6课外补充Critical Sales.docx

6课外补充Critical Sales.docx

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6课外补充CriticalSales

CriticalPointofSalesandProbabilityofDistress:

AComprehensiveFinancialRiskIndicator

JosephM.Cheng

AssociateProfessor

SchoolofBusiness

IthacaCollege

Ithaca,N.Y.,14850

Email:

Cheng@Ithaca.edu

（607）274-3067

CriticalPointofSales:

AComprehensiveFinancialRiskIndicator

Abstract

Thispaperillustratesthedrawbacksofconventionaldebtratiosandproposestheuseofanalternativefinancialratioformeasuringbankruptcyrisk:

CriticalPointofSales,whichmeasurestheminimumsalesaborrowermusthaveinordertogeneratesufficientamountofcashflowtomeetitsinterestobligations.Inpercentageterms,itmeansthepercentagedropinrevenueaborrowercanwithstandbeforebeingunabletomeetitsdebtobligation.Theratioessentiallycombinesallthefinancialandoperatingleverageratiosintoonewhichlendsitselftobemorereadilyunderstoodbystudents.Thisratioismoreuser-friendlyandisshowntoprovideamorecomprehensiveandmeaningfulpictureonthedegreeoffinancialriskoffirmsthanconventionaldebtratios.Thisnewlyintroducedconcepthasbeentaughtwithgreatsuccessinfinanceclassesanddrawnmuchstudentinterest.

Introduction

Eventhebestfinancestudentslearningaboutfinancialstatementanalysis（andperhapsalsosomefinancialanalysts）oftenmisusethefinancialleverageordebtratiosinassessingthedegreeoffinancialriskoffirms.Theconventionaldebtsratioslendthemselvestobeeasilymisinterpretedbecausethefocusofindividualdebtratiosonfinancialriskisnarrowandthereisnosystematicprocedureforinterpretingallratiossimultaneously.Thispaperdemonstrateshowthetimesinterestearnedratio,forexample,canbemisused,andsetsforthaneasy-to-understandfinancialindicatorwhichprovidesadirect,intuitive,andcomprehensivemeansofassessingdefaultrisk.

Thetimesinterestearnedratio,whichisoperatingincomebeforeinterestandtaxesdividedbyinterestexpense,isadebtcoverageratiocommonlyusedbyfinancialanalysts.Itisintendedtobeusedasameasurefortheabilityoffirmsinpayinginterestwithitsearning.Afirmwithhighertimesinterestearnedratioisgenerallyregardedashavinglowerbankruptcyriskthanafirmwithlowertimesinterestearnedratio;however,thisisaninferentialtrapintowhichmanystudentsandfinancialanalystsfall.Thedrawbackofthisratioasafinancialriskindicatorisdemonstratedinthefollowingillustration.Considertwofirmsofequalsize,FirmAandFirmB.LetusassumethatthevariableoperatingcostofAandBare80%ofrevenueand10%ofrevenue,respectively;andthatthefixedoperatingcostofAandBare$40,000and$530,000,respectively.Iftherevenuesforbothfirmsare$700,000,thentheiroperatingcosts,thesumofvariableandfixedcosts,arecalculatedasfollows:

（1）operatingcost（A）=.8x$700,000+$40,000=$600,000

（2）operatingcost（B）=.1x$700,000+$530,000=$600,000

GiventhattheinterestexpensesforFirmAandFirmBare$50,000and$25,000,respectively,thepartialcurrentincomestatementsforFirmsAandBarepresentedinTable1.

Table1.

CurrentIncomeStatements

FirmAFirmB

Revenue$700,000$700,000

Operatingcost$600,000$600,000

________________

Operatingincome$100,000$100,000

Interest$50,000$25,00

________________

Earningsbeforetaxes$50,000$75,000

Thetimesinterestearnedratioare:

（3）TimesInterestEarned（A）=$100,000/$50,000=2

（4）TimesInterestEarned（B）=$100,000/$25,000=4

Accordingtotheaboveresults,FirmAhasalowertimesinterestearnedratioandthusisgenerallyregardedasbeingmorehighlyleveragedwithdebtthanFirmB.AstudentoranunsophisticatedfinancialanalystisoftenledintothinkingthatFirmAhashigherdefaultriskbyvirtueofalowertimesinterestearnedratio.However,suchcommoninferencemaybeflawed,especiallyinthecasewhereFirmAutilizeslessfixedoperatingcoststhanFirmB.

Supposethatrevenuesofbothfirmsdeclineto$500,000,onemightexpectthatAwouldbemorelikelytohaveproblemmeetingitsinterestpaymentthanB.Toanalyzethisproposition,letusexaminetheirrelativeabilitiestomeetinterestobligationsifrevenuesforbothfirmsdeclinefrom$700,000to$500,000.Basedontheoperatingcostformulae

（1）and

（2）,theoperatingcostforFirmAandFirmBare$440,000and$580,000,respectively,atrevenuelevelof$500,000.

Table2

$500,000RevenueScenario（行动的）方案;剧情概要;分镜头剧本;

FirmAFirmB

Revenue$500,000$500,000

OperatingCost$440,000$580,000

_______________

OperatingIncome（Loss）$60,000（$80,000）

InterestExpense$50,000$25,000

________________

EarningsBeforeTaxes$10,000（$105,000）

NoteinTable2thatFirmAstillhassufficientoperatingincometocoverits$50,000interestexpensewhereasFirmBmighthavetodefault,althoughthelatteroriginallyhasahighertimesinterestearnedratio.Thereasonforthisparadoxisthatdebtratiosdonotreflectthedegreeofoperatingleverage（theextenttowhichfixedoperatingcostisutilized）,whichmeasuresthesensitivityofoperatingincometochangesinrevenueandisakeyfactorindeterminingdefaultrisk.Thismeansthatafirmwithmorefavorabledebtratiosmightactuallyhavegreaterdefaultriskduetoitshighoperatingleverage,asisinthecaseofFirmB.

Inlightofthisdrawbackinusingsuchratios,analternativeindicatorwhichincorporatesbothfinancialandoperatingleveragestoyieldamorecomprehensivemeasureofdefaultriskwouldbedesirable.Tothisend,afinancialindicatorcalledCriticalPointofSales（CPS）isdevised,whichrepresentsthepercentagedeclineinrevenuethatwouldreducecashflowsfromoperationtoanamountjustsufficienttocoverinterestpayment.SinceafirmmightdefaultonitsinterestobligationsifitsrevenueinpercentagetermsdeclinesbyanamountgreaterthantheCSPpercentage,theprobabilityofsalesdecliningbytheCSPpercentageamountisdirectlycorrelatedwiththeprobabilityofdefault.Ascanbeseen,theappealoftheCSPliesinitssimplicityofinterpretationanditsdirectrelationshiptobankruptcyrisk.

DerivationoftheCSPFormula

TheCSPcanbederivedbyfirstsolvingforthecriticallevelofrevenuewherecashflowfromoperationisjustequaltointerestexpense（cashflowsfromoperationcanbewrittenasrevenuelessvariablecostandcashfixedoperatingcosts（CFC））:

（5）revenue-variableoperatingcost-CFC=interest

Variableoperatingcostcanberewrittenasvrevenuewherevrepresentsvariablecostas%ofrevenue.

（6）revenue-vrevenue-CFC=interest

Solvingforthatcriticallevelofrevenue（CR）alone,weget

（7）revenue=CR=（interest+CFC）/（1-v）

Asstated,revenuein（7）representsthecriticallevelofrevenue（CR）wherecashflowsfromoperationequalinterestexpense.CSPisdefinedasthemaximumsalesdropinpercentagetermbeforereachingthatcriticallevel:

（8）CSP=（currentrevenue-CR）/currentrevenue,whichcanberewrittenas

（9）CSP=1-CR/currentrevenue

Substituting（7）intoCRin（9）,weget

（10）CSP=1-（interest+CFC）/[currentrevenue（1-v）],

whichrepresentsthecomputationformulaforCSP.

ApplicationoftheCSPFormula

Assumecashfixedcost（CFC）is75%ofthetotalfixedoperatingcostforbothfirms.TheamountsofcashfixedcostforAandBwouldbe:

（11）CFC（A）=.75x$40,000=$30,000

（12）CFC（B）=.75x$530,000=$397,500

HavingcomputedCFC,wecanproceedtocalculatetheCSP'sforFirmAandFirmBbyusing（10）:

（13）CSP（A）=1-（$50,000+$30,000）/[$700,000（1-.8）]=43%

（14）CSP（B）=1-（$25,000+$397,500）/[$700,000（1-.1）]=33%

Basedontheabovecalculations,revenuewouldhavetodeclineby43%beforeFirmAencounterscashflowprobleminmeetingitsinterestobligation,whileFirmBwouldreachthiscriticalthresholdifitssalesdeclinebyonly33%.Thus,ifbothfirmshavesimilarrevenuevariability,thentheCSPsuggeststhatFirmBhasgreaterdefaultrisk,whichisconsistentwiththeanalysisinTable2.However,thefalsesignalgeneratedbythetimesinterestearnedratiomayleadunsophisticatedfinancialstatementusersintomakinganerroneousassessmentoftherelativedefaultriskofthefirms.

Theotherconventionaldebtratiosareplaguedwiththesameshortcomingssincenoneofthemtakesintoconsiderationthedegreeofoperatingleverage.ThekeyadvantagesoftheCSPoverconventionaldebtratiosarethatoperatingleverageisaccountedforandthattheriskisexpressedintermsoftheprimarysourceofuncertainty-revenue.Becauseofitssimplicityincomputationandinterpretation,anditsdirectlinktodefaultrisk,CSPshouldbecomeanessentialfinancialindicatoramongthesetofdebtratioscurrentlybeingusedforfinancialstatementanalysis,inacademiaaswellasintherealworld.

ProbabilityofDistress

Assumethatsalesnextyearhasthesamedistribution（meanandstandarddeviation）asthepast.Theprobabilitythatsalesdropbelowthelevelofcriticalsaleswouldbetheprobabilityofdistress.

Applythistheorytoanactualfirmwithjustoneclassofbondwithknowncouponinterestforsimplicitypurpose.UseValueLineforsalesstandarddeviation.,whichshouldusethestandarddeviationofsales/assetinsteadofsalestoadjustinflationarytrend.

References

Brigham,EugeneF.,FundamentalsofFinancialManagement（Dryden,1995）.

Chambers,DonaldR.,andNelson,J.Lacey.,ModernCorporateFinance（Addison-Wesley,1999）

Collins,RobertA.,"AnEmpiricalComparisonofBankruptcyPredictionModels,"FinancialManagement,Summer1980,pp.52-57.

Fras