Financial-Rations-discriminate-Analysis-and-the-Pr

TheJournalofFINANCEVOL.XXIIISEPTEMBER1968No.4FINANCIALRATIOS,DISCRIMINANTANALYSISANDTHEPREDICTIONOFCORPORATEBANKRUPTCYEDWARDI.ALTMAN*ACADEMICIANSSEEMtobemovingtowardtheeliminationofratioanalysisasananalyticaltechniqueinassessingtheperformanceofthebusinessenterprise.Theoristsdowngradearbitraryrulesofthumb,suchascompanyratiocompari­sons,widelyusedbypractitioners.Sinceattacksontherelevanceofratioanalysisemanatefrommanyesteemedmembersofthescholarlyworld,doesthismeanthatratioanalysisislimitedtotheworldofnutsandbolts?Or,hasthesignificanceofsuchanapproachbeenunattractivelygarbedandthere­foreunfairlyhandicapped?Canwebridgethegap,ratherthanseverthelink,betweentraditionalratioanalysisandthemorerigorousstatisticaltech­niqueswhichhavebecomepopularamongacademiciansinrecentyears?Thepurposeofthispaperistoattemptanassessmentofthisissue-thequalityofratioanalysisasananalyticaltechnique.Thepredictionofcorporatebankruptcyisusedasanillustrativecase.'Specifically,asetoffinancialandeconomicratioswillbeinvestigatedinabankruptcypredictioncontextwhereinamultiplediscriminantstatisticalmethodologyisemployed.Thedatausedinthestudyarelimitedtomanufacturingcorporations.Abriefreviewofthedevelopmentoftraditionalratioanalysisasatechniqueforinvestigatingcorporateperformanceispresentedinsection1.InsectionIItheshortcomingsofthisapproacharediscussedandmultiplediscriminantanal­ysisisintroducedwiththeemphasiscenteringonitscompatibilitywithratioanalysisinabankruptcypredictioncontext.Thediscriminantmodelisdevel­opedinsectionIII,whereaninitialsampleofsixty-sixfirmsisutilizedtoestablishafunctionwhichbestdiscriminatesbetweencompaniesintwomutu­allyexclusivegroups:bankruptandnon-bankruptfirms.SectionIVreviewsempiricalresultsobtainedfromtheinitialsampleandseveralsecondarysam­ples,thelatterbeingselectedtoexaminethereliabilityofthediscriminant*AssistantProfessorofFinance,NewYorkUniversity.TheauthoracknowledgesthehelpfulsuggestionsandcommentsofKeithV.Smith,EdwardF.Renshaw,LawrenceS.RitterandtheJournal'sreviewer.TheresearchwasconductedwhileunderaRegentsFellowshipattheUniversityofCalifornia,LosAngeles.1.Inthisstudythetermbankruptcywill,exceptwhereotherwisenoted,refertothosefirmsthatarelegallybankruptandeitherplacedinreceivershiporhavebeengrantedtherighttore­organizeundertheprovisionsoftheNationalBankruptcyAct.589590TheJournalofFinancemodelasapredictivetechnique.InsectionVthemodel'sadaptabilitytopracti­caldecision-makingsituationsanditspotentialbenefitsinavarietyofsituationsaresuggested.Thefinalsectionsummarizesthefindingsandconclusionsofthestudy,andassessestheroleandsignificanceoftraditionalratioanalysiswithinamodernanalyticalcontext.1.TRADITIONALRATIOANALYSISThedetectionofcompanyoperatingandfinancialdifficultiesisasubjectwhichhasbeenparticularlysusceptibletofinancialratioanalysis.Priortothedevelopmentofquantitativemeasuresofcompanyperformance,agencieswereestablishedtosupplyaqualitativetypeofinformationassessingthecredit­worthinessofparticularmerchants.'Formalaggregatestudiesconcernedwithportentsofbusinessfailurewereevidentinthe1930's.Astudyatthattimeandseverallateronesconcludedthatfailingfirmsexhibitsignificantlydifferentratiomeasurementsthancontinuingentities.Inaddition,anotherstudywasconcernedwithratiosoflargeasset-sizecorporationsthatexperienceddifficul­tiesinmeetingtheirfixedindebtednessobligations.Arecentstudyinvolvedtheanalysisoffinancialratiosinabankruptcy-predictioncontext.Thislatterworkcomparedalistofratiosindividuallyforfailedfirmsandamatchedsampleofnon-failedfirms.Observedevidenceforfiveyearspriortofailurewascitedasconclusivethatratioanalysiscanbeusefulinthepredictionoffailure.Theaforementionedstudiesimplyadefinitepotentialofratiosaspredictorsofbankruptcy.Ingeneral,ratiosmeasuringprofitability,liquidity,andsolvencyprevailedasthemostsignificantindicators.Theorderoftheirimportanceisnotclearsincealmosteverystudycitedadifferentratioasbeingthemosteffectiveindicationofimpendingproblems.II.MULTIPLEDISCRIMINANTANALYSISTheprevioussectioncitedseveralstudiesdevotedtotheanalysisofafirm'sconditionpriortofinancialdifficulties.Althoughtheseworksestablishedcer­tainimportantgeneralizationsregardingtheperformanceandtrendsofpartic­ularmeasurements,theadaptationoftheirresultsforassessingbankruptcy2.Forinstance,theforerunnerofwellknownDun&Bradstreet,Inc.wasorganizedin1849inCincinnati,Ohio,inordertoprovideindependentcreditinvestigations.Foraninterestingandinformativediscussiononthedevelopmentofcreditagenciesandfinancialmeasuresofcompanyperformancesee,RoyA.Foulke,PracticalFinancialStatementAnalysis,5thEd.,(NewYork,McGraw-Hill,1961).3.R.F.SmithandA.H.Winakor,ChangesintheFinancialStructureofUnsuccessfulCorpora­tions.(UniversityofIllinois:BureauofBusinessResearch,1935).4.Forinstance,acomprehensivestudycoveringover900firmscompareddiscontinuingfirmswithcontinuingones,seeC.Merwin,FinancingSmallCorporations(NewYork:BureauofEco­nomicResearch,1942).5.W.B.Hickman,CorporateBondQualityandInvestorExperience(Princeton,N.J.:PrincetonUniversityPress,1958).6.W.H.Beaver,FinancialRatiosasP