第七章 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-StructureQuestionandThePieTheory•Thevalueofafirmisdefinedtobethesumofthevalueofthefirm’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1ROALeverageNINIAssetsROEEquityAssetsEquityEDROAEDROEROAE无税的MM定理•AssumptionsoftheModigliani-MillerModel–HomogeneousExpectations–HomogeneousBusinessRiskClasses–PerpetualCashFlows–PerfectCapitalMarkets:•Perfectcompetition•Firmsandinvestorscanborrow/lendatthesamerate•Equalaccesstoallrelevantinformation•Notransactioncosts•NotaxesTheMMPropositionsI&II(NoTaxes)•PropositionI–FirmvalueisnotaffectedbyleverageVL=VU•PropositionII–Leverageincreasestheriskandreturntostockholdersrs=r0+(B/SL)(r0-rB)rBistheinterestrate(costofdebt)rsisthereturnon(levered)equity(costofequity)r0isthereturnonunleveredequity(costofcapital)BisthevalueofdebtSListhevalueofleveredequityTheMMPropositionI(NoTaxes)ULVV\BrEBITB-receivefirmleveredainrsShareholdeBrBreceivesBondholderThederivationisstraightforward:BrBrEBITBB-)(isrsstakeholdealltoflowcashtotaltheThus,ThepresentvalueofthisstreamofcashflowsisVLEBITBrBrEBITBB-)(ClearlyThepresentvalueofthisstreamofcashflowsisVUTheMMPropositionII(NoTaxes)Thederivationisstraightforward:SBWACCrSBSrSBBr..0setThenrrWACC0rrSBSrSBBSB..SSBbysidesbothmultiply0rSSBrSBSSSBrSBBSSBSB....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ADEDEWACCrrrAATheCostofEquity,theCostofDebt,andWACC:MMPropositionIIwithNoCorporateTaxesDebt-to-equityRatioCostofcapital:r(%)r0rBSBWACCrSBSrSBBr)(00BLSrrSBrr-rBSB有公司税的MM定理TheMMPropositionsI&II(withCorporateTaxes)•PropositionI(withCorporateTaxes)–FirmvalueincreaseswithleverageVL=VU+TCB•PropositionII(withCorporateTaxes)–SomeoftheincreaseinequityriskandreturnisoffsetbyinteresttaxshieldrS=r0+(B/S)×(1-TC)×(r0-rB)rBistheinterestrate(costofdebt)rSisthereturnonequity(costofequity)r0isthereturnonunleveredequity(costofcapital)BisthevalueofdebtSisthevalueofleveredequityTheMMPropositionI(Corp.Taxes)BTVVCUL\)1()(receivefirmleveredainrsShareholdeCBTBrEBIT-.-BrBreceivesBondholderBrTBrEBITBCB-.-)1()(isrsstakeholdealltoflowcashtotaltheThus,ThepresentvalueofthisstreamofcashflowsisVL-.-BrTBrEBITBCB)1()(ClearlyThepresentvalueofthefirsttermisVUThepresentvalueofthesecondtermisTCBBrTBrTEBITBCBC-.--.)1()1(BrBTrBrTEBITBCBBC--.)1(TheMMPropositionII(Corp.Taxes)StartwithM&MPropositionIwithtaxes:)()1(00BCSrrTSBrr-.-.BTVVCULSinceBSVLThecashflowsfromeachsideofthebalancesheetmustequal:BCUBSBrTrVBrSr0BrTrTBSBrSrBCCBS-0)]1([DividebothsidesbySBCCBSrTSBrTSBrSBr-0)]1(1[BTVBSCU)1(CUTBSV-WhichquicklyreducestoTheEffectofFinancialLeverageontheCostofDebtandEquityCapitalwithCorporateTaxesDebt-to-equityratio(B/S)Costofcapital:r(%)r0rB)()1(00BCLSrrTSBrr--SLLCBLWACCrSBSTrSBBr-)1()(00BLSrrSBrr-TotalCashFlowtoInvestorsUnderEachCapitalStructurewithCorp.TaxesAll-EquityRecessionExpectedExpansionEBIT$1,000$2,000$3,000Interest000EBT$1,000$2,000$3,000Taxes(Tc=35%$350$700$1,050TotalCashFlowtoS/H$650$1,300$1,950LeveredRecessionExpectedExpansionEBIT$1,000$2,000$3,000Interest($800@8%)640640640EBT$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$2,174TotalCashFlowtoInvestorsUnderEachCapitalStructurewithCorp.TaxesTheleveredfirmpayslessintaxesthandoestheall-equityfirm.Thus,thesumofthedebtplustheequityoftheleveredfirmisgreaterthantheequityoftheunleveredfirm.SGSGBAll-equityfirmLeveredfirmTotalCashFlowtoInvestorsUnderEachCapitalStructurewithCorp.TaxesThesumofthedebtplustheequityoftheleveredfirmisgreaterthantheequityoftheunleveredfirm.Thisishowcuttingthepiedifferentlycanmakethepielarger:thegovernmenttakesasmallersliceofthepie!SGSGBAll-equityfirmLeveredfirm权衡理论trade-offTheoryIntegrationofTaxEffectsandFinancialDistressCosts•M&Msuggestthatfinancialleveragedoesnotmatter,orimplythattaxescausetheoptimalfinancialstructuretobe100%debt.•Intherealworld,mostexecutivesdonotlikeacapitalstructureof100%debtbecausethatisastateknownas“bankruptcy”.•Thereisatrade-offbetweenthetaxadvantageofdebtandthecostsoffinancialdistress.•Itisdifficulttoexpressthiswithapreciseandrigorousformula.IntegrationofTaxEffectsandFinancialDistressCostsDebt(B)Valueoffirm(V)0PresentvalueoftaxshieldondebtPresentvalueoffinancialdistresscostsValueoffirmunderMMwithcorporatetaxesanddebtVL=VU+TCBV=ActualvalueoffirmVU=ValueoffirmwithnodebtB*MaximumfirmvalueOptimalamountofdebtThePieModelR