《財(cái)務(wù)管理案例分析》Chapter 9 Capital structure and leverage

Chapter9CapitalstructureandleverageThepurposeofthischapteristogiveyouanideaofwhatcapitalstructureandleverageareallabout.Afteryoufinishthechapter,youshouldhaveareasonablygoodideaofwhattargetofcapitalstructureis.Youshouldalsohaveabetterunderstandingof:BusinessandfinancialriskDeterminingtheoptimalcapitalstructureCapitalstructuretheoryVariationsincapitalstructuresUncertaintyaboutfutureoperatingincome,i.e.,howwellcanwepredictoperatingincome?

Whatisbusinessrisk?ProbabilityEBITE(EBIT)0LowriskHighriskBusinessriskvs.FinancialriskBusinessriskdependsonbusinessfactorssuchascompetition,productliability,andoperatingleverage.Financialriskdependsonlyonthetypesofsecuritiesissued.Moredebt,morefinancialriskBusinessriskandtheLeverageAXONCompanyhasfollowingaccountinginformationforyears2001-2003(0,000)

Assumepriceperunitis$20,unitvariablecostis$10,salesamountintheyearof2011,2012and2013are500,000units,600,000unitsand700,000units.WhataretheDOLs?DOL（12)=2.5DOL(13)=2

yearOperatingrevenueGrowthrateonsalesrevenueVariablecostsFixedcostsEBITGrowthrateonEBIT111000--500300200--12120020%60030030050%13140017%70030040033%EBIT=S-V-FHowdowemeasuretheoperatingleverageOperatingLeverage

Whatisoperatingleverage,andhowdoesitaffectafirm’sbusinessrisk?

Fixedcostremainsconstantwhensalesrevenuegoesup.Therefore,thefixedcostperdollarsaleswillbedeclinewhensalesincrease.Inaword,asmallchangeofsalesrevenuecauseabigEBITvariety.Wecallthisphenomenonasoperatingleverage.FinancialRiskandLeverageFinancialrisks：Financialriskisapartofspecificriskofthefirm.Itisexistingbecauseofdebt.Highdebtfinancingbringstheriskofbankruptcyaswellastheriskofstockpricedeclinetothefirm.Factorsthataffectfinancialrisk:--EBIT;--Debtamountandstructure;--Costofdebt；

--Preferredstockdividend；DegreeofFinancialLeverageAXONCompanyhasEBITsfor2011-2013:200m,300m,and400m.Longtermcapitalis50000mwith40%ofdebt.Theaveragecostofdebtis6%.Incometaxrateis40%.Preferreddividendis20mannually.Thenumberofoutstandingsharesis100m.Otherinformationislistedinthefollowingtable:YearEBITEBITGrowthrateInterestEBTTaxesPreferreddividendEPSEPSgrowthrate11200---1208032200.28---1230050%12018072200.88214%1340033%120280112201.4868%DFL(12)=4.29DFL(13)=2.05DegreeofFinancialLeverageTotalLeverage(CompositeLeverage)1.Itiscomposedofoperating&financialleverage.2.Whenoperatingrevenueischangedbyacertainportion,EPSwillbechangedbyabiggerportionbecauseexistingoffixedcosts,interestandpreferreddividend.Therefore:

SalesEPSmoreSalesEPSmore3.Thefactorsthataffectbusinessriskandfinancialriskwillaffecttheleveloftotalleverage.

Degreeoftotalleverage

DTLorDCLProblemsinleverageanalysis1.OperatingleverageworksonlywhenEBIT>0forbasicperiod;2.AssumptionwhencomputeDOL:Priceoftheproduct,unitvariablecostandfixedcosthavenochangeforthetwoperiods;3.FinancialleverageworksonlywhenEPS>0forbasicperiod;4.AssumptionwhencomputeDFL:Debtinterest,preferreddividendandtaxrateremainconstantforthetwoperiods.IllustratingeffectsoffinancialleverageTwofirmswiththesameoperatingleverage,businessrisk,andprobabilitydistributionofEBIT.Onlydifferwithrespecttotheiruseofdebt(capitalstructure).

FirmU

FirmL Nodebt $10,000of12%debt $20,000inassets $20,000inassets 40%taxrate 40%taxrateFirmU:UnleveragedEconomy

BadAvg.GoodProb. 0.25 0.50 0.25EBIT $2,000 $3,000 $4,000Interest 0

0

0EBT $2,000 $3,000 $4,000Taxes(40%) 800

1,200

1,600NI $1,200 $1,800 $2,400FirmL:LeveragedEconomy

BadAvg.GoodProb.* 0.25 0.50 0.25EBIT* $2,000 $3,000 $4,000Interest 1,200

1,200

1,200EBT $800 $1,800 $2,800Taxes(40%) 320

720

1,120NI $480 $1,080 $1,680*SameasforFirmU.RatiocomparisonbetweenleveragedandunleveragedfirmsFIRMU Bad Avg GoodBEP 10.0%15.0%20.0%ROE 6.0%9.0%12.0%FIRML Bad Avg GoodBEP 10.0%15.0%20.0%ROE 4.8%10.8%16.8%RiskandreturnforleveragedandunleveragedfirmsExpectedValues:

FirmU

FirmL E(BEP) 15.0% 15.0% E(ROE) 9.0% 10.8%RiskMeasures:

FirmU

FirmL

σROE 2.12% 4.24% CVROE 0.24 0.39AssetsLiabilities&EquityCurrentAssetsCurrentLiabilitiesFixedAssetsLong-termDebtPreferredStockCommonEquityAssetsLiabilities&EquityCurrentAssetsCurrentLiabilitiesFixedAssetsLong-termDebtPreferredStockCommonEquityTheinvestmentdecisionCorporateFinance:

CostofcapitalLeverageCapitalStructureWherewe’regoing...AssetsLiabilities&EquityCurrentAssetsCurrentLiabilitiesFixedAssetsLong-termDebtPreferredStockCommonEquityAssetsLiabilities&EquityCurrentAssetsCurrentLiabilitiesFixedAssetsLong-termDebtPreferredStockCommonEquityThefinancingdecisionForInvestors,therateofreturnonasecurityisabenefitofinvesting.ForFinancialManagers,thatsamerateofreturnisacostofraisingfundsthatareneededtooperatethefirm.Inotherwords,thecostofraisingfundsisthefirm’scostofcapital.Howcanthefirmraisecapital?BondsPreferredStockCommonStock

Eachoftheseoffersarateofreturntoinvestors.Thisreturnisacosttothefirm.

“Costofcapital”actuallyreferstotheweightedcostofcapital-aweightedaveragecostoffinancingsources.CostofDebtCostofDebtFortheissuingfirm,thecostofdebtis:therateofreturnrequiredbyinvestorsflotationcosts(anycostsassociatedwithissuingnewbonds)adjustedfortaxesExample:Taxeffectsoffinancingwithdebt

withstock

withdebtEBIT 400,000 400,000-interestexpense 0

(50,000)EBT 400,000 350,000-taxes(34%) (136,000)

(119,000)EAT 264,000 231,000Example:Taxeffectsoffinancingwithdebt

withstock

withdebtEBIT 400,000 400,000-interestexpense 0

(50,000)EBT 400,000 350,000-taxes(34%) (136,000)

(119,000)EAT 264,000 231,000Now,supposethefirmpays$50,000individendstothestockholders.Example:Taxeffectsoffinancingwithdebt

withstock

withdebtEBIT 400,000 400,000-interestexpense 0

(50,000)EBT 400,000 350,000-taxes(34%) (136,000)

(119,000)EAT 264,000 231,000-dividends (50,000)

0Retainedearnings214,000231,000=After-taxMarginal%costofdebtBefore-taxMarginal%costofdebtx1-TaxRateKd=kb(1-T)其中：—稅后債券資本成本

—每年支付的利息

—所得稅稅率

—籌集債券數(shù)額

—籌資費(fèi)用率

某企業(yè)向銀行借入9個(gè)月期款項(xiàng)20000元，年利率為8%，每季度支付一次利息，到期還本。借款手續(xù)費(fèi)等為200元。假如該企業(yè)適用18%的所得稅率，那么該借款的成本是多少？解：不考慮資金的時(shí)間時(shí)借款的資本成本為：如果考慮資金的時(shí)間價(jià)值時(shí)該怎么做？借款的年成本率=1.66%*4=6.63%Example:CostofDebtPrescottCorporationissuesa$1,000par,20yearbondpayingthemarketrateof10%.Couponsaresemiannual.Thebondwillsellforpar(平價(jià))sinceitpaysthemarketrate,butflotationcostsamountto$50perbond.Whatisthepre-taxandafter-tax(thetaxrateis34%)costofdebtforPrescottCorporation?Pre-taxcostofdebt:(usingTVM) P/Y=2 N=40 PMT=-50 FV=-1000 PV=950 solve:I=10.61%=kbAfter-taxcostofdebt:

Kd=kb(1-T)

Kd=.1061(1-.34)

Kd=.07=7%CostofPreferredStockRecall:

kp==

Fromthefirm’spointofview:

kp==NPo=price-flotationcosts!DPoDividendPriceDividendNetPriceDNPoCostofPreferredIfPrescottCorporationissuespreferredstock,itwillpayadividendof$8peryearandshouldbevaluedat$75pershare.Ifflotationcostsamountto$1pershare,whatisthecostofpreferredstockforPrescott?CostofPreferredStock

kp==

==10.81%DividendNetPriceDNPo8.0074.00CostofCommonStockTherearetwosourcesofCommonEquity:1)Internalcommonequity(retainedearnings).2)Externalcommonequity(newcommonstockissue).Dothesetwosourceshavethesamecost?CostofInternalEquitySincethestockholdersownthefirm’sretainedearnings,thecostissimplythestockholders’requiredrateofreturn.Ifmanagersareinvestingstockholders’funds,stockholderswillexpecttoearnanacceptablerateofreturn.CostofInternalEquityDividendGrowthModel

kc=+gD1Po1)DividendGrowthModel

knc=+gCostofExternalEquityD1NPoNetproceedstothefirmafterflotationcosts!CostofInternalEquity2)CapitalAssetPricingModel(CAPM)

kj=krf+βj(km-krf

)WeightedCostofCapitalTheweightedcostofcapitalisjusttheweightedaveragecostofallofthefinancingsources.WeightedCostofCapital

CapitalCapital

SourceCostStructuredebt6%20%preferred10%10%common16%70%WeightedCostofCapital=.20(6%)+.10(10%)+.70(16%)=13.4%WeightedCostofCapital

(20%debt,10%preferred,70%common)Whatisoperatingleverage,andhowdoesitaffectafirm’sbusinessrisk?Operatingleverageistheuseoffixedcostsratherthanvariablecosts.Ifmostcostsarefixed,hencedonotdeclinewhendemandfalls,thenthefirmhashighoperatingleverage.Anexample:IllustratingeffectsoffinancialleverageTwofirmswiththesameoperatingleverage,businessrisk,andprobabilitydistributionofEBIT.Onlydifferwithrespecttotheiruseofdebt(capitalstructure).

FirmU

FirmL Nodebt $10,000of12%debt $20,000inassets $20,000inassets 40%taxrate 40%taxrateFirmU:UnleveragedEffectoffinancialleverage:Bigbeeelectronicsfinancedwithzerodebtor50percentdebt(SectionΙ)FirmL:LeveragedEffectoffinancialleverage:Bigbeeelectronicsfinancedwithzerodebtor50percentdebt(SectionⅡ)RelationshipamongExpectedEPS,Risk,andFinancialLeverage

0%a$2.4a$2.96a1.23a102.563.291.29202.753.701.35302.974.231.43403.204.941.5450a3.36a5.93a1.76a603.307.412.25aValuesforD/A=0andD/A=50percentaretakenfromTable12-2.ValuesatotherD/Aratioswerecalculatedsimilarly.DEBT/ASSETSRATIOEXPECTEDEPSCOEFFICIENTOFVARIATIONSTANDARDDEVIATIONOFEPSTheeffectofleverageonprofitabilityanddebtcoverageForleveragetoraiseexpectedROE,musthaveBEP>kd.Why?Ifkd>BEP,thentheinterestexpensewillbehigherthantheoperatingincomeproducedbydebt-financedassets,soleveragewilldepressincome.Asdebtincreases,TIEdecreasesbecauseEBITisunaffectedbydebt,andinterestexpenseincreases(IntExp=kdD).ConclusionsBasicearningpower(BEP)isunaffectedbyfinancialleverage.LhashigherexpectedROEbecauseBEP>kd.LhasmuchwiderROE(andEPS)swingsbecauseoffixedinterestcharges.Itshigherexpectedreturnisaccompaniedbyhigherrisk.OptimalCapitalStructureThatcapitalstructure(mixofdebt,preferred,andcommonequity)atwhichP0ismaximized.TradesoffhigherE(ROE)andEPSagainsthigherrisk.Thetax-relatedbenefitsofleverageareexactlyoffsetbythedebt’srisk-relatedcosts.Thetargetcapitalstructureisthemixofdebt,preferredstock,andcommonequitywithwhichthefirmintendstoraisecapital.StockPriceandCostofCapitalEstimateswithDifferentDebt/AssetRatiosBigbee’sStockPriceandCostofCapitalEstimateswithDifferentDebt/AssetsRatios.(excel連結(jié))Whateffectdoesincreasingdebthaveonthecostofequityforthefirm?Ifthelevelofdebtincreases,theriskinessofthefirmincreases.Wehavealreadyobservedtheincreaseinthecostofdebt.However,theriskinessofthefirm’sequityalsoincreases,resultinginahigherks.TheHamadaEquationBecausetheincreaseduseofdebtcausesboththecostsofdebtandequitytoincrease,weneedtoestimatethenewcostofequity.TheHamadaequationattemptstoquantifytheincreasedcostofequityduetofinancialleverage.Usestheunleveredbetaofafirm,whichrepresentsthebusinessriskofafirmasifithadnodebt.CapitalStructureTheory(1)1.Moderncapitalstructuretheorybeganin1958,whenProfessorsFrancoModiglianiandMertonMiller(hereafterMM)publishedwhathasbeencalledthemostinfluentialfinancearticleeverwritten.CapitalStructureTheory(2)2.Assumptions(1)Therearenobrokeragecosts.(2)Therearenotaxes.(3)Therearenobankruptcycosts.(4)Investorscanborrowatthesamerateas