资本结构和MM定理

第七章资本结构和MM定理MM定理及扩展资本结构的经验证据MM定理及扩展无税的MM定理（1958）有公司税的MM定理trade-offTheory（权衡理论）等加入个人税的MM定理（米勒定理1977）MM定理的其他用途TheCapital-StructureQuestion

andThePieTheoryThevalueofafirmisdefinedtobethesumofthevalueofthefirm’sdebtandthefirm’sequity.V=

B+SIfthegoalofthemanagementofthefirmistomakethefirmasvaluableaspossible,thethefirmshouldpickthedebt-equityratiothatmakesthepieasbigaspossible.ValueoftheFirmSBSBSBSBFinancialLeverageandEPS(2.00)0.002.004.006.008.0010.0012.001,0002,0003,000EPSDebtNoDebtBreak-evenpointEBITindollars,notaxesAdvantagetodebtDisadvantagetodebt杠杆增加了权益收益（returnonequity,ROE）以及股票持有者的收益，然而也增加了股票风险MM定理认为，两方面的效应恰好抵消无税的MM定理AssumptionsoftheModigliani-MillerModelHomogeneousExpectationsHomogeneousBusinessRiskClassesPerpetualCashFlowsPerfectCapitalMarkets:PerfectcompetitionFirmsandinvestorscanborrow/lendatthesamerateEqualaccesstoallrelevantinformationNotransactioncostsNotaxesTheMMPropositionsI&II(NoTaxes)PropositionIFirmvalueisnotaffectedbyleverageVL=VUPropositionIILeverageincreasestheriskandreturntostockholdersrs=r0+(B/SL)(r0-rB)rBistheinterestrate(costofdebt)rsisthereturnon(levered)equity(costofequity)r0isthereturnonunleveredequity(costofcapital)BisthevalueofdebtSListhevalueofleveredequityTheMMPropositionI(NoTaxes)ULVV=\

BrEBITB-receive

firm

levered

ain

rsShareholdeBrBreceive

sBondholderThederivationisstraightforward:BrBrEBITBB+-)(is

rsstakeholde

all

toflowcash

totaltheThus,ThepresentvalueofthisstreamofcashflowsisVL

EBITBrBrEBITBB=+-)(ClearlyThepresentvalueofthisstreamofcashflowsisVU

TheMMPropositionII(NoTaxes)Thederivationisstraightforward:SBWACCrSBSrSBBr.++.+=0setThenrrWACC=0rrSBSrSBBSB=.++.+SSB+by

sidesbothmultiply0rSSBrSBSSSBrSBBSSBSB+=.+.++.+.+0rSSBrrSBSB+=+.00rrSBrrSBSB+=+.)(00BSrrSBrr-+=杠杆率上升时，公司更多进行“低成本”的债务融资，然而其股本风险和成本也随之增大，根据MM，两项效应恰好抵消。不考虑税收，资本结构的改变不影响加权资本成本（WACC）WACC仅为资产的风险决定

TheCostofEquity,theCostofDebt,andWACC:MMPropositionIIwithNoCorporateTaxesDebt-to-equityRatioCostofcapital:r(%)r0rBrBSB有公司税的MM定理

TheMMPropositionsI&II(withCorporateTaxes)PropositionI(withCorporateTaxes)FirmvalueincreaseswithleverageVL=VU+TCBPropositionII(withCorporateTaxes)SomeoftheincreaseinequityriskandreturnisoffsetbyinteresttaxshieldrS=r0+(B/S)×(1-TC)×(r0-rB)

rBistheinterestrate(costofdebt)rSisthereturnonequity(costofequity)r0isthereturnonunleveredequity(costofcapital)BisthevalueofdebtSisthevalueofleveredequityTheMMPropositionI(Corp.Taxes)BTVVCUL+=\

)1()(receive

firm

levered

ain

rsShareholdeCBTBrEBIT-.-BrBreceive

sBondholderBrTBrEBITBCB+-.-)1()(is

rsstakeholde

all

toflowcash

totaltheThus,ThepresentvalueofthisstreamofcashflowsisVL

=+-.-BrTBrEBITBCB)1()(ClearlyThepresentvalueofthefirsttermisVU

ThepresentvalueofthesecondtermisTCB

BrTBrTEBITBCBC+-.--.=)1()1(BrBTrBrTEBITBCBBC++--.=)1(TheMMPropositionII(Corp.Taxes)StartwithM&MPropositionIwithtaxes:)()1(00BCSrrTSBrr-.-.+=BTVVCUL+=

SinceBSVL+=Thecashflowsfromeachsideofthebalancesheetmustequal:BCUBSBrTrVBrSr+=+0BrTrTBSBrSrBCCBS+-+=+0)]1([DividebothsidesbySBCCBSrTSBrTSBrSBr+-+=+0)]1(1[BTVBSCU+=+Þ)1(CUTBSV-+=WhichquicklyreducestoTheEffectofFinancialLeverageontheCostofDebtandEquityCapitalwithCorporateTaxesDebt-to-equity

ratio(B/S)Costofcapital:r

(%)r0rBTotalCashFlowtoInvestorsUnder

EachCapitalStructurewithCorp.Taxes

All-Equity

Recession Expected ExpansionEBIT $1,000 $2,000 $3,000Interest 0 0 0EBT $1,000 $2,000 $3,000Taxes(Tc=35% $350 $700 $1,050TotalCashFlowtoS/H $650 $1,300 $1,950

Levered

Recession Expected ExpansionEBIT $1,000 $2,000 $3,000Interest($800@8%) 640 640 640EBT $360 $1,360 $2,360Taxes(Tc=35%) $126 $476 $826TotalCashFlow $234+640 $468+$640 $1,534+$640(tobothS/H&B/H): $874 $1,524 $2,174EBIT(1-Tc)+TCrBB $650+$224 $1,300+$224 $1,950+$224 $874 $1,524 $2,174TotalCashFlowtoInvestorsUnder

EachCapitalStructurewithCorp.TaxesTheleveredfirmpayslessintaxesthandoestheall-equityfirm.Thus,thesumofthedebtplustheequityoftheleveredfirmisgreaterthantheequityoftheunleveredfirm.SGSGBAll-equityfirm LeveredfirmTotalCashFlowtoInvestorsUnder

EachCapitalStructurewithCorp.TaxesThesumofthedebtplustheequityoftheleveredfirmisgreaterthantheequityoftheunleveredfirm.Thisishowcuttingthepiedifferentlycanmakethepielarger:thegovernmenttakesasmallersliceofthepie!SGSGBAll-equityfirm Leveredfirm权衡理论trade-offTheory

IntegrationofTaxEffectsandFinancialDistressCostsM&Msuggestthatfinancialleveragedoesnotmatter,orimplythattaxescausetheoptimalfinancialstructuretobe100%debt.Intherealworld,mostexecutivesdonotlikeacapitalstructureof100%debtbecausethatisastateknownas“bankruptcy”.Thereisatrade-offbetweenthetaxadvantageofdebtandthecostsoffinancialdistress.Itisdifficulttoexpressthiswithapreciseandrigorousformula.IntegrationofTaxEffects

andFinancialDistressCostsDebt(B)Valueoffirm(V)0Presentvalueoftax

shieldondebtPresentvalueof

financialdistresscostsValueoffirmunder

MMwithcorporate

taxesanddebtVL=VU+TCBV=ActualvalueoffirmVU=ValueoffirmwithnodebtB*Maximum

firmvalueOptimalamountofdebtThePieModelRevisitedTaxesandbankruptcycostscanbeviewedasjustanotherclaimonthecashflowsofthefirm.LetGandLstandforpaymentstothegovernmentandbankruptcylawyers,respectively.VT=S+B+G+LTheessenceoftheM&MintuitionisthatVTdependsonthecashflowofthefirm;capitalstructurejustslicesthepie.SGBL其他相关理论信号理论代理成本理论融资次序理论动态权衡理论SignalingThefirm’scapitalstructureisoptimizedwherethemarginalsubsidytodebtequalsthemarginalcost.Investorsviewdebtasasignaloffirmvalue.Firmswithlowanticipatedprofitswilltakeonalowlevelofdebt.Firmswithhighanticipatedprofitswilltakeonhighlevelsofdebt.Amanagerthattakesonmoredebtthanisoptimalinordertofoolinvestorswillpaythecostinthelongrun.Shirking,Perquisites,andBadInvestments:TheAgencyCostofEquityAnindividualwillworkharderforafirmifheisoneoftheownersthanifheisoneofthe“hiredhelp”.Whobearstheburdenoftheseagencycosts?Whilemanagersmayhavemotivetopartakeinperquisites,theyalsoneedopportunity.Freecashflowprovidesthisopportunity.Thefreecashflowhypothesissaysthatanincreaseindividendsshouldbenefitthestockholdersbyreducingtheabilityofmanagerstopursuewastefulactivities.Thefreecashflowhypothesisalsoarguesthatanincreaseindebtwillreducetheabilityofmanagerstopursuewastefulactivitiesmoreeffectivelythandividendincreases.ThePecking-OrderTheoryTheorystatingthatfirmsprefertoissuedebtratherthanequityifinternalfinanceisinsufficient.Rule1Useinternalfinancingfirst.Rule2Issuedebtnext,equitylast.Thepecking-orderTheoryisatoddswiththetrade-offtheory:ThereisnotargetD/Eratio.Profitablefirmsuselessdebt.CompanieslikefinancialslackGrowthandtheDebt-EquityRatioGrowthimpliessignificantequityfinancing,eveninaworldwithlowbankruptcycosts.Thus,high-growthfirmswillhavelowerdebtratiosthanlow-growthfirms.Growthisanessentialfeatureoftherealworld;asaresult,100%debtfinancingissub-optimal.加入个人税的MM定理

米勒定理，TheMillerModelTheMillerModelshowsthatthevalueofaleveredfirmcanbeexpressedintermsofanunleveredfirmas:BTTTVVBSCUL.úûùêëé--.--+=1)1()1(1Where:TS=personaltaxrateonequityincomeTB=personaltaxrateonbondincomeTC=corporatetaxratePersonalTaxes:TheMillerModelThederivationisstraightforward:)1()1()(receive

firm

levered

ain

rsShareholdeSCBTTBrEBIT-.-.-)1(receive

sBondholderBBTBr-.)1()1()1()(is

rsstakeholde

all

toflowcash

totaltheThus,BBSCBTBrTTBrEBIT-.+-.-.-úûùêëé--.--.-.+-.-.BSCBBSCTTTTBrTTEBIT1)1()1(1)1()1()1(asrewritten

becan

This

PersonalTaxes:TheMillerModel(cont.)úûùêëé--.--.-.+-.-.BSCBBSCTTTTBrTTEBIT1)1()1(1)1()1()1(Thefirsttermisthecashflowofanunleveredfirmafteralltaxes.Itsvalue=VU.

AbondisworthB.ItpromisestopayrBB×(1-TB)aftertaxes.Thusthevalueofthesecondtermis:Thetotalcashflowtoallstakeholdersintheleveredfirmis:ThevalueofthesumofthesetwotermsmustbeVLBTTTVVBSCUL.úûùêëé--.--+=\1)1()1(1PersonalTaxes:TheMillerModel(cont.)ThustheMillerModelshowsthatthevalueofaleveredfirmcanbeexpressedintermsofanunleveredfirmas:InthecasewhereTB=TS,wereturntoM&Mwithonlycorporatetax:BTTTVVBSCUL.úûùêëé--.--+=1)1()1(1BTVVCUL+=EffectofFinancialLeverageonFirmValuewithBothCorporateandPersonalTaxesDebt(B)Valueoffirm(V)VUVL=VU+TCBwhenTS=TBVL<VU+TCB

whenTS<TB

but(1-TB)>(1-TC)×(1-TS)VL=VU

when(1-TB)=(1-TC)×(1-TS)VL<VUwhen(1-TB)<(1-TC)×(1-TS)BTTTVVBSCUL.úûùêëé--.--+=1)1()1(1IntegrationofPersonalandCorporateTaxEffectsandFinancialDistressCostsandAgencyCostsDebt(B)Valueoffirm(V)0Presentvalueoftax

shieldondebtPresentvalueof

financialdistresscostsValueoffirmunder

MMwithcorporate

taxesanddebtVL=VU+TCBV=ActualvalueoffirmVU=ValueoffirmwithnodebtB*Maximum

firmvalueOptimalamountofdebtVL<VU+TCB

whenTS<TB

but(1-TB)>(1-TC)×(1-TS)AgencyCostofEquityAgencyCostofDebtMM定理的延伸远期负债相对短期负债是无关重要股息政策是无关重要风险管理是无关重要资本结构的实证问题CostsofFi