchfield,anoverviewisgivenonthe currentstateofthatresearcharea.Themaintheoriesandviewsarediscussedtoprovidean overviewoftheparticularareaandto(implicitly)giveanindicationoftherobustnessofthe theoriesandviewsthatcurrentlyexist.Thediscussionofthetheoriesalsoservesasa foundationforthemodelingchoicesthataremadeinchapter3ofthisresearchreport. Eachparagraphendswithaconclusionontherelevantsubjectsofanalysisthatcomeforth fromtheparticularresearcharea.Thesesubjectsformthebasisoftheanalysisofthetwo valuationmodelsinchapter3ofthisresearchreport. 2.1 Introduction to valuation theory Valuationisanimportanttoolformanyreasons.Itisusedinmultiplesituationsfordifferent purposes.Valuationmodelscanbedividedinthreecategoriesthateachhaveadifferent approachofdeterminingwhatthevalueofanassetorcompanyis.However,inpractice,one typeofapproach,theincomeapproach,ismostoftenapplied.Also,thevaluationmodelsthat arecomparedinthisresearchprojectaremodelsinthiscategory.Therefore,thisparagraph discussesanumberofdifferentincomeapproachvaluationmodelsandthedifferent parametersthatareusedinmostofthem. Thepurposeofthisparagraphistocomeupwithanumberofsubjectsonwhichthetwo valuationmodelscanbeanalyzed. 2.1.1 Definitions in and rationale of valuation Valuation,forthepurposeofthisresearchproject,isdefinedastheprocessofdetermining thecurrentworthofanassetorcompany.Ingeneral,valuationistheprocessofestimating themarketvalueofafinancialasset(e.g.investmentsinmarketablesecuritiesorintangible assets),liability(e.g.bondsissuedbyacompanyorloans),oracompany 2. Commontermsforthevalueofanassetorliabilityarefairmarketvalue,fairvalue,and intrinsicvalue.Themeaningsofthesetermsdiffer. Acommontermisfairmarketvaluedefinedastheprice,expressedintermofcash equivalents,atwhichpropertywouldchangehandsbetweenahypotheticalwillingandable buyerandahypotheticalwillingandableseller,actingatarmslengthinanopenand unrestrictedmarket,whenneitherisundercompulsiontobuyorsellandwhenbothhave reasonableknowledgeoftherelevantfacts. Fairvalueisusedindifferentcontextsandhasmultiplemeanings.Thetermissometimes usedtomeanthesamethingasfairmarketvalue.Fairvalueisalsoatermusedinlawand accounting.ItisusedintheGenerallyAcceptedAccountingPrinciples(GAAP)forfinancial reportingandinlawinshareholderrightslegalstatutes.Inthesecases,fairvalueisdefinedin theaccountingliteratureorthelaw,respectively.Fairvaluemaydeviatefromfairmarket valueintheaccountandlegalcontexts. Intrinsicvalueisanasset’struevalueregardlessofthemarketprice.Itistheactualvalueofa companyoranassetbasedonanunderlyingperceptionofitstruevalueincludingallaspects ofthecompany,intermsofbothtangibleandintangiblefactors.

2 Damodaran(2002)

MasterThesisSebastianOotjers 13 s0041823 IEMFEM ABCD Enterprisevaluationisaprocessappliedtodeterminethefairmarketvalueofacompanyor anowner’sinteresttherein.AccordingtoDuffhues(1997),inourwestern,onmarket principlesbasedeconomy,differentreasonscanbethoughtofonwhyaproclamationonthe valueofacompanycouldbenecessary. Inthefirstplace,onecanthinkofthevaluationoftheshareholder’sequityofgoingconcerns inrelationtocurrentorfuturetransactions,inwhichtheexplicitgoalofthetransactionis toacquirecontroloverthecompany.Examplesofsuchvaluationissuesare: 1. Thedeterminationofthepriceagainstwhichwillbeintroducedatanexchange (introductionprice). 2. Thedeterminationoftheissuepriceofsecuritiesthatareissued. 3. Thedeterminationoftheconversionpriceofconvertiblesecurities. 4. Thedeterminationoftheexercisepriceofwarrants. 5. Thedeterminationoftheexercisepriceofemployeestockoptions. Second,onecanthinkofthevaluationofcompaniesbytaxauthorities.Inthatcase,the determinationofthevalueofthetaxequityisoneoftheobjectives. Third,valuationissuesarepresentinthecaseofthetradeofmarketablesecurities;publicor private,incidentalorcontinuous.Inthatcase,oneshouldnotonlythinkofthesaleor purchaseofcompletecompaniesthroughmergersoracquisitions,butalsoofthevaluationof securitiesofcompanieswithoutanyspecificrelationtomergersandacquisition,thattake placeonadailybasisonthestockexchanges. 2.1.2 Valuation approaches Therearethreedifferentapproachesthatareusedinenterprisevaluation:theincome approach,theassetbasedapproach,andthemarketapproach 3.Withineachofthese approaches,therearevarioustechniquesfordeterminingthefairmarketvalueofacompany. Generally,theincomeapproachmodelsdeterminevaluebycalculatingthenetpresentvalue ofthebenefitstreamgeneratedbythecompany.Theassetbasedapproachmodels determinetheenterprisevaluebyaddingthesumofthepartsofthecompanyandthemarket approachmodelsdeterminetheenterprisevaluebycomparingthesubjectcompanytoother companiesinthesameindustry,ofthesamesize,and/orwithinthesameregion.Eachmodel hasitsownadvantagesanddrawbacks.Theseshouldbeconsideredwhenapplyingthose modelstoaparticularsubjectcompany. The income approach models determinefairmarketvaluebymultiplyingthebenefitstream generatedbythesubjectcompanytimesadiscountorcapitalizationrate.Thediscountor capitalizationrateconvertsthestreamofbenefitsintopresentvalue.Thereareseveral differentincomeapproaches,includingcapitalizationofearningsorcashflows,discounted futurecashflows(DCF),andtheexcessearningsmethod(whichisahybridofassetsand incomeapproaches).Mostoftheincomeapproachmodelsconsiderthesubjectcompany’s historicalfinancialdata;onlytheDCFmodelsrequirethesubjectcompanytoprovide projectedfinancialdata.Mostoftheincomeapproachmodelsusethecompany’sadjusted historicalfinancialdatafromasingletimeperiod;onlytheDCFmodelsrequiredatafrom multiplefuturetimeperiods.Thesingletimeperioddataisoftenbasedonnormalizeddata overthreehistoricalyears.Thediscountorcapitalizationratemustbematchedtothetypeof benefitsstreamstowhichitisapplied.Theresultofavaluationundertheincomeapproachis generallythefairmarketvalueofacontrolling,marketableinterestinthesubjectcompany, sincetheentirebenefitstreamofthesubjectcompanyismostoftenvalued,andthe capitalizationanddiscountratesarederivedfromstatisticsconcerningpubliccompanies. The asset-based approach models arebasedontheprinciplethatthevalueofacompanyis equaltothesumofitspart.Thisprincipleiscalled value additivity anddefinesthatinperfect capitalmarketsthepresentvalueoftwoassetscombinedisequaltothesumoftheirpresent valuesconsideredseparately 4. Incontrasttotheincomeapproachmodels,whichrequiresubjectivejudgmentsabout capitalizationordiscountrates,theadjustednetbookvaluemethodisrelativelyobjective.In accordancewithaccountingconventions,mostassetsarereportedinthebooksofthesubject

3 Damodaran(2002) 4 Brealey&Myers(2003)

MasterThesisSebastianOotjers 14 s0041823 IEMFEM ABCD companyattheiracquisitionvalue,netofdepreciationwhereapplicable.Thesevaluesmust beadjustedtofairmarketvaluewhereverpossible. Thevalueofacompany’sintangibleassets,suchas,isgenerallyimpossibleto determineapartfromthecompany’soverallenterprisevalue.Forthisreason,theassetbased approachmodelsarenotthemostappropriatemodelsofdeterminingthevalueofgoing concerncompanies. Adjustednetbookvaluemaybethemostrelevantstandardofvaluewhereliquidationis imminentorongoing;whereacompany’searningsorcashflowsarenominal,negativeor worthlessthanitsassets;orwherenetbookvalueisstandardintheindustryinwhichthe companyoperates.Ifthesesituationsdonotapplytothecompanythatisbeingvalued,then theadjustednetbookvaluemaybeusedasa‘sanitycheck’whencomparedtoother methodsofvaluation,suchastheincomeandmarketapproaches. The market approach toenterprisevaluationisbasedontheeconomicprincipleof substitution:buyerswillbeunwillingtopaymoreforanitemthanthepriceatwhichtheycan obtainanequallydesirablesubstitute.Themarketpriceofthestocksofpubliclytraded companiesengagedinthesameorasimilarlineofbusiness,whosesharesareactively tradedinafreeandopenmarket,canbeavalidindicatorofvaluewhenthetransactionsin whichstocksaretradedaresufficientlysimilartopermitmeaningfulcomparison.Thedifficulty liesinidentifyingpubliccompaniesthataresufficientlycomparabletothesubjectcompanyfor thispurpose. Ofthethreeusedapproachesinenterprisevaluation,theincomeapproachismostoften applied.However,sincetheincomeapproachmodelsrelypartiallyonforecasts,aplausibility checkoftheforecastscouldbeusedtoimprovethevaluationaccuracy. Koller et al.(2005,p.361)identifytheseaspectsandarguethat“theincomeapproach appliedthroughvariousdiscountedcashflowmethodsisthemostaccurateandflexible methodforvaluingprojects,divisionsandcompanies.Anyanalysis,however,isonlyas accurateastheforecastsitrelieson.Errorsinestimatingthekeyingredientsofcorporate valuecanleadtomistakesinvaluationand,ultimatelytostrategicerrors. Acarefulmultipleanalysis(whichisanapplicationofthemarketapproachtovaluation)– comparingacompany’smultiplesversusthoseofcomparablecompanies–canbeusefulin makingsuchforecastsandthediscountedcashflowvaluationstheyinformmoreaccurate. Properlyexecuted,suchananalysiscanhelptesttheplausibilityofcashflowforecasts, explainmismatchesbetweenacompany’sperformanceandthatofitscompetitors,and supportusefuldiscussionsaboutwhetherthecompanyisstrategicallypositionedtocreate morevaluethanotherindustryplayers.” Becausebothvaluationmodelsthatarestudiedinthisresearchprojectareincomeapproach models,thefollowingsectionswillgodeeperintotheaspectsofdiscountedcashflow techniques.Beforecontinuingonthoseaspects,itisimportanttonotethatvaluationismore anartthanascience,mainlybecauseitrequiresasignificantdegreeofjudgment: 1. Thereareverydifferentsituationsandpurposesinwhichonevaluesacompany (e.g.,acompanyindistress,fortaxpurposes,inrelationtomergers&acquisitions). Inturnthisrequiresdifferentmodelsoradifferentinterpretationofthesamemodels eachtime. 2. Allvaluationmodelshavetheirlimitations(e.g.,mathematical,complexity, comparability)andcouldbewidelycriticized.Asageneralrulethevaluationmodels aremostusefulwhenthesamevaluationmodelasthe‘partner’youareinteracting withisused. 3. Thequalityofsomeinputdatamayvarywidely. 2.1.3 Parameters normally used in valuation models Thedifferentdiscountedcashflowtechniquesalldeterminevaluebydiscountingcertaincash flowsatacertaindiscountrate.Thissectiondiscussestheparametersthatareusedinalmost alldiscountedcashflowtechniques.Theseparametersarethecashflows,thediscountrate, thecostofdebt,thecostofequity,andthetaxrate.Thecashflowsandthediscountrate formthebasisofmostdiscountedcashflowtechniques.Thecostofdebt,thecostofequity, andthetaxrateinsomecasesdirectlyinfluencetheenterprisevalue,inothercasesthey serveasaninputforthediscountrateorcashflows.

MasterThesisSebastianOotjers 15 s0041823 IEMFEM ABCD MostofthedescriptionsoftheparametersarebasedonBrealey&Myers(2003)andKoller et al (2005).ThedefinitionsoftheparametersthatarederivedfromBrealey&Myers(2003)and Koller et al. (2005)willbeexplicitlylinkedtotheirsourcethroughareference.

Cashflows Acashflowisthedifferencebetweentheamountofcashreceivedandtheamountofcash paidoutoveragivenperiodoftime. 5Cashinflowsusuallyarisefromoneofthreeactivities: operations,financingorinvesting.Cashoutflowsresultfromexpensesorinvestments. Themaintwotypesofcashflowsusedinenterprisevaluationarethefreecashflow(FCF) andequitycashflow(ECF). istheaftertaxcashflowavailableto all investors:debtholdersandequity holders.Unlike“cashflowfromoperations”reportedinacompany’sfinancialstatement,free cashflowisindependentoffinancingandnonoperatingitems.Itcanbethoughtofasthe aftertaxcashflow–asifthecompanyheldonlycoreoperatingassetsandfinancedthe businessentirelywithequity.FreecashflowisdefinedbyKoller et al. (2005)as: FCF=NOPLAT+NoncashOperatingExpenses–InvestmentsinInvestedCapital Cash flow to equity is ameasureofhowmuchcashcanbepaidtotheequityshareholdersof thecompanyafterallexpenses,reinvestmentanddebtrepayment.AccordingtoKoller et al (2005)itiscalculatedas: ECF=NetIncome+NoncashExpenses–NetCapitalExpenditures–ChangeinWorking Capital+NewDebt–DebtRepayment Oras: ECF =Dividends+ShareRepurchases–NewEquityIssues Discountrate Thefirstbasicprincipleoffinanceisthat a Euro today is worth more than a Euro tomorrow , becausetheEurotodaycanbeinvestedtostartearninginterestimmediately.Thus,the presentvalueofadelayedpayoffmaybefoundbymultiplyingthepayoffbyadiscountfactor whichislessthan1.IfC 1denotestheexpectedpayoffatperiod1(oneyearhence),then Presentvalue(PV)=discountfactor*C 1 Thediscountfactoristhevaluetodayof€1receivedinthefuture.Itisusuallyexpressedas thereciprocalof1plusarateofreturn: Discountfactor=1/(1+ r) Therateofreturn ristherewardthatinvestorsdemandforacceptingdelayedpayment. Tocalculatepresentvalue,onediscountsexpectedpayoffsbytherateofreturnofferedby equivalentinvestmentalternativesinthecapitalmarket.Thisrateofreturnisoftenreferredto asthe discount rate, hurdle rate, or opportunity . Itiscalledthe opportunity cost becauseitisthereturnforegonebyinvestingintheinvestmentopportunityathandrather thaninvestinginalternativeinvestmentopportunities,suchassecurities. The company cost of capital isdefinedastheexpectedreturnonaportfolioofallthe company’sexistingsecurities.Itisusedtodiscountthecashflowsoninvestment opportunitiesthathavesimilarrisktothatofthecompanyasawhole. Costofdebt Thecostofdebtistheborrowingrateatwhichthecompanyisexpectedtobeabletoacquire debt,basedonthecompany’scurrent(credit)riskposition.Theappropriatemethodof

5 Brealey&Myers(2003,p.119)

MasterThesisSebastianOotjers 16 s0041823 IEMFEM ABCD determiningthecostofdebtshouldbeselectedbasedonthetypeofdebtthatthecompany hasoutstanding. Koller et al.(2005)givethefollowingoptionsforestimatingthecostofdebt: “Toestimatethecostofdebt,usetheyieldtomaturityofthecompany’slongterm,optionfree bonds.Technicallyspeaking,yieldtomaturityisonlyaproxyforexpectedreturn,becausethe yieldisactuallya promised rateofreturnonacompany’sdebt.Forestimatingthecostofdebt foracompanywithinvestmentgradedebt(debtratedatBBBorbetter),yieldtomaturityisa suitableproxy.Whencalculatingyieldtomaturity,use long-term bonds. Forcompanieswithonlyshorttermbondsorbondsthatrarelytrade,determineyieldto maturitybyusinganindirectmethod.First,determinethecompany’screditratingon unsecuredlongtermdebt.Next,examinetheaverageyieldtomaturityonaportfoliooflong termbondswiththesamecreditrating.Usethisyieldasaproxyforthecompany’simplied yieldonlongtermdebt. Fordebtbelowinvestmentgrade,usingtheyieldtomaturityasaproxyforthecostofdebt cancausesignificanterror.Threefactorsdriveyieldtomaturity:thecostofdebt,the probabilityofdefault,andtherecoveryrate.Whentheprobabilityofdefaultishighandthe recoveryratelow,theyieldtomaturitywilldeviatesignificantlyfromthecostofdebt.Thus,for companieswithhighdefaultriskandlowratings,theyieldtomaturityisapoorproxyforthe costofdebt.Toestimatethecostofhighyielddebt,werelyontheCAPM(ageneralpricing model,applicabletoany).” Costofequity Thecostofequityisestimatedbydeterminingtheexpectedrateofreturnofthecompany's stock.Sinceexpectedratesofreturnareunobservable,assetpricingmodelsthattranslate riskintoexpectedreturnareused. ThemostcommonassetpricingmodelistheSLB(Sharpe–Lintner–Black)CapitalAsset PricingModel(CAPM).OthermodelsincludetheFamaFrenchthreefactormodelandthe arbitragepricingtheory(APT). TheCAPMputsforwardthattheexpectedrateofreturnofanysecurityequalstheriskfree rateplusthesecurity’sbetatimesthemarketriskpremium:

E(Ri ) = rf + βi [E(Rm ) − rf ] whereE(R i)isthesecurity i’sexpectedreturn,r ftheriskfreerate,β ithestock’ssensitivityto themarketandE(R m)theexpectedreturnofthemarket. IntheCAPM,theriskfreerateandmarketriskpremium(definedasthedifferencebetween E(R m)andr f)arecommontoallcompanies;onlybetavariesacrosscompanies.Beta representsastock’sincrementalrisktoadiversifiedinvestor,whereriskisdefinedbyhow muchthestockcovarieswiththeaggregatestockmarket. In1992,EugeneFamaandKennethFrenchstatedthatequityreturnsareinverselyrelatedto thesizeofacompany(asmeasuredbymarketcapitalization)andpositivelyrelatedtothe ratioofacompany’sbookvaluetoitsmarketvalueofequity.Intheirmodelcommonlyknown astheFamaFrenchthreefactormodel,astock’sexcessreturnsareregressedonexcess marketreturns(similartotheCAPM),theexcessreturnsofsmallstocksoverbigstocks (SMB),andtheexcessreturnsofhighbooktomarketstocksoverlowbooktomarketstocks (HML). TheSMBandHMLportfoliosaremeanttoreplicateunobservableriskfactors,factorsthat causedsmallcompanieswithhighbooktomarketvaluestooutperformtheirCAPMexpected returns.TheexpectedrateofreturnaccordingtotheFamaFrenchthreefactormodelis calculatedthrough:

E(Ri ) = rf + β1 (E(Rm ) − rf ) + β 2 E(RS − RB ) + β3 E(RH − RL ) Thecompany’sthreebetasaredeterminedthrougharegressionofthestocksreturnsagainst theexcessmarketportfolio,SMB,andHML.

MasterThesisSebastianOotjers 17 s0041823 IEMFEM ABCD AnotheralternativetotheCAPM,thearbitragepricingtheory(APT),resemblesageneralized versionoftheFamaFrenchthreefactormodel.IntheAPT,asecurity’sactualreturnsare fully specifiedby k factorsandrandomnoise: ~ ~ ~ ~ Ri = α + β1F1 + β 2 F2 +....+ β k Fk + ε Bycreatingwelldiversifiedfactorportfolios,itcanbeshownthatasecurity’sexpectedreturn mustequaltheriskfreerateplusthecumulativesumofitsexposuretoeachfactortimesthe factor’sriskpremium(λ):

E[Ri ] = rf + β1λ1 + β 2λ2 +....+ β k λk Otherwise,arbitrageispossible(positivereturnwithzerorisk). Onpaper,thetheoryisextremelypowerful.Inpractice,implementationofthemodelhasbeen difficult,asthereislittleagreementabouthowmanyfactorsthereare,whatthefactors represent,orhowtomeasurethefactors.Forthisreason,useoftheAPTresidesprimarilyin theclassroom. Tax Companiesareobligedbylawtopaycorporatetaxesontheprofitsthattheyrealize.This corporatetaxthuscausesacashoutflow.However,companiesareallowedtodeductcertain costsfromtheirprofit(taxdeductible)beforethetaxesthathavetobepaidaredetermined. Thisleadstoaformalcashinflowoftheamountdeductedtimesthetaxrate.Thisreductionin corporatetaxesthatresultsfromtakinganallowabledeductionfromtaxableprofitsiscalleda . Debtfinancingalsohasthisimportantadvantageunderthecorporateincometaxsystemin theUnitedStates,theNetherlands,andinmultipleothercountries.Theinterestthatthe companypaysisataxdeductibleexpense.Dividendsandretainedearningsarenot.Thus thereturntobondholdersescapestaxationatthecorporatelevel. Therearetwotaxratesthatareusedinvaluation:themarginalcorporatetaxT candthenet taxsavingperdollarofinterestpaidbythefirmT*. Brealey&Myers(2003)statethatoneshouldalwaysuseT c,themarginalcorporatetaxrate, (1)whencalculatingtheWACCasaweightedaverageofthecostsofdebtandequityand(2) whendiscountingsafe,nominalcashflows.Ineachcasethediscountrateisadjusted only for corporatetaxes. TheAPVmodelinprinciplecallsforT*,thenettaxsavingperdollarofinterestpaidbythe company.Thisdependsontheeffectivepersonaltaxratesondebtandequityincome.T*is almostsurelylessthanT c,butitisverydifficulttopindownthenumericaldifference. ThereforeinpracticeT cisalmostalwaysusedasanapproximation. 2.1.4 Five valuation models Asafinalpartofthisparagraph,fivedifferentcashflowvaluationmodelsarediscussedto showthedifferenceinassumptionsandparametersthatareused.Thisshouldgivesome insightintheaspectsinwhichvaluationmodelscandifferfromeachother.Thefivemethods discussedare: Equitycashflowsdiscountedattherequiredreturntoequity. CapitalcashflowsdiscountedattheWACCbeforetax. ResidualIncomediscountedattherequiredreturntoequity. EVAdiscountedattheWACC. Theriskfreeadjustedequitycashflowdiscountedattheriskfreerate. Therearefourbasicdiscountedcashflowvaluationmodels,twoofthembeingtheenterprise DCFmodelandtheAPVmodel.Theothertwoare(a)themodelinwhichtheequitycash flows(ECF)arediscountedattherequiredreturntoequity(K e)and(b)themodelwhere capitalcashflows(CCF)arediscountedattheWACCbeforetax. For(a),equation(2.1)indicatesthatthevalueofequity(E)isthepresentvalueofthe expectedequitycashflow(ECF)discountedattherequiredreturntoequity(K e).

MasterThesisSebastianOotjers 18 s0041823 IEMFEM ABCD

E0 = PV0[Ket ;ECFt ] (2.1) Theexpectedequitycashflowisthesumofallexpectedcashpaymentstoshareholders, mainlydividendsandsharerepurchases. Equation(2.2)indicatesthatthevalueofthedebt(D)isthepresentvalueoftheexpected debtcashflows(CFd)discountedattherequiredreturntodebt(K d).

D0 = PV0[Kdt ;CFdt ] (2.2) Theexpecteddebtcashflowinagivenperiodisgivenbyequation(2.3)

CFdt = Nt−1rt − (Nt − Nt−1 ) (2.3) whereNisthebookvalueofthefinancialdebtandristhecostofdebt.N t1rtistheinterest paidbythecompanyinperiodt.(N t N t1)istheincreaseinthebookvalueofdebtinperiodt. With(b),thecapitalcashflowsarethecashflowsavailableforallholdersofthecompany’s securities,whetherthesearedebtorshares.Theyareequivalenttotheexpectedequitycash flow(ECF)plustheexpecteddebtcashflows(CFd). Equation(2.4)indicatesthatthevalueofthedebttoday(D)plusthatoftheshareholders’ equity(E)isequaltothecapitalcashflow(CCF)discountedattheWACCbeforetax (WACC BT ). (2.4) E0 + D0 = PV[WACCBTt ;CCFt ] TheexpressionthatrelatestheCCFwiththeECFandtheFCFis(2.5):

CCFt = ECFt + CFdt = ECFt − (Nt − Nt−1 ) + Nt−1rt = FCFt + Nt−1rtTt (2.5) Theotherthreediscountedcashflowmodelsareusedlessoften.Forthemodelthatusesthe residualincome(alsocalledeconomicprofit)andKe(requiredreturntoequity),equation(2.6) indicatesthatthevalueoftheequity(E)istheequity’sbookvalue(Ebv)plusthepresent valueoftheexpectedresidualincome(RI)discountedattherequiredreturntoequity(K e).

E0 = Ebv0 + PV0[Ket ;RIt ] (2.6) Thetermresidualincome(RI)isusedtodefinetheaccountingnetincomeorprofitaftertax (PAT)minustheequity’sbookvalue(Ebv t1)multipliedbytherequiredreturntoequity.

RIt = PATt − Ket Ebvt−1 (2.7) ForthemodelusingtheEVA(economicvalueadded)andtheWACC,equation(2.8) indicatesthatoftheshareholders’equity(E)isthebookvalueoftheshareholders’equityand thedebt(Ebv 0 +N 0)plusthepresentvalueoftheexpectedEVA,discountedattheWACC: (2.8) E0 + D0 = (Ebv0 + N0 ) + PV0[WACCt ;EVAt ] TheEVA(economicvalueadded)istheNOPAT(NetOperatingProfitAfterTax)minusthe company’sbookvalue(N t1 +Evc t1)multipliedbytheweightedaveragecostofcapital (WACC).TheNOPATistheprofitoftheunlevered(debtfree)company.

EVAt = NOPATt − (Nt−1 + Ebvt−1 )WACCt (2.9)

MasterThesisSebastianOotjers 19 s0041823 IEMFEM ABCD Last,forthemodelusingtheriskfreeadjustedequitycashflowsdiscountedattheriskfree rate,equation(2.10)indicatesthatthevalueofthedebt(D)plusthatoftheshareholders’ equity(E)isthepresentvalueoftheexpectedriskfreeadjustedfreecashflows(FCF\\rf)that willbegeneratedbythecompany,discountedattheriskfreerate(r f): (2.10) E0 + D0 = PV0 [Kut ; FCFt \\ rf ] Thedefinitionoftheriskfreeadjustedfreecashflowsis:

FCFt \\ rf = FCFt − (Et−1 + Dt−1 )(WACCt − RFt ) (2.11) 2.1.5 Subjects of analysis regarding the general assumptions of a valuation model Therearemultipleapproachesfordeterminingtheenterprisevalueofacompany.Thetwo modelsthatarestudiedinthisresearchprojectbothbelongtotheincomeapproachandhave theformofadiscountedcashflowmodel.Eachdiscountedcashflowmodelconsistsoffour subjectsofwhichthespecificationdeterminesthefunctioningoftheparticulardiscounted cashflowmodel.Thesefoursubjectsare: 1. Thewayinwhichthecashflowsaremodeled. 2. Thediscountratethatisused. 3. Thecostofequityandthecostofdebtused. 4. Theincorporationoftaxesintothevaluation. Asthefivediscountedcashflowmodelsshowed,discountedcashflowmodelsoftendifferon theirspecificationsinrelationtothesefoursubjects.Therefore,tocomparetheenterprise DCFmodelandtheAPVmodel,bothmodelshavetobeanalyzedonthesefour general subjects of analysis . 2.2 Probability of default Thegoalofthisparagraphistogiveanoverviewofthemaintheoriesonestimatingthe probabilityofdefault.Threetypesofmodelsarecommonlyusedforestimatingtheprobability ofdefault,eachwithadifferenttypeofinputsfortheestimation.Thisparagraphdiscussesthe mainmodelsofeachtypeandthecommentsonthesemodels.Thetotaloverviewofthe modelsisusedtodeterminetheprobabilityofdefaultsubjectsofanalysis. Defaultisdefinedtobetheconditionthatoccurswhenacompanyhasadelayedormissing contractualdebtpayment.Unfortunately,dataondefaultsisnotreadilyavailable.Forthis reason,insteadofdefaults,moststudiesusebankruptciesasthereobjectofanalysis,where abankruptcyisdefinedtooccurwhenacompanymakeseitheraChapter7(liquidation)or Chapter11(reorganization)filing(thesetitlesrefertochaptersoftheUSBankruptcyCode). Ingeneral,thedefaultriskisafunction,verybroadly,oftwovariables:itscapacitytogenerate cashflowsfromoperationsanditsfinancialobligations–includinginterestandprincipal payments.Damodaran(2002)statesthat,keepingeverythingequal: Companieswhichgeneratehighcashflowsrelativetotheirfinancialobligationhave lowerdefaultriskthanfirmswhichgeneratelowcashflowsrelativetotheir obligations.Thus,companieswithsignificantassetsinplace,whichgeneratehigh cashflows,willhavelowerdefaultriskthanfirmsthatdonot. Themorestabilitythereisincashflows,theloweristhedefaultriskinthecompany. Companieswhichoperateinpredictableandstablebusinesseswillhavelower defaultriskthanotherwisesimilarcompanieswhichoperateincyclicateand/or volatilebusinesses. Therearethreebroadsourcesofinformationaboutthecreditworthinessofcompanies,from whichonecandeterminewhattheprobabilityisthatacompanywilldefault.Thesearethe viewsofaspecialistcreditanalyst,informationembeddedinthecompany’ssecurityprices,or theuseofthecompany’sfinancialstatementstomakeanassessment.

MasterThesisSebastianOotjers 20 s0041823 IEMFEM ABCD Awaytoassessacompany’screditstandingistoseektheviewsofaspecialistincredit assessment.Forexample,ratingagencies,suchasMoody’sandStandardandPoor’s, provideausefulguidetotheriskinessofthecompany’sbonds. Bondratingsareusuallyavailableonlyforrelativelylargecompanies.However,information canbeobtainedonmanysmallercompaniesfromacreditagency.DunandBradstreetisby farthelargestoftheseagenciesanditsdatabasecontainsreportsonmorethan10million companies. 6 Inadditiontocheckingwithacreditagencyorabank,itmaymakesensetocheckwhatthe financialcommunitythinksaboutthecompany’screditstandingbylookingattheyieldonthe company’sbondsand/orstockprice. Informationonsecuritypricescanbeusedtoputafigureonthechancesofdefault. Companieshaveanincentivetoexercisetheiroptiontodefaultwhenthevalueoftheirassets islessthantheamountoftheirdebt.So,ifitisknownhowmuchthevalueofthecompany’s assetsmayfluctuate,theprobabilitythattheassetvaluewillfallbelowthedefaultpointcan beestimated. Securitypricedatamaynotbeavailableformanycompanies,andinthesecasesonewill needtorelyonthecompany’sfinancialstatementstomakeanownassessmentofthe company’screditposition. 2.2.1 Ratings TherelativequalityofmosttradedbondscanbejudgedfrombondratingsgivenbyMoody’s andStandardandPoor’s.Forexample,thehighestqualitybondsareratedtripleA(Aaa)by Moody’s,thencomedoubleA(Aa)bonds,andsoon.BondsratedtripleB(Baa)oraboveare knownasinvestmentgradebonds. Brealey&Myers(2003,p.685)statethat:“Bondratingsdoreflecttheprobabilityofdefault. Since1971nobondthatwasinitiallyratedtripleAbyStandardandPoor’shasdefaultedin theyearafterissueandfewerthanoneinathousandhasdefaultedwithintenyearsofissue. Attheotherextreme,overtwopercentofCCCbondshavedefaultedintheirfirstyearandby year10almosthalfhavedoneso.Ofcourse,bondsrarelyfallsuddenlyformgrace.Astime passes,andthecompanybecomesprogressivelymoreunstable,theagenciesrevise downwardthebond’sratingtoreflecttheincreasingprobabilityofdefault.” Thefollowingtableshowsthedefaultprobabilitiesthatarelinkedtothevariouscreditratings. S&P's Default Probability ¹ Moody's Default Probability ² AAA 0.12 Aaa 0.12 AA 0.33 Aa 0.24 Investmentgrade A 0.75 A 0.54 BBB 3.84 Baa 2.16

BB 14.45 Ba 11.17 B 33.02 B 31.99 CCC 61.35 Caa 60.83 Subinvestmentgrade CC Ca CC

¹Percentagedefaultingwithin5yearsbasedondefaultratesbetween19812003 ²Percentagedefaultingwithin5yearsbasedondefaultratesbetween19702003 Tocapturethestatementsgivenaboveinamoreformalfashion,thefollowingexpressioncan beused. AratingofacompanycanbedefinedasthemappingofthePoD,theexpectedprobabilityof default,intoadiscretenumberofqualityclasses,orratingcategories.ThePoDisa continuousvariable,boundedbyzerofrombelowandbyonefromabove. 6 Brealey&Myers(2003)

MasterThesisSebastianOotjers 21 s0041823 IEMFEM ABCD PoD : _ Companies → ]1,0[ APoDistheexpectedrelativefrequencyofacreditevent,wherethelatterisdefinedasa nonpaymentofprincipalorinterestdue(overaperiodofatleast30days,say).ThePoDis onecomponentofalenders’expectedloss,asin: E(L) = PoD * E(LGD) Here,E(L)isexpectedloss,andE(LGD)istheexpectedlossgivendefault.Theexpectations aretakenoveracommontimeinterval,usuallyoneyearinthefuture.Expectedlossisthus theaverageamountalenderisexpectingtolooseoverthenexttwelvemonths. Krahnen&Weber(2001)statethat:“Thoughintheory,PoDsaremappedinratingclasses,in practiceitistheotherwayaround.RatingclassesaremappedintoPoDsonthebasisof historicaldata.Theestablishedagencies,notablyS&PandMoody’s,usehistoricaldefault ratestocalibratetheirmodel.Thedefaultrateisthepercentageofallbondissues outstandingat tthatwillhaveacrediteventbetween t and t + 1, e.g.,a12monthsperiod.” Thebondratingsassignedbyratingagenciesarebasedprimarilyuponpubliclyavailable information,althoughprivateinformationconveyedbythecompanytotheratingagencydoes playarole.Theratingisassignedtoacompany’sbondswilldependinlargepartonfinancial ratiosthatmeasurethecapacityofthecompanytomeetdebtpaymentsandgeneratestable andpredictablecashflows.Whileamultitudeoffinancialratiosexist,thetablebelow summarizessomeofthekeyratiosthatareusedtomeasuredefaultrisk. Financial ratios used to measure default risk Ratio Description PretaxInterestCoverage =(PretaxIncomefromContinuingOperations+InterestExpense)/GrossInterest EBITDAInterestCoverage =EBITDA/GrossInterest FundsfromOperations/TotalDebt =(NetIncomefromContinuingOperations+Depreciation)/TotalDebt FreeOperatingCashFlow/TotalDebt =(FundsfromOperationsCapitalExpedituresChangeinWorkingCapital)/TotalDebt PretaxReturnonPermanentCapital =(PretaxIncomefromContinuingOperations+InterestExpense)/ (AverageofBeginningoftheyearandEndoftheyearoflongandshorttermdebt,minority interestandShareholdersequity) OperatingIncome/Sales =(SalesCOGS(beforedepreciation)SellingExpenses AdministrativeExpensesR&DExpenses)/Sales LongTermDebt/Capital =LongTermDebt/(LongTermDebt+Equity) =TotalDebt/(TotalDebt+Equity) TotalDebt/Capitalization Thereisastrongrelationshipbetweenthebondratingacompanyreceivesandits performanceonthesefinancialratios.Companiesthatgenerateincomeandcashflowsthat aresignificantlyhigherthandebtpayments,thatareprofitable,andthathavelowdebtratios aremorelikelytobehighlyratedthanarecompaniesthatdonothavethesecharacteristics. Therewillbeindividualcompanieswhoseratingsarenotconsistentwiththeirfinancialratios, becausetheratingsagencydoesbringsubjectivejudgmentsintothefinalmix.Formost companies,however,thefinancialratiosshouldprovideareasonablebasisforestimatingthe bondrating. Tworemarkscanbemadewithregardtobondratings.First,basedonthedistributionof creditratingsforallU.S.andEuropeancompanieswithamarketcapitalizationover$1billion accordingtoStandard&Poor’s,isbecomesclearthatthevastmajorityofthecompanies (72%)areintheratingcategoryofA+toBBB.7 Second,Gray et al (2005)findthatinterestcoverageandleverageratioshavethemost pronouncedeffectoncreditratings,andthatprofitabilityvariablesandindustryconcentration measuresarealsoimportant.Theyalsodocumentaconsistenttrendtowardslowerratings– thestandardrequiredtoachieveaparticularratingisincreasingovertime. Thepreviousindicatesthatratingsprovideanindicationoftheprobabilityofdefaultforrated companies.Theseratingsarebasedonfinancialratiosandjudgmentoftheratingagencies. Throughtheusageofthecreditratingofcompany,onecandirectlyacquireanestimateofthe probabilityofdefault. 7 Koller et al. (2005)

MasterThesisSebastianOotjers 22 s0041823 IEMFEM ABCD 2.2.1 Altman’s Z-score Thesecondsourceofinformationonthecreditworthinessofcompaniesistherefinancial statement.Whiletheusageofaratingtoestimatetheprobabilityofdefaultisrestrictedto (mainly)largercompanies,thescoringmethodsbasedonthefinancialstatementsofa companycanbeusedforrating(practically)anycompany. Inrecentdecades,anumberofobjective,quantitativesystemsforscoringcreditshavebeen developed.OneoftheclassicstudiesofratioanalysisandbankruptcyisBeaver(1967). Beaver(1967)defines“failure”astheinabilityofacompanytopayitsfinancialobligationsas theymature.Hefindsthatfinancialratiosanalysiscanbeusefultoclassifyfailedand nonfailedcompaniesforatleastfiveyearsbeforefailureandthattheabilitytopredictfailure isstrongestinthecashflowtototaldebtratio. Anotherconclusionisthattheratiodistributionsofnonfailedcompaniesarequitestable throughoutthefiveyearsbeforefailure.Theratiodistributionsofthefailedcompaniesexhibit amarkeddeteriorationasfailureapproaches.Theresultisawideninggapbetweenthefailed andnonfailedcompanies.Thegapproducespersistentdifferencesinthemeanratiosoffailed andnonfailedcompanies,andthedifferenceincreasesasfailureapproaches. However,theratioanalysiscannotbeusedindiscriminately,becausenotallratiospredict equallywellandratiosdonotcorrectlypredictfailedandnonfailedcompanieswiththesame degreeofsuccess.Nonfailedcompaniescanbecorrectlyclassifiedtoagreaterextentthan thefailedcompanies. Studies,likeBeaver’s,precedingtheAltman(1968)studyimplyadefinitepotentialofratios aspredictorsofbankruptcy.Ingeneral,ratiosmeasuringprofitability,liquidity,andsolvency prevailedasthemostsignificantindicators.Altman(1968)aimedatdeterminingwhichratios aremostimportantindetectingbankruptcypotential,whatweightsshouldbeattachedto thoseselectedratios,andhowtheseweightsshouldobjectivelybeestablished.Theresulting Zscoremodelisamultivariateapproachbuiltonthevaluesofbothratiolevelandcategorical univariatemeasures.Caouette et al (1998)commentthat,thebasicZscoremodelhas enduredtothisdayandhasalsobeenappliedtoprivatecompanies,nonmanufacturing companiesandemergingmarkets. MultipleDiscriminantAnalysis(MDA)isastatisticaltechniqueusedtoclassifyanobservation intooneofseveral a priori groupingsdependentupontheobservation’sindividual characteristics.Itisusedprimarilytoclassifyand/ormakepredictionsinproblemswherethe dependentvariableappearsinqualitativeform,e.g.,maleorfemale,bankruptornon bankrupt.AltmandevelopedhismodelonthebasisoftheMDAtechnique. Fromhisoriginallistoftwentytwopotentiallyhelpfulvariables,Altmanselectedfivevariables asdoingthebestoveralljobtogetherinthepredictionofcorporatebankruptcy.Theoriginal 1968discriminatefunctionisasfollows:

Z = .0 012X1 + .0 014X 2 + .0 033X 3 + .0 006X 4 + .0 999X 5 where X1 =Workingcapital/Totalassets X2 =Retainedearnings/Totalassets X3 =Earningsbeforeinterestandtaxes/Totalassets X4 =Marketvalueequity/Bookvalueoftotaldebt X5 =Sales/Totalassets Z =OverallIndex Thegreateracompany’sbankruptcypotential,theloweritsdiscriminantscore.Allcompanies havingaZscoreofgreaterthan2.99fallintothe“nonbankrupt”sector,whilethose companieshavingaZscorebelow1.81areallbankrupt.Theareabetween1.81and2.99is definedasthe“zoneofignorance”or“grayarea”becauseofthesusceptibilitytoerror classification. Altman(1968)concluded,basedonhisresults,thatthebankruptcypredictionmodelisan accurateforecasteroffailureuptotwoyearspriortobankruptcyandthattheaccuracy

MasterThesisSebastianOotjers 23 s0041823 IEMFEM ABCD diminishessubstantiallyastheleadtimeincreases.Healsoconcluded(1)thatallofthe observedratiosshowadeterioratingtrendasbankruptcyapproaches,and(2)thatthemost seriouschangeinthemajorityoftheseratiosoccurredbetweenthethirdandthesecond yearspriortobankruptcy. InAltman(2000),whereherevisitstheoriginalZscoremodelanddiscussesthe developmentsovertheyears,heformulatesanadjustmenttotheZscoremodelthrough whichthespecificationofthemodelismoreconvenient:

Z = 2.1 X1 + 4.1 X 2 + 3.3 X 3 + 6.0 X 4 + 0.1 X 5 Usingthisformula,oneinsertsthemorecommonlywrittenpercentage,forexample,0.10for 10%,forthefirstfourvariables(X 1X4)androundsthelastcoefficientofftoequal1.0(from 0.99).Thelastvariablecontinuoustobewrittenintermsofnumberoftimes. Healsoadaptedthemodelfortheapplicationtoprivatecompanies,bysubstitutingthebook valuesofequityvalueforthemarketvalueinX 4.Theresultofthisrevisionprocesswitha newX 4variablewas:

Z'= .0 717(X1 ) + .0 847(X 2 ) + .3 107(X 3 ) + .0 420(X 4 ) + .0 998(X 5 ) Thegrayareaforthismodeliswider:thelowerboundaryis1.23insteadof1.81andthe upperboundaryis2.90insteadof2.99. ThenextmodificationoftheZscoremodelwasusedtoanalyzethecharacteristicsand accuracyofamodelwithoutX 5.Thiswasdonetominimizethepotentialindustryeffect,which ismorelikelytooccurwhenanindustrysensitivevariablesuchasassetturnoverisincluded. ThebookvalueofequitywasusedforX 4inthiscase. Theclassificationresultsareidenticaltotherevisedfivevariablemodel.ThenewZ’score modelwas:

Z '' = .6 56(X1 ) + .3 26(X 2 ) + .6 72(X 3 ) + .1 05(X 4 ) Thisparticularmodelisusefulinindustrieswherecompaniesfinancetheirassetsinvery differentwaysandwhereadjustmentssuchasleasecapitalizationarenotmade. In1977,Altman,HaldemanandNarayananconstructedasecondgenerationmodelwith severalenhancementstotheoriginalZscoreapproach.Thepurposeofthisstudywasto construct,analyzeandtestanewbankruptcyclassificationmodelwhichexplicitlyconsiders recentdevelopmentswithrespecttocompanyfailures.Thenewstudyalsoincorporated refinementsintheutilizationofdiscriminantstatisticaltechniques.Thenewmodel,called ZETA,waseffectiveinclassifyingbankruptcompaniesuptofiveyearspriortofailureona sampleofcompaniesconsistingofmanufacturersandretailers.However,sincetheZETA modelisaproprietaryeffort,theparametersofthemarketwerenotdisclosedin1977andare stillunavailabletoday. ThevariablesusedintheZETAmodelare:X1Returnonassets,X 2Stabilityofearnings,X 3 Debtservice,X 4Cumulativeprofitability,X 5Liquidity,X 6Capitalization,andX 7Size, measuredbythecompany’stotalassets. TheZETAmodelforassessingbankruptcyriskofcompaniesdemonstratesimproved accuracyoverexistingfailureclassificationmodel(Zscore),asisshowninthetablebelow, and,perhapsmoreimportantly,isbasedondatamorerelevanttocurrentconditionsandtoa largernumberofindustrialcompanies.

MasterThesisSebastianOotjers 24 s0041823 IEMFEM ABCD Classification accuracy between the ZETA model and various forms of the Z-score model

ZETAmodel Altman's1968model 1968model,ZETAsample Yearsprior Non Non Non Bankrupt Bankrupt Bankrupt tobankruptcy Bankrupt Bankrupt Bankrupt 1 96,2% 89,7% 93,9% 97,0% 86,8% 82,4% 2 84,9% 93,1% 71,9% 93,9% 83,0% 89,3% 3 74,5% 91,4% 48,3% n.a. 70,6% 91,4% 4 68,1% 89,5% 28,6% n.a. 61,7% 86,0% 5 69,8% 82,1% 36,0% n.a. 55,8% 86,2% WhentheZscoreandZETAmodelsweredeveloped,agreatdealofattentionwasgivento choosingtheratiostobeused.Thismayaccountforthecontinuedstabilityoftheirpredictive powerandthemodels’robustness. Oneoftheprimaryusesofcreditscoringmodelsistoassignabondratingequivalenttoeach score.Thisenablestheanalysttoassessthedefaultprobabilityofacompanybyobserving thehistoricalexperienceofeachbondrating. Thefollowingtable 8showstheaverageZscoreforbondsofdifferentbondclassesbasedon themodel Z = 2.1 X 1 + 4.1 X 2 + 3.3 X 3 + 6.0 X 4 + 0.1 X 5 inwhichtheratiosX 1throughX 4 areexpressedasdecimalsandnotpercentages. Average Z-score by Standard & Poor's Bond Rating S&P 500 (1991-1995) 1995 1994 1993 1992 1991

Rating No.ofFirms Avg. Avg. Avg. Avg. Avg.

AAA 11 5.020 4.376 4.506 5.263 6.357 AA 46 4.296 4.047 4.032 4.226 4.386 A 131 3.613 3.472 3.607 3.923 3.736 BBB 107 2.776 2.701 2.839 2.601 2.550 BB 30 2.449 2.276 2.185 2.102 2.219 B 8 1.673 1.876 1.964 1.962 1.887 NotethattheaverageZscorein1995rangedfromabout5.0forAAAbondsdownto1.67for Bbonds.TheaveragescoreforBratedcompaniesactuallyfallsintheZscore’sdistress zone. Altman’sZscoreisnotundisputed.Blums(2003),forinstance,statesthat“thedebateonthe appropriatevaluesforthescoringmodelofAltmanuntilthisdatehaslatentlystalledatthis pointwithmostresearcherssearchingamongtheoreticallyappropriatevariables”,andthat “thegeneralconclusionfrompreviousresearchisthatontheonehandeachstudybyitself seemstoprovideareasonabledegreeofdifferentiationbetweenfailedandnonfailed companies,whileontheotherhandthevariousstudieshardlyshowanyagreementonwhat factorsareimportantforfailureprediction.Morethen30yearsofresearchhavefailedto produceagreementonwhichvariablesaregoodpredictorsandwhy.” 2.2.3 Ohlson’s O-score OppositetotheMDAthatAltmanappliedtoarriveatascoringformula,multipleauthorsusea conditionallogitanalysisapproachtodoso.Ohlson(1980)alsointroducedanalternative scoringmethod.However,asformostlogitapproachmodels,thecreatorsdonotprovidea scaletoconvertthescoreintoaprobabilityofdefault. Ohlson’smodelisbrieflydiscussedbecausehestatessomeclearcommentsonusingMDA andhismodelgivesanindicationofratiosthatareusedinlogitapproachmodels. First,Ohlson(1980)identifiedfourbasicfactorsasbeingstatisticallysignificantinaffecting theprobabilityoffailure(withinoneyear).Theseare:(i)thesizeofthecompany;(ii)a 8 Caouette et al. (1998)

MasterThesisSebastianOotjers 25 s0041823 IEMFEM ABCD measure(s)ofthefinancialstructure;(iii)ameasure(s)ofperformance;(iv)ameasure(s)of currentliquidity.Second,hearguesthatpreviousstudiesappeartohaveoverstatedthe predictivepowerofmodelsdevelopedandtested. Ohlson(1980)arguesthattheeconometricmethodologyofconditionallogitanalysiswas chosentoavoidsomefairlywellknownproblemsassociatedwithMDA:(i)Therearecertain statisticalrequirementsimposedonthedistributionalpropertiesofthepredictors.(ii)The outputoftheapplicationofanMDAmodelisascorewhichhaslittleintuitiveinterpretation, sinceitisbasicallyanordinalranking(discriminatory)device.(iii)Therearealsocertain problemsrelatedtothe“matching”procedureswhichhavetypicallybeenusedinMDA. Healsoarguesthathisresultsagainsupportthecontentionthatsizeisanimportantpredictor ofbankruptcy. ThevariableOscoreisdefinedas: total _ liabil. working _ cap O − score = − .1 32 − .0 407log(total _ assets) + .6 03( ) − .1 43( ) total _ assets total _ assets current _ liabil. + .0 076( ) − .1 72 1( _ if _ total _ liabilities _ > _ total _ assets _, 0 _ if _ otherwise) current _ assets net _ income funds _ from _ operations − .2 37( ) − .1 83( ) total _ assets total _ liabilities + .0 285 1( _ if _ a _ net _ loss _ for _ the _ last _ two _ years _, 0 _ otherwise) net _ income − net _ income − .0 521( t t−1 ) | net _ incomet | + | net _ incomet−1 | 2.2.4 Contingent-claims models Thethirdcategoryofmodelsusesthestockpriceofacompanyasaninputfortheestimation oftheprobabilityofdefault.Thegeneralprincipleofthesecontingentclaimmodelsisthe following. Holdingacorporatebondisequivalenttolendingmoneywithnochanceofdefaultbutatthe sametimegivingstockholdersaputoptiononthecompany’sassets.Whenacompany defaults,itsstockholdersareineffectexercisingtheirput.Theput’svalueisthevalueofthe limitedliability–thevalueofstockholder’srighttowalkawayfromtheircompany’sdebtin exchangeforhandingoverthecompany’sassetstoitscreditors.Thus,valuingbondsshould beatwostepprocess: Bondvalue=bondvalueassumingnochanceofdefault–valueofputoption Owningacorporatebondisalsoequivalenttoowningthecompany’sassetsbutgivingacall optionontheseassetstothecompany’sstockholders: Bondvalue=assetvalue–valueofcalloptiononassets Tocalculatetheprobabilitythatacompanywilldefault,theexpectedgrowthinthemarket valueoftheassets,thefacevalueandmaturityofthedebtandthevariabilityoffutureasset valuesneedtobeknown.However,themarketvalueofassetsforindustrialcompaniesis unobservable.Thislackcanbefilledbyemployingcontingentclaimsmethodologytoinferthe marketvalueofassets,assetvolatility,anddefaultprobabilityfromstockpricehistoryandthe bookvalueofdebt 9. Crouhy et al.(2000)discusthemainfourcontingentclaimmodelswhicharethecredit migrationapproach,thestructuralapproach,CreditRisk+,andCreditPortfolioView. Thecreditmigrationapproach,asproposedbyJPMorganwithCreditMetrics,isbasedon creditmigrationanalysis,i.e.theprobabilityofmovingfromonecreditqualitytoanother, 9 Fang&Zong(2004)

MasterThesisSebastianOotjers 26 s0041823 IEMFEM ABCD includingdefault,withinagiventimehorizon,whichisoftentakenarbitrarilyas1year.The optionpricing,orstructuralapproach,asinitiatedbyKMVandwhichisbasedontheasset valuemodeloriginallyproposedbyMerton(1974)differssomewhatfromCreditMetricsasit reliesuponthe“ExpectedDefaultFrequency”,orEDF,foreachissuer,ratherthanuponthe averagehistoricaltransitionfrequenciesproducedbytheratingagencies,foreachcredit class. Attheendof1997,CreditSuisseFinancialProducts(CSFP)releasedanewapproach, CreditRisk+,whichonlyfocusesondefault.CreditRisk+assumesthatdefaultforindividual bonds,orloans,followsaPoissonprocess. McKinsey’sCreditPortfolioViewisadiscretetimemultiperiodmodel,wheredefault probabilitiesareafunctionofmacrovariablessuchasunemployment,thelevelofinterest rates,thegrowthrateintheeconomy,governmentexpenses,foreignexchangerates,which alsodrive,toalargeextent,creditcycles.

CreditMetrics/CreditVaRIaremethodologiesbasedontheestimationoftheforward distributionofthechangesinvalueofaportfolioofloanandbondtypeproductsatagiven timehorizon,usually1year. CreditMetrics/CreditVaRIdeterminestheprobabilityofdefaultthroughtheuseofarating system,withratingcategories,togetherwiththeprobabilitiesofmigratingfromonecredit qualitytoanotheroverthecreditriskhorizon.Thetransitionmatrixofcreditratingsisas follows. Probabilities of credit rating migrating from one rating quality to another, within one year

Initial Ratingatyearend(%) rating AAA AA A BBB BB B CCC Default AAA 90,81 8,33 0,68 0,06 0,12 0,00 0,00 0,00 AA 0,70 90,65 7,79 0,64 0,06 0,14 0,02 0,00 A 0,09 2,27 91,05 5,52 0,74 0,26 0,01 0,06 BBB 0,02 0,33 5,95 86,93 5,30 1,17 1,12 0,18 BB 0,03 0,14 0,67 7,73 80,53 8,84 1,00 1,06 B 0,00 0,11 0,24 0,43 6,48 83,46 4,07 5,20 CCC 0,22 0,00 0,22 1,30 2,38 11,24 64,86 19,79 Source:Standard&Poor'sCreditWeek(April15,1996) Toacquireacumulativedefaultrate,oneshouldmultiplythemigrationprobabilities. TheweaknessofCreditMetrics/CreditVaRIisnotthemethodology,buttherelianceon transitionprobabilitiesbasedonaveragehistoricalfrequenciesofdefaultsandcredit migration.TheaccuracyofCreditMetrics/CreditVaRIcalculationsreliesupontwocritical assumptions:first,allcompanieswithinthesameratingclasshavethesamedefaultrate,and second,theactualdefaultrateisequaltothehistoricalaveragedefaultrate.Thesame assumptionsalsoapplytotheothertransitionprobabilities.Inotherwords,creditrating changesandcreditqualitychangesareidentical,andcreditratinganddefaultratesare synonymous,i.e.theratingchangeswhenthedefaultrateisadjusted,andviceversa. ThisviewhasbeenstronglychallengedbyKMV.KMVhasshownthroughasimulation exercisethatthehistoricalaveragedefaultrateandtransitionprobabilitiescandeviate significantlyfromtheactualrates.Inaddition,KMVhasdemonstratedthatsubstantial differencesindefaultratesmayexistwithinthesamebondratingclass,andtheoverlapin defaultprobabilityrangesmaybequitelargewith,forinstance,someBBBandAArated bondshavingthesameprobabilityofdefault.KMValsoshowedthattheaveragehistorical defaultprobabilityoverstatesthedefaultrateforatypicalobligor. KMVderivestheactualprobabilityofdefault,theExpectedDefaultFrequency(EDF),foreach obligorbasedonaMerton(1974)’stypemodelofthecompany.Theprobabilityofdefaultis thusafunctionofthecompany’scapitalstructure,thevolatilityoftheassetreturnsandthe currentassetvalue.TheEDFiscompanyspecific,andcanbemappedintoanyratingsystem toderivetheequivalentratingoftheobligor.

MasterThesisSebastianOotjers 27 s0041823 IEMFEM ABCD KMVbestappliestopubliclytradedcompaniesforwhichthevalueofequityismarket determined.Theinformationcontainedinthecompany’sstockpriceandbalancesheetcan thenbetranslatedintoanimpliedriskofdefault. Thederivationoftheprobabilitiesofdefaultproceedsinthreestages:estimationofthe marketvalueandvolatilityofthecompany’sassets;calculationofthedistancetodefault, whichisanindexmeasureofdefaultrisk;andscalingofthedistancetodefaulttoactual probabilitiesofdefaultusingadefaultdatabase.Themarketvalueofequityisusedto estimatethemarketvalueandvolatilityofthecompany’sassetssincetheassetsvaluecan notdirectlybeobserved. KMVhasconstructedatransactionmatrixbasedupondefaultratesratherthanrating classes,whichisshownbelow. KMV 1-year transition matrix based on non-overlapping EDF ranges

Initial Ratingatyearend(%) rating AAA AA A BBB BB B CCC Default AAA 66,26 22,22 7,37 2,45 0,86 0,67 0,14 0,02 AA 21,66 43,04 25,83 6,56 1,99 0,68 0,20 0,04 A 2,76 20,34 44,19 22,94 7,42 1,97 0,28 0,10 BBB 0,30 2,80 22,63 42,54 23,52 6,95 1,00 0,26 BB 0,08 0,24 3,69 22,93 44,41 24,53 3,41 0,71 B 0,01 0,05 0,39 3,48 20,47 53,00 20,58 2,01 CCC 0,00 0,01 0,09 0,26 1,79 17,77 69,94 10,13 Source:KMVCorporation Thedifferencebetweenthevariousprobabilitiesbetweenthetwotablesisstriking.According toKMV,exceptforAAA,theprobabilityofstayinginthesameratingclassisbetweenhalfand onethirdofhistoricalratesproducedbytheratingagencies.KMV’sprobabilitiesofdefaultare alsolower,especiallyforthelowgradequality.Migrationprobabilitiesarealsomuchhigher forKMV,especiallyforthegradeaboveandbelowthecurrentratingclass. CreditRisk+appliesanactuarialscienceframeworktothederivationofthelossdistributionof abond/loanportfolio.Onlydefaultriskismodeled,notdowngraderisk.ContrarytoKMV, defaultriskisnotrelatedtothecapitalstructureofthecompany.InCreditRisk+no assumptionismadeaboutthecausesofdefault:anobligorAiseitherindefaultwith probabilityP A,oritisnotindefaultwithprobability1–P A.Itisassumedthat: - Foraloan,theprobabilityofdefaultinanygivenperiod,say1month,isthesameforany othermonth. - Foralargenumberofobligors,theprobabilityofdefaultbyanyparticularobligorissmall, andthenumbersofdefaultsthatoccurinanygivenperiodisindependentofthenumber ofdefaultsthatoccurinanyotherperiod. CreditPortfolioViewisamultifactormodelwhichisusedtosimulatethejointconditional distributionofdefaultandmigrationprobabilitiesforvariousratinggroupsindifferent industries,foreachcountry,conditionalonthevalueofmacroeconomicfactorslikethe unemploymentrate,therateofgrowthinGDP,theleveloflongterminterestrates,foreign exchangerates,governmentexpendituresandtheaggregatesavingsrate. 2.2.5 Subjects of analysis regarding the probability of default Therearemultipleapproachesforestimatingtheprobabilityofdefaultofacompany.Each approachrequiresaparticulartypeofinput,therebyrestrictingitsusefulnesstothesituations inwhichtheneededinputisavailable. Itistobeexpected,fromapracticalpointofview,thatthepotentialfordefaulthasanimpact onthevalueofacompany.Eachofthetwovaluationmodelsisthereforealsoexpectedto incorporateacertainmeasureorfactoroftheriskofdefaulttorepresentthatimpact. Thefirstsubjectofanalysis,resultingfromthis,iswhetherthevaluationmodelsusea measureoftheprobabilityofdefault.Thesecondsubjectofanalysis,incaseofapositive answeronthefirstsubject,iswhatmodel/approachisusedtodeterminetheprobabilityof default.Thissubjectisrelevantbecausetheapproachimpliedbythemodelcouldimpactthe

MasterThesisSebastianOotjers 28 s0041823 IEMFEM ABCD valuationoutcomeoreventhefactwhethertheprobabilityofdefaultcanbedeterminedatall basedontheavailableinformation. So,thetwosubjectsare: 1. Theusageoftheprobabilityofdefaultinthevaluationmodel. 2. Themodel/approachthatisused(incaseofactualusageoftheprobabilityofdefault) todeterminetheprobabilityofdefault.Whichmodeltousecoulddependentonthe typeofcompanythatisbeingvalued. 2.3 Thepurposeofthisparagraphistogiveanoverviewofthetheoriesoncapitalstructure decisionsofacompany.Theeffectsofanumberoffactorsonleveragearecomparedtothe inferencesthatthedifferenttheoriesoncapitalstructuredecisionsmaketoseewhichtheory describesrealityinthemostaccurateway. Mostoftheliteratureoncapitalstructureisfocusedonthediscussionwhetherthe tax/bankruptcytradeofftheoryorthepeckingordertheoryisthetheorythatbestdescribes reality.Frank&Goyal(2003a)provideanoverviewofthefactorsthatdeterminetheamount ofleveragethatacompanyadopts.Theycomparefivedifferenttheoriesonthebasisofthese factors.Becauseoftheirextensiveandclearreview,theirarticleisusedasoneofthemain sourcesofthisparagraph. 2.3.1 Definition of capital structure AccordingtoDuffhues(1997),capitalstructureisdefinedasthecompositionofthetotal amountofcapitalthatisvisibleattherighthandsideofabalancesheet. Theconceptofcapitalinthedefinitionofcapitalstructurehasthecharacteristicoftotal capital.Themeaningoftotalcapitalisnotunambiguouslydefinedintheoryorinpractice.It hasmultipledefinitions.Threeofthemare:abalancesheetdefinition,anactivecapital definition,anda(middleoftheroad)standalonecapitaldefinition.Toaddinsulttoinjury, thesedefinitionsarealsoexpressedintwodifferentvaluationprinciples:bookvalueand marketvalue. Inthefirstdefinition,totalcapitalequalsthesumoftheliabilitiesaccordingtotheregular dispositionusedinpublishedannualaccounts;thatisincludingtheinducedshorttermdebt. Inducedshorttermdebtisthetotalamountofcapitalthatorganicallygrowswiththesizeof thebusinessactivities,likeaccountspayableanddeferredwages. Theseconddefinitionofcapitalstructureplaysanincreasinglylargerpartinannualreporting. Inthiscase,totalcapitalisequaltoactivecapital.Allshorttermdebtisignored. Thethirddefinitionstaysinbetweenthefirsttwodefinitions.Totalcapitalisinthiscaseequal tothesumofallliabilitiesminustheinducedshorttermdebt. Duffhues(1997)alsostatesthatmultiplecriteriaareavailabletoclassifythedifferent componentsofthetotalcapital.First,thecapitalstructurecanbeclassifiedintwo componentsthatarerelatedtotheabsenceorpresenceofadebtrelationbetweenthe companyandtheprovidersofcapital.Iftherelationisabsent,thenthecapitalcomponentis referredtoasequity.Capitalcomponentsthathaveadebtrelationarenameddebt.Asecond criterionisbasedonthetimetomaturityoftheindividualfinancingtransaction.Permanent capitalhasbeendisposedtothecompanyforanindefiniteperiodoftime.Longtermcapital comprisescapitalwithafinitetimetomaturitylargerthanoneyear.Shorttermcapital comprisescapitalwithatimetomaturityofatmostoneyear.Permanentcapitalcoincides withequity,temporarycapitalcoincideswithdebt. Ifwitheverychoiceofthecapitalstructure(standalonedefinition)themarketvalueofthe totalcapital–ofwhichmaximizationispursued–wouldbethesame,thenthechoiceof capitalstructurewouldbeirrelevant.Thiswouldbethecaseinthefollowingtwoextreme situations: Thereisnoneedforriskbearingcapital. Thereisperfectsubstitutionbetweenthemarketvalueofthecomponentsoftotal capital. Whenthefuturecashflowsofacompanywouldbecertain,thenthedifferencebetweendebt andequitywoulddisappear.Allcapitalproviderswouldreceiveareturninthissituationthatis

MasterThesisSebastianOotjers 29 s0041823 IEMFEM ABCD equaltotheriskfreereturn.Thecapitalstructurecouldthan,withoutanyobjections,be composedofsolelydebt. Whenfuturecashflowsofacompanyareuncertain,aneedexistforequitytocoverpotential futurelosses.However,thisdoesnotmeanthatthinkingoftheexactchoiceofthecapital structurebecomesrelevant.Thissituationcreatesafakeproblemwhenasaresultof exchangingequityfordebt(ortheotherwayaround)themarketvalueoftheonetypeof capitalchangesinthesameamountasthemarketvalueoftheothertypeofcapitalinthe oppositedirectionthusleavingthesumatanequalvalue. 2.3.2 Financial deficit Companiesinvestinlongtermassets(mainlyproperty,plant,andequipment)andnet workingcapital.Fromthetablebelow,itcanbeseenthatbyfarthegreaterpartofthemoney isgeneratedinternally.Inotherwords,itcomesfromcashthatthecompanyhassetasideas depreciationandfromretainedearnings. 1994 1995 1996 1997 1998 1999 2000 CapitalExpenditure 83,2% 77,6% 87,6% 81,0% 89,1% 80,4% 86,6% Investmentinnetworkingcapital 16,8% 22,4% 12,4% 19,0% 10,9% 19,6% 13,4% andotheruses

TotalInvestment 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% 100,0% TotalInvestment,billions 754 789 755 880 872 1116 1162 Internallygeneratedcash 87,7% 78,6% 89,5% 82,7% 85,7% 72,1% 76,7% Financialdeficit 12,3% 21,4% 10,5% 17,3% 14,3% 27,9% 23,3% Financial deficit covered by: Netstockissues 6,9% 7,4% 9,2% 13,0% 30,6% 12,9% 14,3% Netincreaseindebt 19,3% 28,8% 19,7% 30,3% 45,0% 40,8% 37,6%

Source:BoardofGovernorsoftheFederalReserveSystem,DivisionofResearchandStatistics,at www.federalreserve.gov/releases/z1/current/data.htm Inmostyearsthereisagapbetweenthecashthatcompaniesneedandthecashthatthey generateinternally.Thisgapisthe financial deficit .Frank&Goyal(2003b)givethefollowing formulaforcalculatingthefinancialdeficit:

DEFt = DIVt + It + Wt − Ct = Dt + Et WithDIV t ascashdividendsinyeart,I tthenetinvestmentinyeart(i.e.,I t=capital expenditures+increaseinvestments+acquisitions+otheruseoffunds–saleofPPE–sale ofinvestment),W tthechangeinworkingcapitalinyeart,C tthecashflowafterinterestand taxes,D tthenetdebtissuedinyeart,andE t thenetequityissuedinyeart. Tomakeupthedeficit,companiesmusteithersellnewequityorborrow.Socompaniesface twobasicfinancingdecisions:Howmuchprofitshouldbeplowedbackintothebusiness ratherthanpaidoutasdividends?And,whatproportionofthedeficitshouldbefinancedby borrowingratherthanbyanissueofequity? CompaniesintheUnitedStatesarenotaloneintheirheavyrelianceoninternalfunds. InternalfundsmakeupmorethantwothirdsofcorporatefinancinginGermany,Japan,and theUnitedKingdom. 2.3.3 Effects of capital structure Althoughacademicresearchershaveinvestigatedtheissuefordecades,thereisstillnoclear modelforacompany’soptimalleverageratio,theleveragethatwouldcreatethemostvalue forshareholders.Butthereisevidencethatleveragedeliverskeybenefitsaswellasgiving risetocertaincosts 10 . 1. Taxsavings:themostobviousbenefitofdebtversusequityisthereductionoftaxes. However,thistaxreductiondoesnotmakefulldebtfundingoptimal.Forexample, 10 Koller et al.(2005)

MasterThesisSebastianOotjers 30 s0041823 IEMFEM ABCD moredebtfundingmayreducecorporatetaxesbutcouldactuallyleadtohighertaxes forinvestors. 2. Reductionofcorporateoverinvestment:thesocalled free cash flow hypothesis arguesthatdebtcanhelpimposeinvestmentdisciplineonmanagers.Debtcurbs overinvestmentbyforcingthecompanytopayoutfreecashflowaccordingto scheduledinterestandprincipalobligations. 3. Costsofbusinesserosionandbankruptcy:mostnotably,bankruptcycostsarethe legalandadministrativecostsofliquidatingorrestructuringthecompanyforthedebt holdersafterithasdefaultedonitsdebt.Academicresearchindicatesthatthese costsarerelativelysmall,aroundthreepercentofacompany’smarketvalue. Howeverthecostsofbusinesserosionareprobablymuchhigher.Highlyleveraged companiesaremorelikelytoforgoinvestmentopportunitiesorreducebudgetsfor researchanddevelopmentandothercostsforwhichthepayoffsarefurtherinthe future.Asaresult,thesecompaniesmaylosesignificantvaluecreationopportunities. Furthermore,astheriskoffinancialdistressincreases,companiesbecomemore likelytolosecustomers,employees,andsuppliers.Theriskoflosingbusinessis high,particularlywhentheproductsrequirelongtermserviceandmaintenance. 4. Costsofinvestorconflicts:higherleveragemaycauseadditionallossofvalueasa resultofconflictsofinterestamongdebtholders,shareholders,andmanagers. 2.3.4 Capital structure development theories Frank&Goyal(2003a)comparetheempiricalsupportforcertainfactorsthatinfluencecapital structuredecisionsofacompanytopredictionsoffivedifferenttheoriesofcapitalstructure choices.Thesearethefollowing. 1. Thepeckingordertheory:Duetoadverseselection,companiesprefertofinancetheir activitiesusingretainedearningsifpossible.Ifretainedearningsareinadequate,then theyturntotheuseofdebt.Equityfinancingisonlyusedasalastresort.Thepecking ordertheoryisthereforeatheoryofleverageinwhichthereisnonotionofanoptimal leverageratio.Observedleverageissimplythesumofpastevents. 2. Themarkettimingtheory:Thebasicideabehindthemarkettimingtheoryisthat managerslookatcurrentconditionsinbothdebtmarketsandequitymarkets.Ifthey needfinancing,thentheywillusewhichevermarketlooksmorefavorableatthetime. 3. Thetax/bankruptcytradeofftheory:Companiesdetermineaninteriorleverage optimumbyabalancingofthecorporatetaxsavingsadvantageofdebtagainstthe deadweightcostsofbankruptcy. 4. Theagencytheory:Companymanagersmaybetemptedtooverspendtheirfree cashflow,sohighdebtisusefultocontrolthisoverspendingimpulse.Ofcourse,this increaseinleveragedoesincreasethechanceofpayingdeadweightbankruptcy costs.Thereareagencyconflictsbetweendebtholdersandequityholders. 5. Stakeholdercoinvestmenttheory:Inordertoinsurethewillingnessofstakeholders, suchasemployeesandbusinesspartnerstomakevaluablecoinvestments,some companiesprefertouselittledebtwhencomparedtoothercompanies. 2.3.5 Factors that influence capital structure Frank&Goyal(2003a)findempiricalsupportforfourteenfactorsthatinfluencecapital structuredecisionsofacompany.Factorsthathavethemoststatisticallyrobustand economicallylargeeffectsareclassifiedasTier1.Tier2factorsarelessrobust,butarestill generallysupportedbytheevidenceoftheirstudy. InTier1,leverageispositivelyrelatedtomedianindustryleverage,companysizeas measuredbylogofsales,intangibleassets,andcollateral.Leverageisnegativelyrelatedto firmriskasmeasuredbyAltman’sZScore,adummyfordividendpayingcompanies,andthe markettobookratio. InTier2,leverageispositivelyrelatedtocompanygrowthasmeasuredbythechangeintotal assets,thetopcorporatetaxrate,andtheTreasurybillrate.Leverageisnegativelyrelatedto thevolatilityofacompany’sownstockreturns,itsnetoperatinglosscarryforwards(NOLCF), corporateprofits,andtobeingfinanciallyconstrainedasmeasuredbyKorajczyk&Levy’s (2003)financialconstraintdummyvariable.

MasterThesisSebastianOotjers 31 s0041823 IEMFEM ABCD Korajczyk&Levy(2003)theoreticallydefinefinanciallyconstrainedcompaniesasthesetof companiesthatdonothavesufficientcashtoundertakeinvestmentopportunitiesandthat facesevereagencycostswhenaccessingfinancialmarkets. 2.3.6 Support for the different theories by the fourteen factors Frank&Goyal(2003a)comparethefoundinfluenceofthedifferentfactorsonleveragetothe predictionsofthedifferenttheories.Thefollowingisanoverviewofthiscomparisonforeach factor. Ineverycase,companiesinahighleverageindustryhavehigherleverage.Thisisquite naturalwithinatradeoffmodelsincecompaniesinthesameindustrymustfacemany commonforces.Underapurepeckingorderperspective,theindustryshouldonlymatterto thedegreethatitservesasaproxyforthecompany’sfinancingdeficit–aratherindirectlink. Underthemarkettimingtheory,thisresultisnotpredicted. Leverageispositivelyrelatedtocompanysizeasmeasuredbylogofsalesandpositively relatedtointangibleassets.Anintangibleisdefinedtobe“assetsthathavenophysical existenceinthemselves,butrepresenttherighttoenjoysomeprivilege”.Itiseasytoimagine thatintangibleassets,usingtheabovedefinition,couldbeusedascollateraltosupportdebt. Underthisinterpretation,thesigniswhatisaspredictedbytradeofftheory.Itisdifficulttosee howthisfitsundermarkettimingtheory.Underthepeckingorderonemightexpectthat increasedintangibleswouldbeassociatedwithincreasedleveragesincesuchassetsare hardtovalueandthusinsidersmightknowmorethanoutsidersregardingtheirtruevalue. Leverageispositivelyrelatedtocollateral.Fromatradeoffperspective,acompanywithmore assetscanpledgetheminsupportofdebt.Underthepeckingordertheory,acompanywith moreassetshasagreaterworryabouttheadverseselectiononthoseassets.Accordingly, onemightpredictthatleverageispositivelyrelatedtoassets.Underthepeckingordertheory, onemightpredictanegativerelationtodebt.Thisambiguitystemsfromthefactthatcollateral canbeviewedasaproxyfordifferenteconomicforces. LeverageisnegativelyrelatedtocompanyriskasmeasuredbymodifiedAltman’sZScore. Withinthetradeofftheory,thismakessense.Whenthereisagreaterriskofbankruptcycosts, thecompanywilltakeoffsettingactionbyreducingleverage.Similarly,inthestakeholderco investmentversionoftradeofftheory,evenwithoutdirectbankruptcycosts,downsizingor otherdisruptionsinnormalbusinessimposecosts.Companiestakeactionstoavoidthese costsbyreducingleverage.Fromthepeckingorderperspective,itisunclearwhyriskshould matter. Perhapsdividendpayingcompaniescanavoidpayingtransactioncoststounderwriters involvedinaccessingthepublicfinancialmarkets.Ifso,thenunderthetradeofftheory, dividendpayersshouldhavelessleverage.ThisiswhatwasfoundbyFrank&Goyal(2003). Sincethefinancingofdividendisbydebt,theimplicationofthepeckingordertheoryisthat dividendpayingcompaniesshouldhavegreaterleverage.ThisisnotwhatFrank&Goyal (2003a)found.

Themarkettobookratioisnegativelyrelatedtoleverage.Itisusuallyinterpretedasreflecting aneedtoretaingrowthoptions.Thisinterpretationisconsistentwiththetradeofftheory. Underthepeckingordertheory,moreprofitablecompaniesuselessdebt.Moreprofitable companiesshouldalsohaveahighermarketvalue.Thusonemightexpectthatahighmarket tobookcompanywouldhavelowleverage.ThisisconsistentwiththefindingsofFrank& Goyal(2003a). Leverageispositivelyrelatedtocompanygrowthasmeasuredbythechangeintotalassets. Underthetradeofftheorythisreflectsthefactthatassetscanbepledgedascollateral.Under thepeckingordertheory,thisreflectsthefactthatdebtisusedtocoverthefinancingdeficit. Leverageispositivelyrelatedtothetopcorporatetaxrate. Thisisdirectlypredictedbythe taxbasedversionsofthetradeofftheory.Thisisnotpredictedbythemarkettimingtheory, peckingordertheory,ornontaxbasedversionsofthetradeofftheory.

MasterThesisSebastianOotjers 32 s0041823 IEMFEM ABCD Leverageispositivelyrelatedtotheinterestrate.Thisisnotpredictedbythepeckingorder theory,becausehigherinterestrateslowerthedebtcapacity,andthuslowerleverage.The tradeofftheorypredictsthatthenegativeeffectofahigherinterestrateisstrongerforequity thanfordebt,thusincreasingleverage.ThisisconsistentwiththeFrank&Goyal(2003) results. Leverageisnegativelyrelatedtothevolatilityofacompany’sownstockreturns–asimple measureofrisk.Inthetradeofftheorycompaniesreacttoriskbyreducingleverage.Under thepeckingordertheory,riskmatterstothedegreethatitisasymmetric. Leverageisnegativelyrelatedtonetoperatinglosscarryforwards.Thisisadirectimplication ofthetradeofftheory. Itiswellknownthatleverageisnegativelyrelatedtocorporateprofits.Thisisinconsistent withstaticversionsofthetradeofftheory,inwhichthecompanyconstantlyadaptsits financingmixtostayattheirtargetleverageratio.Itisconsistentwithsomedynamicversions ofthetradeofftheory,inwhichthecompanyonlychangesitsfinancingmixiftheleverage ratiopassestheendpointsoftheoptimalleverageratiointerval.Itisalsoconsistentwiththe peckingordertheory. Consistentwiththepreviousliterature,Frank&Goyal(2003)findthatleverageincreaseswith theaverageleverageinanindustry,withcompanysize,andwiththepresenceofcollateral. Alsoconsistentwiththeliterature,riskiercompaniesandhighmarkettobookcompanies havelowerleverage. Theystatethatovertimethesignonprofitismovinginthedirectionofthepredictionsofthe tradeofftheory. Mostoftheevidenceiseasytounderstandwithinthetradeoffclassoftheories.Frank& Goyal(2003a)considerthreeversionsofthetradeofftheory:taxesversusbankruptcycosts, agencycosts,andstakeholdercoinvestment.Sincetaxeffectsappeartobereal,versionsof thetradeofftheorythatallowfortaxeffectsarepreferred. Itiswellunderstoodthatcompanycircumstancesmaybeimportantforleveragedecisions. Forinstance,thelevelofsalesisparticularlyimportantfornondividendpayingcompanies, youngcompaniesandsmallcompanies.Largecompaniesseemmoreconcernedabouttax factorsthandosmallcompanies.However,themajorfactorshavereliableeffectsacross companycircumstances. 2.3.7 Debt capacity Lemmon&Zender(2004)presentevidencethatcompaniesfollowapeckingorderin incrementalfinancingchoiceandoffersubstantialsupportforadynamicversionofthe peckingordertheoryarticulatedinMyers(1984)byexplicitlyrecognizingtheroleofdebt capacityinthetheory. Companiesunconstrainedbyconcernsoverdebtcapacityprimarilyusedebttofilltheir financingdeficitwhileconstrainedcompaniesexhibitaheavyrelianceonexternalequity financing.Lemmon&Zender(2004)showthatcompaniesappearto“stockpile”debtcapacity. Whenpossible,internallygeneratedfundsareusedtofinancenewinvestmentandtoreduce debtlevels.Directlycontrarytothetradeofftheoryweseethatcompanieswithlowleverage expectinghighprofitsandhavinglowexternalfinancingrequirementsexhibitthisbehavior. DebtcapacitywasdefinedbyMyers(1977)asthepointatwhichanincreaseintheuseof debt(fixedcommitments)actuallyreducesthetotalmarketvalueofthecompany’sdebt.More recently,ShyamSunder&Myers(1999)andChirinko&Singha(2000)defineitintermsof “sufficientlyhighdebtratios”implyingthatcostsoffinancialdistresscurtailfurtherdebtissues. Addingdebtcapacitytothepeckingordertheorysuggeststhatcostsofadverseselectionare dominantformoderatecapitalstructuresbutthattradeofftheorylikeforcesbecomeprimary motivatorsoffinancingdecisionsatextremelyhighleveragemakingitmoredifficultto distinguishthetheories. Lemmon&Zender’sprimaryindicatorofwhetherdebtcapacityconcernsconstraina company’schoicesiswhetherthecompanyhasrateddebtoutstandinginagivenyear.

MasterThesisSebastianOotjers 33 s0041823 IEMFEM ABCD ThestudyofLemmon&Zender(2004)showsastrikingcontrast:forthosecompaniesthat shouldfacetighterdebtcapacityconstraints,netissuesofequityarehighlycorrelatedwith thefinancialdeficit(asopposedtoahighcorrelationbetweenthefinancialdeficitandnetdebt issuesaspredictedbythestaticpeckingordertheory). Further,comparedtocompanieswithoutbondratings,companieswithrateddebtoutstanding areonaveragemorehighlylevered.Allofthesefindingsareconsistentwiththeideathat companieswithrateddebthavehigherlevelsofborrowingcapacity. Thefinancingbehaviorofcompanieswithoutrateddebtisfarfromthatpredictedbythestatic peckingorder.Forthecompanieswithrateddebtoutstandingtheresultsarequitedifferent andsupportthepredictionsofthestaticpeckingorder. Thedynamicpeckingordertheorypredictsthatfinancingbehaviorwillbedependentupon bothacompany’sdistancetoitscurrentdebtcapacityandthespeedatwhichthecompany expectstoapproachitsdebtcapacitygivenitscurrentandfuturefinancingneeds. Onceconsiderationofdebtcapacityistakenintoaccountinthepeckingorderitbecomes moredifficulttodistinguishitfromadynamicversionofthetradeofftheorywithissuance costs. Thetwotheoriesprovidecontrastinghypotheses,however,forhighlyprofitablecompanies thatarefarbelowtheirdebtcapacities.Thepeckingordertheory,bothstaticanddynamic, predictsthatprofitablecompanieswithlowleveragehavenoincentivetoincreasetheir leverage. Conversely,thedynamictradeofftheorypredictsthatinsuchsituationsnewdebtfinancing wouldbepreferredtoanincreaseduseof(internal)equity. Theresultsprovideevidencethatinternallygeneratedfundsarethepreferredsourceof financing,regardlessofexistingleverageandexpectedprofitability. Moreover,evencompanieswithlowinitialleverageuseexcessprofitstoreducetheir leverageratiosovertime.Thisfindingisdirectlycontrarytothetradeofftheory. Theseresultssuggestthatthosecompanieswhoissuethemajorityofexternalequitycanbe classifiedasconstrainedbyconcernsoverdebtcapacity,andprovideareconciliationofthe resultsinFama&French(2002)andFrank&Goyal(2003a)withthepeckingorder. Theresultsareconsistentwiththreeinterpretations.Thefirstisthatalthoughthesmall,high growthcompaniesinthelowpredictedratinggroupmayfacemoreasymmetricinformation concerningthevalueoftheirassetsinplace,theyalsofacerelativelymorevaluable investmentopportunitysets.Thesecondisthatthemarketrealizesthat,duetotheconstraint imposedbydebtcapacity,thecompanyhaslittleornoflexibilityinitschoiceoffinancing instrumentsandsotheannouncementofanequityissueislessofabadsignalthanitwould beforasimilarcompanythatcouldalsochoosetoissuelowriskdebt.Last,ifsmall,high growthcompaniesarebetterat“timing”theirequityissueswewouldexpecttoseethis pattern. Nonetheless,Lemmon&Zender’sresultsprovidearationalewithinthepeckingorder frameworkforthefrequentequityissuesbysmall,highgrowthcompanies,whichothershave posedasachallengetothetheory. TheresultsfromtheresearchofFrank&Goyal(2003a)identifyanumberoffactorsthat influencethecapitalstructuredecisionsofcompanies.Aftercomparingtheeffectsofthese factorstothedifferenttheoriesofcapitalstructuretheyconcludethatthetradeofftheories, especiallythetaxes/bankruptcytradeofftheory,aresupportedmost. Lemmon&Zender(2004)respondtotheseresultsbyintegratingtheconceptof‘debt capacity’intheiranalysisofcapitalstructuredecision.Thisleadstothefollowingoverview.

MasterThesisSebastianOotjers 34 s0041823 IEMFEM ABCD

Pecking Market Tax/ Agency/ Stakeholder Factors Found relation Order Timing Bankruptcy Bankruptcy CoInvestment

IndustryLeverage + + + + Zscore Firmsize + + + + Dividendpaying + Tier1 Intangibles + + + + + Markettobookratio Collateral + + + +

Stockvariance + NetOperatingLoss Carryforwards Financiallyconstrained (dc) + Tier2 Profitability + + + Changeintotalassets + + + TaxRate + + TreasuryBillRate + + + +

ThetableshowthefactorsdeterminedbyFrank&Goyal(2003a)andtheireffectonleverage aspredictedbythedifferenttheories,includingthecorrectionfortheeffectofdebtcapacity. 2.3.8 Views of other authors Otherauthorshavealsostudiedtheeffectofdifferentfactorsonthecapitalstructure developmentwithinacompany.Whencomparingthesestudies,onecanconcludethatthere isnotaspecificcompletetheorytodescribecapitalstructuredecisions,butanumberof theoriesthatapplyundercertainconditions. Hovakimian et al. (2001)concludethat“althoughthepeckingorderconsiderationsaffect corporatedebtratiosintheshortrun,companiestendtomakefinancingchoicesthatmove themtowardtargetdebtratiosthatareconsistentwithtradeoffmodelsofcapitalstructure choice”. Myers(2001)commentsthatthetradeofftheorycannotaccountforthecorrelationbetween highprofitabilityandlowdebtratios.Ontheotherhand,healsocommentsthatpotential conflictsofinterestbetweenlendersandstockholderssignificantlyincreasethepotentialcost offinancialdistressthroughsuboptimalinvestmentandoperatingdecisions.Thiscontributes tothetradeofftheoryofwhichfinancialdistresscostareanimportantfactor. Fama&French(2002)concludethatthetradeoffandpeckingordermodelsharemany predictionsaboutdividendsandleverage.Theyalsocommentthatthetradeoffmodelis scarredbythenegativerelationbetweenprofitabilityandleverage,thatthepeckingorderis woundedbythelargeuseofequitybysmalllowleveragegrowthcompaniesandthatthe issueofthemeanreversionofleverageisundecidedsincemeanreversionseemstohappen butataveryslowpace. Korajczyk&Levy(2003)concludethattheirresultsareconsistentwithelementsofboth tradeoffandpeckingordertheories.Theyalsoconcludethatconstrainedcompaniesfitthe peckingordertheorylesswellthanunconstrainedcompanies. 2.3.9 Subjects of analysis regarding capital structure Therearemultipletheoriesonthepredictionofcapitalstructurechoices.Themostwell knownarethe(tax/bankruptcy)tradeofftheoryandthepeckingordertheory.Althoughmany authorshavegivenargumentsoverthepastyearstosupportoneoftheseorboththeories, neitherofthetwohascometobethe‘ultimate’theoryofcapitalstructure.

MasterThesisSebastianOotjers 35 s0041823 IEMFEM ABCD IntheanalysisoftheenterpriseDCFmodelandtheAPVmodel,thefollowingsubjectswith regardtocapitalstructureneedtobeconsidered: 1. Whataretheassumptionsoncapitalstructureofthevaluationmodel? 2. Whataretheconditionsofcapitalstructurerequiredforthemodeltobeused? 3. Ifthemodelcanbeused,howcanthecapitalstructuredecisionsbemodeled?

Thefirstsubjectissimplyameanstoidentifytheinfluenceofcapitalstructureonthe valuationmodel.Thesecondsubjectneedstobeanalyzedtodeterminewhetherthereare certaincapitalstructuresituationsinwhichoneofthetwovaluationmodelscannotbeused. Thelastsubjectrelatestothetheoriesdescribedabove:ifthemodelcanbeused,howare capitalstructuredecisionsmodeled? 2.4 Costs of Thepurposeofthisparagraphistogiveanoverviewofthetheoriesonthecostsoffinancial distress.Mostoftheliteratureonthecostsoffinancialdistressfocusesonestimatingthese costs.Thisparagraphdiscussestheseestimates.Italsodescribessomecommentsonthe costsoffinancialdistress.Theparagraphcloseswiththe(final)subjectsofanalysis,those regardingthecostsoffinancialdistress. 2.4.1 Definition of financial distress Financialdistressoccurswhenpromisestocreditorsarebrokenorhonoredwithdifficulty. Sometimesfinancialdistressleadstobankruptcy.Sometimesitonlymeansskatingonthin ice.Financialdistressgenerallyleadstonegotiationswithatleastoneofthecompany’s creditors.Financialdistressisresolvedinanenvironmentofimperfectinformationand conflictsofinterest.Yetevidenceonthefrequencydistributionofoutcomesforcompaniesin distressprovesthatitisnotsynonymouswithcorporatedeath. Corporatebankruptciesoccurwhenstockholdersexercisetheirrighttodefault.Thatrightis valuable;whenacompanygetsintotrouble,limitedliabilityallowsstockholderssimplytowalk awayfromit,leavingallitstroublestoitscreditors.Theformercreditorsbecomethenew stockholders,andtheoldstockholdersareleftwithnothing. Thedeclineinthevalueofassetsiswhatthemourningisreallyabout.Thathasnonecessary connectionwithfinancing.Thebankruptcyismerelyalegalmechanismforallowingcreditors totakeoverwhenthedeclineinthevalueofassetstriggersadefault.Bankruptcyisnotthe causeofthedeclineinvalue.Itistheresult. Twotypesofbankruptcyfilingsareavailabletocorporations:Chapter 7 andChapter11 (thesetitlesrefertochaptersoftheUSBankruptcyCode).Chapter7providesfortheorderly liquidationofacompany’sassetsbyacourtappointedtrustee,andpaymenttoclaimantsin orderofpriorityisalwaysmaintained.Chapter11providesforreorganizationofacompany. ParticipantsinaChapter11filingmustapproveaplanofreorganization,leavingroomfor negotiationsamongthevariouspartiesandforviolationofpriorityofclaims. Noteverycompanythatgetsintotroublegoesbankrupt.Whenacompanyisintrouble,both bondholdersandstockholderswantittorecover,butinotherrespectstheirinterestsmaybe inconflict. AccordingtoBrealey&Myers(2003),financialdistressiscostlywhentheseconflictsof interestgetinthewayofproperoperating,investment,andfinancingdecisions.Stockholders aretemptedtoforsaketheusualobjectiveofmaximizingtheoverallmarketvalueofthe companyandtopursuenarrowerselfinterestinstead.Theyaretemptedtoplaygamesatthe expenseoftheircreditors. Thefirstgamethatcanbeplayedis risk shifting .Thisgameillustratesthat,stockholdersof leveredfirmsgainwhenbusinessriskincreases.Financialmanagerswhoactstrictlyintheir shareholders’interestwillfavorriskyprojectsoversafeones.Theymayeventakerisky projectswithnegativenetpresentvalues(NPVs). Thisdistortedstrategyforcapitalbudgetingclearlyiscostlytothecompanyandtothe economyasawhole.Thetemptationtoplaythisgameisstrongestwhentheoddsofdefault arehigh.

MasterThesisSebastianOotjers 36 s0041823 IEMFEM ABCD Thesecondgameisrefusingtocontributeequitycapital.Thegameshowsthat,ifoneholds businessriskconstant,anyincreaseincompanyvalueissharedamongbondholdersand stockholders.Thevalueofanyinvestmentopportunitytothecompany’sstockholderis reducedbecauseprojectbenefitsmustbesharedwithbondholders.Thusitmaynotbeinthe stockholders’selfinteresttocontributefreshequitycapitalevenifthatmeansforgoing positiveNPVinvestmentopportunities. Aswithothergames,thetemptationtoplaythenextthreegamesisparticularlystrongin financialdistress: 1. Cashinandrun 2. Playingfortime 3. Baitandswitch Theresultsofthesegamesarepoordecisionsaboutinvestmentsandoperations.Thesepoor decisionsareagencycostsofborrowing. Someassets,likegoodcommercialrealestate,canpassthroughbankruptcyand reorganizationlargelyunscathed;thevaluesofotherassetsarelikelytobeconsidered diminished.Thelossesaregreatestfortheintangibleassetsthatarelinkedtothehealthof thecompanyasagoingconcern–forexample,technology,humancapital,andbrandimage. 2.4.2 Cost effects of financial distress Altman’s(1984)studyassumesthattheexpectedbankruptcycostissueisrelevantandthat firmsdorecognizetheprobabilityofbankruptcyasanimportantingredientwhenmaking operatingandfinancialdecisions. Altmanarguesthat,inadditiontothecostsofliquidation,thereareotherrelevantcosts includingthosewhichariseduetotheprocessofbankruptcy(eitherliquidationor reorganization)andthoseduetotheperceivedsignificantpotentialofbankruptcy(lost opportunitiesandabnormallossofsalesandprofits). Indirectbankruptcycostsarenotlimitedtocompanieswhichactuallydofail.Companies whichhavehighprobabilitiesofbankruptcy,whethertheyeventuallyfailornot,stillcanincur thesecosts. Wruck(1990)describesthecostsoffinancialdistressas: 1. Directcosts.Theoutofpocketordirectcostsoffinancialdistressaretheeasiestto measure.Theyincludelegal,administrative,andadvisoryfeespaidbythecompany. Comparingthedirectcostsofprivateworkoutswithdirectcostsofbankruptcy suggeststhatdirectcostsarealmosttentimeslesswhenthecompanyisableto restructuredebtprivately. 2. Indirectcosts.Indirectcostsareopportunitycostsimposedonthecompanybecause financialdistressaffectsitsabilitytoconductbusinessasusual.Adistressed companyishamperedonthreefronts.First,itlosestherighttomakecertain decisionswithoutlegalapproval.Second,financialdistresscanreducedemandfor thecompany’sproductandincreaseitsproductioncosts.Third,managementspends considerabletimeresolvingfinancialdistress. Andrade&Kaplan,intheir1998studyonhighlyleveragedtransactions(HLT)thatbecame financiallydistressed,alsoconsiderqualitativemeasuresoffinancialdistresscostsintheir analysis.Thecompaniesintheirsampleappeartoincurthreesuchcostsmostfrequently. First,anumberofcompaniesareforcedtocurtailcapitalexpenditures,sometimes substantially.Second,anumberofcompaniesappeartosellassetsatdepressedprices. Third,anumberofcompaniesdelayrestructuringorfilingforChapter11inawaythat appearstobecostly.Incontrast,theyfindnoevidencethatthedistressedcompaniesengage inriskshifting/assetsubstitutionofanykind.Inadditiontocostsoffinancialdistress,theyalso findbenefits:manycompaniescutcostsandreplacemanagement. Totheextenttheyoccur,thecostsoffinancialdistressthattheyidentifyareheavily concentratedintheperiodafterthefirmsbecomedistressed,butbeforetheyenterChapter 11.TheyfindlittleevidencethatChapter11isinefficientorcostly. Finally,Andrade&Kaplan(1998)estimatethecrosssectionaldeterminantsofthecostsof financialdistress.TheyfindthatthesecostsdeclinewithHLTvalueandthefractionoftotal debtowedtobanks,butarenotrelatedtocapitalstructurecomplexity,thepresenceofjunk

MasterThesisSebastianOotjers 37 s0041823 IEMFEM ABCD bonds,thepresenceofbuyoutsponsors,timeindistress,orindustryperformance.These resultsarenotconsistentwithincreasedcomplexityincreasingthecostsoffinancialdistress. Theyalsosuggestthatcostsoffinancialdistresshaveafixedcomponent. 2.4.3 Estimation of the costs of financial distress AccordingtoAndrade&Kaplan(1998),financialeconomistshavefounditdifficulttomeasure thecostsoffinancialdistress.Theystatethatthedifficultyisdrivenbyaninabilityto distinguishwhetherpoorperformancebyacompanyinfinancialdistressiscausedbythe financialdistressitselforiscausedbythesamefactorsthatpushedthecompanyinto financialdistressinthefirstplace.Thosecompaniesarenotonlyfinanciallydistressed,but alsoeconomicallydistressed,makingitdifficulttoidentifywhetherthepapersofthese financialeconomistmeasurecostsoffinancialdistress,economicdistress,oraninteractionof them Altman(1984)concludesthat,basedonhissampleofeighteencompanies,theaveragetotal costsoffinancialdistressare12.4%ofthevalueofthecompaniesthreeyearsbefore bankruptcyto16.7%ofthevalueofthecompanyatbankruptcy.Thetablebelowshowsthe relationbetweenthedirectandindirectcostsoffinancialdistressfoundbyAltman. Average bankruptcy costs relative to company value for the combined corporate sample (N = 18 firms)

Yearspriortobankruptcy

3 2 1 0

Directbankruptcycosts/Value 4.3% 4.6% 4.6% 6.2% Indirectbankruptcycosts/Value 8.1% 7.1% 6.6% 10.5% Totalbankruptcycosts/Value 12.4% 11.7% 11.2% 16.7% Altmanusesthetermbankruptcycosts,butstatesthat“Indirectbankruptcycostsarenot limitedtofirmswhichactuallydofail.Firmswhichhavehighprobabilitiesofbankruptcy, whethertheyeventuallyfailornot,stillcanincurthesecosts.”Thismeansthathisbankruptcy costsareasynonymforthecostsoffinancialdistressusedbyotherauthorsandasitisused inthisresearchproject. Weiss(1990)usesthreemeasurestoassessthemagnitudeofthedirectcostsofbankruptcy: (1)marketvalueofequity,(2)bookvalueofdebtplusthemarketvalueofequity,and(3)book valueoftotalassets,allmeasuredatthefiscalyearendpriortothebankruptcyfiling.On average,thedirectcostsofbankruptcyare20.6%ofthemarketvalueofequity(rangingfrom 2.0%to63.6%),3.1%ofthebookvalueofdebtplusthemarketvalueofequity(rangingfrom 1.0%to6.6%),and2.8%ofthebookvalueoftotalassets(rangingfrom0.9%to7.0%). Wruck(1990)concludesthatdirectcostsoffinancialdistressaverage3.5%ofmarketvalue. Estimatesofindirectcostsarelessreliable,butevidencetodateindicatestheylieinthe rangeof9%to15%ofmarketvalue. Andrade&Kaplan(1998)provideseveralestimatesofthemagnitudeofthenetcostsof financialdistress.Fortheirentiresample,theyestimatethatthesecostsare10to20%of companyvalueoneyearpriortothefinancialdistress.Theirmostconservativeestimatesdo notexceed25%ofcompanyvalueoneyearpriortothefinancialdistress. However,theystate:“Overall,then,wecannotconcludethatourresultswouldholdfor companiesinhighR&Dor,possibly,highgrowthbusinesses.(Infact,webelievetheresults areunlikelytoholdforsuchcompanies.)However,amongcompaniesinmoremature businesses,itseemslikelythattheresultsforoursampleHighlyLeveragedTransactions wouldhold.” Chen&Merville(1999)concludethatithasbeenacceptedthatthedirectcostsoffinancial failureareontheorderof5%ofcompanyvalueatthetimeofoccurrenceofthefinancial distress(Warner(1977))andindirectcostsaround810%ofcompanyvalueatthetimeof occurrenceofthefinancialdistress(Altman(1984)).

MasterThesisSebastianOotjers 38 s0041823 IEMFEM ABCD Branch(2002)concludesthatontheaverage,theeffectofthefinancialdistressonthe predistresscompanyvalueisallocatedasfollows: 1. Theloss,whichcausedthebankruptcy,consumesabout28%; 2. Thecostofdealingwithdistressconsumesabout16%; 3. Thenetvalueavailabletodistributetotheclaimholdersamountstoabout56%. 2.4.4 Comments on the costs of financial distress Pindado&Rodrigues(2005)findthatfinancialdistresscostsarepositivelyrelatedtothe probabilityoffinancialdistress,andnegativelytoleverageandtheholdingofliquidassets. Theyalsofindthattheunderinvestmentproblemismorerelevantthantheoverinvestment one.Theirresultssupporttherelevanceofinstitutionaldifferencesacrosscountriesforthe analysisoffinancialdistresscosts. Chen&Merville(1999)relyontheZscoremodelofAltman(1968)asaproxyforthe probabilityoffinancialdistressfortworeasons:becauseitsparametersarepubliclyavailable andbecausetheinterpretationsofthescoresarewidelyknown. Wruck(1990)alsostatesthatpreviousstudiesoffinancialdistressfocusonthecostsand ignorethepossibilitythatdistresscanresultinbeneficialoutcomes.Thesebenefitsof financialdistressare,accordingtoWruck(1990),asfollows: 1. Changesinmanagementandgovernance.Wruck(1990)’sresultsareconsistentwith theideathatleverageactsasacatalystfororganizationalchange.Poorstockprice performanceisnotenoughtoremoveincumbentmanagers,butfinancialdistress providesamechanismtoinitiatetopmanagementchanges. 2. Changesinorganizationalstrategyandstructure.Financialstructureinteractswith investmentdecisions;financialdistressforcesachangeinthecompany’seconomic activitiesandthewaytheseactivitiesareorganized.Financialdistresscan,therefore, forcemanagerstoundertakevalueincreasingorganizationalchangestheywouldnot haveotherwiseundertaken.Whencompanyvaluedeterioratesasaresultofpoor managementorwhencompanyvalueishighestinliquidationandmanagement refusestoliquidate,financialdistresscreatesvalue. 3. Benefitsofchapter11.Insomespecialsituations,theabilitytoenterChapter11isa valuablealternativeforsecurityholders.Forexample,tradecreditorsandclaimantsin productliabilitysuits,arenumerousandhaveheterogeneousclaims.Reachinga privateagreementwithallofthemisverydifficult.UnderChapter11,diffusecreditors canbedealtwithasasingleclass,makingnegotiationmanageableandsettling protracteddisputesonceandforall. Wruck(1990)alsocommentsthat:“Althoughthebenefitsofdistresshavenotyetbeen quantified,turnoverintopmanagementandchangesingovernanceindicatethatcorporate insidersaredisciplinedforpoorperformance.Evidencefromclinicalstudiesandcasestudies documentschangesinstrategyandorganizationalstructurefollowingfinancialdistressthat areconsistentwithaprocessofcorporaterevitalization.” 2.4.5 Subjects of analysis regarding the costs of financial distress Financialdistressiscausedbythecompany’sinabilitytomeetthepromisesthatweremade tocreditors.Thecostsoffinancialdistresscanbesplitupindirectandindirectcosts.The probabilityofdefaultcanbeusedasaproxyfortheprobabilityoffinancialdistressandthus astheprobabilitythattheexpectedcostoffinancialdistresswilloccur.Thedirectcostsof distressareestimatedat35%ofthebookvalueofdebtplusthemarketvalueofequityatthe yearpriortotheoccurrenceofthefinancialdistressandtheindirectcostareestimatedat7 15%cumulatingtototalcostsoffinancialdistressof1020%ofthebookvalueofdebtplus themarketvalueofequityattheyearpriortotheoccurrenceofthefinancialdistress. Basedontheelaborationonthecostsoffinancialdistressabove,thefollowingsubjectsof analysiscanbeanalyzed: 1. Whetherthevaluationmethodincorporatespotentialcostsoffinancialdistress. 2. Thewayinwhichthefinancialdistresscostsareintegratedinthevaluation(ifthe methoddoesinfactusefinancialdistresscosts).

MasterThesisSebastianOotjers 39 s0041823 IEMFEM ABCD Conclusion TheobjectiveofthisresearchprojectistoidentifythedifferencesbetweentheenterpriseDCF modelandtheAPVmodel.Inordertocomparethetwomodelsinadistinctivemanner,they bothneedtobecomparedonthesamesetofsubjects. Thischapterdiscussedfourresearchareasthatarerelatedtotheaspectsofthetwo valuationmodels.Anumberofsubjectscameforthfromeachresearcharea,whichcanbe usedtoanalyzethetwovaluationmodels. General subjects of analysis Therearemultipleapproachesfordeterminingtheenterprisevalueofacompany.Thetwo modelsthatarestudiedinthisresearchprojectbothbelongtotheincomeapproachandhave theformofadiscountedcashflowmodel.Eachdiscountedcashflowmodelconsistsoffour subjectsofwhichthespecificationdeterminesthefunctioningoftheparticulardiscounted cashflowmodel.Thesefoursubjectsare: 1. Thewayinwhichthecashflowsaremodeled. 2. Thediscountratethatisused. 3. Thecostofequityandthecostofdebtused. 4. Theincorporationoftaxesintothevaluation. Subjects of analysis regarding the probability of default Therearemultipleapproachesforestimatingtheprobabilityofdefaultofacompany.Each approachrequiresaparticulartypeofinput,therebyrestrictingitsusefulnesstothesituations inwhichtheneededinputisavailable. Itistobeexpected,fromapracticalpointofview,thatthepotentialfordefaulthasanimpact onthevalueofacompany.Eachofthetwovaluationmodelsisthereforealsoexpectedto incorporateacertainmeasureorfactoroftheriskofdefaulttorepresentthatimpact. Thefirstsubjectofanalysis,resultingfromthis,iswhetherthevaluationmodelsusea measureofprobabilityofdefault.Thesecondsubjectofanalysis,incaseofapositiveanswer onthefirstsubject,iswhatmodel/approachisusedtodeterminetheprobabilityofdefault. Thissubjectisrelevantbecausetheapproachimpliedbythemodelcouldimpactthe valuationoutcomeoreventhefactwhethertheprobabilityofdefaultcanbedeterminedatall basedontheavailableinformation. So,thetwosubjectsare: 1. Theusageoftheprobabilityofdefaultinthevaluationmodel. 2. Themodel/approachthatisused(incaseofactualusageoftheprobabilityofdefault) todeterminetheprobabilityofdefault.Whichmodeltousecoulddependentonthe typeofcompanythatisbeingvalued. Subjects of analysis regarding the capital structure Therearemultipletheoriesonthepredictionofcapitalstructurechoices.Themostknownare the(tax/bankruptcy)tradeofftheoryandthepeckingordertheory.Althoughmanyauthors havegivenargumentsoverthepastyearstosupportoneoftheseorboththeories,neitherof thetwohascometobethe‘ultimate’theoryofcapitalstructure. IntheanalysisoftheenterpriseDCFmodelandtheAPVmodel,thefollowingsubjectswith regardtocapitalstructureneedtobeconsidered: 1. Whataretheassumptionsoncapitalstructureofthevaluationmodel? 2. Whataretheconditionsofcapitalstructurerequiredforthemodeltobeused? 3. Ifthemodelcanbeused,howcanthecapitalstructuredecisionsbemodeled?

Thefirstsubjectissimplyameanstoidentifytheinfluenceofcapitalstructureonthe valuationmodel.Thesecondsubjectneedstobeanalyzedtodeterminewhetherthereare certaincapitalstructuresituationsinwhichoneofthetwovaluationmodelscannotbeused. Thelastsubjectrelatestothetheoriesdescribedabove:ifthemodelcanbeused,howare capitalstructuredecisionsmodeled?

MasterThesisSebastianOotjers 40 s0041823 IEMFEM ABCD Subjects of analysis regarding the costs of financial distress Financialdistressiscausedbythecompany’sinabilitytomeetthepromisesthatweremade tocreditors.Thecostsoffinancialdistresscanbesplitupindirectandindirectcosts.The probabilityofdefaultcanbeusedasaproxyfortheprobabilityoffinancialdistressandthus astheprobabilitythattheexpectedcostoffinancialdistresswilloccur.Thedirectcostsof distressareestimatedat35%ofthebookvalueofdebtplusthemarketvalueofequityatthe yearpriortotheoccurrenceofthefinancialdistressandtheindirectcostareestimatedat7 15%cumulatingtototalcostsoffinancialdistressof1020%ofthebookvalueofdebtplus themarketvalueofequityattheyearpriortotheoccurrenceofthefinancialdistress. Basedontheelaborationonthecostsoffinancialdistressabove,thefollowingsubjectsof analysiscanbeanalyzed: 1. Whetherthevaluationmethodincorporatespotentialcostsoffinancialdistress. 2. Thewayinwhichthefinancialdistresscostsareintegratedinthevaluation(ifthe methoddoesinfactusefinancialdistresscosts). Application of the subjects of analysis Thischapterprovidesthetheoreticalframeworkfortheanalysisofthetwovaluationmodels. Thetwovaluationmodelsarethesocalled research objects onwhichthecollectionof subjectsofanalysis,thesocalled research perspective ,isapplied.Theresearchperspective isthereforelikeapairofglassesusedtolookatthetwovaluationmodels. Thenextchapterdiscussestheapproachwhichistakentoanalyzetheresearchobjects.It alsoenrollsajustificationfortheapproachtakenbasedontheresearchcontext. Inchapter3,thetwovaluationmodelsareactuallyassessedatthesubjectsofanalysisand thancomparedtoeachother.

MasterThesisSebastianOotjers 41 s0041823 IEMFEM ABCD

Chapter 3: The two models compared

Introduction Thischapteristhemainchapterofthisresearchreport.Inthischaptereachofthetwo valuationmodelsisanalyzed.Inthefirsttwoparagraphsthevaluationmodelsareassessed atthegeneralsubjectsofanalysis.InthethirdandfourthrespectivelytheenterpriseDCF modelandtheAPVmodelareassessedattheotherthreesubjectsofanalysiscategories. Thisprovidesanoverviewontheassumptionsandthefunctioningofeachmodel.Thetwo valuationmodelsarecomparedinthefifthparagraphwithregardtotheirtheoretical differencesandthesedifferencesaretranslatedto(expected)differencesinthevaluation outcomeinthesixthparagraph. ThefirstparagraphdiscussesthebasicassumptionsoftheenterpriseDCFmodelrather extensive.Therationalebehindthisisthatanumberofmethodsfordeterminingthevalueof theinputvariablesoftheenterpriseDCFmodelarealsovalidfortheAPVmodel.Relevant methodsareforinstancethedeterminationofthefreecashflowsandthecostofdebt. 3.1 Basic assumptions of the enterprise DCF model ThepurposeofthisparagraphistoassesstheenterpriseDCFmodelonthebasisofthe generalsubjectsofanalysis.Theseare,asdiscussedinchapter2: 1. Thewayinwhichthecashflowsaremodeled. 2. Thediscountratethatisused. 3. Thecostofequityandthecostofdebtused. 4. Theincorporationoftaxesintothevaluation. Thefirstthreesubjectsareexplicitlydiscussed.Thefourthsubject,thetaxrate,returnsin multiplesections(forinstanceinthediscussionofthediscountrate)andisthereforeonly discussedimplicitly. Koller et al.(2005)discusstheenterpriseDCFmodelextensively.Thisbookisthereforeone ofthemainsourcesofthisparagraph.Damodaran(2002)alsodiscussestheenterpriseDCF modelingreatlength.HisviewsarecombinedwiththoseofKoller et al .(2005)toarriveata comprehensiveoverviewoftheenterpriseDCFmodel.Commentsfromsomeotherauthors areusedtorefinethedescriptionsfromDamodaran(2002)andKoller et al. (2005). 3.1.1 Definition of the enterprise DCF model TheenterpriseDCFmodeldiscountsfuturecashflowsattheweightedaveragecostof capital. TheenterpriseDCFmodelisthefavoritevaluationmodelsofmanypractitionersand academics,accordingtoKoller et al. (2005),becauseitreliessolelyontheflowofcashinand outofthecompany,ratherthanonaccountingbasedearnings(whichcanbemisleading). Inthe1950s,FrancoModiglianiandMertonMillerpostulatedthatthevalueofacompany’s economicassetsmustequalthevalueoftheclaimsagainstthoseassets. 11 Thus,inorderto valuetheequityofacompany,twooptionsarise.Thefirstistovaluethecompany’s operationsandsubtractthevalueofallnonequityfinancialclaims;thesecondistovaluethe equitycashflowsdirectly. Koller et al. (2005,p.103)statethat:“Althoughbothmethodsleadtoidenticalresultswhen appliedcorrectly,theequitymethodisdifficulttoimplementinpractice.Consequently,to valueacompany’sequity,werecommendvaluingtheenterprisefirstandthensubtractingthe valueofanynonequityfinancialclaims.” 11 Miller&Modigliani(1958)

MasterThesisSebastianOotjers 42 s0041823 IEMFEM ABCD 3.1.2 Steps in the enterprise DCF model Tovalueacompany’scommonstockusingtheenterpriseDCFmodel,thefollowingstepsare tobetaken: 1. Valuethecompany’soperationsbydiscountingfreecashflowfromoperationsatthe weightedaveragecostofcapital. 2. Valuenonoperatingassets,suchasexcessmarketablesecurities,nonconsolidated subsidiaries,andotherequityinvestments.Combiningthevalueofoperatingassets andnonoperatingassetsleadstoenterprisevalue. 3. Identifyandvalueallnonequityfinancialclaimsagainstthecompany’sassets. Nonequityfinancialclaimsinclude(amongothers)fixedandfloatingratedebt, pensionshortfalls,employeeoptions,andpreferredstock. 4. Subtractthevalueofnonequityfinancialclaimsfromenterprisevaluetodetermine thevalueofcommonstock.Todetermineshareprice,divideequityvaluebythe numberofsharesoutstanding. Thevalueofoperationsequalsthediscountedvalueoffuturefreecashflow.Freecashflow equalsthecashflowgeneratedbythecompany’soperations,lessanyreinvestmentbackinto thebusiness.Freecashflowisthecashflowavailableto all investors,andis independent of leverage.Consistentwiththisdefinition,freecashflowmustbediscountedusingthe weightedaveragecostofcapital.TheWACCisthecompany’sopportunitycostofcapitaland representsablendedrequiredreturnbythecompany’sdebtandequityholders 3.1.3 Modeling of the cash flows Damodaran(2002,p.382)usesthetermfreecashflowtothefirminsteadoffreecashflow. Hestatesthat:“Thefreecashflowtothefirm(FCFF)isthesumofthecashflowstoall claimholdersinthecompany,includingstockholders,bondholders,andpreferred stockholders.Therearetwowaysofmeasuringthefreecashflowtothefirm. Oneistoaddupthecashflowstotheclaimholders,whichwouldincludecashflowstoequity (definedeitherasfreecashflowtoequityordividends),cashflowtolenders(whichwould includeprincipalpayments,interestexpenses,andnewdebtissues),andcashflowsto preferredstockholders(usuallypreferreddividends): FCFF=Freecashflowtoequity+Interestexpense(1–Taxrate)+principalrepayments– newdebtissues+preferreddividends Asimplerwayofgettingtofreecashflowtothefirmistoestimatethecashflowspriortoany oftheseclaims.Thusonecouldbeginwiththeearningsbeforeinterestandtaxes,netout taxesandreinvestmentneeds,andarriveatanestimateofthefreecashflowtothefirm: FCFF=EBIT(1–Taxrate)+Depreciation–Capitalexpenditure–workingcapital where EBIT =Earningsbeforeinterestandtaxes =Differencein Sincethiscashflowispriortodebtrepayments,itisoftenreferredtoasanunleveredcash flow.” TheDamodaran(2002)FCFFisalmostequaltotheKoller et al. (2005)freecashflow.The differenceisthatDamodaran(2002)usesEBIT(1T)andKoller et al.(2005)usesNOPLAT. NOPLATisslightlymodifiedversionofEBIT(1T)anditremovesanynonoperatingitemsthat mightaffectthereportedEBIT.TheseconddefinitionofDamodaran(2002)isusedthrough theremainderofthisresearchreportbecausetheFCFFusestermsthataredirectly retrievablefromthefinancialstatements,andisthuseasiertouseinpractice.Thisfreecash flowtothefirmwillbecalled free cash flow or FCFF . 3.1.4 Structure of the enterprise DCF model ThevalueofthecompanyisobtainedbydiscountingtheFCFFattheweightedaveragecost ofcapital.Embeddedinthisvaluearethetaxbenefitsofdebt(intheuseoftheaftertaxcost ofdebtinthecostofcapital)andexpectedadditionalriskassociatedwithdebt(intheformof

MasterThesisSebastianOotjers 43 s0041823 IEMFEM ABCD highercostsofequityanddebtathigherdebtratios).Theversionofthemodelusedwill dependonassumptionsmadeaboutfuturegrowth.

Thevalueofthecompany,inthemostgeneralcase,canbewrittenasthepresentvalueof expectedfreecashflows: t=∞ FCFF Value _ of _ company = t ∑ t t=1 1( + WACC) where FCFF t =Freecashflowtothefirminyeart WACC =Weightedaveragecostofcapital Ifthecompanyreachessteadystateafternyearsandstartsgrowingatastablegrowthrate gnafterthat,thevalueofthecompanycanbewrittenas: t=n FCFF [FCFF /(WACC − g )] Value _ of _ company = t + n+1 st n ∑ t n t=1 1( +WACChg ) 1( + WACChg ) where WACC=Costofcapital(hg:highgrowth;st:stablegrowth) 3.1.5 Asacompanygrows,itbecomesmoredifficultforittomaintainhighgrowthanditeventually willgrowataratelessthanorequaltothegrowthrateoftheeconomyinwhichitoperates. Thisgrowthrate,labeledstablegrowth,canbesustainedinperpetuity,allowingforthe estimationofthevalueofallcashflowsbeyondthatpointasaterminalvalueforagoing concern. Sincecashflowscannotbeestimatedforever,closureindiscountedcashflowvaluationis generallyimposedbystoppingtheestimationofcashflowsometimeinthefutureanthen computingaterminalvaluethatreflectsthevalueofthecompanyatthatpoint: t=n CF Termi _ nal _ value Value _ of _ a _ company = t + n ∑ t n t=1 1( + kc ) 1( + kc ) Theterminalvaluecanbefoundinthreeways.Oneistoassumealiquidationofthe company’sassetsintheterminalyearandestimatewhatotherswouldpayfortheassetsthat thecompanyhasaccumulatedatthatpoint.Theothertwoapproachesvaluethecompanyas agoingconcernatthetimeoftheterminalvalueestimation.Oneappliesamultipleto earnings,revenues,orbookvaluetoestimatethevalueintheterminalyear.Theother assumesthatthecashflowsofthecompanywillgrowataconstantrateforever–astable growthrate. Damodaran(2002)statesthattherearetwowaysinwhichtheliquidationvaluecanbe estimated.Oneistobaseitonthebookvalueoftheassets,adjustedforanyinflationduring theperiod. averagelifeofassets Expectedliquidationvalue=Bookvalueofassets termyear *(1+Inflationrate) Thelimitationtothisapproachisthatitisbasedonaccountingbookvalueanddoesnot reflecttheearningpoweroftheassets. Thealternativeapproachistoestimatethevaluebasedontheearningpoweroftheassets. Tomakethisestimate,theexpectedcashflowsfirsthavetobeestimatedfromtheassetsand thenthesecashflowshavetobediscountedbacktothepresent,usinganappropriate discountrate.

Inthemultipleapproach,thevalueofacompanyinafutureyearisestimatedbyapplyinga multipletothecompany’searningsorrevenuesinthatyear.

MasterThesisSebastianOotjers 44 s0041823 IEMFEM ABCD Whilethisapproachhasthevirtueofsimplicity,themultiplehasahugeeffectonthefinal valueandwhereitisobtainedcanbecritical. Damodaran(2002)thereforestatesthat:“Usingmultiplestoestimateterminalvalue,when thosemultiplesareestimatedfromcomparablefirms,resultsinadangerousmixofrelative anddiscountedcashflowvaluation.Theonlyconsistentwayofestimatingterminalvalueina discountedcashflowmodelistouseeitherliquidationvalueortouseastablegrowthmodel.” Inthestablegrowthmodel,whichassumesthatcashflows,beyondtheterminalyear,will growataconstantrateforever,theterminalvaluecanbeestimatedasfollows: Terminalvalue t=Cashflow t+1 /(r–stablegrowthrate) Ifvaluingacompany,theterminalvaluecanbewrittenas: Terminalvalue n=Freecashflowtofirm n+1 /(Costofcapital n+1 –g n) wherethecostofcapitalandthegrowthrateinthemodelaresustainableforever. Ofalltheinputsintoadiscountedcashflowvaluationmodel,nonecanaffectthevaluemore thanthestablegrowthrate. Thefactthatastablegrowthrateisconstantforever,however,putsstrongconstraintsonhow highitcanbe.Sincenocompanycangrowforeverataratehigherthanthegrowthrateofthe economyinwhichitoperates,theconstantgrowthcannotbegreaterthantheoverallgrowth rateoftheeconomy.Inmakingajudgmentonwhatthelimitsonstablegrowthrateare,the followingthreequestionshavetobeconsidered: 1. Isthecompanyconstrainedtooperateasadomesticcompany,ordoesitoperate(or havethecapacitytooperate)internationally?Ifacompanyisapurelydomestic company,thegrowthrateinthedomesticeconomywillbethelimitingvalue.Ifthe companyisamultinationalorhasaspirationstobeone,thegrowthrateintheglobal economywillbethelimitingvalue. 2. Isthevaluationbeingdoneinnominalorrealterms? 3. Whatcurrencyisbeingusedtoestimatecashflowsanddiscountratesinthe valuation? Whilethestablegrowthratecannotexceedthegrowthrateoftheeconomyinwhicha companyoperates,itcanbelower.Settingthestablegrowthratetobelessthanorequalto thegrowthrateoftheeconomyisnotonlytheconsistentthingtodo,accordingtoDamodaran (2002),butitalsoensuresthatthegrowthratewillbelessthanthediscountrate. Ineverydiscountedcashflowvaluation,therearethreecriticalassumptionsthatneedtobe madeonstablegrowth.Thefirstrelatestowhenthecompanyundervaluationwillbecomea stablegrowthcompany,ifitisnotalready.Thesecondrelatestowhatthecharacteristicsof thecompanywillbeinstablegrowth,intermsofreturnoninvestmentsandcostofequityand capital.Thefinalassumptionrelatestohowthecompanyundervaluationwillmakethe transitionfromhighgrowthtostablegrowth. AccordingtoDamodaran(2002),threefactorsshouldbelookedatwhenconsideringhow longacompanywillbeabletomaintainhighgrowth. 1. Sizeofthecompanies.Smallercompaniesaremuchmorelikelytoearnexcess returnsandmaintaintheseexcessreturnsthanotherwisesimilarlargercompanies. 2. Existinggrowthrateandexcessreturns.Companiesthathavebeenreportingrapidly growingrevenuesaremorelikelytoseerevenuesgrowrapidlyatleastinthenear future. 3. Magnitudeandsustainabilityofcompetitiveadvantage.Thisisperhapsthemost criticaldeterminantofthelengthofthehighgrowthperiod.Iftherearesignificant barrierstoentryandsustainablecompetitiveadvantages,companiescanmaintain highgrowthforlongerperiods. Ascompaniesmovefromhighgrowthtostablegrowth,theyneedtobegiventhe characteristicsofstablegrowthcompanies.Acompanyinstablegrowthisdifferentfromthat samecompanyinhighgrowthonanumberofdimensions.Ingeneral,stablegrowth

MasterThesisSebastianOotjers 45 s0041823 IEMFEM ABCD companiesareexpectedtohaveaveragerisk,usemoredebt,havelower(orno)excess returns,andreinvestlessthanhighgrowthcompanies. Whenlookingatthecostofequity,highgrowthcompaniestendtobemoreexposedto marketrisk(andhavehigherbetas)thanstablegrowthcompanies.Asthesecompanies mature,theyareexpectedtohavelessexposuretomarketriskandbetasthatarecloserto1 –theaverageforthemarket.Damodaran(2002)recommendthat,asaruleofthumb,stable periodbetasdonotexceed1.2. Sinceentireindustriesoftenearnexcessreturnsoverlongperiods,assumingacompany’s returnsonequityandcapitalwillmovetowardindustryaverageswillyieldmorereasonable estimatesofvalue. Highgrowthcompaniestendtouselessdebtthanstablegrowthcompanies.Ascompanies mature,theirdebtcapacityincreases.Whenvaluingcompanies,thiswillchangethedebtratio thatisusedtocomputethecostofcapital. Stablegrowthcompaniestendtoreinvestlessthanhighgrowthcompanies,anditiscritical thattheeffectsoflowergrowthonreinvestmentarecapturedandthatitisensuredthatthe companyreinvestsenoughtosustainitsstablegrowthrateintheterminalphase.Lookingat freecashflow,theexpectedgrowthinoperatingincomeisestimatedasafunctionofthe returnoncapitalandthereinvestmentrate: Expectedgrowthrate=Reinvestmentrate*Returnoncapital Algebraicmanipulationyieldsthefollowingmeasureofthereinvestmentrateinstablegrowth: Reinvestmentrateinstablegrowth=Stablegrowthrate/ROC n wheretheROC nisthereturnoncapitalthatthecompanycansustaininstablegrowth.This reinvestmentratecanthenbeusedtogeneratethefreecashflowtothefirminthefirstyear ofstablegrowth.Linkingthereinvestmentrateretentionratiotothestablegrowthratealso makesthevaluationlesssensitivetoassumptionsaboutthestablegrowthrate. If the return on capital is equal to the stable growth rate, increasing the stable growth rate will have no effect on value .Inthiscase,accordingtoDamodaran(2002): Terminalvalue ROC=WACC =EBIT n+1 (1–t)/Costofcapital n Therearethreedistinctscenariosregardingthetransitiontostablegrowth.Inthefirst scenario,thecompanywillmaintainitshighgrowthrateforaperiodoftimeandthenbecome astablegrowthcompanyabruptly.Inthesecond,thecompanywillmaintainitshighgrowth rateforaperiodandthenhaveatransitionperiodwhereitscharacteristicschangegradually towardstablegrowthlevels.Inthethird,thecompanycharacteristicschangeeachyearfrom theinitialperiodtothestablegrowthperiod. 3.1.6 The weighted average cost of capital TovalueacompanyusingtheenterpriseDCFmodel,thefreecashflowsarediscountedby theweightedaveragecostofcapital(WACC).Theweightedaveragecostofcapital representstheopportunitycostthatinvestorsfaceforinvestingtheirfundsinoneparticular businessinsteadofotherswithsimilarrisk. Themostimportantprincipleunderlyingsuccessfulimplementationofthecostofcapitalis consistencybetweenthecomponentsofWACCandthefreecashflows.Toassure consistency,accordingtoKoller et al.(2005),thecostofcapitalmustmeetseveralcriteria: - Itmustincludetheopportunitycostsfromallsourcesofcapital–debt,equity,andsoon– sincefreecashflowisavailabletoallinvestors,whoexpectcompensationfortherisks theytake. - Itmustweigheachsecurity’srequiredreturnbyitstargetmarketbasedweight,notbyits historicalbookvalue. - Itmustbecomputedaftercorporatetaxes(sincefreecashflowiscalculatedinaftertax terms).Anyfinancingrelatedtaxshieldsnotincludedinthefreecashflowsmustbe incorporatedintothecostofcapitalorvaluedseparately(asdoneintheadjustedpresent value). - Itmustbedenominatedinthesamecurrencyasthefreecashflows. - Itmustbedenominatedinnominaltermswhencashflowsarestatedinnominalterms.

MasterThesisSebastianOotjers 46 s0041823 IEMFEM ABCD Todeterminetheweightedaveragecostofcapital,itsthreecomponentsmustbecalculated: thecostofequity,theaftertaxcostofdebt,andthecompany’stargetcapitalstructure.Since noneofthevariablesaredirectlyobservable,variousmodels,assumptions,and approximationsareemployedtoestimateeachcomponent. Initssimplestform,theweightedaveragecostofcapitalisthemarketbasedweighted averageoftheaftertaxcostofdebtandcostofequity: D E WACC = k 1( −T ) + k D + E d m D + E e where D/V=Targetlevelofdebttoenterprisevalueusingmarketbased(notbook)values E/V=Targetlevelofequitytoenterprisevalueusingmarketbasedvalues kd =Costofdebt ke =Costofequity Tm =Company’smarginalincometaxrate Forcompanieswithothersecurities,suchaspreferredstock,additionaltermsmustbeadded tothecostofcapital,representingeachsecurity’sexpectedrateofreturnandpercentageof totalenterprisevalue. Toestimatethecostofequity ,theexpectedrateofreturnofthecompany’sstockmustbe determined.Sinceexpectedratesofreturnareunobservable,onecanrelyonassetpricing modelsthattranslateriskintoexpectedreturn.Themostcommonassetpricingmodelisthe capitalassetpricingmodel(CAPM). BecausetheCAPMisdiscussedatlengthinmodernfinancetextbooks,itsbackgroundwill notbediscussedanyfurtherhere.Instead,thefocusisonbestpracticesforimplementation. TheCAPMpostulatesthattheexpectedrateofreturnonanysecurityequalstheriskfreerate plusthesecurity’sbetatimesthemarketriskpremium:

E(Ri ) = rf + βi [E(Rm ) − rf ] where E(R i) =Security i’sexpectedreturn rf =Riskfreerate βi =Stock’ssensitivitytothemarket E(R m) =Expectedreturnofthemarket IntheCAPM,theriskfreerateandmarketriskpremium(definedasthedifferencebetween E(R m)andr f)arecommontoallcompanies;onlybetavariesacrosscompanies.Beta representsastock’sincrementalrisktoadiversifiedinvestor,whereriskisdefinedbyhow muchthestockcovarieswiththeaggregatestockmarket. Koller et al. (2005)’sgeneralconclusionswithregardtotheimplementationofCAPMareas follows. - Toestimatetheriskfreerateindevelopedeconomies,usehighlyliquid,longterm governmentsecurities,suchasthe10yearzerocouponstrip. - Basedonhistoricalaverageandforwardlookingestimates,theappropriatemarketrisk premiumiscurrentlybetween4,5and5,5%. - Toestimateacompany’sbeta,useanindustryderivedunleveredbetaleveredtothe company’stargetcapitalstructure. Toestimatetheriskfreerate,looktothegovernmentdefaultfreebonds.Whenvaluinga companyorlongtermproject,ashorttermTreasurybillshouldnotbeusedtodeterminethe riskfreerate.Theshorttermbondratemisestimatestheopportunitycostofinvestmentfor longertermprojects. Methodstoestimatethemarketriskpremiumfallinthreegeneralcategories: 1. Estimatingthefutureriskpremiumbymeasuringandextrapolatinghistoricalexcess returns. 2. Usingregressionanalysistolinkcurrentmarketvariables,suchastheaggregate dividendtopriceratio,toprojecttheexpectedmarketriskpremium.

MasterThesisSebastianOotjers 47 s0041823 IEMFEM ABCD 3. UsingDCFvaluation,alongwithestimatesofreturnoninvestmentandgrowth,to reverseengineerthemarket’scostofcapital. Althoughmanyinthefinanceprofessiondisagreeabouthowtomeasurethemarketrisk premium,Koller et al.(2005)believe4,5to5,5%isanappropriaterange.(Brealey&Myers (2003)arriveattheconclusionthatoveraperiodof75yearsthemarketriskpremiumhas averagedabout9%peryearandKaplan&Ruback(1995)findthatthemedianimplied marketequityriskpremiumequals7,78%andtheystatethatthisvalueiscomparabletothe historicarithmeticaveragemarketequityriskpremium.) Inordertoestimatebeta,firstarawbetahastobemeasuredthroughtheuseofaregression andthentheestimateshouldbeimprovedbyusingindustrycomparablesandsmoothing techniques.Themostcommonregressionusedtoestimateacompany’srawbetaisthe marketmodel:

Ri = α + βRm + ε Inthemarketmodel,thestock’sreturnisregressedagainstthemarket’sreturn. Toimprovetheprecisionofbetaestimation,oneshoulduseindustry,ratherthancompany specificbetas.Companiesinthesameindustryfacesimilar operating risks,sotheycould havesimilaroperatingbetas.Theeffectofleveragemustfirstbestrippedouttocompare companieswithsimilaroperatingrisks.Onlythencanthebetabecomparedacrossan industry. So,  D  βu = β e /1+   E  where βe =Leveredbetaofthecompany βu =Unleveredbetaofthecompany D/E =Currentdebt/equityratio Sinceunleveredbetafocussolelyonoperatingrisk,theycanbeaveragedacrossanindustry (assumingindustrycompetitorshavesimilaroperatingcharacteristics). Koller et al.(2005)describethefollowingfourstepprocesstoestimateanindustryadjusted companybeta.First,regresseachcompany’sstockreturnsagainstthemarketindexto determinerawbeta.Next,tounlevereachbeta,calculateeachcompany’smarketdebtto equityratio.Applyingthelastgivenequationleadstounleveredcompanybetas.Instepthree, determinetheindustryunleveredbetabycalculatingthemedian.Inthefinalstep,releverthe industryunleveredbetatoeachcompany’s target debttoequityratio(usingcurrentmarket valuesasproxies)accordingtothefollowingformula:  D β = β 1+  e u E  Forestimatingthecostofdebt foracompanywithinvestmentgradedebt(debtratedatBBB orbetter),yieldtomaturityisasuitableproxy.Usingthecompany’sbondratingstodetermine theyieldtomaturityisagoodalternativetocalculatingtheyieldtomaturitydirectly.However, Koller et al. (2005)commentto“neverapproximatetheyieldtomaturityusingabond’s couponrate.” Fordebtbelowinvestmentgrade,usingyieldtomaturityasaproxyforthecostofdebtcan causesignificanterror.Threefactorsdrivetheyieldtomaturity:thecostofdebt,the probabilityofdefault,andtherecoveryrate.Whentheprobabilityofdefaultishighandthe recoveryrateislow,theyieldtomaturitywilldeviatesignificantlyfromthecostofdebt.Thus, forcompanieswithhighdefaultriskandlowratings,theyieldtomaturityisapoorproxyfor thecostofdebt.Toestimatethecostofhighyielddebt,thefollowingmethodfrom Damodaran(2002)canbeused.First,estimateacompany’sdollardebtandinterest expenses.Second,computeafinancialratioorratiosthatmeasuresdefaultriskandusethe

MasterThesisSebastianOotjers 48 s0041823 IEMFEM ABCD ratio(s)toestimatearatingforthecompany.Third,adefaultspread,basedontheestimated rating,isaddedtotheriskfreeratetoarriveatthepretaxofdebt. Damodaran(2002)assumethatbondratingsaredeterminedsolelybyinterestcoverageratio, whichisdefinedas: Interestcoverageratio=Earningsbeforeinterestandtaxes/Interestexpense Theinterestcoverageratioischosenforthreereasons.First,itisaratiousedbyboth Standard&Poor’sandMoody’stodetermineratings.Second,thereissignificantcorrelation notonlybetweentheinterestcoverageratioandbondratings,butalsobetweeninterest coverageratioandotherratiosusedinanalysis,suchasthedebtcoverageratioandthe capitalflowratios.Third,theinterestcoverageratiochangesasacompanychangesits financingmixanddecreasesasthedebtratioincreases.Theratingagencieswouldargue, however,thatsubjectivefactors,suchastheperceivedqualityofmanagement,arepartofthe ratingsprocess.Onewaytobuildthesefactorsintotheanalysiswouldbetomodifytherating obtainedfromthefinancialratioanalysisacrosstheboardtoreflecttheratingsagencies’ subjectiveconcerns. Thedatainthefollowingtableswereobtainedfromananalysisoftheinterestcoverageratios ofthreetypesofcompaniesindifferentratingsclasses.Thetablesalsoshowtheinterest spread/ratingrelationship.Theriskfreeinterestratehastobeaddedtothespreadtoacquire thecostofdebt. For large manufacturing firms InterestCoverageRatio Rating Spread >8.5 AAA 0.35% 6.508.50 AA 0.50% 5.506.50 A+ 0.70% 4.255.50 A 0.85% 3.004.25 A 1.00% 2.503.00 BBB 1.50% 2.252.50 BB+ 2.00% 2.002.25 BB 2.50% 1.752.00 B+ 3.25% 1.501.75 B 4.00% 1.251.50 B 6.00% 0.801.25 CCC 8.00% 0.650.80 CC 10.00% 0.200.65 C 12.00% <0.20 D 20.00% www.bondsonline.com(February2004) For financial service firms InterestCoverageRatio Rating Spread >3 AAA 0.70% 2.503 AA 0.90% 2.002.50 A+ 1.25% 1.502.00 A 1.40% 1.201.50 A 1.50% 0.901.20 BBB 2.00% 0.750.90 BB+ 4.25% 0.600.75 BB 4.75% 0.500.60 B+ 5.75% 0.400.50 B 6.00% 0.300.40 B 6.25% 0.200.30 CCC 10.50% 0.100.20 CC 12.50% 0.050.10 C 14.00% <0.05 D 16.00% www.bondsonline.com(February2004)

MasterThesisSebastianOotjers 49 s0041823 IEMFEM ABCD

For smaller and riskier firms InterestCoverageRatio Rating Spread >12.5 AAA 0.35% 9.5012.50 AA 0.50% 7.509.50 A+ 0.70% 6.007.50 A 0.85% 4.506.00 A 1.00% 4.004.50 BBB 1.50% 3.504.00 BB+ 2.00% 3.003.50 BB 2.50% 2.503.00 B+ 3.25% 2.002.50 B 4.00% 1.502.00 B 6.00% 1.251.50 CCC 8.00% 0.801.25 CC 10.00% 0.500.80 C 12.00% <0.50 D 20.00% www.bondsonline.com(February2004) Tocalculatefreecashflow,taxesarecomputedasifthecompanywereentirelyfinancedby equity.Byusingallequitytaxes,comparisonscanbemadeacrosscompaniesandovertime, withoutregardtocapitalstructure.Yet,sincethetaxshieldhasvalue,itmustbeaccounted for.IntheenterpriseDCFmodelusingtheWACC, the tax shield is valued as part of the cost of capital .Tovaluethetaxshield,thecostofdebtisreducedbythemarginaltaxrate: Aftertaxcostofdebt=Costofdebt*(1Tm) AccordingtoresearchbyJohnGraham(1996),thestatutorymarginaltaxrateoverstatesthe future marginaltaxratebecauseofrulesrelatedtotaxlosscarryforwards,taxloss carrybacks,investmenttaxcredits,andalternativeminimumtaxes. Grahamfindsthatforinvestmentgradecompanies,oneshouldusethestatutoryrate.Fora typicalcompanythatdoesnotalwaysfullyuseitstaxshields,Graham(1996)estimatesthat themarginaltaxrateisonaverage5percentagepointsbelowthestatutoryrate. Targetweights shouldbeusedtodeterminethecostofcapital.Usingmarketvaluestoweight expectedreturnsinthecostofcapitalfollowsdirectlyfromtheformula’sderivation.Buta moreintuitiveexplanationcanalsobeconsidered:theWACCrepresentstheexpectedreturn onan alternative investmentwithidenticalrisk.Ratherthanreinvestinthecompany, managementcouldreturncapitaltoinvestors,whocouldreinvestelsewhere.Toreturncapital withoutchangingthecapitalstructure,managementcanrepaydebtandrepurchaseshares, butmustdosoattheir market value.Conversely,bookvaluerepresentsasunkcost,soitis nolongerrelevant. Thecostofcapitalshouldrelyontargetweights,ratherthancurrentweights,becauseatany point,acompany’scurrentcapitalstructuremaynotreflectthelevelexpectedtoprevailover thelifeofthebusiness.Thecurrentcapitalstructuremaymerelyreflectashorttermswingin thecompany’sstockprice,aswingthathasyettoberebalancedbymanagement.Thus, usingtoday’scapitalstructuremaycauseoverestimating(orunderestimating)ofthevalueof taxshieldsforcompanieswhoseleverageisexpectedtodrop(orrise). AccordingtoKoller et al. (2005),manycompaniesarealreadyneartheirtargetcapital structure.Ifthecompanyundervaluationisnot,thentherehastobedecidedhowquicklythe companywillachievethetarget.Inthesimplestscenario,thecompanywillrebalance immediatelyandmaintainthenewcapitalstructure.Inthiscase,usingthetargetweightsand aconstantWACC(forallfutureyears)willleadtoareasonablevaluation.Iftherebalancingis expectedtohappenoverasignificantperiodoftime,thenadifferentcostofcapitalshouldbe usedeachyear,reflectingthecapitalstructureatthetime.Inpractice,thisprocedureis complex;notonlyhavetheweightstobemodeledcorrectly,butalsothechangesinthecost ofdebtandequity(becauseofincreaseddefaultriskandhigherbetas).Forextremechanges incapitalstructure,modelingenterpriseDCFusingaconstantWACCcanleadtosignificant error.

MasterThesisSebastianOotjers 50 s0041823 IEMFEM ABCD Koller et al. (2005)recommendtheuseacombinationofthreeapproachestodevelopatarget capitalstructureforacompany: 1. Estimatethecompany’scurrentmarketvaluebasedcapitalstructure. 2. Reviewthecapitalstructureofcomparablecompanies. 3. Reviewmanagement’simplicitorexplicitapproachtofinancingthebusinessandits implicationsforthetargetcapitalstructure. Thecompany’scurrentcapitalstructurecanbedeterminedbymeasuringthemarketvalueof allclaimsagainstenterprisevalue.Forthemostcompanies,theclaimswillconsistprimarily ofdebtandequity.Ifacompany’sdebtandequityarepubliclytraded,simplymultiplythe quantityofeachsecuritybyitsmostrecentprice.Mostdifficultiesarisewhensecuritiesare nottradedsuchthatpricescanbereadilyobserved. Ifanobservablemarketvalueisnotreadilyavailable,thedebtsecuritiescanbevaluedat bookvalueorthroughtheuseofdiscountedcashflow.Inmostcases,bookvaluereasonably approximatesthecurrentmarketvalue.Thiswillnotbethecase,however,ifinterestrates havechangeddramaticallysincethetimeofissuanceorthecompanyisinfinancialdistress. Inthesesituations,eachbondshouldbevaluedseparatelybydiscountingpromisedcash flowsattheappropriateyieldtomaturity.Determinetheappropriateyieldtomaturityby examiningtheyieldsfromcomparablyrateddebtwithsimilarmaturities. Ifcommonstockispubliclytraded,multiplythemarketpricebythenumberofshares outstanding . Forprivatelyheldcompanies,nomarketbasedvaluesareavailable.Inthiscase,theequity value(forthecostofcapital)hastobedeterminedbyeitherusingamultiplesapproachor throughDCFiteratively.Toperformaniterativevaluation,assumeareasonablecapital structure,andvaluetheenterpriseusingDCF.Usingtheestimateofdebttoenterprisevalue ratio,repeatthevaluation.Continuethisprocessuntilthevaluationnolongermaterially changes. Toplacethecompany’scurrentcapitalstructureinthepropercontext,compareitscapital structurewiththosesimilarcompanies. Asafinalstep,management’shistoricalfinancingphilosophyshouldbereviewed. 3.1.7 Nonoperating assets and nonequity claims Nonoperatingassetscanbesegmentedintotwogroups,marketablesecuritiesandilliquid investments. InternationalAccountingStandardsrequirecompaniestoreportliquiddebtandequity investments(e.g.,excesscashandmarketablesecurities)atafairmarketvalueonthe company’sbalancesheet.Therefore,whenvaluing liquid nonoperatingassets,usetheirmost recentreportedbalancesheetvalue,ratherthantodiscountfuturenonoperatingflows. Whenvaluingacompanyfromtheinside,illiquidinvestmentsshouldbevaluedbyusing enterpriseDCF.Ifthecompanyisvaluedfromtheoutside,accordingtoKoller et al. (2005), valuationoftheseassetsisroughatbest.Companiesdiscloseverylittleinformationabout illiquidinvestments,suchasdiscontinuedoperations,excessrealestate,nonconsolidated subsidiaries,andotherequityinvestments. Fornonconsolidatedsubsidiaries,informationdisclosuredependsonthelevelofownership. Whenacompanyhassomeinfluencebutnotacontrollinginterestinanothercompany,it recordsitsportionofthesubsidiary’sprofitsonitsownincomestatementandtheoriginal investmentplusitsportionofreinvestedprofitsonitsbalancesheet.Thisinformationcanbe usedtocreateasimplecashflowstatement.Todiscountthecashflow,acostofcapital, commensuratewiththeriskoftheinvestmentshouldbeused,nottheparentcompany’scost ofcapital. Whenownershipislessthan20%,investmentsarereportedathistoricalcost,andthe company’sportionofprofitsisrecorded only whenpaidouttotheparent.Inmostsituations, nothingmorethantheinvestment’soriginalcostsarevisible.Inthiscase,useamultipleof thebookvalueoratrackingportfoliotovaluetheinvestment.

MasterThesisSebastianOotjers 51 s0041823 IEMFEM ABCD Thevalueofnonoperatingassetshastobeaddedtothevalueofoperationstodetermine enterprisevalue.Toestimateequityvalue,subtractanynonequityclaims,suchasdebt, unfundedretirementliabilities,capitalizedoperatingleases,andoutstandingemployee options.Themostcommonnonequityclaimsare: 1. Debt 2. Unfundedretirementliabilities 3. Operatingleases 4. Contingentliabilities 5. Preferredstock 6. Employeeoptions 7. Minorityinterest Onceallthenonequityclaimshavebeenidentifiedandvalued,theycanbesubtractedfrom enterprisevaluetodetermineequityvalue. 3.1.8 Conclusion AfteranalyzingtheenterpriseDCFmodelonthegeneralsubjectsofanalysis,itcanbe concludedthattheenterprisevalueequalsthesumofthevalueoftheoperationaland nonoperationalassetsofthecompany.Theoperationalassetsarevaluedbydiscountingthe freecashflowsattheweightedaveragecostofcapital.Theeffectofthetaxdeductibilityof interestisintegratedintheweightedaveragecostofcapital.Thenonoperationalassetsare valuedinadifferentwaydependingonthetypeofasset.Toarriveatthevalueofequity,the nonequityclaimshavetobesubtractedfromtheenterprisevalue. Figure3.1givesaschematicoverviewofthebuildingblocksoftheenterpriseDCFmodel.

MasterThesisSebastianOotjers 52 s0041823 IEMFEM ABCD

Enterprisevalue Operatingassets Nonoperatingassets Forecastperiod Terminalvalue Marketablesecurities Illiquidinvestments FCFF WACC Liquidation Multiple EBIT(1T) D/Eratio Stablegrowth Depreciation Targetratio • EstimatecurrentCS Expectedgrowthrate Capex • ReviewCScomparable companies Workingcapital • Reviewmanagement’s approach Aftertaxcostofdebt Riskfreerate Taxrate Formula overview Spread t=n FCFF t Forecastperiod: ∑ t Creditrating t=1 1( +WACChg ) Interestcoverageratio FCFF=EBIT(1– Taxrate)+Depreciation– Capex – WC D E WACC= kd 1( −Tm ) + ke Costofequity D + E D + E Liquidationvalue= CAPM Bookvalueofassets *(1+Inflationrate) average lifeofassets term year Marketriskpremium Stablegrowth: FCFFn+1 Riskfreerate (WACCst − gn ) Expectedgrowthrate=Reinvestmentrate*Returnoncapital Leveredequitybeta Aftertax cost ofdebt =cost ofdebt *(1– Tm) • Unlever peergroupbetas Interestcoverage ratio=EBIT/Interestexpense • Averageunleveredpeer groupbetas CAPM: E(Ri ) = rf + βi[E(Rm − rf )] • Relever averagebetato company D Levered equity beta: β = β 1( + ) e u E Figure 3.1: Schematic overview of enterprise DCF model building blocks

MasterThesisSebastianOotjers 53 s0041823 IEMFEM ABCD 3.2 Basic assumptions of the APV model ThepurposeofthisparagraphistoassesstheAPVmodelatthegeneralsubjectsofanalysis. However,theparagraphisstructuredinsuchawaythatitdoesnotexplicitly assessthese subjects.TheparagraphdiscussesthethreecomponentsoftheAPVmodel:theunlevered companyvalue,thevalueoftheinteresttaxshieldsandthecostsoffinancialdistress. Koller et al. (2005),Brealey&Myers(2003)andDamodaran(2002)eachgiveadescriptionof theAPVmodel.Theirdescriptionsareusedtoillustratethefirstandthethirdcomponent.The valuationoftheinteresttaxshieldsisamuchdebatedtopicandisthereforediscussedmore extensivelythroughtheuseofmultiplescientificarticles. 3.2.1 Definition of the APV model SeveralauthorshavediscussedtheAPVmodel.Ingeneral,theyagreeonthefundamentals oftheAPVmodel,whichareasfollows. Theadjustedpresentvalue(APV)modelseparatesthevalueofoperations intotwo components:thevalueofoperationsasifthecompanywereallequityfinancedandthevalue oftaxshieldsthatarisesfromdebtfinancing: Adjustedpresentvalue=Enterprisevalueasifthecompanywasallequityfinanced+present valueoftaxshields TheAPVvaluationmodelfollowsdirectlyfromtheteachingsofMiller&Modigliani,who proposedthatinamarketwithnotaxes(amongotherthings),acompany’schoiceoffinancial structurewillnotaffectthevalueofitseconomicassets.Onlymarketimperfections,suchas taxesanddistresscosts,affectenterprisevalue. Ratherthanmodeltheeffectofcapitalstructurechangesintheweightedaveragecostof capital,theAPVmodelexplicitlymeasuresandvaluesthecashfloweffectsoffinancing separately. MostauthorsbuildanAPVbasedvaluationbyvaluingthecompanyasifitwereallequity financed.Theydothisbydiscountingfreecashflowbytheunleveredcostofequity(whatthe costofequitywouldbeifthecompanyhadnodebt).Theythenaddanyvaluecreatedbythe company’suseofdebttothisvalue. 3.2.2 Value of the unlevered company ThefirststepintheAPVmodelistheestimationofthevalueoftheunleveredcompany.This canbeaccomplishedbyvaluingthecompanyasifithasnodebt: t=n FCFF Value _ unlevered _ company = t ∑ t t=1 1( + ku ) where FCFF t =Freecashflowtothefirmattimet ku =Unleveredcostofequity ThefreecashflowstothefirmarecalculatedinthesamemannerasintheenterpriseDCF model. Inthespecialcasewherecashflowsgrowataconstantrateinperpetuity, FCFF Value _ unlevered _ company = 1 (ku − g) where FCFF 1 =Expectedaftertaxoperationcashflowtothecompany g =Growthrate Theinputsneededforthisvaluationaretheexpectedcashflows,growthrates,andthe unleveredcostofequity.TheunleveredcostofequitycanbederivedbymeansoftheCAPM framework(asdiscussedinthepreviousparagraph)withtheunleveredbetaofthecompany asininput,insteadoftheleveredbetaofthecompany.Damodaran(2002)givesthefollowing

MasterThesisSebastianOotjers FinalDraft 54 s0041823 IEMFEM ABCD formulafortheunleveringofthebeta.Thisformula,however,istiedtotheassumptionthat the company maintains a fixed amount over time .Theformulaisasfollows.

βunlevered = β levered /(1+ 1( − T )D / E) where βunlevered =Unleveredbetaofthecompany βlevered =Leveredbetaofthecompany T =Taxrateforthecompany D/E =Currentdebtequityratio Incaseoftheassumptionthatthecompanymaintainsaconstantleverageratio,the unleveringformula,asstatedbyKoller et al. (2005),becomes:  D  βu = β e /1+   E  where βe =Leveredbetaofthecompany βu =Unleveredbetaofthecompany D/E =Currentdebt/equityratio Soasageneralbasis,thevalueofanenterpriseisbasedonthevalueoftheunlevered companyandthepresentvalueoftheinteresttaxshields(whichwillbediscussedfurtheron inthisparagraph).Damodaran,however,extendsthebasicAPVmodelwithatermthat accountsfortheexpectedcostsofbankruptcy.Otherauthorsacknowledgethetheoretical existenceofthecomponent,butignoreitmostofthetimes.Theignoranceoftheexpected costsofbankruptcy,accordingDamodaran(2002),leadstheseotherauthorstothe conclusionthatenterprisevalueincreasesascompaniesborrowmoneyandthatitwilleven yieldtheconclusionthattheoptimaldebtratioforacompanyis100%debt.Sincethisisan unrealisticconclusion,theinclusionofacomponentfortheexpectedcostsofbankruptcyis supported. TheDamodaran(2002)APVmodelconsistsofthreestepstodeterminethevalueofthe company: 1. Estimatingthevalueofthecompanywithnoleverage. 2. Consideringthepresentvalueoftheinteresttaxsavingsgeneratedbyborrowinga givenamountofmoney. 3. Evaluatingtheeffectofborrowingtheamountontheprobabilitythatthecompanywill gobankrupt,andtheexpectedcostofbankruptcy. 3.2.3 The expected bankruptcy cost ThethirdcomponentoftheAPVmodelistheevaluationoftheeffectofdebtonthedefault riskofthecompanyandtheexpectedcostsofbankruptcy.Damodaranstatesthat:Intheory, atleast,thisrequirestheestimationoftheprobabilityofdefaultandthedirectandindirect costsofbankruptcy.IfπistheprobabilityofdefaultandBCisthepresentvalueofthe bankruptcycost,thepresentvalue(PV)ofexpectedbankruptcycostcanbeestimated: PVofexpectedbankruptcycost=Probabilityofbankruptcy*PVofbankruptcycost =πBC Damodaran(2002,p.401)commentsthat:“Thiscomponentoftheadjustedpresentvalue approachposesthemostsignificantestimationproblems,sinceneithertheprobabilityof bankruptcynorthebankruptcycostcanbeestimateddirectly.” Furtherdetailsontheeffectandcalculationofthebankruptcycostscomponentinthe adjustedpresentvaluemodelwillbediscussedinalaterparagraphofchapter4. 3.2.4 Interest tax shields AlthoughageneralbasisoftheAPVmodelcanbeformulatedbasedontheapproachesof thethreeauthors,differencesariseinthedeterminationofthevalueoftheinteresttax shields.

MasterThesisSebastianOotjers 55 s0041823 IEMFEM ABCD Damodaran(2002,p.401)statesthat:“ThesecondstepintheAPVisthecalculationofthe expectedtaxbenefitfromagivenlevelofdebt.Thistaxbenefitisafunctionofthetaxrate andinterestpaymentsofthefirmandisdiscountedatthecostofdebttoreflecttheriskiness ofthiscashflow.Ifthetaxsavingsareviewedasaperpetuity, Valueoftaxbenefits =(Taxrate*Costofdebt*Debt)/CostofDebt =Taxrate*Debt=T mD Thetaxrateusedhereisthefirm’smarginaltaxrate,anditisassumedtostayconstantover time.” Koller et al. (2005,p.124)statethat:“Ifyoubelievethecompanywillmanageitsdebtto valuetoatargetlevel,thenthevalueofthetaxshieldswilltrackthevalueofoperating assets.Thus,theriskoftaxshieldswillequaltheriskofoperatingassets(k txa equalsk u).The majorityofcompanieshaverelativelystablecapitalstructures(asapercentageofexpected value),sowefavorthismethod. Ifyoubelievethedebttoequityratiowillnotremainconstant,thenthevalueofinteresttax shieldswillbemorecloselytiedtothevalueofforecasteddebt,ratherthanoperatingassets. Inthiscasetheriskoftaxshieldsisequivalenttotheriskofdebt(whenacompanyis unprofitable,itcannotuseinteresttaxshields,theriskofdefaultrises,andthevalueofdebt drops).Inthiscase,thefollowingequationgivesthevalueoftheinteresttaxshieldsin perpetuity:

(D * kd *) Tm Vtxa = = D *Tm kd where Tm =Marginaltaxrate kd =Costofdebt Thissituationoccursfrequentlyinperiodsofhighdebtsuchfinancialdistressandleveraged .” Thecostofdebtusedinthevaluationoftheinteresttaxshieldsisdeterminedinthesame wayasintheenterpriseDCFmodel. Brealey&Myers(2003,p.541)begintheirevaluationoftheinteresttaxshieldswiththe statingoftwofinancingrules.Thefocusonthevaluationofprojects,buttheirreasoningis alsovalidforenterprisevaluation.Theystatethefollowing: “Whataretaxshieldsworth?Itdependsonthe financing rule thecompanyfollows.Thereare twocommonrules: - Financingrule1:debtfixed.Borrowafractionofinitialprojectvalueandmakeanydebt repaymentsonapredeterminedschedule. - Financingrule2:debtrebalanced.Adjustthedebtineachfutureperiodtokeepitata constantfractionoffutureprojectvalue.” Theyillustratethesetworulesbymeansofexamplebasedonwhichtheyconcludethatthe calculationofAPV(debtrebalanced)getstheimplicationsofFinancingRule2only approximatelyright.Brealey&Myers(2003,p.542)commentthefollowingontheerrorinthe valuation: “Evenwhendebtisrebalanced,nextyear’sinteresttaxshieldsarefixes.Year1’sinteresttax shieldisfixedbytheamountofdebtatdate0,thestartoftheproject.Therefore,year1’s interesttaxshieldshouldhavebeendiscountedatk d,notatk u. Year2’sinteresttaxshieldisnotknownatthestartoftheproject,sincedebtisrebalancedat date1,dependingonthefirstyear’sperformance.Butoncedate1’sdebtlevelisset,the interesttaxshieldisknown.Thereforetheforecastedinteresttaxshieldatdate2shouldbe discountedforoneyearat12%andoneyearat8%. Thereasoningrepeats.Everyyear,oncedebtisrebalanced,nextyear’sinteresttaxshieldis fixed.SotheprocedureforcalculatingtheexactvalueoftaxshieldsunderFinancingRule2is asfollows: 1. Discountattheunleveredcostofequity,becausefuturetaxshieldsaretiedtoactual cashflows.

MasterThesisSebastianOotjers 56 s0041823 IEMFEM ABCD

2. Multiplytheresultingpresentvalueby(1+k u)/(1+k d),becausethetaxshieldsarefixed oneperiodbeforereceipt.Thek ustandsfortheunleveredcostofequityandk disthe costofdebt.” Brealey&Myers(2003,p.539)alsoposetwopointsofinterestregardingthevalueofthe interesttaxshields.Thefirstregardsthetruepresentvalueofthetaxshieldscomparedtothe valuethatresultsfromtheperpetuityformulafortheinteresttaxshieldsincaseofFinancing Rule1(T m*interest): “ThetruepresentvalueofthetaxshieldsisalmostsurelylessthanT m*interest: - Youcan’tusetaxshieldsunlessyoupaytaxes,andyoudon’tpaytaxesunlessyoumake money.Fewfirmscanbesurethatfutureprofitabilitywillbesufficienttouseupthe interesttaxshields. - Thegovernmenttakestwobitesoutofcorporateincome:thecorporatetaxandthetaxon bondholders’andstockholders’personalincome.Thecorporatetaxfavorsdebt;the personaltaxfavorsequity. - Aproject’sdebtcapacitydependsonhowwellitdoes.Whenprofitsexceedexpectations, thefirmcanborrowmore;iftheprojectfails,itwon’tsupportanydebt.Ifthefutureamount ofdebtistiedtofutureprojectvalue,thentheinteresttaxshieldsareestimates,notfixed amounts.” Theirsecondpointisthatoftherelevanceoftheaccuracyofthevaluationoftheinteresttax shields:“Inpracticeitrarelypaystoworrywhetherinteresttaxshieldsarevalued approximatelyorexactly.Yourworryingtimewillbemuchbetterspentinrefiningforecastsof operatingcashflowsandthinkingthroughwhatifscenarios. Butwhichfinancingruleisbetter–debtfixed,ordebtrebalanced?Asageneralrulewevote fortheassumptionofrebalancing,thatis,forFinancingRule2.” Asshownbytheabove,Koller et al. (2005)andBrealey&Myers(2003)considertwo scenariosforvaluingtheinteresttaxshields:afixed(dollar)amountofdebtoraconstant leverageratio(debtgrowsinlinewiththecompanyvalue).Damodaran(2002)onlydiscusses thesituationofthefixedamountofdebt. Thesetwoscenariosforthedeterminationoftheinteresttaxshieldsarebasedoneitherthe 1963studyofMiller&Modiglianioronthe1980and1985studiesofMiles&Ezzell.The remainderofthisparagraphwillfocusonthesetwoscenariosandthediscussioninthe corporatefinanceliteratureontheircorrectness. Miller&Modigliani(1963)describeavaluationmodelforleveredcompaniesinwhichthey assumethatthecompanymaintainsafixedamountofdebt.Theystate: “WewouldexpectthevalueofaleveredfirmofsizeX,withapermanentlevelofdebtD Linits capitalstructure,tobegivenby”: 1( −τ )X τR V = + = V +τD L ρτ r U L where VL =leveredcompanyvalue VU =unleveredcompanyvalue τ =marginaltaxrate Theformuladoesnotincludeacomponentforthepotentialcostsoffinancialdistressbut Miller&Modiglianigivethefollowingargumentwithregardtothevaluemaximizingamountof debt:“Itmaybeusefultoremindreadersonceagainthattheexistenceofataxadvantagefor debtfinancing–eventhelargeradvantageofthecorrectedversion–doesnotnecessarily meanthatcorporationsshouldatalltimesseektousethemaximumpossibleamountofdebt intheircapitalstructures. Thereareadditionalconsiderations,whicharetypicallygroupedundertherubricof“theneed forpreservingflexibility”,whichwillnormallyimplythemaintenancebythecorporationofa substantialreserveofuntappedborrowingpower.Thetaxadvantageofdebtmaywelltendto lowertheoptimalsizeofthatreserve,butitishardtobelievethatadvantagesofthesize contemplatedunderourmodelcouldjustifyanysubstantialreduction,letalonetheircomplete elimination.”

MasterThesisSebastianOotjers 57 s0041823 IEMFEM ABCD Miller&Modigliani(1963)alsoassumethatcashflowshaveagrowthrateofzero. InMiles&Ezzell(1980)theauthorscommentontheMillerModiglianiAPVmodelwithregard totheriskinessoftheinteresttaxshields.Theystatethat:“Whenmanagementactsto maintainaconstantdebttototalvalueratio,intermsofrealizedmarketvalues,the investmentdecisionimpactsupontheriskinessaswellasthemagnitudeoffuturetaxshields createdbydebtfinancing.Eventhoughthefirmmightissuerisklessdebt,iffinancingpolicyis targetedtorealizedmarketvalues,theamountofdebtoutstandinginfutureperiodsisnot knownwithcertainty(unlesstheinvestmentisriskless)andconsequently,themagnitudeof thetaxshieldscannotbeknownwithcertainty.” ThepurposeoftheMiles&Ezzell(1985)studywastoexaminetheimplicationsfortaxshield valuationofmaintainingaconstantmarketvalueleverageratioinsteadofaconstantdebt level.InthispaperMiles&Ezzellshowthatwhenthecompany’sfinancingstrategyisto maintainaconstantmarketvalueleverageratio,themarginalvalueofachangeindebtlevel resultingfromachangeinthisleverageratioismuchlowerthanthecorporatetaxrate.They alsoderivetherelationshipbetweenthecompany’sequitybetaanditsunleveredbetaunder theassumptionofaconstantleverageratio. Miles&Ezzellstarttheirreasoningwiththeassumptionthatcompaniesmaintainaconstant leverageratio.Theydevelopanequationforthemarketvalueofaleveredcashflowstream ~ ~ ~ ~ ~ ~ ~ (X 1 + TS1 ) , (X 2 + TS 2 ) ,…, (X T + TST ) where X j arerandomunleveredcashflowsand ~ TS j arerandomdebtrelatedtaxshieldsinperiodj,respectively,forj=1,…,T. ~ ~ AttimeT–1,theyexpressthevalueof (X T + TST ) bytheCAPMas ~ ~ ~ ~ E (X + TS ) − φCov(X + TS ,~r ) V = T −1 T T T T mT (3.1) T −1 1+ r where Ei() =Timeiexpectationoperator Cov() =Covarianceoperator Ф =Marketpriceofriskassumedconstantacrosstime ~ rmj =Timejmarketrateofreturn r =Risklessrateofinterest Asaresultoftheconstantleverageratioassumption,thevalueoftheinteresttaxshieldsat timeTcanbeexpressedas: ~ TST = τrLVT −1 (3.2) where τ =Marginalcorporatetaxrate L =Leverageratio(Debt/(Debt+Equity)) ~ AttimeT1,V T1isknownwithcertainty.Hence,Equation(3.2)showsthatTST seenfrom timeT1,isalsoknownwithcertainty.However,attimeT–2,thetimeTinteresttaxshield,

TST = τrLVT −1 isuncertainduetoV T1beingarandomvariable. Afteranumberofrearrangementsandassumptions,Miles&Ezzellarriveatthefollowing expression: ˜ ˜ ET −2 (X T ) τrL[ET −2(VT −1)] π T −2(VT −1) = 2 + (3.3) (1+ ku ) (1+ ku )(1+ r) Fromthisequation(3.3),itisapparentthattoobtainthetimeT–2valueofthetimeTinterest taxshield,theappropriatediscountrateforperiodTistheriskfreerate,r,andtheunlevered costofcapital,k u,istheappropriatediscountrateforperiodT–1.Thus,attimeT–1,the marketknowsthetimeTtaxshieldwithcertainty.However,viewedfromtimeT–2,thetime T–1expectationaboutthetimeTtaxshieldissubjecttouncertainty.

MasterThesisSebastianOotjers 58 s0041823 IEMFEM ABCD Thenextstepisiteratingformula(3.3)toarriveatthevalueV 0: T ˜ T ˜ E 0(X j ) E0 (TS j ) V0 = ∑ j +∑ j−1 (3.4) j=1 (1+ ku ) j=1 (1+ ku ) (1+ r) where ~ ~ E0 (TS j ) = τrL[E0 (V j−1 )] Equation(3.4)showsthatwhenthemarketvalueleverageratioisheldconstant,itisnot generallycorrecttodiscountinteresttaxshieldsattherisklessrate.Thetaxshieldexpected attimejisdiscountedbackoneperiodattherisklessrateandtheremainingj–1periodsat theunleveredcostofcapital. Thisresulthasanumberofimplicationsforthevaluationofinteresttaxshields.Thestandard analysisofthepresentvalueoftaxshieldsinaMiller&Modiglianitaxworldassumesthatthe ~ expectedunleveredcashincomestream, X j isalevelperpetuityandderivesthefollowing expressionforleveredmarketvalue: ˜ ˜ E0 (X ) τrD0 E0 (X ) V0 = + = + τD0 (3.5) ku r ku whereD 0isthecurrentlevelofdebt.Implicitinequation(3.5)isthatD 0ispermanentdebt, andthatallfuturetaxshieldsarenonstochastic.Onlyinthiscasewilleachdollarofadditional debtaddτdollarstototalleveredvalue.Theresult,however,isnotconsistentwithequation (3.4). dV ComparedtotheMiller&Modiglianianalysisthatimplies o = τ ,Miles&Ezzellfindthat: dDo dV0 1+ ku  r  =   τ (3.6) dD0  1+ r ku  Theystate,basedonthisexpression,thattwotestablepredictionscanbeinferredfrom equation(3.6).First, dV0 / dD0 canbemuchlessthanτevenintheabsenceofpersonaltax biases.Second, dV0 / dD0 isadecreasingfunctionofthecompany’sbusinessrisk(as measuredbyeitherk uorβ u,theunleveredcoefficient).Ifthecompanyhasnobusinessrisk, thenk u=r,andequation(3.6)implies dV0 / dD0 =τwhichistheMiller&Modiglianiresult.

However,ifk u>r,then dV0 / dD0 <τ. Anotherimplicationofequation(3.5)relatestotheunleveringofthebeta.Thereasoningof Miles&Ezzellisasfollows. Hamada(1972)assumedthatequation(3.5)wascorrectanddevelopedthefollowing equationforunleveringtheequitybeta: 1− L β * = ( )β (3.7) u 1−τL e * where βu and β e are,respectively,theunleveredbetaandtheequitybeta.Theasterisk indicatesthatHamada’sunleveringprocedureisused.Toderive(3.7),itmustbeassumed thatfutureinteresttaxwriteoffsarecertainandthisholdsonlyifthecompany’sfuturedebt

MasterThesisSebastianOotjers 59 s0041823 IEMFEM ABCD levelsarecertain.However,ifthecompanymaintainsaconstantleverageratio,thenthe correctunleveringprocedureisquitedifferentfromtheonespecifiedabovesincetaxshields occurringbehindtime1areuncertain. Miles&Ezzellbeginbywritingleveredvaluefromequation(3.3)as ˜ ˜ u ˜ τ E0 (X1 + V1 ) τrLV0 E 0 (V1 ) V0 = + + (3.8) (1+ ku ) (1+ r) (1+ ku ) ~ u ~τ where V1 isthetime1valueoftheunleveredcashflowsbeyondtime1and V1 isthetime1 valueofallinteresttaxwriteoffsbeyondtime1.Thefirstcomponentissimplytheunlevered value,thesecondisthepresentvalueofthetime1taxshield,andthethirdisthevalueofall interesttaxwriteoffsbeyondtime1.Theleveredbetacoefficients,β L,canbespecifiedasa weightedaverageofthebetasofthesethreecomponents. Thebetacoefficientofthefirstvaluecomponentofequation(3.8)isβ u,theunleveredbeta coefficient.Sincethethirdcomponenthasthesameexpectedrateofreturnasthefirst component,itsbetacoefficientisalsoβ u.Sincetherateofreturnonthesecondvalue componentisriskless,itsbetacoefficientiszero. Thisresultsin,  τrL  (3.9) β L = 1− β u  1+ r  Sinceitisalsoknownthat

β L = Lβ d + 1( − L)β e (3.10) andfollowingtheHamadaassumptionthatβ d,thedebtbeta,iszero,thefollowingrelationship betweentheβ e andβ u canbeobtainedfromequations(3.9)and(3.10):    1− L  βu = β e   τrL 1−   1+ r  ThisistheMiles&Ezzell(1985)betaunleveringformulaundertheassumptionofaconstant leverageratio. 3.2.5 Comments on the Miller-Modigliani and the Miles-Ezzell framework Multipleauthorsofcorporatefinanceandvaluationtextbooks,asshownearlierinthis paragraph,haveadoptedthetheoriesofMiller&ModiglianiandMiles&Ezzell.However, Fernández(2004)takesadifferentpointofview,concludingtoanoverallincorrectnessof boththeMillerModiglianiandtheMilesEzzellframework. Fernández(2004)arguesthatthepresentvalueeffectofthetaxsavingondebtcannotbe calculatedassimplythepresentvalueofthetaxshieldsassociatedwithinterest.Instead,he claimsthattheonlywaytoobtainthecorrectvalueofthetaxshieldsfromdebtistodotwo presentvaluecalculations,onefortheunleveragedfirmandtheotherfortheleveragedfirm, andthensubtracttheformerfromthelatter.Theseresultsarepotentiallyimportant,because theycontradictstandardresultsintheliterature.Inaddition,hisresultsimplythat,even thoughthecapitalmarketiscomplete,valueadditivityisviolatedbecausethevalueofa streamofcashflowsisnotindependentofaddingtoanothersetofcashflows. Cooper&Nyborg(2006)correctthereasoningfromFernández(2004)andgiveanoverview oftheMillerModiglianiandMilesEzzellframework.

MasterThesisSebastianOotjers 60 s0041823 IEMFEM ABCD Intheirpaper,Cooper&NyborgreconciletheFernándezresultswithstandardvaluation formulaeforthetaxsavingfromdebt.Theyshowthat,asonewouldexpectinacomplete market,thevalueofthedebttaxsavingisthepresentvalueofthetaxsavingsfrominterest. Theirreviewisasfollows.ThetwomainapproachestoleveragepolicyaretheMiller& Modigliani(1963)andtheMiles&Ezzell(1980).ThedifferenceisthatMiles&Ezzellassume thattheamountofdebtisadjustedtomaintainafixedmarketvalueleverageratio,whereas Miller&Modiglianiassumethattheamountofdebtineachfutureperiodissetinitiallyandnot revisedinlightofsubsequentdevelopments. Becausethelevelofriskinthetaxsavingsisdifferent,relationsbetweenkeyparametersare differentforthetwoassumedleveragepolicies.FortheMiller&Modiglianipolicy,therelation betweenthecostofequityk eandk uisgivenby D k = k + ()k − k ()1− T e u E u d whereTisthetaxrateandk disthecostofdebt.FortheMiles&Ezzellleveragepolicywith continuousrebalancing,itisgivenby D k = k + ()k − k e u E u d ThevalueofthetaxsavingswhentheMiller&Modiglianipolicyisfollowedis Dk T VTSMM (g = 0) = d = DT kd ThevalueoftaxsavingswhentheMiles&Ezzellpolicyisfollowedis: Dk T VTSME = d (ku − g) Thefirstperiodtaxsavingisequaltotheinterestcharge,DK D,multipliedbythetaxrate.With theMiles&Ezzellconstantdebttovalueleveragepolicy,thetaxsavingschangesatthe samerateastheunleveragedcashflows,andtheriskofthetaxsavingisthesameasthe riskofthecompany. Miller&ModiglianidoesnotrepresentsimplytheMiles&Ezzellassumptionwithzerogrowth. Itisacompletelydifferentfinancingstrategy. Tocalculateanadjustedpresentvalue,theamountoftheinteresttaxshieldsshouldbe addedtotheunleveredvalueofthecompany,whichcanbecalculatedusingadiscountrate setwiththeunleveredbeta.Theunleveredbetacannotbeobserveddirectly.Assuming risklessdebt,itcanbeestimatedfromtheobservableequitybetaby MM βu = β e /(1+ 1( − T )(D / E)) IncaseoftheusageoftheMiles&Ezzellassumptionofaconstantleverageratiotheformula fortheunleveredequitybetais ME βu = β e (E /(D + E)) Cooper&Nyborg(2006)concludewiththecommentthat“noconsensusexistsastowhich setofassumptionstouse”. InCooper&Nyborg(2007),theauthorsgivetheirviewontheapplicationofoneofthetwo frameworkstoavaluationsituation.Intheiropinion,thekeytovaluingtaxshieldsis

MasterThesisSebastianOotjers 61 s0041823 IEMFEM ABCD consistency.“First,themethodusedshouldbeconsistentwiththeactualdebtpolicyofthe companybeingvalued.Second,thereleveringformulashouldbeconsistentwiththedebt policiesofthecompanieswhoseequitybetasareusedtoestimatediscountrates.Third, differentmethodsthatassumedifferentassumptionsshouldnotbemixedinthesame valuation. Thechoicebetweenthetwopossiblereleveringformulasisimportant.Bothapproaches persistinpartbecausetheformulasareoftenusedtounleveradiscountrateandthenrelever itbacktoaleverageratiosimilartowhereitstarted.Inthatapplication,itdoesn’tmattermuch whichapproachoneusesaslongasoneusesthesameapproachtounleverastoreleverthe rate.Inothercases,wheretheunleveredrateitselfisbeingusedinavaluation,itdoesmatter whichapproachoneuses,andthedifferenceissignificant.”TheyalsonotethattheMiles& EzzellformulasforreleveringareusuallymorelikelytobeaccuratethantheMiller& Modiglianiformulas. 3.2.6 Which author, which beta? Asshownabove,therearetwobetaunleveringformulas.OnebasedontheMiller& ModiglianileveragepolicyandtheotherbasedontheMiles&Ezzellpolicy.Damodaran (2002),asdescribedinthebeginningofthisparagraph,usestheModigliani&Miller framework.Heunleversthebetathrough

βu = β e /(1+ 1( − T )(D / E)) anddeterminesthevalueoftheinteresttaxshieldsthrough VTS = D *T Cooper&Nyborg(2006)give ME βu = β e (E /(D + E)) astheformulaforunleveringthebetaundertheMiles&Ezzellframework.However,the originalMiles&Ezzellformulafortheunleveringofthebetaformulatedin1985was:    1− L  β = β u e  τrL  1−   1+ r  TheCooper&Nyborg(2006)formulaisaproxyfortheoriginalMiles&Ezzell(1985)formula, becausethemultiplicationof τrL becomesverysmallundernormalcircumstances,which resultsinthefactthatthedenominatorapproachesone.Thesenormalcircumstanceswould beataxratesmallerthan50%,aninterestratearound5%andaleverageratiounder50%. Thesemultipliedgivesavaluefor τrL of0,0125.Inordertoillustratethedifferencebetween theoriginalMiles&Ezzell(1985)andtheCooper&Nyborg(2006)proxy,considerthe followingsituationsandtheerrorinthefoundproxyforthe β u :

MasterThesisSebastianOotjers 62 s0041823 IEMFEM ABCD

Most likely cases: Error 35%tax,leverage30%,interest5% 0,007 35%tax,leverage20%,interest5% 0,005 35%tax,leverage30%,interest4% 0,006 35%tax,leverage20%,interest4% 0,004 30%tax,leverage30%,interest5% 0,006 30%tax,leverage20%,interest5% 0,005 30%tax,leverage30%,interest4% 0,005 30%tax,leverage20%,interest4% 0,004 The table shows the maximum difference between the official Miles & Ezzell formula and Cooper & Nyborg's proxy. Sincethedifferencesareverysmall,theCooper&Nyborg(2006)formulawillbeusedinthe remainderofthisresearchproject. 3.2.7 Comments on the correctness of the Miller-Modigliani framework TheAPVmodelhastwoversions,eachbasedonadifferentleveragepolicy.Thismeansthat thechoiceforoneofthetwoversionsshouldbebasedontheleveragepolicythatthe companyundervaluationappliesinpractice. TheissueaddressedbyEhrhardt&Daves(1999)iswhethertheMillerModigliani(MM) versionoftheAPVmodeliscorrect.Theystatethat“Anestimateoftheunleveredcostof equityisnecessaryformanyapplicationsofcorporatevaluation.However,thewidelyused MM/Hamadaformulaisbasedontwoassumptionsthatmaynotbetrue.First,theMM formulaassumesthatthefirmwillnotgrow.Thisassumptionisalmostcertainlyviolatedin practice,sincealmostallfirmsareexpectedtogrow.Asecondissueisthechoiceofdiscount rateforthetaxshield.TheMMAPVmodelassumesthatthediscountrateforthetaxshield shouldbethecostofdebt.However,therearesoundargumentsforusingalargerrate, perhapsevenashighastheunleveredcostofequity.Thisimpliesthatdespiteitswidespread usebypractitioners,researchers,andtextbookwriters,itisalmostalwaysinappropriateto usetheMM/Hamadamodel,sincevirtuallyallfirmsareexpectedtogrow.Giventhatgrowth shouldbeincorporatedexplicitlyintothemodel,theonlyremainingdecisionisthechoiceof discountrateforthetaxshield.Unfortunately,therearenoempiricalteststoprovidean answertothisquestion,andtwomajoreconometricproblemswillconfoundfutureresearchin thisarea.First,theunleveredbetaandunleveredcostofequityforafirmareunobservable. Second,therearelargemeasurementerrorsintheotherrequiredvariables.” Ehrhardt&Daves(1999)showthatusingthecostofdebtasthediscountforthetaxshield canleadtoaleveredcostofequitythatislessthantheunleveredcostofequity.Sincethis contradictsbothintuitionandcasualobservationsofleveredcompanies,theybelievethata ratehigherthanthecostofdebtshouldbeused. Ehrhardt&Daves(1999)alsoshowthatifaratelessthantheunleveredcostofequityis usedtodiscountthetaxshield,thenthepartialderivativeofthecostofcapitalwithrespectto growthisnegative,anditbecomesmorenegativeforhigherdegreesofleverage.Taken alone,thiswouldimplythatahighgrowthcompanycouldsubstantiallyreduceitscostof capital,andhenceincreaseitsvalue,ifithadahighdegreeofleverage.Butthisis inconsistentwiththeobservedcapitalstructuresofhighgrowthcompanies,whichtypically havelowlevelsofdebt.Theystatethat:“Althoughthereareotherexplanationsforthe phenomenon,suchasagencycostsandasymmetricinformation,thissuggestsonceagain thatarelativelyhighrate,perhapseventheunleveredcostofequityitself,shouldbeusedto discountthetaxshieldofdebt.” 3.2.8 Conclusion BasedontheworksofKoller et al. (2005),Brealey&Myers(2003)andDamodaran(2002)it canbeconcludedthattheadjustedpresentvaluemodelisbasedonthreesteps: 1. Determiningthevalueoftheunleveredcompany 2. Valuingthetaxshields 3. Determiningthecostofpotentialdistress

MasterThesisSebastianOotjers 63 s0041823 IEMFEM ABCD ThiscanberepresentedbythefollowinggeneralAPVmodelformula: t=n FCFF t=n ITS EV = t + t + π * DC ∑ t ∑ t a t=1 1( + ku ) t=1 1( + kts ) where FCFF t =Freecashflowtothefirmattimet ku =Unleveredcostofequity ITS t =Interesttaxshieldattimet kts =Appropriatetaxshielddiscountrate π =Probabilityofdefault DC =Distresscosts Therearetwoframeworksforthevaluingofthetaxshields.Thefirstisbasedonthe assumptionofMiller&Modigliani(1963)thatacompanymaintainsafixedamountofdebt. ThisleadstoataxshieldvalueinperpetuityofD*T m(debt*tax). ThesecondisbasedontheassumptionofMiles&Ezzell(1985)thatacompanymaintainsa Dk T constantleverageratio.Thisleadstoataxshieldvalueinperpetuityof d m . (ku − g) Thereisnoclearconsensusintheliteratureonwhichassumption(andapproach)isthe correctone. Althoughdifferentauthors(Cooper&Nyborg(2006,2007);Ehrhardt&Daves(1999))have pointedoutthattheMiller&Modiglianiassumptionisunrealisticorevenincorrect,theworks allofthethreeauthorsthatwerediscussedinthisparagraphstillholdontoMiller& Modigliani’sassumption,withDamodaran(2002)discussingonlytheMillerModigliani framework. Thevalueoftheunleveredfirmisdeterminedbydiscountedfreecashflowtothefirm (FCFFs)attheunleveredcostofequity.Thisunleveredcostofequityisderivedbyusingthe CAPMframeworkandtheunleveredequitybetaasaninput.Thisunleveredequitybetahas tobederivedfromtheleveredequitybeta,sincethelattercanbeobservedinthemarketin contrasttotheformerwhichisunobservable. Dependingontheassumptiontaken(fixeddebtamountoraconstantratio),theequationfor determiningtheunleveredequitybetachanges.Assumingaconstantratioresultsinthe formulafoundbyMiles&Ezzell(1985)whichcanbeapproximatedbytheunleveringformula givenbyCooper&Nyborg(2006): ME βu = β e (E /(D / E)) AssumingafixeddebtamountgivestheformulastatedbyDamodaran(2002):

βu = β e /(1+ 1( − T )(D / E)) Thevalueofthepotentialcostoffinancialdistressdependsonthecostoffinancialdistress andtheprobabilityoftheoccurrenceofthesecosts. 3.2.9 Comment on this paragraph ThegoalofthisparagraphistoapplythegeneralsubjectsofanalysistotheAPVmodel.It seemsasifthereisnoyetaconsensusonthecorrectshapeoftheAPVmodelinthe literature:thenewestpublicationsonthedifferentrelatedtopicsarefrom2007.Inthe followingparagraphs,theothersubjectofanalysiswillbeappliedtotheAPVmodelandan overviewwillbegivenontheapplicabilityoftheAPVmodelunderdifferentcircumstances. ThatwillalsoleadtoacomparisonwiththeenterpriseDCFmodel.Thereforethisparagraph doesnotconcludeindefinitelyonany“right”or“wrong”assumptions. Figure3.2givesaschematicoverviewofthebuildingblocksoftheAPVmodel.

MasterThesisSebastianOotjers 64 s0041823 IEMFEM ABCD

Enterprisevalue Operatingassets Nonoperatingassets Unleveredfirm Interesttaxshields Financialdistresscosts Marketablesecurities Illiquidinvestments Forecastperiod Terminalvalue Amountofdebt Distress cost Tax rate Probabilityofdefault Liquidation Costofdebt Multiple Riskfreerate Stablegrowth Formula overview Taxrate t=n Forecastperiod: FCFF t Expectedgrowthrate ∑ t Spread (unleveredfirm) t=1 1( + ku ) FCFF=EBIT(1– Taxrate)+Depreciation– Capex – WC Creditrating CAPM: E(Ri ) = rf + βi[E(Rm − rf )] β Interestcoverageratio e FCFF Unleveredcostofequity Unleveredbeta (MM): D 1+ 1( −T ) m E CAPM EBIT(1T) βe Unleveredbeta (ME): D Marketriskpremium 1( + ) Depreciation E Riskfreerate Liquidationvalue= Capex Bookvalueofassets *(1+Inflationrate) average lifeofassets term year Unleveredequitybeta Workingcapital TVStablegrowth: FCFFn+1 • Unlever peergroupbetas (k − g ) • Averageunleveredpeer u n groupbetas Expectedgrowthrate=Reinvestmentrate*Returnoncapital Interestcoverage ratio=EBIT/Interestexpense Interesttax shields (MM):for (g=0) D*Tm Tm Dkd 1+ ku  Interesttax shield (ME): *  (k − g ) 1+ k u n  d  Distress cost (DC)=unleveredfirm value *15% PVfinancial distress costs = DC * PoD Figure 3.2: Schematic overview of APV model building blocks

MasterThesisSebastianOotjers 65 s0041823 IEMFEM ABCD 3.3 The enterprise DCF model assessed at the nongeneral subjects of analysis Paragraph3.1discussedthebasicassumptionsoftheenterpriseDCFmodel.Thecashflows aremodeledasfreecashflowstothefirm(FCFFs),whicharediscountedattheweighted averagecostofcapital.Thecostofdebtisdeterminedbasedonbondpricesorcreditratings andthecostofequitycanbeestimatedbyusingtheCAPMframework. Inthisparagraph,theenterpriseDCFmodelisanalyzedonthebasisoftheotherthree subjectsofanalysis(capitalstructure,probabilityofdefault,costsoffinancialdistress). 3.3.1 Capital structure InthecapitalstructureparagraphofChapter2,twotheorieswereidentifiedasthemain theoriesoncapitalstructuredecisionmakingwithincompanies.Thesewerethetradeoff theoryandthepeckingordertheory.Neitherofthetwotheoriescameforthasthe‘ultimate’ theorythatcouldexplainalltheeventsregardingcapitalstructuredevelopmentofdifferent companies. Thetradeofftheorystatesthatcompaniesmanagetheircapitalstructuretoanoptimaltarget leverageratio.Thisoptimalleverageistheoutcomeofthetradeoffbetweenthepotentialcost offinancialdistresscausedbytheincreasedleverage,andthetaxbenefitsofdebt.Afactor thatneedstobetakenintoaccountisthefactthatcompaniesmaytakeonatargetleverage ratiothatislowerthantheoptimalpointbasedonthetradeoffbetweendistresscostandtax savingsbecauseoftheneedforaccessdebtcapacity. Inthisparagraphandthenextitisassumedthatthetradeofftheoryistherighttheory.The reasonsforthisassumptionareasfollows. 1. Practicality.Ifcompanieswouldnotuseatargetleverageratio,thennoinferences couldbemadeontheexpectedcapitalstructure.Theleverageratiowoulddepend onlyontheleverageratiooftheprevioustimeperiodandthiswouldresultina Markovprocesswithaninfinitenumberofresultsbasedonanunknowndistribution ofthelikelihoodofthecompanyeitherissuingdebt,equityorusingretainedearnings. 2. Longtermview.Hovakimianet al. (2001)statedthatalthoughthepeckingorder considerationsaffectcorporatedebtratiosintheshortrun,companiestendtomake financingchoicesthatmovethemtowardtargetdebtratiosthatareconsistentwith tradeoffmodelsofcapitalstructurechoice.Sincealargeportionofthevalueofa companyisderivedfromitsterminalvalue,themainfocusinthevaluationshouldbe onthelongterm,thusleadingtoapreferenceforthetradeofftheory. 3. Interdependenceofthevaluationinputs.Ifthepeckingordertheoryisassumedtobe correct,thentheestimationofthecapitalstructuredecisionshastobebasedonthe financialdeficit.Ifthereisafinancialdeficit,thenthecompanywillhavetoacquire newcapitalanditsdecisionforthetypeofcapitalwilldependontheamountof retainedearnings.Thismeansthatchangesincapitalstructurewilldependonthe estimatedcashflows.ThismakestheWACCandthecashflowsareinterdependent whichcreatesroomforpossibleerrorsinbothofthemwhenoneofthetwois incorrect.Thisproblemdoesnotoccurwhenthetradeofftheoryisassumedtobe correct,sincetheleverageratioisindependentofthecashflowsinthistheory. Assumptions TheenterpriseDCFmodelassumesaconstantmarketleverageratio.Thatis,themarket valueofdebtdividedbythemarketvalueoftotalcapitalisconstantovertime. Thisassumptionisinlinewiththetradeofftheoryofcapitalstructurediscussedinthecapital structureparagraphofChapter2.Thismeansthatthecompanyisexpectedtocorrectits leverageattheendofitstimeperiodinawaysothatitmatchesittargetleverageratioagain. Thespeedofreversiontothistargetishoweverapointofdebate.Certainauthorsstatethata companyreversestothetargetleverageinaveryslowmanner.TheenterpriseDCFmodel, however,implicitlyassumesthatthespeedofreversionishighenoughtoresultinareversion totheoptimalpointattheendofeachtimestep,sothattheleverageratiocanbeconsidered constant. Theothertheoryofcapitalstructurediscussedinthecapitalstructurechapter,thepecking ordertheory,statesthatacompanybasesitsdecisionsofcapitalstructuringontheadverse selectioneffectsofthedifferentpossibilitiesofacquiringcapital.Thepeckingordertheory

MasterThesisSebastianOotjers 66 s0041823 IEMFEM ABCD assumesthatafirmdoesnothaveatargetleverageratio.Thecapitalstructureofacompany issimplytheresultofallpreviousfinancingdecisions.Itisclearthatthistheorydoesnot coincidewiththeassumptionoftheconstantleverageratio,whichisadoptedbythe enterpriseDCFmodel.

Conditions InorderfortheenterpriseDCFmodeltobeused,theleverageratiohastobe(atleast approximately)constant.Iftheleverageratioisnotconstant,theusedWACCwilldifferfrom theactual/correctWACC.ThisisbecausetheWACChastheleverageratioasaninput variable.Alsotheusedcostofequityisdependentontheleverageratio,thereforeitgivesan errorwhentheleverageratiochanges. TranslatingthisconditiontocapitalstructureeventsinwhichtheenterpriseDCFmodel cannotbeusedgivesthefollowingproblemscenarios: 1. Thecompanyhasalargeportionofdebtonitsbalancesheet,whichitwillrepayin thecomingtimeperiods.Thismeansthattheleverageratiowilldeclineeachperiod. Anexampleofthissituationisamanagementbuyoutorleveragedbuyout. 2. Thecompanyisfinanciallyconstrainedinawaythatpreventsthemfromfurther acquiringofdebt.Thisinhibitsthecompanyinacquiringnewcapitalinthedesired ratio. 3. Thecompanyisaspecialpurposevehiclecreatedtofinanceacertainproject.Inthis socalledprojectfinancesituation,thecompanyfirstbuildsupalargedebt(uptoa leverageratioof90%)andthenrepaysthisdebtovertime.Thiscausesanon constantleverageratio. Anothersituationinwhichanonconstantleverageratiocanoccuriswhenthecompany decidestofinanceitsfinancialdeficitinacertaintimeperiodbyonlyonefinancialinstrument (debtorequity).Weassumehowever,basedonthetradeofftheoryofcapitalstructure,that thecompanywillcorrectthisdifferencebetweenthecurrentleverageratioandthetarget leverageratioattheendofthatperiod. Modeling IftheenterpriseDCFmethodcanbeusedbecauseofaconstantleverageratio,thenthe targetleverageratiohastobedetermined.Themethodfordeterminingthetargetcapitalratio hasalreadybeendiscussedonthechapterofthebasicassumptionsoftheenterpriseDCF model.Inshort,todevelopatargetcapitalstructureforacompany,useacombinationof threeapproaches: 1. Estimatethecompany’scurrentmarketvaluebasedcapitalstructure. 2. Reviewthecapitalstructureofcomparablecompanies. 3. Reviewmanagement’simplicitorexplicitapproachtofinancingthebusinessandits implicationsforthetargetcapitalstructure. Theresultsofthesethreeapproachesshouldbecombinedtodetermineatargetleverage ratio.ThistargetratioistheinputfortheWACC. 3.3.2 Probability of default Usage TheenterpriseDCFmodeldoesnotexplicitlyusetheprobabilityofdefaultasaninputforthe valuationofafirm.TheWACCisbasedonthecostofdebt,costofequity,themarginaltax rateandtheleverageratio.Thefreecashflowsdonotincorporateanyfactorthatcorrectsfor thepossibilityofdefault. However,thepresenceofaprobabilityofdefaultmightbeimpliedinthecostofdebtandthe costofequity.Theprovidersofdebtofthecompanyareassumedtomakeanestimationof theriskofdefaultforthecompanyandwillincorporatethisintheinterestrate,whichthey demand.Also,thecostofequitycouldincorporatetheprobabilityofdefault.Thiscouldbe throughahigherequitybeta.However,thisbetaisderivedbytakentheaverageofthe unleveredindustrybetasandreleveringittothecompany’sleverageratio.Thereforeitcan onlyrepresenttheaverageprobabilityofdefaultofthecompaniesintheindustryinwhichthe companyoperates.Nonetheless,thesepossibleimplicationsoftheprobabilityofdefaultare notenoughtostatethattheprobabilityofdefaultisincorporatedintheenterpriseDCFmodel. AsaresultoftheabsenceoftheprobabilityofdefaultintheenterpriseDCFmodel,errormay occurinthevaluationofcompaniesthathaveasignificantprobabilityofdefault.Thecompany

MasterThesisSebastianOotjers 67 s0041823 IEMFEM ABCD isvaluedbasedontheexpectationthatitwillremainagoingconcernandthatitscashflows existinthefuture.Whentheprobabilityofdefaultissignificant,thecashflowsarenolonger certainandtheterminalvaluethatiscalculatedwilloverstatethecorrectterminalvalue. Therefore,theenterpriseDCFmodelgivesanincorrectestimationofthevalueofacompany thathasasignificantprobabilityofdefault. Thereisoneexceptiontothisflaw,andthatiswhenaliquidationofthecompanyisforeseen directlyaftertheforecastperiod.Thiscausestheterminalvaluetobetheliquidationvalue. However,thisexceptiononlyoccurswhenitisstatedwithcertaintythatthecompanywillbe liquidatedattheassumedpointintime.Ifthecompanybecomesdistressedorgoesbankrupt butdoesnotliquidateorendsupinastablegrowthpatternandisliquidatedanumberof periodslater,thentheerrorwillstillremaininthevaluation.

Modeling SincetheprobabilityofdefaultisnotincorporatedintheenterpriseDCFmodel,themethod fordeterminingtheprobabilityofdefaultisnotrelevanthere. 3.3.3 Costs of financial distress Incorporation ThecostsoffinancialdistressarenotincorporatedintheenterpriseDCFmodel.The enterpriseDCFmodelassumesthatthecompanyendsupinastablegrowthstateorthatthe companyisliquidated.Inthelastcase,theliquidationvaluebecomestheterminalvalue. Thereare,however,twointermediatestatesbetweenstablegrowthandliquidation:financial distressandbankruptcy.Withfinancialdistressthecompanyhasproblemsmeetingitsdebt obligations.Thiscausesindirectcostoffinancialdistresstooccur.Asaresultofaperiodof financialdistress,acompanycaneithermanagetoovercomethesituationandreturntobeing ahealthycompanyorthecompanycangobankrupt.Whenthecompanygoesbankrupt, directbankruptcycostsoccur.Bankruptcy,however,doesnotmeanthatthecompanyis liquidated.Thecompanycanbereorganizedandcaneventuallybecomeahealthycompany. Therefore,theenterpriseDCFmodeldoesnotincorporatethe(full)costsoffinancialdistress.

Mannerofusage SincetheenterpriseDCFmodeldoesnotincorporatethecostoffinancialdistress,the methodofintegratingtheseinthevaluationisnotrelevant. 3.3.4 Conclusion Thetradeofftheoryofcapitalstructureisassumedtobethecorrecttheoryfortheprediction ofcapitalstructuredecisionswithincompanies.TheenterpriseDCFmodelassumesa constantleverageratio.Insituationswherethisassumptionisviolated,themodelwillgivean incorrectvalueofthecompany.TheenterpriseDCFmodelalsodoesnotincorporatea measurefortheprobabilityofdefaultandthecostsoffinancialdistress.Thevaluationofa companywithasignificantprobabilityoffinancialdistressthroughtheenterpriseDCFmodel willthereforealsoresultinanincorrectvaluation. 3.4 The APV model assessed at the nongeneral subjects of analysis Paragraph3.2discussedthebasicassumptionsoftheAPVmodel.Thecashflowsare modeledasfreecashflowstothefirm(FCFFs),whicharediscountedattheunleveredcostof equitytodeterminethevalueoftheunleveredcompany.Theinteresttaxshieldsare discountedateitherthecostofdebtortheunleveredcostofequitydependingonthe leveragepolicyadoptedbythecompany.Thecostofdebtisdeterminedbasedonbond pricesorcreditratingsandtheunleveredcostofequitycanbeestimatedbyusingtheCAPM frameworkwiththeunleveredbetaasaninput.Thecostsoffinancialdistressarethethird componentoftheAPVmodelofwhichthethreecomponentscombinedgivethevalueofthe operatingassetsofthecompany. Inthisparagraph,theAPVmodelisanalyzedonthebasisoftheotherthreesubjectsof analysis(capitalstructure,theprobabilityofdefault,thecostsoffinancialdistress).

MasterThesisSebastianOotjers 68 s0041823 IEMFEM ABCD 3.4.1 Capital Structure Assumptions TherearetwoversionsoftheAPVmodel,eachbasedonadifferentassumptionofcapital structure.TheModiglianiMillerversionisbasedontheassumptionthattheleverageratioofa companyisnotconstantbutthattheamountofdebtisfixed.Sothecompanyhasacertain amountofdebtattime0andthisdebtwillremaininplaceforever.Linkedtotheassumption ofthefixedamountofdebtisthattheriskoftheinteresttaxshieldsisequaltotheriskof debt.Therefore,thetaxshieldsarediscountedatthecostofdebt. TheMilesEzzellversionassumesthattheleverageratioisconstantovertime.Theriskof interesttaxshieldsisthereforelinkedtotheriskofthecompany’soperations.Miles&Ezzell thereforeassumethattheinteresttaxshieldsshouldbediscountedattheunleveredcostof equity,exceptforthefirstperiod’staxshield,whichisdiscountedatthecostofdebt. Conditions TherearethreeconditionsunderwhichtheAPVmodelcanbeused.Thefirstisthesameas fortheenterpriseDCFmodel,namelyaconstantleverageratio.Iftheleverageratiois constant,thencertaininferencescanbemadeontheamountofdebtatcertainpointsintime enablingthevaluertocalculateaterminalvaluebasedonaperpetuityformula. Thesecondpossibleconditionisthefixedamountofdebt,whichalsoallowsfordetermining thecontinuingvaluebymeansofaperpetuityformula. Asthefirsttwoconditionsshow,thedifficultyinvaluingacompanybymeansoftheAPV modelisthefactthatsomeclosureisneedonthevalueaftertheforecastperiod.Aslongas someinferencecanbemadeontheamountofdebt,thevalueoftheinteresttaxshieldscan bedeterminedandthecompanycanbevalued.Ifthereisnofixedamountofdebtandalso noconstantleverageratio,thenthecompanythatisvaluedhastohaveafixedtermination date.Thisway,nocontinuingvaluehastobedeterminedandnoinferencesonthedebthave tobemade.Thisisthusthethirdcondition:acompanyhastohaveaknownterminationdate ifitdoesnothaveafixedamountofdebtandnoconstantleverageratio.Anotetothethird conditionisthattheamountofdebthastobeknownforeachyearintheforecastperiod. Otherwise,theinteresttaxshieldscannotbevalued.InthiscasethegeneralAPVmodel applies: t=n FCFF t=n ITS EV = t + t + π * DC ∑ t ∑ t a t=1 1( + ku ) t=1 1( + kts ) where FCFF t =Freecashflowtothefirmattimet ku =Unleveredcostofequity ITS t =Interesttaxshieldattimet kts =Appropriatetaxshielddiscountrate π =Probabilityofdefault DC =Distresscosts BecausetheAPVmodelcanbeusedunderanyoneofthethreeconditions,mostofthe scenariosofcapitalstructuredecisionsarecovered.TheonlyscenariounderwhichtheAPV modelcannotbeusedisthatofacompanythatisexpectedtostayagoingconcern,thathas avariableamountofdebtandthisamountofdebtisnotbasedonaconstantleverageratio. Inthiscase,noinferencescanbemadeontheamountofdebtandthecompanycannotbe valuedthroughtheAPVmodel. However,sinceweassume(asdiscussedinthepreviousparagraph)thatcompaniesfollow thetradeofftheoryofcapitalstructuredecision,companiesareassumedstrivetostayattheir targetleverageratioiftheyarenotasituationwheretheyhaveafixedamountofdebt. Modeling IncaseoftheMilesEzzellversionoftheadjustedpresentvalue,wherethecompanyis assumedtomaintainaconstantleverageratio,thesituationbecomescomparabletothe modelingofthecapitalstructuredevelopmentfortheenterpriseDCFmodel:thetarget leverageratioofthecompanyhastobedetermined.Thisratiocanthenbeusedasaninput forthevaluation. IncaseoftheMillerModiglianiversionoftheAPVmodel,wherethecompanyisassumedto maintainafixedamountofdebt,nomodelingofthecapitalstructureisneeded.Sinceonlythe

MasterThesisSebastianOotjers 69 s0041823 IEMFEM ABCD amountofdebt(andnottheamountofequity)isusedasaninputintheAPVmodel,any othercapitalstructurerelatedelementsarenotusedandthusirrelevant. 3.4.2 Probability of default Usage TheAPVmodelusestheprobabilityofdefaultasaproxyfortheprobabilityoffinancial distress.The1yearprobabilityoffinancialdistressismultipliedbythepresentvalueofthe costsoffinancialdistresstodeterminetheexpectedcostsoffinancialdistress. Modeling Todeterminetheprobabilityofdefaultforacompany,wehaveacoupleofpossible scenarios.Thecompanycanhaveacreditrating,inwhichcasetheprobabilityofdefaultcan directlybedetermined,orthecompanydoesnothaveacreditrating,inwhichcasethenext stepistodeterminewhetherthecompanyisapublicorprivatecompany. TheratingagenciesMoody’sandStandard&Poor’stracktheperformancesofcompanies andratetheircredibilityonthebaseofanumberofratios.Theratingagenciesalsodetermine theprobabilityofdefaultforcompaniesinthedifferentratingclassesbasedonhistorical defaultdata.Therefore,whenacompanyhasacreditrating,theprobabilityofdefaultcanbe determined.Table3.1showstheprobabilitiesofdefaultforthedifferentratingclasses. TheAltmanZscoreformulaisbasedonfivefinancialratios.TheZscorecanbeconvertedto acreditrating.ThisconversionisbasedonhistoricaldataontheZscoresofcompaniesthat haveacertaincreditrating.Fromthiscreditrating,theprobabilityofdefaultcanbe determined. Forpubliccompanieswithoutacreditrating,thefollowingAltmanZscoreformulaistobe used:

Z = 2.1 X1 + 4.1 X 2 + 3.3 X 3 + 6.0 X 4 + 0.1 X 5 where X1 =Workingcapital/Totalassets X2 =Retainedearnings/Totalassets X3 =Earningsbeforeinterestandtaxes/Totalassets X4 =Marketvalueequity/Bookvalueoftotaldebt X5 =Sales/Totalassets Z =OverallIndex Usingthisformula,oneinsertsthemorecommonlywrittenpercentage,forexample,0.10for 10%,forthefirstfourvariables(X 1X4).Thelastvariableistobewrittenintermsofnumberof times. Forprivatecompanieswithoutacreditrating,thefollowingadjustedAltmanZscoreformulais tobeused,inwhichthemarketvalueofequityisreplacedbythebookvalueofequityinthe X4variable:

Z'= .0 717(X1 ) + .0 847(X 2 ) + .3 107(X 3 ) + .0 420(X 4 ) + .0 998(X 5 ) Thevalueoftheinputvariablesshouldbebasedontheaccountinginformationretrievedfrom thelatestfinancialreportofthecompany. AfterdeterminingtheZscoreofacompany,thefollowingstepistotranslatethisscoretoa creditratingfromwhichtheprobabilityofdefaultcanbedetermined.Thevaluesinconversion arecreatedasfollows: 1. Thebasicinputsarethedefaultprobabilitiesthatbelongtocertainratingsaccording toStandard&Poor’sandMoody’s.Theseprobabilitiesaregivenintheparagraphon theprobabilityofdefaultinChapter2.Theseprobabilitiesarepercentagesof companiesdefaultingwithinfiveyears.Recalculatingthesevaluesto1yearvalues andtakingtheaverageofthetwodifferentratingagenciesgivesthefollowingresult.

MasterThesisSebastianOotjers 70 s0041823 IEMFEM ABCD

Average 1-year Credit rating default probability AAA 0,02 AA 0,06 A 0,13 BBB 0,61

BB 2,71 B 7,56 CCC 17,20 Table 3.1: Probability of default for different rating classes 2. TheZscorescanbelinkedtoacreditratingonthebasisofthefollowingintervals: Interval Z-score per rating Lower Upper PoD% AAA 4,641 infinity 0,02 AA 3,967 4,641 0,06 A 3,117 3,967 0,13 BBB 2,470 3,117 0,61 BB 2,075 2,470 2,71 B 1,617 2,075 7,56 CCC infinity 1,617 17,20 Therearemultiplewaysofdeterminingtheprobabilityofdefault,aswaysshowninthe paragraphontheprobabilityofdefault.Themethoddescribedaboveisabasedona combinationoftheprobabilitiesofdefaultthatarelinkedtodifferentcreditratingsandthe AltmanZscore.Thereasonsforthiscombinationareasfollows. 1. TheKMVmodelrequiresthevalueofthecompanyasaninputforthedetermination. However,thevalueispreciselywhatthecompletevaluationissupposedto determine.Socompanyvalueisanoutputnotaninput.Therefore,theKMVmodelis notuseful. 2. TheOhlsonscorecanbeusedtoestimatethelikelihood,wereitnotforthefactthat thereisnoscaleavailabletoconverttheOhlsonscoretoanactualprobabilityof default. 3. TheZETAmodelofAltmangivesmoreaccuratepredictionsoftheactualprobability ofdefault,asAltman(2000)showed.However,thecoefficientsofthevariablesare notpubliclyavailable.Therefore,thismodelcannotbeused. 4. TheCreditMetricsmodelbasestheprobabilityofdefaultontheratingmigration probabilities.Themodeldiscussedisthusasimpleversionofthismodelsincethe probabilitiesofdefaultforcertainratingclassesaretheprobabilitiesofmigratingfrom thatratingclasstodefaultwithinoneperiod.Forsimplicityreasons,themodel describedaboveassumesthatcompanieseitherdefaultorremainintheirrating class. 5. TheAltmanZscorecanbeusedforprivatecompaniessinceitonlyrequires accountinginformationasaninputinsteadofamarketvalueofpubliclytradedequity. 3.4.3 Cost of financial distress Incorporation Thecostsoffinancialdistressareincorporatedintheadjustedpresentvaluemodelthrougha separateterm.The1yearprobabilityofdefaultismultipliedbythepresentvalueofthecosts offinancialdistress. Integration Asdiscussedinthechapteronthecostofdefault,thetotalcostsoffinancialdistressare estimatedat1020%ofthebookvalueofdebtplusthemarketvalueofequity.When calculatingthecostoffinancialdistressforacompany,15%(themiddleof1020%)istaken asabasicestimate.Andinsteadoftakingthis15%fromthebookvalueofdebtplusthe marketvalueitistakenfromthevalueoftheunleveredcompany.Thereasonforthis

MasterThesisSebastianOotjers 71 s0041823 IEMFEM ABCD approachisthefactthatthevalueoftheunleveredcompanycanbedetermined,butthebook valueofdebtandthemarketvalueofequitycannot,sinceitistheendresultofthevaluation. Usingtheunleveredcompanyvalueasthebasisforthecostoffinancialdistressisclearlyan approximation.ThisapproximationwasintroducedbyDamodaran(2002). 3.4.4 Conclusion TherearetwoversionoftheAPVmodel:onethatassumesaconstantleverageratioanother thatassumesafixedamountofdebt.ThegeneralAPVmodel,whichmakesnoassumption onthedevelopmentofthecapitalstructure,canbeusedincaseofafinitelifeofthe company.TheAPVmodelalsocontainsaseparatetermtoincorporatethepotentialcostsof financialdistress.Thesepotentialcostsarebasedonthedistresscostsandtheprobabilityof default.Theprobabilityofdefaultcanbeestimatedbasedonamethodthatcombinesthe creditratingofacompanyanditsZscore. 3.5 Theoretical differences between the enterprise DCF model and the APV model Basedonthepreviouschapters,thedifferencesbetweentheenterpriseDCFmodelandthe APVmodelcanbedividedintotwocategories:thedifferencesinbasicassumptionsandthe differencesregardingcapitalstructure,theprobabilityofdefaultandthecostsoffinancial distress. 3.5.1 The differences and similarities in basic assumptions TheenterpriseDCFmodelandtheAPVmodelhavetwobasicassumptionsincommon.They bothusefreecashflowstothefirm(FCFFs)andusethesamecostofdebt. Theydifferinthestructureofthevaluationmodel,inthecostofequityusedandinthe discountrate(s)used.TheenterpriseDCFmodeldiscountsthefreecashflowstothefirmof eachtimeperiodattheweightedaveragecostofcapital.Thesumofthesediscountedcash flowsisthevalueoftheoperatingassetsofthecompany. TheAPVmodelsplitsthevaluationinthreeseparateparts:thevaluationoftheunlevered company,thevaluationofthetaxbenefitsofdebtandthevaluationofthecostsoffinancial distress.Thefreecashflowsarediscountedattheunleveredcostofequitytoarriveatthe valueoftheunleveredcompany.Theinteresttaxshieldsarediscountedateitherthe unleveredcostofequityorthecostofdebt.Thecostsoffinancialdistressarebasedonthe valueoftheunleveredcompany. SotheenterpriseDCFmodelusesonediscountrate,theAPVmodelusestwodifferent discountrates. TheenterpriseDCFmodelusestheleveredcostofequityasininputfortheWACC calculation.TheAPVmodelusestheunleveredcostofequityasmentioned.Sincethecostof equityisderivedthroughtheCAPMtheoremwithanequalriskfreerateandanequalmarket riskpremiumforboththeAPVmodelandenterpriseDCFmodel,thisimpliesthatthe enterpriseDCFmodelusestheleveredequitybetaandtheAPVtheunleveredequitybeta. 3.5.2 The differences regarding capital structure, the probability of default and the costs of financial distress AlthoughtheAPVmodelandtheenterpriseDCFmodelmakedifferentassumptionsonthe capitalstructureofthecompany,companiesinbothmodelsareassumedtofollowatradeoff theoryofcapitalstructuredevelopment.Thereasonsforthisassumptionwereexplainedin thechapterontheapplicationofthesubjectsofanalysisontheenterpriseDCFmodel.This meansthatthecompanywillingeneralstrivetomaintainatargetleverageratio. TheenterpriseDCFmodelassumesthatcompaniesdomaintainaconstantleverageratio thatremainsatatargetvalueovertime.TheAPVmodelhastwodifferentversions,each basedonadifferentassumptionofthecapitalstructure.Thefirstversionassumesthatthe companymaintainsafixedamountofdebtovertime.Soeachoccurringcapitalrequirement ismetbyeitherretainedearningsorbynewlyissuedequity.Thesecondversionassumes (liketheenterpriseDCFmodel)aconstantleverageratio.TheAPVmodelcouldalsobeused

MasterThesisSebastianOotjers 72 s0041823 IEMFEM ABCD inathirdsituationinwhichnoclearcapitalstructureismaintainedbutwhereallthe developmentsofcapitalstructureareknownateachtimeperiod. TheenterpriseDCFmodelandtheAPVmodelcanthushaveadifferentoranequal assumptionofcapitalstructuredependingonthesituation.However,incaseofanequal assumption,namelybothassumeaconstantleverageratio;thefunctionofthatconstant leverageratioisdifferentineachmethod.TheenterpriseDCFmodelusestheleverageratio todeterminetheWACC(discountrateeffect);theAPVmodelusestheleverageratioto determinetheamountofdebtandtheresultinginteresttaxshield(cashfloweffect). TheenterpriseDCFmodeldoesnotexplicitlytakethecostoffinancialdistressandthe probabilityofdefaultintoaccount.TheonlyaspectsintheenterpriseDCFmodelthatcouldbe relatedtoaprobabilityofdefaultarethecostofequityandthecostofdebt.Sincethecostof debtisderivedfromtheyieldtomaturityofthecompany’sbonds(inwhichtheprovidersof debtareassumedtotakeintoaccountanydefaultrisk)orfromthecreditratingofthe company(inwhichathespreadovertheriskfreerateisrelatedtotheprobabilityofdefault), onecansaythatsomemeasureoftheprobabilityofdefaultisincorporatedinit.Thecostof equitycouldincorporateameasureoftheprobabilityofdefaultthroughtheuseofthebetain itsdetermination.Thisbetaisameasureoftheriskinessofthecompany,butthebetais derivedbytakinganaverageindustrybetaandthusdoesnotrelatetothecompany’sriskof default.Anotherargumentonwhythecostofequityandthecostofdebtdonotaddan explicitmeasureoftheprobabilityofdefaultisthefactthatthecostofdebtandthecostof equityarealsousedintheAPVmodel.ThismeansthateventhoughtheenterpriseDCF modelmightincorporatetheprobabilityofdefaultintothevaluation,itdoesnotaddanyextra detailinrelationtotheAPVmodel.Asalastnotice,theenterpriseDCFmodeldoesnotadjust thecashflowsfortheprobabilityofdefaultanditalsodoesnotuseacashflowcomponentfor thecostoffinancialdistress. TheAPVmodelconsistsofaseparatepartthatincorporatesthepotentialcostoffinancial distress.Thispartisamultiplicationofthe1yearprobabilityofdefaultandthecostof financialdistress(whichisbasedonthevalueoftheunleveredcompany).Theprobabilityof defaultisaproxyfortheprobabilityoffinancialdistress.Iffinancialdistressoccurs,bothdirect andindirectcostsoffinancialdistressarerealized.Thesecostsareproportionaltothevalue oftheunleveredcompany.TheAPVmodelthustakesintoaccountthatacompanymight incurcostswhenitbecomesdistress. 3.5.3 Overview Thetablebelowshowsanoverviewofthedifferences.Theeffectofthesedifferencesonthe valuationoutcomewillbediscussedinthenextparagraph. Enterprise DCF model APV model

Cashflow FCFF FCFF

Discountrate WACC KuorKd

Costofequity Levered Unlevered

Costofdebt Creditratingbased Creditratingbased

Constantleverageratio Capitalstructure Constantleverageratio orfixeddebt Notexplicitlytakeninto Separateterminthe Probabilityofdefault account valuation Notexplicitlytakeninto Separateterminthe Costsoffinancialdistress account valuation 3.5.4 Method choice AsdiscussedintheapplicationchaptersoftheenterpriseDCFmodelandtheAPVmodel, eachmodelisapplicableundercertainconditions.TheenterpriseDCFmodelisonly

MasterThesisSebastianOotjers 73 s0041823 IEMFEM ABCD applicablewhenaconstantleverageratioisassumed.Thisleadstoanumberofsituationsin whichtheusageoftheenterpriseDCFmodelisproblematic: Projectfinance,inwhichtheleverageratioincreasesinthebeginningoftheproject anddeclineslateron. Amanagementorleveragedbuyout,wherethecompanyhasalargeamountofdebt onitsbalancesheet,whichitrepaysovertime. Afinanciallyconstrainedcompany,wherethecompanyisunabletoacquire additionalcapitalthroughdebt. Thecompanyundervaluationhasalargeprobabilityofdefault. TheAPVmodelcanbeusedinpracticallyeverysituation.Onlyinthecaseofacompanywith anonfinitelifewheretheamountofdebtoutstandingateachpointintimeisunknowncan theAPVmodelnotbeapplied. Inordertodecidewhichmodelcanbestbeusedtovalueacertaincompany,onecanfollow thedecisiontreeinAppendixI. InthesituationwhereboththeAPVmodelandtheenterpriseDCFmodelcanbeused (constantleverageratio,nonsignificantprobabilityofdefault),thechoicebetweenthetwo shouldbebasedontheprioritiesofthevaluer.TheenterpriseDCFmodelgivesavaluation basedontheWACC.ThisWACChasacommunicationalvalue,sinceit,asMiles&Ezzell (1980)state,facilitatesdecentralizedcapitalexpenditureanalysesandchoiceswherethe financingandinvestmentdecisionsareorganizationallyseparated.Thus,lowerlevel managersareprovidedwithasinglediscountratewhichisintendedtoreflectnotonlythe company’soperatingrisk,butalsothefirm’sfinancingpoliciesandwhichistobeusedto evaluate,atadecentralizedlevel,thecompany’sinvestmentopportunities.Theenterprise DCFmodelalsodoesnotneedtoestimatetheprobabilityofdefault,whichcanbedifficult andwhichcancontainerrors,thereforebeingthemoreefficientvaluationmodelofthetwo.If thevaluer,however,wantstoknowthedistincteffectsofthefinancingactivitiesandthe potentialfinancialdistresscostonthevalueofthecompany,thentheAPVmodelprovides thedesiredinformation.

3.5.5 Adjustment to the enterprise DCF to include distress ThisresearchprojectaimstoidentifythedifferencesbetweentheenterpriseDCFmodeland theAPVmodelforthevaluationofcompanies.Thetheoreticaldifferencesthatwere discussedabovearethedifferencesthatexistbetweenthegenerallyacceptedformsofthe enterpriseDCFmodelandtheAPVmodeltoday.Theimpactofthedifferencesonthe valuationoutcomewillbediscussedinthenextchapterbasedonthestateofthemodelsas discussedinthepreviouschapters.However,Damodaran(2006)discussespossible alterationstotheenterpriseDCFmodeltoincludethepotentialoffinancialdistress.Togivea completeoverviewofthedevelopmentsoftheenterpriseDCFmodel,thesealterationswill nowbediscussed. Damodaran(2006)introducesanumberofadjustmentsthatcanbemadetotheenterprise DCFmodelinordertoincludetheeffectsofpotentialfinancialdistress.Hestatesthat “distressedfirms,i.e.,firmswithnegativeearningsthatareexposedtosubstantiallikelihood offailure,presentachallengetoanalystsvaluingthembecausesomuchofconventional valuationisbuiltonthepresumptionthatfirmsaregoingconcerns.” Hesuggestsfourwaysinwhichonecanincorporatedistressintovalue–simulationsthat allowforthepossibilitythatacompanywillhavetobeliquidated,modifieddiscountedcash flowmodels,wheretheexpectedcashflowsanddiscountratesareadjustedtoreflectthe likelihoodofdefault,separatevaluationsofthecompanyasagoingconcernandindistress andadjustedpresentvaluemodels.” Damodaran(2006)furtherstatesthat:“Thefailuretoexplicitlyconsiderdistressindiscounted cashflowvaluationwillnothaveamaterialimpactinvalueifanyofthefollowingconditions hold: 1. Thereisnopossibilityofbankruptcy,eitherbecauseofthefirm’ssizeandstandingor becauseofagovernmentguarantee. 2. Easyaccesstocapitalmarketsallowfirmswithgoodinvestmentstoraisedebtor equitytosustainthemselvesthroughbadtimes,thusensuringthatthesefirmswill neverbeforcedintoadistresssale. 3. Weuseexpectedcashflowsthatincorporatethelikelihoodofdistressandadiscount ratethatisadjustedforthehigherriskassociatedwithdistress.Inaddition,wehave

MasterThesisSebastianOotjers 74 s0041823 IEMFEM ABCD toassumethatthefirmwillreceivesaleproceedsthatareequaltothepresentvalue ofexpectedfuturecashflowsasagoingconcernintheeventofadistresssale. Iftheseconditionsdonothold,anditiseasytomakeanargumentthattheywillnotforsome firmsatsomepointsintime,discountedcashflowvaluationwilloverstatefirmvalue.” Damodaran(2006)proposestoadoptaformofmodifieddiscountedcashflowvaluation .He statesthat“wecanadaptdiscountedcashflowvaluationtoreflectsomeormostoftheeffects ofdistressonvalue.Todothis,wewillhavetobringintheeffectsofdistressintoboth expectedcashflowsanddiscountrates. 1. Estimatingexpectedcashflows.Toconsidertheeffectsofdistressintoadiscounted cashflowvaluation,wehavetoincorporatetheprobabilitythatafirmwillnotsurvive intotheexpectedcashflows. j=n Expected _ cash _ flow = ∑π jt (Cashflow jt ) j=1 whereπ jt istheprobabilityofscenariojinperiodtandCashflow jt isthecashflow underthatscenarioandinthatperiod.Theseinputshavetobeestimatedeachyear, sincetheprobabilitiesandthecashflowsarelikelytochangefromyeartoyear. Ashortcut,albeitanapproximateone,wouldrequireestimatedforonlytwoscenarios –thegoingconcernandthedistressscenario.

Expecte _ cash _ flowt = (CashflowGoingconcern,t *) π Goingconcern,t (CashflowDistress,t 1(*) − π Goingconcern,t ) whereπ Goingconcern,t isthecumulativeprobabilitythatthefirmwillcontinueasagoing concernthroughperiodt.Theprobabilitiesofdistresswillhavetobeestimatedfor eachyearandthecumulativeprobabilityofsurvivingasagoingconcerncanthenbe writtenasfollows: n=t Cumulative _ probability _ of _ survival − period _ t = π t = ∏ 1( − π distress,n ) n=1 whereπ distress,t istheprobabilitythatthefirmwillbecomedistressedinperiodt. 2. Estimatingdiscountrates.Inconventionalvaluation,weoftenestimatethecostof equityusingaregressionbetaandthecostofdebtbylookingatthemarketinterest ratesonpubliclytradedbondissuedbythefirm.Forfirmswithsignificantprobability ofdistress,theseapproachescanleadtoinconsistentestimates.Considerfirstthe useofregressionbetas.Sinceregressionbetasarebaseduponpastpricesover longerperiods(twotofiveyears,forinstance),anddistressoccursovershorter periods,wewillfindthatthesebetaswillunderstatethetrueriskinthedistressed firm.Withtheinterestratesoncorporatebonds,werunintoadifferentproblem.The yieldstomaturityonthecorporatebondsoffirmsthatareviewedasdistressedreach extremelyhighlevels,largelybecausetheinterestratesarecomputedbasedupon promisedcashflows(couponsandfacevalue)ratherthanexpectedcashflows.The presumptioninagoingconcernvaluationisthatthepromisedcashflowshavetobe madeforthefirmtoremainagoingconcern,anditisthusappropriatetobasethe costofdebtonpromisedratherthanexpectedcashflows.Forafirmwithasignificant likelihoodofdistress,thispresumptionisclearlyunfounded. Toestimatethecostofequity,wehavetwooptionsthatprovidemorereasonable estimatedthanregressionbetas: a. CAPMbetaadjustedfordistress:Insteadofusingregressionbetas,wecould usethebottomupunleveredbeta(theweightedaverageofunleveredbetas ofthebusinessesthatthefirmoperatesin)andthecurrentmarketdebtto equityratioofthefirm. b. Distressfactormodels:Inadditiontothestandardfactorformarketrisk,we couldaddaseparatedistressfactorforthecostofequity.”

MasterThesisSebastianOotjers 75 s0041823 IEMFEM ABCD Damodaran(2006)recommendsusingtheinterestratebaseduponthecompany’sbond ratingtoestimatethecostofdebtforadistressedcompany.Tocomputethecostofcapital, anestimateoftheweightsondebtandonequityisneeded.Intheinitialyear,thecurrent marketdebttocapitalratio(whichmaybeveryhighforadistressedcompany)shouldbe used.Astheforecastsforfutureyearsaremadeandbuildintheexpectationsof improvementsinprofitability,thedebtratioshouldbeadjustedtowardsmorereasonable levels.Theconventionalpracticeofusingtargetdebtratiosfortheentirevaluationperiod (whichreflecttheindustryaveragesortheoptimalmix)canleadtomisleadingestimatesof valueforcompaniesthataresignificantlyoverlevered. AnotheralternativethatDamodaran(2006)proposesisdealingwithdistressseparately .He statesthat“analternativetothemodifieddiscountedcashflowmodelistoseparatethegoing concernassumptionsandthevaluethatemergesfromitfromtheeffectsofdistress.The valueofthefirmcanthenbewrittenas: Firmvalue=goingconcernvalue*(1–π distress )+distresssalevalue*π distress whereπ distress isthecumulativeprobabilityofdistressoverthevaluationperiod.” Tovalueacompanyasagoingconcern,onlythosescenariosareconsideredwherethe companysurvives.Whenestimatingdiscountrates,theassumptionismadethatdebtratios will,infact,decreaseovertime,ifthecompanyisoverlevered,andthatthecompanywill derivetaxbenefitsfromdebtasitturnsthecornertoprofitability. Damodaran(2006)considers,threewaysinwhichtheprobabilityofdistresscanbe estimated.Thefirstisastatisticalapproach,wheretheprobabilityofdistressisrelatedtoa company’sobservablecharacteristics–companysize,leverageandprofitability,forinstance –bycontrastingcompaniesthathavegonebankruptinprioryearswithcompaniesthatdid not.Thesecondisalessdataintensiveapproach,wherethebondratingforacompanyis used,andtheempiricaldefaultratesofcompaniesinthatratingclasstoestimatethe probabilityofdistress.Thethirdistousethepricesofcorporatebondsissuedbythe companiestobackouttheprobabilityofdistress,whichisbasedonthefollowingformula: t=n Coupon 1( − π )t Face _Value _ of _ Bond 1( − π ) n BondP _ rice = distress + Distress ∑ t n t=1 1( + Riskfree _ Rate) 1( + Riskfree _ Rate) Thisequationcannowbeused,inconjunctionwiththepriceonatradedcorporatebondto backouttheprobabilityofdefault. Consequently,akeyinputthatneedstobeestimatedaretheexpectedproceedsintheevent ofadistresssale.Therearethreechoices: 1. Estimatingthepresentvalueoftheexpectedcashflowsinadiscountedcashflow model,andassumethatthedistresssalewillgenerateonlyapercentage(lessthan 100%)ofthisvalue. 2. Estimatingthepresentvalueofexpectedcashflowsonlyfromexistinginvestmentas thedistresssalevalue. 3. Themostpracticalwayofestimatingdistresssaleproceedsistoconsiderthe distresssaleproceedsasapercentofbookvalueofassets,baseduponthe experienceofotherdistressedcompanies. ByincorporatingthechangesdescribedbyDamodaran(2006),onecouldadjustthe enterpriseDCFmodelforthepotentialfinancialdistress.But,asdiscussedbefore,these adjustmentsarenotpartofthisresearchproject.Thisresearchproject’sobjectiveisto determinethedifferencesbetweentheenterpriseDCFmodelandtheAPVmodelascurrently acceptedinliterature. 3.5.6 Conclusion TheenterpriseDCFmodelandtheAPVmodelusethesamecashflowsandthesamecostof debt.Thedifferencesbetweenthetwomodelsarecreatedbythefactthattheyuseadifferent discountrateandadifferentcostofequity.TheenterpriseDCFmodelhasonlyoneversion whereaconstantleverageratioisassumed.TheAPVmodelhastwoversions,onewitha

MasterThesisSebastianOotjers 76 s0041823 IEMFEM ABCD constantleverageratioassumptionandonewithafixedamountofdebtassumption.A generalformoftheAPVmodelcanalsobeusedinspecialsituations. Thechoiceforoneofthetwomodelsindifferentsituationsismainlybasedonthecapital structureandtheprobabilityofdefault. ThereareanumberofadjustmentsthatcouldbemadetotheenterpriseDCFmodelto incorporatethecostsoffinancialdistressmoreaccurately.Theseadjustmentslieoutsidethe scopeofthisresearchprojectandwillnotbediscussedanyfurther. 3.6 Impact of the differences on the valuation outcome ThedifferencesinassumptionsbetweentheenterpriseDCFmodelandtheAPVmodelwere discussedinthepreviousparagraph.Inthisparagraphtheimpactofthesedifferencesonthe valuationoutcomewillbeanalyzed. ThedecisiontreeinAppendixIshowsthedifferentcriteriabasedonwhichonecanchooseto useaversionoftheAPVmodelortheenterpriseDCFmodeltovalueacompany.The decisiontreelinkseitheranAPVmodelortheenterpriseDCFmodeltoaparticularcondition becausetheassumptionsunderlyingthechosenmodelcorrespondtothiscondition.The chosenmodelshouldgivethemostaccuratevaluationofthecompany. TodeterminetheeffectsofthedifferencesbetweentheenterpriseDCFmodelandtheAPV modelonthevaluationoutcome,each‘bestchosen’modeliscomparedwithitsalternative. Sinceeach‘bestchosen’modelisanAPVmodel,the‘bestchosen’modelwillbecompared tothevaluationoutcomeundertheenterpriseDCFmodel.Thespecialcaseinwhichboththe enterpriseDCFmodelandtheAPVmodelcanbeusedwillalsobeaddressed. Thefollowingtablegivesanoverviewofthedifferentscenariosandthe‘bestchosen’model. Theremainderofthischapterisusedtoaddresseachscenario. Scenario Model Compare to Constantleverageratio& 1 DCForAPV(ME) n.a. no significantPoD

Constantleverageratio& 2 APV(ME) DCF significantPoD

3 Fixedamountofdebt APV(MM) DCF

4 Finitelife&debtknown APV(general) DCF

Debtknownuptot,then APV(general)+ 5 DCF constantleverageratio APV(ME)

3.6.1 Scenario 1: Constant leverage ratio & no significant probability of default Differencesbetweenvaluationoutcomesarisebecauseofthefactthatoneofthetwomodels isbasedonassumptionsofcapitalstructureand/ortheprobabilityofdefaultthatdifferfrom thestateoftheseelementsinthescenario. Sincethisfirstscenariocomprisesnosuchdifferences,thevaluationoutcomesofboth modelsshouldbethesame.TheMEAPVmodelandtheenterpriseDCFmodelbothassume aconstantleverageratioandsincethereisnosignificantprobabilityofdefaultthetermofthe costsoffinancialdistressintheMEAPVmodelhasnosignificanteffect. 3.6.2 Scenario 2: Constant leverage ratio & significant probability of default Thisscenarioisthesameasthepreviousexceptforthefactthattheprobabilityofdefaultis significant.Thismeansthatthedifferencebetweenthetwovaluationoutcomesisbasedon thethirdtermoftheMEAPVmodel.TheMEAPVmodelisstatedas:

MasterThesisSebastianOotjers 77 s0041823 IEMFEM ABCD t= n   FCFFt Tm Dkd 1+ ku ∑ t + * − πDC t=1 (1+ ku ) (ku − gn ) 1+ kd  Thethirdterm,πDC,representsthecostsoffinancialdistress. Sincethepresentvalueofthecostsoffinancialdistressareestimatedat15%ofthevalueof theunleveredfirm,thedifferencebetweentheenterpriseDCFmodelvaluationoutcomeand theMEAPVmodelvaluationoutcomewillbe:

= 0.15*Vu *π where Vu =thevalueoftheunleveredcompany π =probabilityofdefault Thevalueofthedifference()willdependonthevalueoftheunleveredcompany:

Since 0 ≤ π ≤1and Vu ≥ 0 , < 0 .Thismeansthatinthisscenario,thevaluationoutcome oftheMEAPVmodelwillbelowerthanthevaluationoutcomeoftheenterpriseDCFmodel.

So VenterpriseDCF > VAPV / acutal underthisscenario. 3.6.3 Scenario 3: Fixed amount of debt ThedifferenceinvaluationoutcomebetweentheMMAPVmodelandtheenterpriseDCF modelinthescenarioofafixedamountofdebtconsistsoftwoparts.Thedifferencein valuationoutcomebasedonthedifferenceinthecapitalstructureassumptiondependsonthe developmentofthecapitalstructure.TheMMAPVmodelisformulatedas: t= n FCFFt ∑ t + DTm − πDC t=1 (1+ ku ) Thecapitalstructurehasanimpactonthevaluethroughthesecondterm,DT m,whereDis theamountofdebtandT m isthemarginaltaxrate.Ifthecompanyisexpectedtoincreaseits totalamountofcapitalundertheconditionofafixedamountofdebt,thenthismeansthatthe company’sleverageratiowilldecrease.TheenterpriseDCFmodel,however,assumesa constantleverageratio.ThismeansthattheenterpriseDCFmodeloverestimatestheamount ofdebtandthusoverestimatesthebenefitsofdebt.Thisresultsinahighervalueunderthe enterpriseDCFmodelthanundertheMMAPVmodel.Ifthecompanyisexpectedto decreaseitstotalamountofcapitalwhilekeepingitsamountofdebtfixed,thentheopposite occurs:theenterpriseDCFmodelassumeslessdebtthanisactuallypresentthereby underestimatingthebenefitsofdebtandthusunderestimatingthevalueofthecompany.This canbesummarizedinthefollowingway. d(D + E) For > 0 , D > D ,whichleadsto V > V . dt enterpriseDCF APV / actual enterpriseDCF APV / acutal Andintheoppositedevelopmentofthecapitalstructureofthecompany: d(D + E) for < 0 , D < D ,whichleadsto V < V . dt enterpriseDCF APV / actual enterpriseDCF APV / acutal Theseconclusionsontherelationofthecompanyvalueunderthetwovaluationmodelsare onlycorrectiftheprobabilityofdefaultisnotsignificant. IncaseofasignificantprobabilityofdefaultthethirdtermoftheMMAPVmodel,thecostsof financialdistress,alsoaffectsthevaluationoutcome.Inthecaseofanincreasingamountof capitalthe VenterpriseDCF > VAPV / acutal relationremainsthesame,onlythedifferencewillbe largersincethecostsoffinancialdistressalwayslowerthevalueofthecompany(aswas showninscenario2). Inthesituationwheretheamountofcapitaldecreasesandtherelationbetweenthecompany valuesunderthetwomethodsbasedonthedifferenceonthecapitalstructureassumptionis

MasterThesisSebastianOotjers 78 s0041823 IEMFEM ABCD givenby VenterpriseDCF < VAPV / acutal ,theeffectofthecostsoffinancialdistressreducesthe companyvalueundertheMMAPVmodelandthusreducesthedifferencebetweenthe valuationoutcomeundertheenterpriseDCFmodelandtheMMAPVmodel.Whether

VenterpriseDCF < VAPV / acutal or VenterpriseDCF > VAPV / acutal dependsonthechangeintheamount ofcapitalinrelationtotheprobabilityofdefault.Itmightevenbethecasethat

VenterpriseDCF = VAPV / acutal ,becauseofthefactthatthetwoerrorsintheenterpriseDCFmodel canceleachotherout. 3.6.4 Scenario 4: Finite life and a known amount of debt at each point in time Inthisscenario,thereisneitherafixedamountofdebtnoraconstantleverageratio.This resultsinthefactthatthevalueoftheinteresttaxshieldscannotbecalculatedbymeansofa perpetuityformula.Instead,eachinteresttaxshieldhastobevaluedseparately.Thevalueof thecompanycanbedeterminedbytheuseofthegeneralAPVmodel: t= n FCFF t= n ITS t t ∑ t + ∑ t − πDC t=1 (1+ ku ) t=1 (1+ kts) where kts =thediscountrateoftheinteresttaxshields ITS t =theinteresttaxshieldattimet Sincetheamountofdebtisknownateachpointintime,theappropriatediscountrateforthe taxshieldsisthecostofdebt:k ts =k d. ThedifferenceinthevaluationoutcomebetweenthegeneralAPVmodelandtheenterprise DCFmodeldependsonthedifferenceintheamountofdebtassumedateachpointintime. Forinstance,iftheamountofcapitalincreasesbytheamountofXthentheamountofdebt assumedbytheenterpriseDCFmodelisX*leverageratio+previousdebt.Thebenefitsof debtarerelatedtothisamountofdebt.Iftheactualamountofdebtinaperiodishigherthan thedebtassumedbytheenterpriseDCFmodelthenthevalueofthebenefitsofdebtatthat pointintimeareunderestimatedbytheenterpriseDCFmodel.Theoppositeistrueisthe actualamountofdebtisbelowtheassumedamountofdebtoftheenterpriseDCFmodel. ThefinaldifferencebetweenthevaluationoutcomesoftheenterpriseDCFmodelandthe generalAPVmodelwilldependonthepresentvalueofthedifferencesbetweentheassumed interesttaxshields.Thisfinaldifferencealsohastobecorrectedforthecostsoffinancial distressiftheprobabilityofdefaultissignificant.Theeffectofthiscorrectionisthesameas discussedunderscenario3. ThedifferencebetweenthevaluationoutcomesoftheenterpriseDCFmodelandthegeneral APVmodelunderthisscenariothusdependsonthesituation. 3.6.5 Scenario 5: Debt known up to time t, followed by a constant leverage ratio Thisscenarioisacombinationofscenario4andscenario1(iftheprobabilityofdefaultisnot significant)oracombinationofscenario4andscenario2(iftheprobabilityofdefaultis significant). Forthefirstpartofthevaluation,uptopointtwheretheamountofdebtisknown,scenario4 applies.Thismeansthatitdependsonthesituationwhetherthevaluationoutcomeofthe APV(general)modelishigherorlowerthanthevaluationoutcomeoftheenterpriseDCF model. Forthesecondpart,afterpointt,thecompanyisassumedtohaveaconstantleverageratio. Inthecaseofaprobabilityofdefaultthatisnotsignificant,boththeMEAPVmodelandthe enterpriseDCFmodelgivethesamevaluationoutcomeasdiscussedinscenario1.Incase ofasignificantprobabilityofdefault,thevaluationoutcomeoftheMEAPVmodelwillgivea lowervaluethantheenterpriseDCFmodelasdiscussedinscenario2. ThetotaldifferencebetweenthegeneralAPVmodel/MEAPVmodelcombinationandthe enterpriseDCFmodelisthesumofthedifferencesofthetwoparts. Thisscenarioisnotanindependentscenariosinceitisacombinationofanumberofthe previousscenarios.Thereasonfordiscussingitbrieflyistoindicatethatthemethodscanbe combined.Thisparticularscenarioisalsothemodelofthesituationthatiscreatedbya

MasterThesisSebastianOotjers 79 s0041823 IEMFEM ABCD managementorleveragedbuyout.Inabuyoutsituationacompanystartswithahighleverage ratioasaresultofthebuyoutand,afterreachingthedesiredleverageratiothroughdebt repayments,thecompanyisassumedtotakeonaconstantleverageratio. 3.6.6 Conclusion Foreachscenariodescribed,anAPVmodelcanbeusedtodeterminethevalueofthe company.UsinganenterpriseDCFmodelinthesesituationsgivesanincorrectvaluation, exceptforscenario1.ThedifferencebetweentheenterpriseDCFmodelvaluationoutcome andtheAPVmodelvaluationoutcomearegiveninthetablebelow.Inthecaseofaconstant leverageratioandaninsignificantprobabilityofdefaultonecanuseboththeenterpriseDCF modelandtheMEAPVmodeltodeterminethecorrectcompanyvalue. Scenario Model Compare to Effect on valuation outcome Constantleverageratio& DCForAPV(ME) n.a. V(APV)=V(DCF) no significantPoD

Constantleverageratio& APV(ME) DCF V(APV)<V(DCF) significantPoD V(APV)>V(DCF)or Fixedamountofdebt APV(MM) DCF V(APV)=V(DCF)or V(APV)<V(DCF) V(APV)>V(DCF)or Finitelife&debtknown APV(general) DCF V(APV)=V(DCF)or V(APV)<V(DCF) Combinationofscenario4and Debtknownuptot,then APV(general)+ DCF 1oracombinationofscenario4 constantleverageratio APV(ME) and2 Conclusion Inthischaptereachofthetwovaluationmodelsisanalyzed.Thevaluationmodelsare assessedatthesubjectsofanalysis.Thisprovidesanoverviewontheassumptionsandthe functioningofeachmodel.Thetwovaluationmodelsarecomparedwithregardtotheir theoreticaldifferencesandthesedifferencesaretranslatedto(expected)differencesinthe valuationoutcome. Basic assumptions of the enterprise DCF model AfteranalyzingtheenterpriseDCFmodelonthegeneralsubjectsofanalysis,itcanbe concludedthattheenterprisevalueequalsthesumofthevalueoftheoperationaland nonoperationalassetsofthecompany.Theoperationalassetsarevaluedbydiscountingthe freecashflowsattheweightedaveragecostofcapital.Theeffectofthetaxdeductibilityof interestisintegratedintheweightedaveragecostofcapital.Thenonoperationalassetsare valuedinadifferentwaydependingonthetypeofasset.Toarriveatthevalueofequity,the nonequityclaimshavetobesubtractedfromtheenterprisevalue. Basic assumptions of the APV model BasedontheworksofKoller et al. (2005),Brealey&Myers(2003)andDamodaran(2002)it canbeconcludedthattheadjustedpresentvaluemodelisbasedonthreesteps: 1. Determiningthevalueoftheunleveredcompany 2. Valuingthetaxshields 3. Determiningthecostofpotentialdistress ThiscanberepresentedbythefollowinggeneralAPVmodelformula: t=n FCFF t=n ITS EV = t + t + πDC ∑ t ∑ t t=1 1( + ku ) t=1 1( + kts ) where FCFF t =Freecashflowtothefirmattimet ku =Unleveredcostofequity

MasterThesisSebastianOotjers 80 s0041823 IEMFEM ABCD

ITS t =Interesttaxshieldattimet kts =Appropriatetaxshielddiscountrate π =Probabilityofdefault DC =Distresscosts Therearetwoframeworksforthevaluingofthetaxshields.Thefirstisbasedonthe assumptionofMiller&Modigliani(1963)thatacompanymaintainsafixedamountofdebt. ThisleadstoataxshieldvalueinperpetuityofD*T m(debt*tax). ThesecondisbasedontheassumptionofMiles&Ezzell(1985)thatacompanymaintainsa Dk T constantleverageratio.Thisleadstoataxshieldvalueinperpetuityof d m . (ku − g) Thereisnoclearconsensusintheliteratureonwhichassumption(andapproach)isthe correctone. Althoughdifferentauthors(Cooper&Nyborg(2006,2007);Ehrhardt&Daves(1999))have pointedoutthattheMiller&Modiglianiassumptionisunrealisticorevenincorrect,theworks allofthethreeauthorsthatwerediscussedinthisparagraphstillholdontoMiller& Modigliani’sassumption,withDamodaran(2002)discussingonlytheMillerModigliani framework. Thevalueoftheunleveredfirmisdeterminedbydiscountedfreecashflowtothefirm (FCFFs)attheunleveredcostofequity.Thisunleveredcostofequityisderivedbyusingthe CAPMframeworkandtheunleveredequitybetaasaninput.Thisunleveredequitybetahas tobederivedfromtheleveredequitybeta,sincethelattercanbeobservedinthemarketin contrasttotheformerwhichisunobservable. Dependingontheassumptiontaken(fixeddebtamountoraconstantratio),theequationfor determiningtheunleveredequitybetachanges.Assumingaconstantratioresultsinthe formulafoundbyMiles&Ezzell(1985)whichcanbeapproximatedbytheunleveringformula givenbyCooper&Nyborg(2006): ME βu = β e (E /(D / E)) AssumingafixeddebtamountgivestheformulastatedbyDamodaran(2002):

βu = β e /(1+ 1( − T )(D / E)) Thevalueofthepotentialcostoffinancialdistressdependsonthecostoffinancialdistress andtheprobabilityoftheoccurrenceofthesecosts. The enterprise DCF model assessed at the nongeneral subjects of analysis Thetradeofftheoryofcapitalstructureisassumedtobethecorrecttheoryfortheprediction ofcapitalstructuredecisionswithincompanies.TheenterpriseDCFmodelassumesa constantleverageratio.Insituationswherethisassumptionisviolated,themodelwillgivean incorrectvalueofthecompany.TheenterpriseDCFmodelalsodoesnotincorporatea measurefortheprobabilityofdefaultandthecostsoffinancialdistress.Thevaluationofa companywithasignificantprobabilityoffinancialdistressthroughtheenterpriseDCFmodel willthereforealsoresultinanincorrectvaluation. The APV model assessed at the nongeneral subjects of analysis TherearetwoversionoftheAPVmodel:onethatassumesaconstantleverageratioanother thatassumesafixedamountofdebt.ThegeneralAPVmodel,whichmakesnoassumption onthedevelopmentofthecapitalstructure,canbeusedincaseofafinitelifeofthe company.TheAPVmodelalsocontainsaseparatetermtoincorporatethepotentialcostsof financialdistress.Thesepotentialcostsarebasedonthedistresscostsandtheprobabilityof default.Theprobabilityofdefaultcanbeestimatedbasedonamethodthatcombinesthe creditratingofacompanyanditsZscore.

MasterThesisSebastianOotjers 81 s0041823 IEMFEM ABCD Differences between the enterprise DCF model and the APV model TheenterpriseDCFmodelandtheAPVmodelusethesamecashflowsandthesamecostof debt.Thedifferencesbetweenthetwomodelsarecreatedbythefactthattheyuseadifferent discountrateandadifferentcostofequity.TheenterpriseDCFmodelhasonlyoneversion whereaconstantleverageratioisassumed.TheAPVmodelhastwoversions,onewitha constantleverageratioassumptionandonewithafixedamountofdebtassumption.A generalformoftheAPVmodelcanalsobeusedinspecialsituations. Thechoiceforoneofthetwomodelsindifferentsituationsismainlybasedonthecapital structureandtheprobabilityofdefault. ThereareanumberofadjustmentsthatcouldbemadetotheenterpriseDCFmodelto incorporatethecostsoffinancialdistressmoreaccurately.Theseadjustmentslieoutsidethe scopeofthisresearchprojectandarenotdiscussedanyfurther. Impact of the differences on the valuation outcome Foreachscenariodescribed,anAPVmodelcanbeusedtodeterminethevalueofthe company.UsinganenterpriseDCFmodelinthesesituationsgivesanincorrectvaluation, exceptforscenario1.ThedifferencebetweentheenterpriseDCFmodelvaluationoutcome andtheAPVmodelvaluationoutcomearegiveninthetablebelow.Inthecaseofaconstant leverageratioandaninsignificantprobabilityofdefaultonecanuseboththeenterpriseDCF modelandtheMEAPVmodeltodeterminethecorrectcompanyvalue. Scenario Model Compare to Effect on valuation outcome Constantleverageratio& DCForAPV(ME) n.a. V(APV)=V(DCF) no significantPoD

Constantleverageratio& APV(ME) DCF V(APV)<V(DCF) significantPoD V(APV)>V(DCF)or Fixedamountofdebt APV(MM) DCF V(APV)=V(DCF)or V(APV)<V(DCF) V(APV)>V(DCF)or Finitelife&debtknown APV(general) DCF V(APV)=V(DCF)or V(APV)<V(DCF) Combinationofscenario4and Debtknownuptot,then APV(general)+ DCF 1oracombinationofscenario4 constantleverageratio APV(ME) and2 Practice Thesecond,thirdandfourthpartoftheresearchframeworkdiscussedinchapter1have beenimplementedinthischapter.Theresultofthesethreestepsisanoverviewofthe differencesbetweentheenterpriseDCFmodelandtheAPVmodelandtheeffectsofthese differencesonthevaluationoutcome. ThefounddifferencesarepurelybasedonthetheoriesunderlyingtheenterpriseDCFmodel andtheAPVmodel.Inordertodeterminethesignificanceofthedifferences,thesetheories havetobetranslatedtoapracticaltoolforthevaluationofcompanies.AppendixIIfocuseson theformulationanddemonstrationofapracticalAPVmodel. Chapter4servesasatestingchapter.Thepurposeofthischapteristotestthetheories statedinthischapterondifferentscenarios.Theresultofchapter4isatestedsetoftheories onthedifferencesbetweentheenterpriseDCFmodelandtheAPVmodel.

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Chapter 4: Validation

Introduction Thepurposeofthischapteristotestthetheoriesstatedinchapter3throughofthevaluation tooldevelopedanddiscussedinappendixII.Thetheoriesaretestedthroughthevaluationof afictitiouscompany.Thefirstparagraphofthischapterdiscussesthekeyfinancialsofthe fictitiouscompany(CompanyX).Thesecondparagraphfocusesonthevalidationofthefive scenariosdiscussedinchapter3.Thethirdparagraphisdedicatedtotheidentificationofthe factorsthatcausethevaluationoutcomestodeviatefromthevaluespredictedbythechapter 3theories.Thesefactorsformtheconditionalframeworkunderwhichthetheorieshold.The lastparagraphconcludesontheretrievedvalidationresultsandlinkstothefinalchapterof theresearchreport:theconclusions. AlltheEuroamountsmentionedinthischapterareinthousandsofEuros. 4.1 Validation approach CompanyX,thecompanythatservesasthemeanstotestthetheoriesfromchapter3,isa stablegrowthcompany.Thecompanyisassumedtohave15.000EURofsalesin2003and theexpectedannualsalesgrowthis2,0%.Thedirectcostscomprise50%ofsales;the operatingcostsarefixedat4.000EURperyear.Thecorporatetaxrateisbasedontheactual rateintheNetherlandsandthelongtermcorporatetaxrateisassumedtobe25,5%. CompanyXisassumedtoowntangiblefixedassetswithavalueof9.000EURin2003,60% ofsales,andisassumedtohavedepreciationcostsof1.000EURperyear.Theinvestments inthetangiblefixedassetsaresuchthatthevalueofthefixedassetsremainsat60%ofsales inthecorrespondingyear.Theintangiblefixedassetsareassumedtohaveavalueof3.000 EURin2003,20%ofsalesinthecorrespondingyear.Theyearlytaxdeductibleamortization isassumedtobe250EUR,thenontaxdeductibleamortizationisassumedtobe200EUR. Theyearlyinvestmentsintheintangiblefixedassetsaresuchthatthevalueoftheintangible fixedassetsremainsat20%ofsalesinthecorrespondingyear. Theinventory(stock)isassumedtobe2,5%ofsalesandthedebtoutstandingwithcreditors isassumedtobe1,5%ofdirectcosts.CompanyXisassumedtopayouttwothirdsofitsnet profittoitsshareholdersintheformofdividends. Theassumedriskfreerateis4,0%,themarketriskpremium5,0%,theadditionalrisk premium3,0%andtheassumedspreadisalso3,0%.Thecompanyisassumedtohavea leveredbetaof1,0andtheD/Eratiousedforthecalculationofthecostofcapitalissetat 20,4%(whichtranslatestoadebttovalueratioof17,0%).Thedevelopmentofthecapital structuredependsonthescenariothatisstudied. Thevalidationoutcomesresultingfromthisvalidationapproachwillbediscussedforeach basicscenariointhenextparagraph. 4.2 Basic scenarios Thisparagraphdiscussesthefive(basic)scenariosdiscussedinchapter3.Thefive scenariosandtheirresults,aspredictedinchapter3,areshowninthetablebelow.

MasterThesisSebastianOotjers 83 s0041823 IEMFEM ABCD

Scenario Model Compare to Effect on valuation outcome Constantleverageratio& DCForAPV(ME) n.a. V(APV)=V(DCF) no significantPoD

Constantleverageratio& APV(ME) DCF V(APV)<V(DCF) significantPoD V(APV)>V(DCF)or Fixedamountofdebt APV(MM) DCF V(APV)=V(DCF)or V(APV)<V(DCF) V(APV)>V(DCF)or Finitelife&debtknown APV(general) DCF V(APV)=V(DCF)or V(APV)<V(DCF) Combinationofscenario4and Debtknownuptot,then APV(general)+ DCF 1oracombinationofscenario4 constantleverageratio APV(ME) and2 4.2.1 Scenario 1: Constant leverage ratio & no significant probability of default Thefirstscenario,whichisbasedonaconstantleverageratioandnosignificantprobabilityof defaultassumption,shouldresultinavaluationoutcomefromtheenterpriseDCFmodelthat isequaltothevaluationoutcomeoftheAPVmodel. Theinputsforthisscenarioarebaseduponthevaluationapproachdescribedinthefirst paragraphofthischapter.Thefollowingtablesshowtheinputsinthedifferentsectionsofthe valuationtool. Thefirstinputs(shownintable4.1)arethesalesand(directandoperational)costs.These adduptotheEBITDA,which,afterdeductionofthedepreciationcosts,resultsintheEBITA. Theotherbluecoloredcellsarealsoinputcellsforrespectivelytheamortizationcostsandthe dividendspaidout. Theassetsaremodeledasshownintable4.2,4.3and4.4.Theamountofexcesscashfor eachyearisdeterminedthroughthecalculationofthecashflows.Thiscashflowcalculation isshownintable4.5. Thedebtequitydistributionthatresultsfrommaintainingafixedmarketleverageratioof17% isshownintable4.6.Thevalueoftheassetsin2003is12.375EUR.Forthefirstfouryears, a30%bookleverageratioisused.Thisinputischosenarbitrarily,andisirrelevantforthe valuationoutcomesincethevaluationisbasedontheyears2007andonward. ThemarketleverageratioisdeterminedthroughaniterationoftheDCFanalysis.Astarting debttovalueratioisinsertedintheWACCcalculationleadingtoacompanyvalue.Thisvalue isrealizedwithacertainamountofdebtattimetiszero.Theamountofdebtoutstanding dividedbytheenterprisevalue(fromtheDCFanalysis)givestheimpliedleverageratio.This impliedleverageratioisinsertedintotheWACCcalculationtoarriveatanewcompanyvalue andanewimpliedleverageratio.Thisprocedureisrepeateduntiltheimplieddebttovalue ratioisequaltotheleverageratioinsertedintheWACCcalculation.Thisisthefinalimplied marketleverageratio,whichisusedasaninputfortheunleveredcostofequitycalculation. Thenextstepistodeterminetheamountofdebtateachpointintime.Theseamountsare determinedbycalculatingthevalueofthecompanyateachpointintimeandmultiplyingthis valuewiththemarketleverageratio.Sincethevalueofthecompanydependsontheamount ofexcesscash,theamountofexcesscashontheamountofdebt,andtheamountofdebton thevalueofthecompany,iterationhastotakeplacetofindtherightvalues. TheprobabilityofdefaultforCompanyXis(automatically)determinedthroughtheAltmanZ scoreformulaandisestimatedat0.06%(equaltoaAArating). Thelast(relevant)inputsareinsertedinthecostofcapitalcalculation.Theseinputsare shownintable4.7and4.8.TherelevantunleveredcostofequityistheMEunleveredcostof equity,sincethemainassumptioninthisscenarioisthatofaconstantleverageratio.

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Company X - profit and loss statement EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Net sales 15.000 15.300 15.606 15.918 16.236 16.561 16.892 17.230 17.575 17.926 18.285 18.650 % growth 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0%

Directcost1 (7.500) (7.650) (7.803) (7.959) (8.118) (8.281) (8.446) (8.615) (8.787) (8.963) (9.142) (9.325) Totaldirectcosts (7.500) (7.650) (7.803) (7.959) (8.118) (8.281) (8.446) (8.615) (8.787) (8.963) (9.142) (9.325)

Gross profit 7.500 7.650 7.803 7.959 8.118 8.281 8.446 8.615 8.787 8.963 9.142 9.325 % of sales 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0%

Operatingcost1 (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.080) Otheroperatingcosts Totaloperationalcosts (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.080) % of sales -26,7% -26,1% -25,6% -25,1% -24,6% -24,2% -23,7% -23,2% -22,8% -22,3% -21,9% -21,9%

EBITDA 3.500 3.650 3.803 3.959 4.118 4.281 4.446 4.615 4.787 4.963 5.142 5.245 % of sales 23,3% 23,9% 24,4% 24,9% 25,4% 25,8% 26,3% 26,8% 27,2% 27,7% 28,1% 28,1%

Depreciation (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.020) EBITA 2.500 2.650 2.803 2.959 3.118 3.281 3.446 3.615 3.787 3.963 4.142 4.225 % of sales 16,7% 17,3% 18,0% 18,6% 19,2% 19,8% 20,4% 21,0% 21,6% 22,1% 22,7% 22,7%

Nontaxdeductibleamortisation (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (204) Taxdeductibleamortisation (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (255) EBIT 2.050 2.200 2.353 2.509 2.668 2.831 2.996 3.165 3.337 3.513 3.692 3.766 % of sales 13,7% 14,4% 15,1% 15,8% 16,4% 17,1% 17,7% 18,4% 19,0% 19,6% 20,2% 20,2%

Interestondebt (245) (264) (275) (286) (325) (367) (411) (457) (504) (554) (605) (631) Interestoncash Profit before tax 1.805 1.936 2.078 2.223 2.343 2.463 2.585 2.708 2.833 2.959 3.088 3.136

Incometax (692) (737) (718) (717) (648) (679) (710) (742) (773) (806) (838) (852) Net profit 1.113 1.199 1.360 1.506 1.695 1.784 1.875 1.967 2.060 2.154 2.249 2.284 % of sales 7,4% 7,8% 8,7% 9,5% 10,4% 10,8% 11,1% 11,4% 11,7% 12,0% 12,3% 12,2%

Dividendpayments (742) (799) (907) (1.004) (1.130) (1.189) (1.250) (1.311) (1.373) (1.436) (1.500) (1.523) Retained earnings 371 400 453 502 565 595 625 656 687 718 750 761 Table 4.1: Profit & loss statement of Company X

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Company X - tangible fixed assets EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Tangiblefixedassetsbeginofperiod 9.000 9.180 9.364 9.551 9.738 9.938 10.138 10.338 10.548 10.758 10.968 Grossinvestmentstangiblefixedassets 1.180 1.184 1.187 1.187 1.200 1.200 1.200 1.210 1.210 1.210 1.020 Bookvalueofdisposaloffixedassets Depreciation (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.020) Tangible fixed assets end of period 9.000 9.180 9.364 9.551 9.738 9.938 10.138 10.338 10.548 10.758 10.968 10.968 % of sales 60,0% 60,0% 60,0% 60,0% 60,0% 60,0% 60,0% 60,0% 60,0% 60,0% 60,0% 58,8%

Company X -intangible fixed assets EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Intangiblefixedassetsbeginofperiod 3.000 3.060 3.121 3.184 3.247 3.310 3.373 3.438 3.507 3.577 3.648 Grossinvestmentsintangiblefixedassets 510 511 513 513 513 513 515 519 520 521 523 Nontaxdeductibleamortisation (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (204) Taxdeductibleamortisation (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (255) Intangible fixed assets end of period 3.000 3.060 3.121 3.184 3.247 3.310 3.373 3.438 3.507 3.577 3.648 3.712 % of sales 20,0% 20,0% 20,0% 20,0% 20,0% 20,0% 20,0% 20,0% 20,0% 20,0% 20,0% 19,9% Table 4.2 & 4.3: Tangible fixed assets and intangible fixed assets of Company X

MasterThesisSebastianOotjers 86 s0041823 IEMFEM ABCD

Company X - Balance sheet - Assets EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Tangible fixed assets 9.000 9.180 9.364 9.551 9.738 9.938 10.138 10.338 10.548 10.758 10.968 10.968

Intangible fixed assets 3.000 3.060 3.121 3.184 3.247 3.310 3.373 3.438 3.507 3.577 3.648 3.712

Nonconsolidatedsubsidiaries Deferredtaxassets Otherfinancialfixedassets1 Otherfinancialfixedassets2 Financial fixed assets ------

Stock(Inventory) 375 383 390 398 406 414 422 431 439 448 457 466 Debtors Otherreceivables Prepaymentsandaccruedincome Operationalcash Current assets 375 383 390 398 406 414 422 431 439 448 457 466

Excess cash - 707 679 1.466 2.036 2.633 3.270 3.951 4.643 5.380 6.155 6.895

ASSETS 12.375 13.329 13.554 14.599 15.427 16.295 17.203 18.158 19.137 20.163 21.229 22.042 Table 4.4: Assets overview of Company X

MasterThesisSebastianOotjers 87 s0041823 IEMFEM ABCD

Company X - Cash flow statement EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

EBITA 2.500 2.650 2.803 2.959 3.118 3.281 3.446 3.615 3.787 3.963 4.142 4.225 Nontaxdeductibleamortisation (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (204) Taxdeductibleamortisation (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (255) EBIT 2.050 2.200 2.353 2.509 2.668 2.831 2.996 3.165 3.337 3.513 3.692 3.766

Operationaltaxes (776) (828) (804) (802) (731) (773) (815) (858) (902) (947) (993) (1.012) NOPLAT 1.274 1.372 1.549 1.707 1.937 2.058 2.181 2.307 2.435 2.566 2.700 2.754 % growth 7,7% 12,9% 10,2% 13,4% 6,2% 6,0% 5,8% 5,6% 5,4% 5,2% 2,0%

Changeinprovisions 2 2 2 Depreciation 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.020 Amortisation 450 450 450 450 450 450 450 450 450 450 450 459 Gross cash flow 2.724 2.824 3.001 3.159 3.387 3.508 3.631 3.757 3.885 4.016 4.150 4.233

Bookvalueofdisposaloffixedassets Capitalgainondisposaloffixedassets(netoftax) Investmentstangiblefixedassets (1.180) (1.184) (1.187) (1.187) (1.200) (1.200) (1.200) (1.210) (1.210) (1.210) (1.020) Investmentintangiblefixedassets (510) (511) (513) (513) (513) (513) (515) (519) (520) (521) (523) Investmentsnetworkingcapital (5) (5) (5) (6) (6) (6) (6) (6) (6) (6) (6) Operational free cash flow 1.129 1.301 1.454 1.681 1.789 1.912 2.036 2.150 2.280 2.413 2.683

Extraordinaryresult(netoftax) Resultnonconsolidatedsubsidiaries(netoftax) Interestondebt(netoftax) (160) (194) (188) (227) (240) (254) (267) (282) (295) (309) (323) Interestoncash(netoftax) Cashflowfromchangeinfixedassets Changeinequity Changeindebt 546 (231) 534 256 260 263 272 259 266 266 Changeindebtequivalents Financing cash flow 386 (425) 346 29 20 9 5 (23) (29) (43) (323)

Generated cash 1.515 876 1.800 1.710 1.809 1.922 2.041 2.128 2.251 2.370 2.361 Dividendpayments (808) (903) (1.013) (1.140) (1.212) (1.285) (1.360) (1.436) (1.514) (1.594) (1.621) Change in cash 707 (28) 787 570 597 637 681 692 737 776 740 Table 4.5: Cash flow statement of Company X

MasterThesisSebastianOotjers 88 s0041823 IEMFEM ABCD

Company X - Balance sheet - Equity & Liabilities EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Sharecapital 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 Minorityinterests Cumulativeretainedearnings 371 775 1.227 1.733 2.303 2.909 3.551 4.231 4.949 5.706 6.503 Exchangeratedifferences Equityfromchangefinancialfixedassets Changeinequity Retainedearningscurrentyear 371 404 452 506 570 606 642 680 718 757 797 810 Equity 8.662 9.066 9.518 10.024 10.594 11.200 11.842 12.522 13.240 13.997 14.794 15.604

Provision1 100 102 104 106 106 106 106 106 106 106 106 106 Provision2 Provision3 Operating provisions 100 102 104 106 106 106 106 106 106 106 106 106

Bankloans 3.500 4.046 3.815 4.349 4.605 4.865 5.128 5.400 5.659 5.925 6.191 6.191 Bonds Otherlongterminterestbearingdebt Long-term liabilities 3.500 4.046 3.815 4.349 4.605 4.865 5.128 5.400 5.659 5.925 6.191 6.191

Preferredequity Longtermoperatingprovisions Nonoperatingprovisions Debt equivalents ------

Creditinstitutions Creditors 113 115 118 120 122 124 127 129 132 134 137 140 Taxation&socialsecurity Otherliabilities Accrualsanddeferredincome Current liabilities 113 115 118 120 122 124 127 129 132 134 137 140

EQUITY & LIABILITIES 12.375 13.329 13.554 14.599 15.427 16.295 17.203 18.157 19.137 20.162 21.228 22.041 Table 4.6: Balance sheet of Company X

MasterThesisSebastianOotjers 89 s0041823 IEMFEM ABCD

Company X - Weighted Average Cost of Capital

Riskfreerate 4,0% Riskfreerate 4,0% Marketriskpremium 5,0% Spread 3,0% Additionalriskpremium 3,0% Taxrate 25,5% Unleveredbetapeergroup 0,83 D/E 20% Leveredbeta 1,00

Cost of equity 12,0% After-tax cost of debt 5,2%

E/(E+D) 83% D/(E+D) 17%

WACC 10,8% Table 4.7: WACC calculation of Company X

Company X - Unlevered cost of equity (ME)

Riskfreerate 4,0% Riskfreerate 4,0% Marketriskpremium 5,0% Spread 3,0% Additionalriskpremium 3,0% Taxrate 25,5% Unleveredbetapeergroup 0,83

Unlevered cost of equity 11,2% Cost of debt 7,0% After-tax cost of debt 5,2% D/E 20% E/(E+D) 83% Table 4.8: Unlevered cost of equity calculation of Company X

MasterThesisSebastianOotjers 90 s0041823 IEMFEM ABCD Theseinputsresultinthefollowingvaluationoutcomes: Scenario 1 DCFanalysis APVanalysis in EUR x1000 Enterprisevalue 25.626 25.767

Shareholdervalue 21.277 21.418 Abs.differencein 141 EV Rel.differencein 0,55% EV ThevaluationoutcomeoftheAPVanalysiscanbedividedintothefollowingfourcomponents: Unleveredcompanyvalue:23.303EUR Valueofinteresttaxshields:999EUR Costsoffinancialdistress:2EUR Excesscash:1.466EUR Theseresultsshowthatthetheoryonscenario1,statedinchapter3,holds. 4.2.2 Scenario 2: Constant leverage ratio & significant probability of default Thissecondscenarioisidenticaltoscenario1acceptforthedifferenceintheprobabilityof default.Thisresultsinadifferenceinthecostsoffinancialdistress.Inscenario1,CompanyX receivedaAAratingbasedonitsZscore.Inthisscenario,theprobabilityofdefaultis manuallyadjustedtoaCCCrating,whichresultsinaprobabilityofdefaultof17.20%.The costsoffinancialdistressincrease,asaresultoftheincreasedprobabilityofdefault,to601 EUR(anincreaseof599EUR).Thevaluationoutcomesafterthisadjustmentareasfollows. Scenario 2 DCFanalysis APVanalysis in EUR x1000 Enterprisevalue 25.626 25.168

Shareholdervalue 21.277 20.819 Abs.differencein 458 EV Rel.differencein 1,79% EV Thisresultsupportsthetheorystatedinchapter3thatincaseofasignificantprobabilityof default,thevaluationoutcomeundertheAPVmodelislowerthanthevaluationoutcome undertheenterpriseDCFmodel. 4.2.3 Scenario 3: Fixed amount of debt Themainassumptioninthethirdscenarioisthatthecompanyundervaluationmaintainsa fixedamountofdebt.Debt,inthiscase,referstointerestbearingdebt.Theamountof interestbearingdebthastobefixedsothattheinteresttaxshieldsareknownateachpointin time. Tosimulatethisscenario,thefinancialdataintheequity&liabilitiesoverviewofCompanyX areadjusted.Thebankloansarefixedatthe2006value(whichis4.349EUR).Alltheother inputsremainthesameasinthepreviousscenarios.Thevaluationoutcomesforthefixedthe amountofdebtscenarioareasfollows.

MasterThesisSebastianOotjers 91 s0041823 IEMFEM ABCD

Scenario 3 DCFanalysis APVanalysis in EUR x1000 Enterprisevalue 25.626 25.375

Shareholdervalue 21.277 21.026 Abs.differencein 251 EV Rel.differencein 0,98% EV Thisresultsupportsthetheorystatedinchapter3that,incaseofafixedamountofdebtand anincreasingamountofcapital,theenterpriseDCFmodeloverestimatesthebenefitsofdebt. TheenterpriseDCFmodelassumesaconstantleverageratio,andsincethetotalamountof capitalincreases,theamountofdebtisalsoassumedtogrow.However,thisisnotcorrect sincetheamountofdebtisfixed.TheenterpriseDCFmodelthereforegivesanincorrect valuation. IftheCompanyXwouldhaveaCCCrating,insteadofanAArating(basedontheZscore), thenthedifferencebetweentheenterpriseDCFmodelandtheAPVmodelwouldincreaseto 3.27%.Thiseffectisalsoasstatedinchapter3. Thetheoryinchapter3onthedifferenceinvaluationoutcomebetweentheenterpriseDCF modelandtheAPVmodelunderscenario3alsostatedthatincaseofadecreasingamount oftotalcapital,theAPVmodelwouldgiveahighercompanyvaluethantheenterpriseDCF modeliftheprobabilityofdefaultwasnotsignificant.Thisiscausedbythefactthatthe enterpriseDCFmodelunderestimatesthebenefitsofdebt. ThefinancialdataofCompanyXhavetobeadjustedatanumberofpointstocreatea scenarioinwhichtheamountofdebtisfixedandthetotalamountofcapitalisdecreasing. Theseadjustmentsarethefollowing: Salesgrowthrateof1,0%. Depreciationincreasedto2.000EUR. Nontaxdeductibleamortizationreducedto100EURfortheyear20032011andto zerofor2012andonward. Taxdeductibleamortizationincreasedto500EURfortheyears20032011andto 600for2012andonward. Tangiblefixedassetsvalueremainedconstantat9.000EURthroughinvestmentsin theseassets. Intangiblefixedassetsvalueremainedconstantat3.000EURthroughinvestmentsin theseassets. Fixedamountofsharecapitalwithavalueof7.628EUR. Dividendpayoutratiosetto100%. Amountofdebtfixedat4.500EUR. Thesechangesresultinanoveralldecreaseintheamountoftotalcapitalof1,9%overthe period2003–2013.Thevaluationoutcomesafterthesechangesareshowninthetable below. Scenario 3b DCFanalysis APVanalysis in EUR x1000 Enterprisevalue 1.930 2.694

Shareholdervalue 2.570 1.806 Abs.differencein 764 EV Rel.differencein 39,59% EV ThisshowsthattheenterpriseDCFmodelunderestimatesthebenefitsofdebtincaseof scenariowherethetotalamountofdebtisfixedandtheamountoftotalcapitalisdecreasing. Thisisinlinewiththetheorystatedinchapter3.

MasterThesisSebastianOotjers 92 s0041823 IEMFEM ABCD 4.2.4 Scenario 4: Finite life & known amount of debt ThefinancialdataofCompanyXinscenario4areidenticaltothoseinscenario3butwithan amountofdebtin2003of3.500EUR.CompanyXisassumedtopaydownitsdebtinthe10 yearsafter2003.Thismeansthattheamountofdebtiseachyearreducedby350EUR.The equity&liabilitiesoverviewthatresultsfromtheseadjustmentsisshownintable4.9. Afterinsertingtheseadjustmentstothebasicscenario,theenterprisevalueofthecompany becomesasfollows. Scenario 4 DCFanalysis APVanalysis in EUR x1000 Enterprisevalue 9.225 9.123

Shareholdervalue 6.775 6.673 Abs.differencein 102 EV Rel.differencein 1,11% EV Thesefindingssupportthetheorystatedinchapter3onthedifferenceinvaluationoutcome betweenthetwovaluationmodelsunderthisscenario.Theamountofcapitalisgrowing,so whenusingtheenterpriseDCFmodel,anincreasedbenefitofdebtisassumed.However,the amountofdebtoutstandingisdecreasedovertimetozeroin2013.Thismeansthatthe enterpriseDCFmodeloverestimatesthebenefitsofdebtwhichcausesthevaluationoutcome undertheenterpriseDCFmodeltobehigherthanthevaluationoutcomeundertheAPV model.Thiswaspredictedinchapter3. IftheCompanyXwouldhaveaCCCrating,insteadofanArating(basedontheZscore), thenthedifferencebetweentheenterpriseDCFmodelandtheAPVmodelwouldincreaseto 3.72%.Thiseffectisalsoasstatedinchapter3. 4.2.5 Scenario 5: Debt known up to time t, then a constant leverage ratio Inthisscenario,CompanyXisassumedtostartwithanamountofdebtof9.000in2003 (whichgivesabookleverageratioof65%).ThiscouldforinstancebethecaseafteraLBOor MBO.CompanyXisalsoassumedtohaveaconstantleverageratiofrom2011andonward. Theotherinputfinancialsarethesameasprescribedinthevalidationapproachparagraph. Theequity&liabilitiesoverviewofthisscenarioisshownintable4.10.

MasterThesisSebastianOotjers 93 s0041823 IEMFEM ABCD

Company X - Balance sheet - Equity & Liabilities EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Sharecapital 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 Minorityinterests Cumulativeretainedearnings 371 775 1.241 1.764 2.367 3.016 3.713 4.458 5.251 6.094 6.988 Exchangeratedifferences Equityfromchangefinancialfixedassets Changeinequity Retainedearningscurrentyear 371 404 466 523 603 649 697 745 794 843 894 918 Equity 8.662 9.066 9.532 10.055 10.658 11.307 12.004 12.749 13.542 14.385 15.279 16.197

Provision1 100 102 104 106 106 106 106 106 106 106 106 106 Provision2 Provision3 Operating provisions 100 102 104 106 106 106 106 106 106 106 106 106

Bankloans 3.500 3.150 2.800 2.450 2.100 1.750 1.400 1.050 700 350 Bonds Otherlongterminterestbearingdebt Long-term liabilities 3.500 3.150 2.800 2.450 2.100 1.750 1.400 1.050 700 350 - -

Preferredequity Longtermoperatingprovisions Nonoperatingprovisions Debt equivalents ------

Creditinstitutions Creditors 113 115 118 120 122 124 127 129 132 134 137 140 Taxation&socialsecurity Otherliabilities Accrualsanddeferredincome Current liabilities 113 115 118 120 122 124 127 129 132 134 137 140

EQUITY & LIABILITIES 12.375 12.433 12.553 12.731 12.986 13.288 13.637 14.034 14.480 14.976 15.522 16.443 Table 4.9: Scenario 4 Equity & liabilities overview

MasterThesisSebastianOotjers 94 s0041823 IEMFEM ABCD

Company X - Balance sheet - Equity & Liabilities EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Sharecapital 3.860 3.860 3.860 3.860 3.860 3.860 3.860 3.860 3.860 3.860 3.860 3.860 Minorityinterests Cumulativeretainedearnings 302 637 1.034 1.488 2.020 2.602 3.233 3.916 4.649 5.422 6.234 Exchangeratedifferences Equityfromchangefinancialfixedassets Changeinequity Retainedearningscurrentyear 302 335 396 454 533 582 631 682 734 772 812 825 Equity 4.162 4.497 4.894 5.348 5.880 6.462 7.093 7.776 8.509 9.282 10.094 10.919

Provision1 100 102 104 106 106 106 106 106 106 106 106 106 Provision2 Provision3 Operating provisions 100 102 104 106 106 106 106 106 106 106 106 106

Bankloans 8.000 7.500 7.000 6.500 6.000 5.500 5.000 4.500 4.774 5.048 5.321 5.321 Bonds Otherlongterminterestbearingdebt Long-term liabilities 8.000 7.500 7.000 6.500 6.000 5.500 5.000 4.500 4.774 5.048 5.321 5.321

Preferredequity Longtermoperatingprovisions Nonoperatingprovisions Debt equivalents ------

Creditinstitutions Creditors 113 115 118 120 122 124 127 129 132 134 137 140 Taxation&socialsecurity Otherliabilities Accrualsanddeferredincome Current liabilities 113 115 118 120 122 124 127 129 132 134 137 140

EQUITY & LIABILITIES 12.375 12.214 12.115 12.074 12.108 12.192 12.326 12.511 13.521 14.570 15.658 16.486 Table 4.10: Scenario 5 Equity & liabilities overview

MasterThesisSebastianOotjers 95 s0041823 IEMFEM ABCD ThecalculationoftheenterprisevalueofCompanyXthroughtheAPVmodelhastobe manuallyadjustedtomatchthesituationathand.Theyears20072010aremodeled accordingtotheMMAPVmodel,sincetheamountofinterestbearingdebtoutstandingis assumedtobeknownintheseyears.Fortheyears2011andonward,theMEAPVmodelis used,sinceaconstantleverageratioisassumed. Asaresultofthissplitinthevaluation,thefreecashflowsfortheyears20072010havetobe discountedattheMMunleveredcostofequityandthefreecashflowsfor2011andonward havetobediscountedattheMEunleveredcostofequity. Also,theinteresttaxshieldsfor20072010havetobediscountedatthecostofdebtandthe interesttaxshieldsfor2011andonwardhavetobediscountedattheMEunleveredcostof equity.Thisresultsinthefollowingvaluationoutcomes. Scenario 5 DCFanalysis APVanalysis in EUR x1000 Enterprisevalue 23.138 23.248

Shareholdervalue 16.638 16.748 Abs.differencein 110 EV Rel.differencein 0,48% EV TheleverageratioinsertedintheWACCcalculationis17,2%.Thisistheassumedvalueof theconstantleverageratiointheperiod2011andonward. Theimpliedleverageratioattimetiszerois28,1%.ThismeansthatCompanyXiscurrently notatitstargetleverageratio.ThiscausestheDCFanalysistounderestimatethebenefitsof debt.ThisleadstoavaluationoutcomeoftheDCFanalysisthatislowerthanthe(correct) APVmodelvaluationoutcome. Thedifferenceinvaluationoutcomesthatisfoundisinlinewiththetheorystatedinchapter4 forthisscenario.TheleverageratiodecreasesandcausestheenterpriseDCFmodelto underestimatethebenefitsofdebt.However,theleverageratioisassumedtobeconstant from2011andonward,whichcausestheerrorinthevaluationoutcometostabilize. WhenmanuallyadjustingthecreditratingfromtheArating(basedontheZscore)toaCCC rating,thevaluationoutcomeoftheAPVanalysisis2,11%lowerthanthevaluationoutcome oftheDCFanalysis.Thisshowsthattheeffectsofunderestimatingthebenefitsofdebtand underestimatingthecostsoffinancialdistressbytheenterpriseDCFmodelcancanceleach otherout.IfCompanyXwouldhaveaBBrating,thedifferenceinvaluationoutcomeswould bereducedto0,06%. 4.3 Sensitivity analysis Thevalidationofthebasicscenariosinthepreviousparagraphisbasedonafictitious company.Thefinancialdatathatformthebasisforthevaluationareartificial.Therefore,the validationoutcomesmightbebiasedbythevalidationapproachchosen.Thisparagraph discussestheeffectsofchanginganumberofinputvariablestogivesomeindicationofthe sensitivityofthevalidationoutcomestothevalidationapproachthatwaschosen. Thefivevariablesofwhichtheinfluenceonthedifferenceinvaluationoutcomesisanalyzed aretheleveredbeta,thecostofdebt,themarketleverageratio,theamountofsalesin2003 andthetaxrate.Theinfluenceofthesevariablesistestedforbothscenario1and3. 4.3.1 Levered beta Theleveredbetahasastandardvalueof1,0inthevalidationapproach.Adjustingthelevered betahaspracticallynoeffectontherelativedifferencebetweentheenterpriseDCFmodel andtheAPVmodelvaluationoutcomeforbothscenario1&3,asisshowninthetables below.

MasterThesisSebastianOotjers 96 s0041823 IEMFEM ABCD S1 Beta 0,1 0,4 0,7 1 1,3 1,65 2 Abs.Diff 256 200 164 141 125 111 102 Rel.Diff 0,59% 0,57% 0,56% 0,55% 0,55% 0,54% 0,55% S3 Beta 0,1 0,4 0,7 1 1,3 1,65 2 Abs.Diff 429 346 291 251 219 191 166 Rel.Diff 0,99% 0,99% 0,99% 0,98% 0,96% 0,94% 0,90% Thismeansthatthevalidationoutcomesareindependentoftheleveredbetainsertedinthe validationapproach. 4.3.2 Cost of debt Thevalidationoutcomesarealsoinsensitivetothecostofdebtthatischoseninthevalidation approach(standardvalueofthecostofdebtis7,0%).Thesizeoftherelativedifference betweenthetwovaluationoutcomesisaffectedbyachangeinthecostofdebtunder scenario1,however,thesignofthedifferenceremainsthesameandtherelativedifference staysunder1%asshowninthetablesbelow. S1 Kd 4% 5% 6% 7% 8% 9% 10% Abs.Diff 123 132 138 141 144 146 148 Rel.Diff 0,34% 0,41% 0,49% 0,55% 0,62% 0,68% 0,74% S3 Kd 4% 5% 6% 7% 8% 9% 10% Abs.Diff 357 313 278 251 227 209 190 Rel.Diff 0,98% 0,98% 0,98% 0,98% 0,97% 0,97% 0,96% Thismeansthatthevalidationoutcomesareindependentofthecostofdebtinsertedinthe validationapproach. 4.3.3 Tax rate Thevalueofthetaxrateusedasaninputinthevalidationapproachhasnoeffectonthesign oftherelativedifferencebetweenthetwovaluationoutcomes.Itdoeshaveaneffectonthe sizeoftherelativedifference.Thiseffect,forbothscenario1&3,isshowninthetables below. S1 Taxrate 10,0% 15,0% 20,0% 25,5% 30,0% 35,0% 40,0% Abs.Diff 51 80 108 141 170 202 237 Rel.Diff 0,17% 0,28% 0,40% 0,55% 0,70% 0,89% 1,11% S3 Taxrate 10,0% 15,0% 20,0% 25,5% 30,0% 35,0% 40,0% Abs.Diff 101 149 198 251 292 337 381 Rel.Diff 0,33% 0,52% 0,73% 0,98% 1,20% 1,48% 1,79% Thisshowsthatthevalidationoutcomesareindependentofthetaxrateselectedasaninput inthevalidationapproach. 4.3.4 Market leverage ratio Thesensitivityofthevalidationoutcomestothevalueofthemarketleverageratioinsertedin thevalidationapproachshowsthesamepatternasthesensitivitytothetaxrateinsertedin thevalidationapproach:thesignoftherelativedifferenceinvaluationoutcomesisinsensitive tothemarketleverageratiochosen,butthesizeoftherelativedifferencedoeschangewhen adifferentmarketleverageratioisinsertedinthevalidationapproach.Theresultsofthe sensitivityanalysisareshownbelow. S1 D/VRatio 4,42% 8,58% 12,52% 16,97% 21,62% 26,30% 34,94% Abs.Diff 23 49 78 141 190 219 356 Rel.Diff 0,10% 0,21% 0,33% 0,55% 0,72% 0,82% 1,24%

MasterThesisSebastianOotjers 97 s0041823 IEMFEM ABCD S3 D/VRatio 4,42% 8,58% 12,52% 16,97% 23,12% 27,83% 32,20% Abs.Diff 64 131 200 251 428 549 692 Rel.Diff 0,28% 0,56% 0,83% 0,98% 1,65% 2,04% 2,48% Thisshowsthatthevalidationoutcomesareindependentofthemarketleverageratio selectedasaninputinthevalidationapproach. 4.3.5 Amount of sales in 2003 Forthepreviousfourvariablesthatwerediscussed,thevalidationoutcomewasinsensitiveto thevaluesofthevariablesinsertedinthevalidationapproach.Thelastvariablediscussedin thisparagraph,theamountofsalesin2003,hasadifferenteffectonthevalidationoutcome. Thevalidationoutcomeissensitivetolowvaluesoftheamountofsalesin2003. Theamountofsalesisassumedtogroweachyearwithafixedpercentage,asdothedirect coststhatareassumedtoremainat50%ofsales.Theothercosts,suchasoperatingcosts anddepreciationareassumedtoremainconstantandthuscausethefreecashflowtogrow. Thegrowthofthefreecashflowiswhatultimatelyaffectsthevaluationoutcome. Incaseofscenario3,therelativedifferenceinthevaluationoutcomesoftheAPVmodeland theenterpriseDCFmodelincreasessignificantlyforlowervaluesoftheamountofsalesin 2003(below12.500).Theresultsofthesensitivityanalysisareshowninthetablebelow. S3 Sales'03 11.000 12.500 15.000 20.000 25.000 30.000 Abs.Diff 779 370 251 187 164 153 Rel.Diff 9,08% 2,49% 0,98% 0,39% 0,24% 0,17% Thisshowsthatthechosenvaluefortheamountofsalesin2003thatisinsertedinthe validationapproachunderscenario3hasaneffectonthesizeoftherelativedifference betweenthevaluationoutcomes.However,thesignoftherelativedifferencestaysthesame. Thesituationbecomesmorepeculiarunderscenario1.Thecostsoffinancialdistress,that lowerthevaluationoutcomeundertheAPVmodel,increasestepwise.Thisresultsinthefact thattherelativedifferenceinvaluationoutcomesispositive(thatistheAPVmodelgivesa highervaluationoutcomethantheenterpriseDCFmodel)foranamountofsalesin2003of 11.100EURandnegativeforanamountofsalesin2003of11.000EUR.Theseresultsare showninthetablebelow. S1 Sales'03 11.000 11.100 11.500 12.500 15.000 20.000 Abs.Diff 59 41 20 116 141 153 Rel.Diff 0,69% 0,46% 0,19% 0,78% 0,55% 0,32% PoD 17% 8% 8% 1% 0% 0% “PoD”standsfortheprobabilityofdefaultbasedontheAltmanZscore.Theseresultsshow thatthesignofthevalidationoutcomeissensitivetothevalueoftheamountofsalesin2003. Conclusion Thepurposeofthischapteristotestthetheoriesstatedinchapter3.Thesetheoriesare formulatedasscenariosunderwhichadifferencebetweentheAPVmodelvaluationoutcome andtheenterpriseDCFmodelvaluationoutcomeshouldoccur.Thetablebelowshowsthese scenariosandtheirpredictedresults.

MasterThesisSebastianOotjers 98 s0041823 IEMFEM ABCD

Scenario Model Compare to Effect on valuation outcome Constantleverageratio& DCForAPV(ME) n.a. V(APV)=V(DCF) no significantPoD

Constantleverageratio& APV(ME) DCF V(APV)<V(DCF) significantPoD V(APV)>V(DCF)or Fixedamountofdebt APV(MM) DCF V(APV)=V(DCF)or V(APV)<V(DCF) V(APV)>V(DCF)or Finitelife&debtknown APV(general) DCF V(APV)=V(DCF)or V(APV)<V(DCF) Combinationofscenario4and Debtknownuptot,then APV(general)+ DCF 1oracombinationofscenario4 constantleverageratio APV(ME) and2 Basedonthevalidationapproachchosen,scenarios2to5werevalidated.Theory1wasonly weaklyvalidated. Adifferenceof0,55%betweenthetwovaluationoutcomesunderscenario1wasfound,while thetheoryinchapter3statedthatthetwomodelsshouldgivethesamevaluationoutcome. Oneofthecausesofthenonzerodifferenceinscenario1isthegrowthrateofboththefree cashflowsandtheinteresttaxshieldsinsertedinthevalidationapproach.Thefreecash flowsandinteresttaxshieldsareassumedtohaveayearlygrowthrateof2,0%inperpetuity. Thedifferenceinvaluationoutcomescanbereducedbysettingthegrowthratetothevalue ofthegrowthimpliedbythefreecashflowsandinteresttaxshields.Forinstance,thefree cashflowisassumedtobe2.413EURin2013and2.683EURinthetimeperiodafter2013 (thisistheinputfreecashflowforthecalculationoftheterminalvalue).Thischangeinfree cashflowimpliesa11,2%growthrate.Thedifferencebetweenthevaluationoutcomesunder scenario1oftheAPVmodelandtheenterpriseDCFmodelisreducedto0.12%ifthegrowth rateofthefreecashflowsandinteresttaxshieldsissetto11,2%. However,assumingan11,2%growthrateinperpetuityisnotveryrealisticsincethechange infreecashflowbetweenthelastyearoftheforecastperiodandtheinputfortheterminal valuecalculationiscausedbyacoupleofmodelingdecisionthatallowforthedetermination ofthisterminalvalue.Thisisalsoindicatedbythefactthattheaveragegrowthinfreecash flowintheyears20072013is6%.Therefore,thegrowthrateofthefreecashflowsand interesttaxshieldsisassumedtobeequaltothegrowthinsales,whichgivesamorerealistic longtermviewoftheexpectedfreecashflowandinteresttaxshieldgrowth. Asaresultofthisdecision,thedifferencebetweenthevaluationoutcomeoftheAPVmodel andtheenterpriseDCFmodelisnonzero.However,sincethedifferenceisverysmall (0,55%),theory1isassumedtobevalidatedbythetestperformedinthischapter. Thetestofscenario3bshowsthestrongestvalidationresult:adifferencebetweenthe valuationoutcomesofthetwomodelsof40%.Theothertestsshowvalidationresultsthat validatethetheoriesstatedinchapter3,buttheseresultsarelesssignificantthantheresult fromthetestofscenario3b. Thevalidationoutcomesareinsensitivetotheleveredbeta,thecostofdebt,themarket leverageratioandthetaxrateinsertedinthevalidationapproachforbothscenario1and3. Thevalidationoutcomeofscenario1issensitivetotheamountofsalesin2003insertedin thevalidationapproach.Underscenario3,insertingalowvaluefortheamountofsalesin 2003resultsinalargerdifferencebetweenthevaluationoutcomesofthetwomodels (differenceincreasesfrom0,98%for15.000EURofsalesin2003to9,08%for11.000EUR ofsalesin2003).However,thesignofthedifferenceremainsthesamewhichmeansthat theory3isvalidatedregardlessofthevalidationapproachchosen. Underscenario1,thedifferencebetweenthevaluationoutcomesofthetwomodelschanges signforaninsertedamountofsalesin2003ofaround11.000EUR(11.000EURgivesa differenceof0,69%and11.100EURgivesadifferenceof0,46%).Thischangeinsignis causedbythestepwiseincreaseofthecostsoffinancialdistress.However,thedifference betweenvaluationoutcomesstayswithinplusorminus1%.Sincetheory1statesthatincase

MasterThesisSebastianOotjers 99 s0041823 IEMFEM ABCD ofaconstantleverageratiobothvaluationmodelsshouldgivethesamevaluationoutcome,a changeinsignofthedifferenceisnotdamagingthevalidityoftheory1. ThetheoriesonthedifferencebetweenthevaluationoutcomesoftheAPVmodelandthe enterpriseDCFmodelunderfivedifferentscenariosarefoundtobevalid,basedonthe resultsfromthetestsdiscussedinthischapter.Theimplicationsofthesevalidated differencesforthedecisiononwhichvaluationmodeltouseinwhichsituationwillbe discussedinchapter5.

MasterThesisSebastianOotjers 100 s0041823 IEMFEM ABCD

Chapter 5: Conclusion

Introduction Theresearchobjectiveofthisresearchproject,asstatedinchapter1,is: To formulate a theory onthedifferencesbetweentheenterpriseDCFmodelandtheAPV model,andtheeffectsofthesedifferencesonthevaluationoutcome by analyzing thebasic assumptionsofbothmodels,thecircumstancesinwhicheitheroneshouldbeused,the impactofthenonconstantcapitalstructureandthenonzerocostsoffinancialdistressonthe valuationoutcomeundertheAPVmodel,andthewayinwhichthesetwofactorscanbe modeledtoobtainthemostaccuratevaluationoutcome. Thepurposeofthischapteristoconcludeontheextentthattheresearchobjectivehasbeen met.ThisisdonebydiscussingthedifferencesfoundbetweentheenterpriseDCFmodeland theAPVmodelandbycommentingontheirvaliditybasedonthevalidationresultsfrom chapter4.Thesituationalconditionsofthedifferencesinthevaluationoutcomesare discussedinthesecondparagraph.Theimplicationsofthevalidatedconditionaldifferences arediscussedinthethirdparagraph. Thechapterendswithaparagraphonthefurtherresearchsuggestionsthatcomeforthfrom theoverallresultsoftheanalysisofthedifferencesbetweentheenterpriseDCFmodeland theAPVmodelandthetheoreticalframeworkthatwasformulatedinchapter2,which functionedasameansfortheanalysis. 5.1 Overview of (valid) differences ThereareanumberofdifferencesbetweentheenterpriseDCFmodelandtheAPVmodel. Thesedifferencesaresummarizedinthetablebelow. Enterprise DCF model APV model

Cashflow FCFF FCFF

Discountrate WACC KuorKd

Costofequity Levered Unlevered

Costofdebt Creditratingbased Creditratingbased

Constantleverageratio Capitalstructure Constantleverageratio orfixeddebt Notexplicitlytakeninto Separateterminthe Probabilityofdefault account valuation Notexplicitlytakeninto Separateterminthe Costsoffinancialdistress account valuation Theimpactofthedifferencesonthevaluationoutcomeisbasedonthedifferenceincapital structureassumptionandtheinclusionofthecostsoffinancialdistressinthevaluation models.TheenterpriseDCFmodelisassumedtogiveacorrectvaluationinthecaseofa companythatmaintainsaconstantleverageratioovertimeandthathasnosignificant probabilityofdefault.TheenterpriseDCFmodelgivesanincorrectcompanyvalueifoneof theseassumptionsisviolated. TherearefivescenariosinwhichtheAPVmodelcanbeusedtodeterminethecorrectvalue ofthecompany,ifthecapitalstructureand/ortheprobabilityofdefaultassumptionofthe enterpriseDCFmodelareviolated.Theexpecteddifferencesinvaluationoutcomesare showninthetablebelow.

MasterThesisSebastianOotjers 101 s0041823 IEMFEM ABCD

Scenario Model Compare to Effect on valuation outcome Constantleverageratio& DCForAPV(ME) n.a. V(APV)=V(DCF) no significantPoD

Constantleverageratio& APV(ME) DCF V(APV)<V(DCF) significantPoD V(APV)>V(DCF)or Fixedamountofdebt APV(MM) DCF V(APV)=V(DCF)or V(APV)<V(DCF) V(APV)>V(DCF)or Finitelife&debtknown APV(general) DCF V(APV)=V(DCF)or V(APV)<V(DCF) Combinationofscenario4and Debtknownuptot,then APV(general)+ DCF 1oracombinationofscenario4 constantleverageratio APV(ME) and2 Thefivescenariosweresimulatedinchapter4totestwhetherthestatedeffectsonthe valuationoutcomedoindeedoccur.Theoutcomeofthetestsisthatallthepredictedeffects onthevaluationoutcomearevalidated.Thismeansthatthefollowingtheoriescanbestated withregardtotheeffectofthedifferencesbetweentheAPVmodelandtheenterpriseDCF modelonthedifferenceinvaluationoutcomes. Theory1:Ifthecompanyundervaluationisassumedtomaintainaconstantleverageratio andifthecompanyhasnosignificantprobabilityofdefault,thenthevaluationoutcomesof bothmodelsarethesame. Theory2:Ifthecompanyundervaluationisassumedtomaintainaconstantleverageratio andifthecompanyhasasignificantprobabilityofdefault,thentheenterpriseDCFmodel valuationoutcomeisincorrectandhigherthanthecorrectvaluationoutcomeoftheAPV model. Theory3:Ifthecompanyisassumedtomaintainafixedamountofdebt,thentheenterprise DCFmodeloverestimatesthebenefitsofdebtincaseofanincreasingtotalamountofcapital andunderestimatesthebenefitsofdebtincaseofadecreasingtotalamountofcapital.This errorintheestimationofthebenefitsofdebtiscomplementedbyapotentialerrorinthe estimationofthecostsoffinancialdistress.Ifthecompanyundervaluationhasasignificant probabilityofdefault,thentheAPVmodelcorrectlyincludesaseparatetermforthesecosts whereastheenterpriseDCFmodelignoresthesecosts.Combiningtheerrorsinthe estimationofthebenefitsofdebtandtheestimationofthecostsoffinancialdistressresultin thetotalerrorinthecompanyvaluedeterminedthroughtheenterpriseDCFmodelcompared tothecorrectcompanyvaluedeterminedbytheAPVmodel. Theory4:Ifthecompanyundervaluationisassumedtohaveafinitelifeandaknownamount ofdebtateachpointintime,thenerrorinthevaluationoutcomeoftheenterpriseDCFmodel dependsonthedifferencebetweentheamountofdebtassumedbytheenterpriseDCF modelandtheactualamountofdebtateachpointintime.Theerrorintheestimationofthe benefitsofdebthastobeaddedtotheerrorthatresultsfromignoringthecostsoffinancial distresswhenthecompanyundervaluationhasasignificantprobabilityofdefault. Theory5:Ifthecompanyundervaluationisassumedtohaveaknownamountofdebtat eachpointintimeuptotimetandifthecompanyisassumedtohaveaconstantleverage ratiofromtimetandonward,thenthedifferencebetweenthevaluationoutcomesofboth modelsisbasedonacombinationoftheory4and1oronacombinationoftheory4and2. Thecombinationoftheory4and1impliesthattheerrorinthevaluationoutcomeofthe enterpriseDCFmodelisbasedontheincorrectestimationofthebenefitsofdebtoverthe timeperioduptotimetsincetheenterpriseDCFmodelgivesacorrectvaluefortheperiod aftertinwhichthecompanymaintainsaconstantleverageratioandhasnosignificant probabilityofdefaultasisstatedintheory1.Thecombinationoftheory4and2impliesthat theerrorinthevaluationoutcomeoftheenterpriseDCFmodelisbasedontheincorrect estimationofthebenefitsofdebtoverthetimeperioduptotimetandonthefactthatthe

MasterThesisSebastianOotjers 102 s0041823 IEMFEM ABCD costsoffinancialdistressareignoredregardlessofthesignificantprobabilityofdefaultofthe companyundervaluation. 5.2 Situational conditions of valuation outcome differences Thevaliddifferencesdiscussedinthepreviousparagraphoccurunderidealcircumstances. Thisparagraphdiscusseswhichfactorscouldcausethevaluationoutcomestodeviatefrom thetheoreticallystatedvalues.Thisparagraphalsoaddressestheextentofthedeviation causedbyeachfactor. Inparagraph4.3,thesensitivityofthevalidationoutcomestofivedifferentvariableswas analyzed.Thesefivevariablesarethetaxrate,thecostofdebt,themarketleverageratio,the leveredbetaandtheamountofsales.Theresultofthesensitivityanalysiswasthattheeffect onthevaluationoutcomeundereachscenariowasinsensitivetochangesinoneofthefive variables.Thismeansthateachofthefivetheoriesregardingtheeffectsonthedifference betweenthevaluationoutcomesoftheAPVmodelandtheenterpriseDCFmodelholdsfor anyreasonablevalueofthefivevariables. The extent oftheeffectonthevaluationoutcomeissensitivetosomeofthefivevariables. Theleveredbetaandcostofdebthavenoinfluenceonthedifferencebetweenthevaluation outcomes.However,thetaxrate,marketleverageratioandtheamountofsalesdoinfluence thesizeofthedifferencebetweenthevaluationoutcomes.Thedifferenceinvaluation outcomesincreasesforhighervaluesofthetaxrateandmarketleverageratioandforlower valuesoftheamountofsalesincaseofanassumedfixedamountofdebt(scenario3). Thiscanbeexplainedasfollows.Thedifferencebetweenthevaluationoutcomesofthetwo valuationmodelsunderscenario3iscausedbythefactthattheenterpriseDCFmodel assumesagrowingamountofdebtincaseofanincreasingamountoftotalcapital.The amountofdebtoutstandingishoweverfixed.Thiscausesanoverestimationofthebenefitsof debtbytheenterpriseDCFmodel.Ahighertaxrateand/orahighermarketleverageratio amplifiestheoverestimationoftheamountofdebt:ifthemarketleverageratiois50%instead of20%,eachincreaseintotalcapitalisassumedtogive2,5timesmorebenefitsofdebtand thusa2,5timeslargererrorinthevaluationoutcomeoftheenterpriseDCFmodel. Theinfluenceoftheamountofsalesisacaseonitsown.Supposethatthecompanyunder valuationisfirstassumedtohaveafixedamountofdebtof1.000EURandsalesinthe amountof5.000EUR.Thisamountofsalesgeneratesfreecashflowandthisleadstoan enterprisevalue.Theimpliedmarketleverageratioisbasedontheratiooftheamountofdebt totheenterprisevalue.Nowsupposethattheamountofsalesisreducedto3.000EUR.This meansthatthefreecashflowdecreasesandsodoestheenterprisevalue.Theimplied marketleverageratioincreasessincetheamountofdebtisassumedtobefixed.Thechange intheimpliedmarketleverageratioislargerforlowenterprisevaluesthanforhighenterprise valuesandthuslargerforlowamountsofsales.Thesehighimpliedmarketleverageratios arethecauseoftheerrorinthevaluationoutcomeoftheenterpriseDCFmodelforlow amountsofsales. TheenterpriseDCFmodelassumesaconstantleverageratioandnosignificantprobabilityof default.Ifoneofthesetwoassumptionsisviolated,thenthevaluationoutcomeofthe enterpriseDCFmodelisincorrect.Thedifferenceinvaluationoutcomesdependsonthe capitalstructureandtheprobabilityoffinancialdistressofthecompanyundervaluation. Thesedifferenceswherediscussedinthepreviousparagraph.Thetestsperformedinchapter 4showedthatthestateddifferencesarevalid.Thevalidityofthetheoriesthatpredictthe differenceinvaluationoutcomesdoesnotdependonthecostofdebt,taxrate,leveredbeta, marketleverageratioandtheamountofsales,aswasalsoshowninchapter4.Thesizeof thedifferencehoweverdoesdependonthemarketleverageratio,taxrateand(indirect)on theamountofsales.Ahighertaxrateandmarketleverageratioamplifiesthedifferenceand sodoesaloweramountofsales.Thismeansthatitbecomesmoreimportanttousetheright modelineachsituationwhenthemarketleverageratioandtaxratearehighandtheamount ofsalesarelow.Theactualvalueofthesizeofthedifferenceinvaluationoutcomesdepends onthecharacteristicsofthecompanyundervaluation.

MasterThesisSebastianOotjers 103 s0041823 IEMFEM ABCD Itisimportanttonotethattheconclusiononthevalidityofthedifferencesbetweenthe valuationoutcomesoftheAPVmodelandtheenterpriseDCFmodelunderdifferent scenariosarebasedontestsonthevaluationofasingle,fictitiouscompany.Thismeansthat isunrealistictostatethatthedifferencesformulatedaregenerallycorrect.However,the statedtheoriesonthedifferencesbetweenthevaluationoutcomesarebasedamultitudeof sourcesandhavenotberejectedbythetestsperformedinchapter4. Thenextparagraphdiscussestheimplicationofthedifferencesbetweenthetwovaluation modelsandrespectivelytheeffectofthesedifferencesonthevaluationoutcomesforthe decisionontheusageofeithertheenterpriseDCFmodelortheAPVmodelundercertain circumstances. 5.3 Implications of the differences between the two valuation models Thefirstparagraphofthischapterdiscussedthevaliddifferencesbetweentheenterprise DCFmodelandtheAPVmodelandtheeffectofthosedifferencesonthevaluationoutcome foranumberofscenarios.Aswasshowninchapter4,thedifferencebetweenthevaluation outcomesundertheenterpriseDCFmodelandtheAPVmodelisinsomecasessignificant (40%underscenario3withadecliningamountoftotalcapital)andinothercasesnegligible. ThefunctionoftheAPVmodelforthevaluationofcompaniescanthereforebeformulatedas follows: - IncertaincasestheAPVmodelistheoreticallymorecorrectandalsogivesasignificantly differentvaluationoutcomethantheenterpriseDCFmodel.Thesecasesare(withthe differenceinvaluebetweenbrackets): 1. Companieswithafixedamountofdebtandadecreasingamountoftotalcapital (40%). 2. Companieswithafixedamountofdebtandlowamountsofsales(9%). 3. Companiesthatmaintainaconstantleverageratioandthathaveasignificant probabilityofdefault(2%). Thesethreecaseshaveincommonthatthecompanyundervaluationisinsomesortof financialdistress:thetotalamountofcapitaldecreases,whichcanbecausedby decliningsales,highfixedcostsandhighdividendpayoutratios;theamountsofsalesare low,whichcombinedwithsignificantfixedcostsresultinlowprofitsandlowfreecash flow;andasignificantprobabilityofdefault,whichalsoindicatesfinancialdistress. Based on this mutual aspect of the three cases, the APV model seems to be especially appropriate for the valuation of a company that suffers from financial distress. - Inothercases,theAPVmodelistheoreticallymorecorrectbutthedifferenceinvaluation outcomewithregardtotheenterpriseDCFmodelisnegligible.Thesecasesare(withthe differenceinvaluebetweenbrackets): 1. Companieswithaknownamountofdebtuptoacertainpointintimeandwitha constantleverageratiofromthatpointonward(0,5%). 2. Companieswithafinitelifeandknownamountsofdebtateachpointintime(1%). 3. Companieswithafixedamountofdebtandhighamountsofsales(1%). Thesmalldifferencesbetweenthevaluationoutcomesinthefirsttwocasesarecaused bytheinfluenceoftheterminalvalueontheenterprisevalue.Inthefirstcase,the assumptionsoftheenterpriseDCFmodelarenotviolatedafterpointt,whichmeansthat theerrorinthevaluationoutcomeisonlycreatedbytheyearsuptopointt.Theterminal value,whichcontributesamajorpartoftheenterprisevalue,doesnotcontainanerror. Inthesecondcase,thecompanyisassumedtohaveafinitelife.Sincetheerrorinthe enterpriseDCFmodelvaluationoutcomeaccumulatesovertheyears,thesizeofthe errorremainsnegligibleforcompanieswithashort,finitelife. Thedifferencebetweenthevaluationoutcomesforthefirsttwocasesthusdependson therelationbetweentheforecastperiodandtheterminalvalue.Thelongertheforecast period,thelargerthedifference.Thismeansthatitatacertainlengthoftheforecast period,thedifferencebetweenthevaluationoutcomesoftheAPVmodelandthe enterpriseDCFmodelbecomessignificant. Asaresultofthenonsignificantdifference,theAPVmodelandtheenterpriseDCFmodel canbothbeusedtovaluethecompanyeventhoughtheAPVmodelgivesatheoretically morecorrectcompanyvalue.ThechoiceforeithertheAPVmodelortheenterpriseDCF

MasterThesisSebastianOotjers 104 s0041823 IEMFEM ABCD modelshouldbebasedontheinformationrequirementsofthevaluerandthequalityof theavailableinputinformationrequiredbyeachofthemodels. Thepracticalsituationsthatrelatetothecasesinwhichthedifferencebecomes insignificantarethatofamanagementorleveragebuyout(thefirstcase)andproject finance(thesecondcase).ForthesecasesboththeenterpriseDCFmodelandtheAPV modelcanbeusediftheperiodinwhichtheenterpriseDCFmodelassumptionsare violatedissmall. - Intheremainingcases,eitherboththeenterpriseDCFmodelandtheAPVmodelcanbe usedtodeterminethecompanyvalueornoneofthetwomodelsisfitforthe determinationofthecompanyvalue. Notehoweverthatfromapracticalpointofviewthatthevaluationtooldiscussedinappendix IIautomaticallycalculatesthecompanyvaluethroughboththeenterpriseDCFmodelandthe APVmodelaftertheinsertionoftherequired(general)inputdata.Thismeansthatthevaluer doesnothavetodecidewhichmodelhechoosestouse.Thedecisioncanbepostponedup tothepointwherebothvaluationoutcomesareknown. 5.4 Further research suggestions Thesuggestionsforfurtherresearchfocusontwotopics: 1. Theestimationofthecostsoffinancialdistress. 2. Thedeterminationoftheexactdifferencesinvaluationoutcomesunderdifferent circumstances. 5.4.1 Costs of financial distress Thecostsoffinancialdistressareoftenignoredindiscussionoftheadjustedpresentvaluein thecorporatefinanceliterature.Damodaran(2002)doesincludeanddiscusstheseparate termthatisaddedintheadjustedpresentvaluefortheexpectedcostsoffinancialdistress. However,Damodaran(2002)doesnotspecifyanyspecificwaysfordeterminingthe probabilityofdefaultandthecostsoffinancialdistress. Thecostsoffinancialdistressareestimatedbydifferentauthors,asdescribedinchapter2, buttheresultsarediverse.Furtherresearchintothecostsoffinancialdistresscouldimprove theaccuracyoftheestimationofthecostsoffinancialdistress. Therearevariouswaystoestimatetheprobabilityofdefaultofacompany.TheAltmanZ scoreisusefulforestimatingtheprobabilityofdefaultofnonlistedandnonratedcompanies. FurtherresearchintotherelationbetweentheZscoreandtheprobabilityofdefaultfor differenttypesofcompaniesindifferentindustriescouldprovideconversiontablestomore accuratelyestimatetheprobabilityofdefaultforthesecompanies. Bycombiningtheimprovedestimationofboththecostsoffinancialdistressandthe probabilityofdefaultandthroughadiscussionontheinclusionofthedistresstermintothe APVmodel,theaccuracyoftheAPVmodeloughttobeimproved. 5.4.2 Exact differences in valuation outcomes Inchapter4,thedifferencesbetweenthevaluationoutcomesoftheAPVmodelandthe enterpriseDCFmodelwereshownfordifferentvaluesofinputvariables.However,these resultsarebasedonthevaluationofonefictitiouscompany.Furtherresearchondifferent scenarios,companiesandvaluesofinputvariablesshouldprovidea quantitative overviewof thedifferencesinvaluationoutcome.Theresultsfromthesecasescanbeusedtoconclude ontheexactsizeofthedifferencebetweenthevaluationoutcomesoftheAPVmodelandthe enterpriseDCFmodelindifferentsituationswhichcanbeusedtomakeabetterfounded decisiononthetypeofvaluationmodeltouseforthecompanyvaluation.

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Literature

Altman,E.I.,1968.FinancialRatios,DiscriminantAnalysisandthePredictionofCorporate Bankruptcy.The Journal of Finance 23 ,pp.589609. Altman,E.I.,1984.AFurtherInvestigationoftheBankruptcyCostQuestion. The Journal of Finance 39 ,pp.10671089. Altman,E.I.,2000.PredictingFinancialDistressofCompanies:RevisitingtheZscoreand ZetaModels.UnpublishedworkingpaperNewYorkUniversity,NewYork,USA. Altman,E.I.,Haldeman,R.G.,Narayanan,P.,1977.ZetaAnalysis,ANewModeltoIdentify BankruptcyRiskofCorporations.Journal of Banking and Finance 1,pp.2954. Andrade,G.,Kaplan,S.N.,1998.HowCostlyisFinancial(NotEconomic)Distress?Evidence fromHighlyLeveragedTransactionsThatBecameDistressed. The Journal of Finance 53 , pp.14431493. Beaver,W.H.,1966.FinancialRatiosasPredictorsofFailure.Journal of Accounting Research 5,pp.71111. Blums,M.,2003.Dscore:BankruptcyPredictionModelforMiddleMarketPublicFirms. UnpublishedworkingpaperMacalesterCollege,St.Paul,USA. Branch,B.,2002.TheCostsofBankruptcy:AReview. International Review of Financial Analysis 11 ,pp.3957. Brealey,R.A.,Myers,S.C.,2003.Principles of .SeventhEdition.New York:McGrawHill. Caouette,J.B.,Narayanan,P.,Altman,E.I.,1998,Managing Credit Risk: The Next Great Financial Challenge ,NewYork:Wiley. ChenG.M.,MervilleL.J.,1999.AnAnalysisoftheUnderreportedMagnitudeoftheTotal IndirectCostsofFinancialDistress. Review of quantitative finance and accounting 13 ,pp. 277293. Chirinko,R.,Singha,A.,2000.TestingStaticTradeoffAgainstPeckingOrderModelsof CapitalStructure:ACriticalComment. Journal of Financial Economics 58 ,pp.412425. Cooper,I.,Nyborg,K.G.,2006.TheValueofTaxShieldsISEqualtothePresentValueof TaxShields.Journal of Financial Economics 81 ,pp.215225. Cooper,I.,Nyborg,K.G.,2007.ValuingtheDebtTaxShield.Journal of Applied Corporate Finance 19 ,pp.5059. Crouhy,M.,Galai,D.,Mark,R.,2000.AComparativeAnalysisofCurrentCreditRiskModels. Journal of Banking & Finance 24 ,p.59117. Damodaran,A.,2002. Investment Valuation: Tools and Techniques for Determining the Value of Any Asset .SecondEdition.NewYork:Wiley. Damodaran,A.,2006.TheCostofDistress:Survival,TruncationRiskandValuation. UnpublishedworkingpaperNewYorkUniversity–DepartmentofFinance,NewYork,USA. Duffhues,P.J.W.,1997. Ondernemingsfinanciering en vermogensmarkten 2 ,SecondEdition. Groningen:WoltersNoordhoff.

MasterThesisSebastianOotjers 106 s0041823 IEMFEM ABCD Ehrhardt,M.C.,Daves,P.R.,1999.TheAdjustedPresentValue:TheCombinedImpactof GrowthandtheTaxShieldofDebtontheCostofCapitalandSystematicRisk. UnpublishedworkingpaperUniversityofTennessee,Tennessee,USA. Fama,E.F.,French,K.R.,2002.TestingTradeOffandPeckingOrderPredictionsabout DividendsandDebt.The Review of Financial Studies 15, pp.133. Fang,M.,Zhong,R.,2004.DefaultRisk,Firm’sCharacteristics,andRiskShifting.YaleICF WorkingPaperNo0421,YaleUniversity,NewHaven,USA. Fernández,P.,2004.TheValueofTaxShieldsisNOTEqualtothePresentValueofTax Shields.Journal of Financial Economics 73 ,pp.145165. Frank,M.Z.,Goyal,V.K.,2003a.CapitalStructureDecisions.Unpublishedworkingpaper UniversityofBritishColumbia,Vancouver,Canada. Frank,M.Z.,Goyal,V.K.,2003b.TestingthePeckingOrderTheoryofCapitalStructure. Journal of Financial Economics 67 ,pp217248. Graham,J.R.,1996.DebtandtheMarginalTaxRate. Journal of Financial Economics 41 ,pp. 4173. Hamada,R.S.,1972.TheEffectoftheFirm’sCapitalStructureontheSystematicRiskof CommonStocks.The Journal of Finance 27 ,pp.435452. Hovakimian,A.,Opler,T.,Titman,S.,2001.TheDebtEquityChoice. The Journal of Financial and Quantitative Analysis 36 ,pp.124. Gray,S.,Mirkovic,A.,Ragunathan,V.,2005.TheDeterminantsofCreditRatings:Australian Evidence. Australian Journal of Management 31 ,pp.333354. Kaplan,S.N.,Ruback,R.S,1995.TheValuationofCashFlowForecasts:AnEmpirical Analysis.The Journal of Finance 50 ,pp.10591093. Koller,T.,Wessels,D.,Goedhart,M.,2005. Measuring and Managing the Value of Companies ,FourthEdition,NewYork:Wiley. Korajczyk,R.A.,Levy,A.,2003.CapitalStructureChoice:MacroeconomicConditionsand FinancialConstraints.Journal of Financial Economics 68 ,pp.75109. Krahnen,J.P.,Weber,M.,2001.GenerallyAcceptedRatingPrinciples:APrimer.The Journal of Banking and Finance 25 ,pp.323. Kruschwitz,L.,Löffler,A.,1998.WACC,APV,andFTErevisited.Unpublishedworkingpaper FreieUniversitätBerlin,Berlin,Germany. Lemmon,M.L.,Zender,J.F.,2004.DebtCapacityandTestsofCapitalStructureTheories. UnpublishedworkingpaperUniversityofUtah,SaltLakeCity,USA. Merton,R.,1974.Onthepricingofcorporatedebt:TheRiskStructureofInterestRates. Journal of Finance 28 ,pp.449470. Miles,J.A.,Ezzell,J.R.,1980.TheWeightedAverageCostofCapital,PerfectCapital Markets,andProjectLife:AClarification.The Journal of Finance and Quantitative Analysis 15 ,pp.719730. Miles,J.A.,Ezzell,J.R.,1985.ReformulatingTaxShieldValuation:ANote.The Journal of Finance 40 ,pp.14851492.

MasterThesisSebastianOotjers 107 s0041823 IEMFEM ABCD Modigliani,F.,Miller,M.H.,1958.TheCostofCapital,CorporationFinanceandtheTheoryof Investment.The American Economic Review 48 ,pp.261297. Modigliani,F.,Miller,M.H.,1963.CorporateIncomeTaxesandtheCostofCapital:A Correction.The American Economic Review 53 ,pp.433443. Myers,S.C.,1977.DeterminantsofCorporateBorrowing. Journal of Financial Economics 5 , pp.147175. Myers,S.C.,1984.TheCapitalStructurePuzzle. The Journal of Finance 39 ,pp.575592. Myers,S.C.,2001.CapitalStructure. The Journal of Economic Perspectives 15 ,pp.81102. Ohlson,J.A.,1980.FinancialRatiosandtheProbabilisticPredictionofBankruptcy.Journal of Accounting Research 18 ,pp.109131. Pindado,J.,Rodrigues,L.,2005.DeterminantsofFinancialDistress.Financial Markets and Portfolio Management 19 ,pp.343359. ShyamSunder,L.,Myers,S.C.,1999.TestingStaticTradeoffagainstPeckingOrderModels ofCapitalStructure. The Journal of Financial Economics 51 ,pp.219244. Warner,J.,1977.BankruptcyCost:SomeEvidence, The Journal of Finance 32 ,pp.337347. Weiss,L.A.,1990.BankruptcyResolution:DirectCostsandViolationofPriorityofClaims. Journal of Financial Economics 27 ,pp.285314. Wruck,K.H.,1990.FinancialDistress,Reorganization,andOrganizationalEfficiency.Journal of Financial Economics 27 ,pp.419444.

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Appendix I: Decision tree

yes yes Constantleverageratio? SignificantPoD? APV(ME)

no no

yes DCFor Fixedamountofdebt? APV(MM) APV(ME)

no

yes Finitelife&debtknown? APV(general)

no

Debtknownuptot,then yes APV(general) constantleverageratio? +APV(ME)

no

APV&DCF notsuitedfor thissituation

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Appendix II: Valuation tool

Introduction Thepurposeofthisappendixistotranslatethetheoriesfoundinchapter3intoapracticaltool thatcanbeusedtovaluecompaniesonthebasisofboththeenterpriseDCFmodelandthe APVmodel.Thefirstparagraphwillfocusonthestructureofthetool,whichhastheformatof aMicrosoftExcelworkbook.ThetoolwasprovidedbyKPMGandalreadycontainedthe functionalitytovalueacompanyonthebasisoftheenterpriseDCFmodel.Thesecond paragraphcommentsonthespecificadjustmentandadditionsthatweremadetoincludethe functionalityoftheAPVmodel.Thelastparagraphdiscussesanexampleofacompany valuationthroughtheuseofthetool. II.1 Model assumptions Themodelconsistsofthirteenworksheets: 1. Mainassumptions 2. AbsPrognose 3. Prognose% 4. WACC 5. UnleveredCoE 6. Probabilityofdefault 7. CoCo 8. CoTrans 9. Outcomes 10. Graph 11. Sensitivity(WACC) 12.Sensitivity(APV) 13. Summary TherelationbetweentheworksheetsisdescribedinAppendixIII. II.1.1 General guidelines Thegreycoloredcellsareinputcellsandtheusershouldsettheirvalue.Thewhitecolored cellsareoutputcells;theseshouldnotbechangedsincetherevalueislinkedtoothercells. II.1.2 The input sheets Inthe'mainassumptions'sheet,themainassumptionsthatwillbeusedinalltheothersheets canbeselected.Mostoftheaspectsareobviousanddonotneedanyexplanation.Thelast fourmightrequiresomeexplanation,thereforethefollowingcomments: - Financialfiguretypes:theusercanchoosewhethertheabsoluteforecastsortherelative forecastsshouldbeusedinthevaluation. - Networkingcapital:therearethreeoptionsforthecalculationofthenetworkingcapital. Thedecisionforeitheroneofthemisamatteroftheuser'spreference. - Capitalstructure:ifthecompanyundervaluationisexpectedtomaintainafixedamount ofdebt,thenthefirstoptionshouldbeselected.Ifthecompanyundervaluationis expectedtomaintainaconstantleverageratio,thenthesecondoptionshouldbe selected.ThechoiceforeithertheMiller&ModiglianiortheMiles&Ezzellassumption hasitsimpactonthevaluationoutcomedeterminedbytheAPVmodelpartofthetool. - Costsoffinancialdistress:asdiscussedinchapter3,theestimateforthecostsof financialdistressis15%oftheunleveredcompanyvalue.Iftheuserhasareasonto believethatthisvalueisincorrect,thenthecostsoffinancialdistresscanbechangedto thedesiredvalue. The‘CoCo’sheetisthesecondinputsheet.Theuserissupposedtoinsertthedatafromthe peergroupofthecompanyundervaluationtoacquirethetargetdebt/equityratioandthe unleveredbeta.

MasterThesisSebastianOotjers 110 s0041823 IEMFEM ABCD The‘CoTrans’sheetisthelastinputsheet,inwhichtheusercanenteranyavailable transactiondatafromrelevanttransaction.Thesedataserveasinputforthetransaction multiples. II.1.3 The processing sheets Thesesheetsaretheonesthatimplementthetheoriesfromchapter3.Basedonthe assumptionsmadeinthefirstsheets('mainassumptions'),theappropriatevaluationmodelis usedtodeterminethevaluationoutcome. The'AbsPrognose'sheetandthe'Prognose%sheetarethesheetsthatcalculatethecash flowsbasedonthefinancialdataofthecompany.The'AbsPrognose'sheetcanbestbeused ifthecompanyundervaluationhasprovidedforecastsinabsolutevalues.Thesecanbe insertedattheassignedlocations(greycoloredcells).Incaseoffinancialdataintheformof percentages,the'Prognose%'sheetshouldbeused. Eachofthesetwosheetshasthesamestructure.Mostofthesectionsofthesheetsspeakfor themselves.Greycoloredcellsshouldbeusedtoinsertdatafromthefinancialstatement(s) ofthecompany. TheDCFanalysisderivesthefreecashflowthroughtheuseofNOPLAT.Thisdiffersfrom thedefinitiondiscussedinchapter3,butsincetheAPVanalysisisbasedonthesamefree cashflowsandsincetheNOPLATdefinitiondiffersonlymarginallyfromthedefinitionin chapter4,usingfreecashflowdeterminedthroughNOPLATdoesnotsignificantlyaffectthe valuationoutcome. ThediscountfactorusedintheDCFanalysisistheWACC.ThefreecashflowsintheAPV analysisarediscountedattheunleveredcostofequity.Theinteresttaxshieldsare discountedattheunleveredcostofequityiftheMiles&Ezzellassumptionisselectedandat thecostofdebtiftheMiller&Modiglianiassumptionisselected.However,thefirstinterest taxshieldisalwaysdiscountedatthecostofdebt. ThecostsoffinancialdistressintheAPVanalysisaredeterminedthroughthemultiplicationof thecostsoffinancialdistresstimestheprobabilityofdefaulttimestheunleveredcompany value. The'Probabilityofdefault'sheettakesinputvariablesfromeitherthe'AbsPrognose'sheetor fromthe'Prognose%'sheetdependingontheassumptionselected.Theprobabilityofdefault isdeterminedonthebasisofthecreditratingofthecompany.Intheabsenceofacredit rating,theAltmanZscore(asdiscussedinparagraph3.4)isusedtodeterminethe probabilityofdefault. The'UnleveredCoE'sheetdeterminestheunleveredcostofequitybasedonthechosen capitalstructureassumption.ThedifferencebetweentheMillerModiglianiandMilesEzzell determinationoftheunleveredcostofequityoccursthroughthedifferenceintheunlevered beta.Theunleveredbetaisretrievedfromthe'CoC'sheet.Theuserissupposedtoinsertthe desiredriskfreerate,marketriskpremium,additionalriskpremiumandspread. The'WACC'sheetisthelastprocessingsheet.TheWACCiscalculatedonthebasisofthe costofequityandtheaftertaxcostofdebt.Theuserissupposedtoinserttherequired inputs,therebymakingsurethattheseinputsareconsistentwiththeinputsinthe'Unlevered CoE'sheet. II.1.4 The output sheets Thefirstoutputsheet,the'Outcomes'sheet,determinesthemarketmultiplesandtransaction multiplesbasedontheinputsinthe'CoCo'sheetandthe'CoTrans'sheet. The'Graph'sheetcanbeusedtoacquireagraphofthekeyfinancialsofthecompany. The'Sensitivity(WACC)'sheetandthe'Sensitivity(APV)'sheetusesaduplicatedoverview ofrespectivelytheDCFanalysisandtheAPVanalysistodeterminethesensitivitywithregard torespectivelythelongtermEBITmargin/WACCandthelongtermEBITmargin/unlevered costofequity.Anintervalof2%istakenforeachparametertotestitssensitivity.

MasterThesisSebastianOotjers 111 s0041823 IEMFEM ABCD The'Summary'sheetisthefinalsheetoftheMicrosoftExceltool.Thesheetshowsthe valuesfoundthrougheachofthefourvaluationmodels.Theintervalsarebasedonthe sensitivityanalyses. II.2 Comments on the model TheenterpriseDCFpartoftheMicrosoftExceltoolwasprovidedbyKPMG.TheAPVmodel isbuiltintothetoolthroughanumberofadditionaladjustmentsandassumptions.AppendixV containsalistofalltheadjustmentthatwheremadetotheoriginalMicrosoftExceltool.This appendixcanbeusedtofurtherexpandthetool. II.3 Example ThisparagraphdiscussesanexampleoftheapplicationoftheMicrosoftExceltooltoillustrate itsfunctioning.AlltheEuroamountsmentionedinthisparagraphareinthousandsofEuros. Thescenariothatisimplementedisscenario1fromparagraph3.4:thecompanyisassumed tomaintainaconstantleverageratioandtheprobabilityofdefaultisassumedtobenot significant. ThefinancialdatafromCompanyXarenotbasedonarealcompany.Mostofthe componentsoftheprofitandlossaccountaremodeledinsuchawaythattheyrepresenta yearlygrowthof2.0%.Nexttothat,theamountofdebtoutstandingisbeingadjustedateach periodtomaintainaconstantmarketleverageratioof17%(debt/totalcapital).Thelongterm taxrateisassumedtobe25,5%andthecostsoffinancialdistressare15%oftheunlevered companyvalue.Thecompanyisalsoassumedtohavealeveredbetaof1,0. Thefirststepinthevaluationprocessisselectingthepeergroup.Sincethecompanyunder valuationisafictitiouscompany,noexistingcompaniesareusedinthepeergroup.Tomake surethatthebetaanalysisshowsaleveredbetaof1,0andaD/Eratioof20,4%(which correspondstotheleverageratioof17%),thepeergroupcompaniesaregivenexactlythe samespecificsasthecompanyundervaluation.Thisresultsinthefollowing. Company X - beta analysis

Tax Levered Unlevered Unlevered Country D/E rate beta beta (MM) beta (ME)

CompanyA NL 20,4% 25,5% 1,00 0,87 0,83 CompanyB NL 20,4% 25,5% 1,00 0,87 0,83 CompanyC NL 20,4% 25,5% 1,00 0,87 0,83 CompanyD NL 20,4% 25,5% 1,00 0,87 0,83 CompanyE NL 20,4% 25,5% 1,00 0,87 0,83

Average 20,44% 25,50% 1,00 0,87 0,83 Median 20,44% 25,50% 1,00 0,87 0,83 Thesecondstepistoestimateandforecastthefinancialdatainthe‘AbsPrognose’sheet andthe‘Prognose%’sheet.TheestimateddataareshownintableII.1(profit&loss account),tableII.2(networkingcapitaloverview),tableII.3(balancesheet–assetsoverview) andtableII.4(balancesheets–liabilitiesoverview).Thegreycoloredcellsaretheinputcells inwhichfinancialdataretrievedfromthefinancialstatement(s)ofthecompanyshouldbe inserted.Inthiscase,thevaluesarechoseninawaythatthesalesgrowat2,0%ayear,the grossmargininstableat50%andtwothirdsofthenetprofitsarepaidoutasdividends.The amountofbankloansoutstandingischosenateachpointintimesuchthatthemarket leverageratioremainsconstant.

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Company X - profit and loss statement EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Net sales 15.000 15.300 15.606 15.918 16.236 16.561 16.892 17.230 17.575 17.926 18.285 18.650 % growth 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0% 2,0%

Directcost1 (7.500) (7.650) (7.803) (7.959) (8.118) (8.281) (8.446) (8.615) (8.787) (8.963) (9.142) (9.325) Totaldirectcosts (7.500) (7.650) (7.803) (7.959) (8.118) (8.281) (8.446) (8.615) (8.787) (8.963) (9.142) (9.325)

Gross profit 7.500 7.650 7.803 7.959 8.118 8.281 8.446 8.615 8.787 8.963 9.142 9.325 % of sales 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0% 50,0%

Operatingcost1 (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.080) Otheroperatingcosts Totaloperationalcosts (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.000) (4.080) % of sales -26,7% -26,1% -25,6% -25,1% -24,6% -24,2% -23,7% -23,2% -22,8% -22,3% -21,9% -21,9%

EBITDA 3.500 3.650 3.803 3.959 4.118 4.281 4.446 4.615 4.787 4.963 5.142 5.245 % of sales 23,3% 23,9% 24,4% 24,9% 25,4% 25,8% 26,3% 26,8% 27,2% 27,7% 28,1% 28,1%

Depreciation (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.000) (1.020) EBITA 2.500 2.650 2.803 2.959 3.118 3.281 3.446 3.615 3.787 3.963 4.142 4.225 % of sales 16,7% 17,3% 18,0% 18,6% 19,2% 19,8% 20,4% 21,0% 21,6% 22,1% 22,7% 22,7%

Nontaxdeductibleamortisation (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (204) Taxdeductibleamortisation (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (255) EBIT 2.050 2.200 2.353 2.509 2.668 2.831 2.996 3.165 3.337 3.513 3.692 3.766 % of sales 13,7% 14,4% 15,1% 15,8% 16,4% 17,1% 17,7% 18,4% 19,0% 19,6% 20,2% 20,2%

Interestondebt (245) (245) (283) (267) (304) (322) (341) (359) (378) (396) (415) (433) Interestoncash Profit before tax 1.805 1.955 2.070 2.242 2.364 2.508 2.656 2.806 2.959 3.117 3.278 3.333

Incometax (692) (743) (715) (723) (654) (691) (728) (767) (806) (846) (887) (902) Net profit 1.113 1.212 1.355 1.519 1.710 1.818 1.927 2.040 2.154 2.271 2.391 2.431 % of sales 7,4% 7,9% 8,7% 9,5% 10,5% 11,0% 11,4% 11,8% 12,3% 12,7% 13,1% 13,0%

Dividendpayments (742) (808) (903) (1.013) (1.140) (1.212) (1.285) (1.360) (1.436) (1.514) (1.594) (1.621) Retained earnings 371 404 452 506 570 606 642 680 718 757 797 810 Table II.1: Profit & loss statement of Company X

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Company X - net working capital EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Stock(Inventory) 375 383 390 398 406 414 422 431 439 448 457 466 Current assets 375 383 390 398 406 414 422 431 439 448 457 466

Creditors 113 115 118 120 122 124 127 129 132 134 137 140 Taxation&socialsecurity Otherliabilities Accrualsanddeferredincome Total current liabilities 113 115 118 120 122 124 127 129 132 134 137 140

Net working capital 263 268 273 278 284 290 296 302 308 314 320 326 as % of sales 1,8% 1,7% 1,7% 1,7% 1,8% 1,8% 1,8% 1,8% 1,8% 1,8% 1,8% 1,8%

Investments in net working capital 55566666666 Table II.2: Net working capital overview of Company X Company X - Balance sheet - Assets EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Tangible fixed assets 9.000 9.180 9.364 9.551 9.738 9.938 10.138 10.338 10.548 10.758 10.968 10.968

Intangible fixed assets 3.000 3.060 3.121 3.184 3.247 3.310 3.373 3.438 3.507 3.577 3.648 3.712

Financial fixed assets ------

Stock(Inventory) 375 383 390 398 406 414 422 431 439 448 457 466 Debtors Otherreceivables Prepaymentsandaccruedincome Operationalcash Current assets 375 383 390 398 406 414 422 431 439 448 457 466

Excess cash - 707 679 1.466 2.036 2.633 3.270 3.951 4.643 5.380 6.155 6.895

ASSETS 12.375 13.329 13.554 14.599 15.427 16.295 17.203 18.158 19.137 20.163 21.229 22.042 Table II.3: Asset overview of Company X

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Company X - Balance sheet - Equity & Liabilities EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

Sharecapital 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 8.291 Minorityinterests Cumulativeretainedearnings 371 775 1.227 1.733 2.303 2.909 3.551 4.231 4.949 5.706 6.503 Exchangeratedifferences Equityfromchangefinancialfixedassets Changeinequity Retainedearningscurrentyear 371 404 452 506 570 606 642 680 718 757 797 810 Equity 8.662 9.066 9.518 10.024 10.594 11.200 11.842 12.522 13.240 13.997 14.794 15.604

Provision1 100 102 104 106 106 106 106 106 106 106 106 106 Provision2 Provision3 Operating provisions 100 102 104 106 106 106 106 106 106 106 106 106

Bankloans 3.500 4.046 3.815 4.349 4.605 4.865 5.128 5.400 5.659 5.925 6.191 6.191 Bonds Otherlongterminterestbearingdebt Long-term liabilities 3.500 4.046 3.815 4.349 4.605 4.865 5.128 5.400 5.659 5.925 6.191 6.191

Preferredequity Longtermoperatingprovisions Nonoperatingprovisions Debt equivalents ------

Creditinstitutions Creditors 113 115 118 120 122 124 127 129 132 134 137 140 Taxation&socialsecurity Otherliabilities Accrualsanddeferredincome Current liabilities 113 115 118 120 122 124 127 129 132 134 137 140

EQUITY & LIABILITIES 12.375 13.329 13.554 14.599 15.427 16.295 17.203 18.157 19.137 20.162 21.228 22.041 Table II.4: Equity & liabilities overview of Company X

MasterThesisSebastianOotjers 115 s0041823 IEMFEM ABCD Thethirdstepistodeterminetheprobabilityofdefault,theunleveredcostofequityandthe weightedaveragecostofcapital(WACC).Theprobabilityofdefaultcanbedeterminedby enteringthecreditratingofthecompany.Sincethefictitiouscompanydoesnothaveacredit rating,choosingthisoptioninthedropdownmenuleadstoanestimationoftheprobabilityof defaultonthebasisoftheAltmanZscore.Theestimationoftheprobabilityofdefaultis showninthetablebelow. Company X - Probability of default

Companytype 1Public Creditrating norating Zscore used

Estimated probability of default 0,06%

Input variables current year Workingcapital 278 Retainedearnings 506 EBIT 2.509 Marketvalueofequity 21.418 Bookvalueofequity 10.024 NetSales 15.918 Bookvalueofdebt 4.575 Totalassets 14.599

Z-score 4,54

TheestimationoftheunleveredcostofequityislinkedtotheMiles&Ezzellassumptionofthe constantleverageratio.Thedatafromthefollowingtablearethereforeusedinthefurther calculationsofthecompanyvalue. Company X - Unlevered cost of equity (ME)

Riskfreerate 4,0% Riskfreerate 4,0% Marketriskpremium 5,0% Spread 3,0% Additionalriskpremium 3,0% Taxrate 25,5% Unleveredbetapeergroup 0,83

Unlevered cost of equity 11,2% Cost of debt 7,0% After-tax cost of debt 5,2% D/E 20% E/(E+D) 83% TheinputfortheWACCispracticallythesameasfortheunleveredcostofequity.Thegrey coloredcellsaretheinputcells.Thetaxrateisretrievedfromthe‘Mainassumptions’sheet andthebetafromthe‘CoCo’sheet.ThecalculationoftheWACClooksasfollows. Company X - Weighted Average Cost of Capital

Riskfreerate 4,0% Riskfreerate 4,0% Marketriskpremium 5,0% Spread 3,0% Additionalriskpremium 3,0% Taxrate 25,5% Unleveredbetapeergroup 0,83 D/E 20% Leveredbeta 1,00

Cost of equity 12,0% After-tax cost of debt 5,2%

E/(E+D) 83% D/(E+D) 17%

WACC 10,8% Afterinsertingalltheinputvaluesintheinputsheets,thevaluationoutcomethroughboththe enterpriseDCFmodelandtheAPVmodelisdetermined.Thefreecashflowsaredetermined asdefinedbyKoller et al. (2005):

MasterThesisSebastianOotjers 116 s0041823 IEMFEM ABCD FCF=NOPLAT+NoncashOperatingExpenses–InvestmentsinInvestedCapital ThisresultsintheDCFanalysisshownintableII.5andtheAPVanalysisshownintableII.6. Thecompanyisalsovaluedthroughtheuseofthedeterminedmarketmultiplesand transactionmultiples.AsensitivityanalysisisperformedforboththeDCFanalysisandthe APVanalysis.ThisisdonefortheDCFanalysisbytakinganintervalfortheWACCof9,8% 11,8%andanintervalforthelongtermEBITmarginof19,2%21,2%.FortheAPVanalysis, anintervalfortheunleveredcostofequityistakenof10,2%12,2%andanintervalforthe longtermEBITmargin(thesameasfortheDCFanalysis)of19,2%21,2%. Combiningtheresultsofthesensitivityanalysisintoanoverviewofthevaluationoutcomes underthefourdifferentvaluationapproachesgivesthefollowingchartsfortheshareholder valueandtheenterprisevalue. (EURm)

APVmodel 20,5 22,4

DCFmodel 20,3 22,3

Marketmultiples 21,3 21,9

Transaction 17,9 23,0 multiples

,0 10,0 20,0 30,0 40,0 50,0

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Company X - DCF analysis EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

EBITA 2.500 2.650 2.803 2.959 3.118 3.281 3.446 3.615 3.787 3.963 4.142 4.225 Nontaxdeductibleamortisation (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (204) Taxdeductibleamortisation (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (255) EBIT 2.050 2.200 2.353 2.509 2.668 2.831 2.996 3.165 3.337 3.513 3.692 3.766

Operationaltaxes (776) (828) (804) (802) (731) (773) (815) (858) (902) (947) (993) (1.012) NOPLAT 1.274 1.372 1.549 1.707 1.937 2.058 2.181 2.307 2.435 2.566 2.700 2.754 % growth 10,2% 13,4% 6,2% 6,0% 5,8% 5,6% 5,4% 5,2% 2,0%

Changeinprovisions 2 2 2 Amortisation 450 450 450 450 450 450 450 450 450 450 450 459 Depreciation 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.020 Operational cash flow 2.724 2.824 3.001 3.159 3.387 3.508 3.631 3.757 3.885 4.016 4.150 4.233

Bookvalueofdisposaloffixedassets Capitalgainondisposaloffixedassets(netoftax) Investmentstangiblefixedassets (1.187) (1.200) (1.200) (1.200) (1.210) (1.210) (1.210) (1.020) Investmentintangiblefixedassets (513) (513) (513) (515) (519) (520) (521) (523) Investmentsinnetworkingcapital (6) (6) (6) (6) (6) (6) (6) (6) Free cash flow 1.681 1.789 1.912 2.036 2.150 2.280 2.413 2.683

Terminaladjustmentfactor 1,000 1,000 1,000 1,000 1,000 1,000 1,000 11,301 Timetocashflow 1,000 2,000 3,000 4,000 5,000 6,000 7,000 7,000 Discountfactor:10,8% 0,902 0,814 0,734 0,662 0,598 0,539 0,486 0,486 Present value operational free cash flow 1.516 1.456 1.404 1.349 1.285 1.229 1.173 14.747

Value of operations 24.159 Nonconsolidatedsubsidiaries Deferredtaxassets Otherfinancialfixedassets1 Otherfinancialfixedassets2 Taxlossescarryforwards Excesscash 1.466 (EV) 25.626 Ratio Value Debt Totalnonequityclaims (4.349) ImpliedD/E 20,44% 4.349 Shareholder value (SV) 21.277 ImpliedD/V 16,971% 4.349

Implied multiples EV/Sales 1,6x 1,5x 1,5x 1,5x 1,5x 1,4x 1,4x EV/EBITDA 6,2x 6,0x 5,8x 5,6x 5,4x 5,2x 5,0x EV/EBITA 8,2x 7,8x 7,4x 7,1x 6,8x 6,5x 6,2x SV/Netprofit 12,4x 11,7x 11,0x 10,4x 9,9x 9,4x 8,9x Table II.5: DCF analysis of Company X

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Company X - APV analysis - ME EUR '000 2003-A 2004-A 2005-A 2006-A 2007-F 2008-F 2009-F 2010-F 2011-F 2012-F 2013-F RV

EBITA 2.500 2.650 2.803 2.959 3.118 3.281 3.446 3.615 3.787 3.963 4.142 4.225 Nontaxdeductibleamortisation (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (200) (204) Taxdeductibleamortisation (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (250) (255) EBIT 2.050 2.200 2.353 2.509 2.668 2.831 2.996 3.165 3.337 3.513 3.692 3.766

NOPLAT 1.274 1.372 1.549 1.707 1.937 2.058 2.181 2.307 2.435 2.566 2.700 2.754 % growth 10,2% 13,4% 6,2% 6,0% 5,8% 5,6% 5,4% 5,2% 2,0%

Operational cash flow 2.724 2.824 3.001 3.159 3.387 3.508 3.631 3.757 3.885 4.016 4.150 4.233

Free cash flow 1.681 1.789 1.912 2.036 2.150 2.280 2.413 2.683

Terminaladjustmentfactor 1,000 1,000 1,000 1,000 1,000 1,000 1,000 10,927 Timetocashflow 1,000 2,000 3,000 4,000 5,000 6,000 7,000 7,000 Discountfactor:11,2% 0,900 0,809 0,728 0,655 0,589 0,530 0,477 0,477 Present value operational free cash flow 1.512 1.448 1.393 1.334 1.267 1.209 1.151 13.989

Value of operations 23.303

Interestondebttaxshield 78 82 87 92 96 101 106 111 Interestoncashtaxshield Interest tax shield 78 82 87 92 96 101 106 111

Terminaladjustmentfactor,assumedgrowth:2,0% 1,000 1,000 1,000 1,000 1,000 1,000 1,000 10,927 Timetocashflow 1,000 2,000 3,000 4,000 5,000 6,000 7,000 7,000 Discountfactor:11,2% 0,935 0,809 0,728 0,655 0,589 0,530 0,477 0,477 Present value interest tax shield 73 67 63 60 57 54 50 576

Value of interest tax shields 999 Value of operations 23.303 Costs of financial distress (2) Excesscash 1.466 Enterprise value (EV) 25.767 APVDCF 0,55% Totalnonequityclaims (4.349) Shareholder value (SV) 21.418

Implied multiples EV/Sales 1,6x 1,6x 1,5x 1,5x 1,5x 1,4x 1,4x EV/EBITDA 6,3x 6,0x 5,8x 5,6x 5,4x 5,2x 5,0x EV/EBITA 8,3x 7,9x 7,5x 7,1x 6,8x 6,5x 6,2x SV/Netprofit 12,5x 11,8x 11,1x 10,5x 9,9x 9,4x 9,0x Table II.6: APV analysis of Company X

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APVmodel 24,8 26,8

DCFmodel 24,6 26,7

Marketmultiples 25,9 26,2

Transaction 22,2 27,4 multiples

,0 10,0 20,0 30,0 40,0 50,0

ThefinalresultofthevaluationexampleisthattheenterprisevaluefoundundertheAPV modelis25.767EURand25.626EURundertheenterpriseDCFmodel. Thedifferencebetweenthetwovaluationoutcomesis0,55%ofthevaluefoundunderthe enterpriseDCFmodel.Accordingtothetheorystatedinparagraph3.4,thereshouldnotbea differencebetweenthevaluationoutcomesofbothmethods.Consideringtheassumptions thathadtobemaderegarding,forinstance,theprobabilityofdefault,therelationbetweenthe amountofdebtoutstandingandthefreecashflowsthatarerealized,itcanbeconcludedthat theAPVmodel,asimplementedintheMicrosoftExceltool,correctlyrepresentsthetheoryof theAPVmodelasstatedinchapter3. Conclusion Inthisappendix,thetheoriesformulatedinchapter3aretranslatedintoapracticaltoolforthe valuationofcompaniesintheformofaMicrosoftExcelworkbook.Theexamplediscussed showstheworkingofthetoolandalsoindicatesthattheresultsfoundthroughtheuseofthe practicaltoolmatchthevaluationoutcomepredictedbythetheoryinchapter3incaseof scenario1. Thenextchapterisconcernedwiththevalidationofthetheoriesstatedinchapter3onthe effectofthedifferencesbetweentheenterpriseDCFmodelandtheAPVmodelthroughthe implementationofdifferentscenarios.Amongthesescenariosarethescenariosdiscussedin chapter3.

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Appendix III: Relations between tool worksheets

Summary Graph

Outcomes SensitivityAPV SensitivityWACC

CoCo AbsPrognose

CoTrans Prognose % UnleveredCoE

PoD

WACC

Mainassumptions

MasterThesisSebastianOotjers 121 s0041823 IEMFEM ABCD

Appendix IV: Comments on valuation tool

Sheet(s):Mainassumptions Added: 1. CapitalStructure–Dropdownlist.Goal:toallowforthechoicebetweentheMMand MEassumption 2. Costoffinancialdistress–Inputvariablesthatisusedtodeterminethepresentvalue ofthecostsoffinancialdistress,displayedasthepercentageofunleveredcompany value. Sheet(s):AbsPrognose&Prognose% Added: 1. APVanalysis a. UptoFreeCashFlowsthesameasDCFanalysis b. Discountfactor(B442)=thecorrectdiscountratebasedonthecapital structureassumption. c. Taxshieldsarebasedontheinterestpaid/receivedandthetaxrate(row447 &448). d. Taxshieldgrowthrate(B451)=thecorrectgrowthratebasedonthecapital structureassumption. e. Discountfactor(B454)=thecorrectdiscountratebasedonthecapital structureassumption.However,thefirstinteresttaxshieldisalways discountedatthecostofdebt,becauseitisknownattime=0.Theperpetuity iscaseoftheMEscenarioisnotmultipliedbythecorrectionfactor,sincethis wouldcreateadoubleeffect.Thisisadeviationfromthemodeldescribedin thetheory. f. Costsoffinancialdistress=themultiplicationofthecostsoffinancialdistress andtheprobabilityofdefault. Sheet(s):UnleveredCoE(Costofequity)(=newsheet) Added: 1. Unleveredcostofequity(MM) a. Unleveredbeta(MM)(C9)isusedasaninputinCAPMtodeterminethe unleveredcostofequity. 2. Unleveredcostofequity(ME) a. Unleveredbeta(ME)(I9)isusedasaninputinCAPMtodeterminethe unleveredcostofequity. 3. Unleveredcostofequity,showthecurrentassumptionandthecurrentunleveredcost ofequity. Sheet(s):Probabilityofdefault(=newsheet) Added: 1. Inputcells a. Companytype(C6)toindicatewhetherthecompanyundervaluationisa publicorprivatecompany. b. Creditrating(C7),whereonecanenterthecreditratingofthecompanythat wasdeterminedbyacreditratingagency. 2. InputvariablesZscore(C13C20).Cellsareusedtocalculatethezscore(C22). 3. Estimatedprobabilityofdefault(C10),basedoneitherthecreditratingor,inabsence ofarating,onthezscore.CellC8showswhetherthezscoreisusedfordetermining theprobabilityofdefault. Sheet(s):CoC Added: 1. Unleveredbeta(MM)(ColumnBR),basedontheunleveringformulaofModigliani& Miller. 2. Unleveredbeta(ME)(ColumnBS),basedontheunleveringformulaofMiles& Ezzell.

MasterThesisSebastianOotjers 122 s0041823 IEMFEM ABCD Sheet(s):Sensitivity(APV)(=newsheet) Added: 1. APVanalysis,basedonthechosenSELECTOR(whichisthetypeoffinancial figures,statedinMainAssumptions!.D19. 2. Sensitivityanalysisbasedonchangesintheunleveredcostofequityandthelong termEBITmargin. Sheet(s):Summary Added: 1. An‘APVmethod’seriesinthechartsoftheshareholdervalueandtheenterprise value.

MasterThesisSebastianOotjers 123 s0041823 IEMFEM ABCD

Word of thanks

Thisresearchprojecthasbeenrealizedwiththehelpofseveralpeople.Eachofthemhas contributedtothefinalresultand/orotheractivitiesthatarerelatedtothecompletionofmy masterIndustrialEngineering&Management. Firstofall,IwouldliketothankJeroenWeimer&FrankSibleszfortheirsupportand supervision,feedbackandquestions. Second,IwouldliketothankHenkKroonforhissupervision,hisflexibilityandhispractical pointofview. Third,IwouldliketothankJanBilderbeekforhisassistancewithmyexplorationofthe corporatefinanceworldandforbeingthesecondcorrectorofthisresearchreport. Andlast,butcertainlynotleast,IwouldliketothankRickertIwema,FrisoStofferandJohan Lommersfortheireffortsduringthepastyearsonalltheassignmentandprojectsthatwe completedtogether.

MasterThesisSebastianOotjers 124 s0041823 IEMFEM