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财务管理江萍2010年秋季Handout3Outline1.RiskandReturn2.CAPM(资本资产定价模型)3.DiscountRates4.RaisingCapital(融资)5.CapitalStructure6.CapitalBudgetingwithDebt(有负债情况下的资本预算)1.RiskandreturnStatisticsreviewIntroductiontostockpricebehaviorExamplesInNovember1990,AT&TwasconsideringanofferforNCR,the5thlargestU.S.computermaker.HowcanAT&TmeasuretherisksofinvestinginNCR?WhatdiscountrateshouldAT&Tusetoevaluatetheinvestment? Underwriter承销商 IPO首次公开发行 SEO新股增发 Marketmaker做市商 Bidprice卖价Randomvariable随机变量 Parameter参数 Mean均值variance方差 Skewness曲度
observation观察值Median中位数(样本观测值中小于其的数占50%)VaR风险价值(给定置信区间的一个持有期内的最坏的预期损失) Normalrandomvariable正态分布随机变量 Symmetricdistribution对称分布confidenceinterval置信区间 Covary共同变化 Covariance协方差 Correlation相关系数 Stdev.标准差Predict
return预测收益 Timeseries时间序列 Volatility波动性Stocksarequiterisky.Individualstocks(私企股票)aremuchriskier.Stockstendtomovetogetherovertime:whenonestockgoesup,otherstocksarelikelytogoupaswell.Thecorrelationisfarfromperfect.Stockreturnsarenearlyunpredictable.Forexample,knowinghowastockdoesthismonthtellsyouverylittleaboutwhatwillhappennextmonth.Thegreatertherisk,thehigherthereturn.
IntroductiontostockpricebehaviorMarketvolatilitychangesovertime(市场价格波动率随时间变化)Pricesaresometimesquitevolatile.Thestandarddeviationofmonthlyreturns(月收益率)variesfromroughly2%to20%.Introductiontostockpricebehavior代表性的Size公司规模 Sorted分选,分类 decile十分位数代表性特征规模效应小企业的表现通常好于大企业,尤其在一月。一月效应各企业一月的平均收益均高于其他月份。市帐比(价值)效应市场价值与账面价值比值较低的公司绩效较好。惯性效应
过去3到12个月股票收益率较高的企业在未来一
段时间股票的表现依旧会好于收益率低的企业。
资本资产定价模型度量风险系统性和可分散风险风险收益之间的权衡取舍投资多元化(分散化)只要股票之间不是完全正相关,分散就投资可以降低风险。投资组合的方差主要取决于各股之间的协方差,而非个股方差。系统性风险不可分散。NumberofSecuritiesSt.DeviationMarketRisk市场风险或systematicrisk系统性风险UniqueRisk独特风险或Diversifiablerisk可分散风险或Unsystematicrisk非系统性风险为什么分散化可以降低风险?资本资产定价模型股票价格取决于公司本身的经营状况和整个市场
环境。但是投资者往往只关心不可分散风险,即系统性的市场风险。个股的不可分散风险可以通过beta来度量,即个
股收益对市场收益做回归所得斜率。预期收益率是betas的线性函数。(市场风险溢价)Beta
回归斜率个股对于整个市场波动的敏感程度如何?其他股票价格波动是所研究股票的价格如何变化?à=企业本身经营带来的不可风散的、非系统性的风险。ß=个股之于市场收益的敏感度。R2=拟合优度,度量整个方差能被市场收益变化解释的比例。无风险收益率=国库券收益率(mutualfunds共同基金)CAPM应用量化风险股票或投资所对应的ß越大,则投资风险越大。有效估值提供了估计企业资本成本(风险调整后的贴现率)
的有效手段。提供基准
估计股票或投资基金考虑风险情况下的表现。
(美国有近74%的企业用CAPM模型估计资本成本)3.(growingstart-up成长性企业)如果是开辟新的生产线或多元化的企业,则用企业ß来衡量项目的资本成本是不当的。市场收益率用市场指数如标普500来衡量该企业的产品或服务要在不同的市场出售吗?期限匹配,求长期项目资本成本用长期国债利率,短期项目用短期国债。(税后加权资本成本)(权数为债务和权益在总资产或企业总价值中的占比,t为公司税)(使行业ß的使用复杂化)多因素模型ß通常不能涵盖所有的和重要的风险因素。风险度量将企业的预期收益对影响其的所有宏观经济风险因子做回归。预期收益与风险线性相关。4.4.1Overview融资内部融资企业内部产生的现金流,通常指留存收益举借债务债券或商业票据、银行贷款(贷款承诺或信贷限额等)、私募资金和租赁等权益性再融资普通股或优先股、权证和私募资金等DifferencesBetweenDebtandEquityDebtNotanownershipinterestCreditorsdonothavevotingrightsInterestisconsideredacostofdoingbusinessandistax-deductibleCreditorshavelegalrecourseifinterestorprincipalpaymentsaremissedExcessdebtcanleadtofinancialdistressandbankruptcyEquityOwnershipinterestCommonstockholdersvotetoelecttheboardofdirectorsandonotherissuesDividendsarenotconsideredacostofdoingbusinessandarenottaxdeductibleDividendsarenotaliabilityofthefirmuntildeclared.StockholdershavenolegalrecourseifnodividendsaredeclaredAnall-equityfirmcannotgobankrupt债权和股权的区别债权非所有权利益债权人无投票权利息作为经营成本在税前扣除债务人违约不能正常支付利息和本金的时候,债权人可以诉诸法律举债过多使企业陷入财务困境,增加代理成本股权所有权利益在选举董事会成员或公司重大决策时普通股东有投票权股息在税后扣除,无税收屏蔽作用股息非强制发放,但是一旦公告即成法定债务全权益融资的公司不会走向破产术语可转换、可赎回债券和优先股优先股零息债券、纯贴现债权、附息债券垃圾债(信用评级公司发行的债券)Thedebtratingsdependon(1)thelikelihoodthatthefirmwilldefaultand(2)theprotectionaffordedbytheloancontractintheeventofdefault.债券评级取决于:(1)企业违约的可能性;(2)贷款合同所规定的企业违约时对债务的补救措施。Issuebond穆迪和标准普尔评级CreditAnalysis5C’sofCredit1.Character(借款人品德)Characterreferstoborrower’swillingnesstomeetcreditobligation.(借款人履行借款义务的意愿)Management’sintegrityandcommitmenttorepaytheloan(管理者正直诚实,归还贷款的承诺)Management’sbusinessqualificationsandoperatingrecord(管理者的业务素养和经营业绩)Management’sabilitytoreactappropriatelytounexpectedevents(管理者有效应对不可预知事件的能力)Corporategovernancestructure(公司的治理结构)CreditAnalysis---5C’sofCredit2.Collateral(担保)Collateralincludestheassetsofferedassecurityforthedebtaswellasotherassetscontrolledbytheissuer.3.Capital(资本):thefirm’sfinancialreserves.4.Conditions(经营情况)Generaleconomicconditions,includingrecenttrendsintheindustryandhowchangingeconomicconditionsmightaffecttheloan.CreditAnalysis---5C’sofCredit5.Capacity(借款能力)Capacityreferstotheborrower’sabilitytomeetcreditobligationsoutofoperatingcashflows.Moody’susesthefollowingfactorsinassessingtheissuer’scapacitytopayindustrytrends,regulatoryenvironment,operatingandcompetitiveposition,financialpositionandsourcesofliquidity,parentcompanysupportagreementsandspecialeventrisk.穆迪评级公司分析企业借款能力所考虑的因素有:行业趋势、监管环境、经营和竞争环境、财务状况、流动性来源、母公司的贷款保证、特定风险等。IssueEquity4.2FinancingPatternsFinancingPatterns4.3StockMarketReactionPriceImpact(信用贷款,无担保的)(财务杠杆增大即债务融资增加)发行新股,股价下跌股价将随着银行贷款的增加而上升,但对公募债券发行反应微小。稀释效应?(高估,即市帐比高于市场平均水平)(企业经营前景惨淡)5.
CapitalstructureM&Mtheorem(M&M理论)Trade-offTheory(权衡理论)PeckingOrderTheory(优序融资理论)Modigliani-MillerTheoremAssume假定Efficientmarketsandnoasymmetricinformation资本市场完全有效,信息完全对称Notaxes无税Notransactionorbankruptcycosts
无交易和破产成本MMPropositionIThevalueofthefirmisindependentof(与……无关)itscapitalstructure.Financingchoicesareirrelevant!(不重要,无关的)M&M1:Arbitrageargument
——ThesetupTwofirmsidentical(相同的)ininvestmentsbutdifferentcapitalstructureCashflowsof$Cperperiodinperpetuity(永续)Allcashflowspaidoutasdividends–nogrowthSinceidenticalrisk,alsohaveidenticalrequiredreturnsofr0iftheyareallequityfinancedBut,oneofthefirmsislevered(withvalueVL=BL+SL),theotherisunlevered(withvalueVU)M&M1:ArbitrageargumentM&M1:VL=VUShowarbitrageifthepropositiondoesn’tholdPortfolio1Composition:fractionaofequityintheleveredfirm.Initialcost:aSLReturns:perpetualcashflowsofa(C-rBBL)
VL=BL+SLVUPortfolio2Composition:InvestaVUdollarsintheequityoftheunleveredfirm,PartiallyfinancebyborrowingaBL
Initialnetcost:aVU-aBLReturns:perpetualcashflowsofaC(fromtheequity)–rBaBL(fromthedebt)Totalperpetualreturn:a(C-rBBL).M&M1:ArbitrageargumentM&M1:Arbitrageargument
(important)WhathappensifVU>VL?Theperpetualcashflowstoportfolio1areequaltotheperpetualreturnstoportfolio2.BuyP1,sellP2.Cashflowattimezero:(aVU-aBL)-aSL=(aVU-aBL)-a(VL-BL)=a(VU–VL)>0Obligationinthefuture:a(C-rBBL)-a(C-rBBL)=0Thisisarbitrage.M&M1:ArbitrageargumentWhathappensifVU<VL?ArbitrageintheotherdirectionConclusion:VU=VLwhichprovesMM1.Notetheimportanceofassumingthatinvestorscanborrowatsamerate(inP2)astherateatwhichfirmsborrow(inP1).M&MII(notaxes)Proposition:WACCisinvarianttocapitalstructureunderthepreviousassumptions.Proof(DirectimplicationofMM1).Thevalueofthefirm,V,iscashflowsdiscountedbyWACCConsidertheleveredandunleveredfirmsintheprevioussetupBothhadthesamecashflows.Bothhadthesamevalue(byMM1).ThereforetheymusthavethesameWACC.MMPropositionIILeverageExample(MMII)Assets=$10,000Returnondebt=5%AllstatesareequallylikelyAll-equityfirm:S=10,000&B=0StateABCDEROA0%5%10%15%20%Earnings0500100015002000Interest00000NI0500100015002000ROE0%5%10%15%20%Leveredfirm(D/V=.5)
S=5,000&B=5,000StateABCDEROA0%5%10%15%20%Earnings0500100015002000Interest250250250250250NI-25025075012501750ROE-5%5%15%25%35%IfthereistaxAssumecorporatetaxrateTC.Interestistaxdeductible.PropositionIchangesto:VL=VU+PV(taxshield)Interesttaxshield=rdebt*D*TaxRateProof:Showtherearearbitrageopportunitiesifthepropositiondoesn’tholdPortfolio1Composition:fractionaofequityintheleveredfirm.Initialcost:aSLReturns:perpetualcashflowsofa(C-rBBL)(1-TC).IfthereistaxPortfolio2Composition:InvestaVUdollarsintheequityoftheunleveredfirm,PartiallyfinancebyborrowingaBL(1-TC)Initialnetcost:aVU-aBL(1-TC)Returns:perpetualcashflowsofaC(1-TC)(fromtheequity)–rBaBL(1-TC)(fromthedebt)Totalperpetualreturn:a(C-rBBL)(1-TC).IfthereistaxIfthereistaxValueofleveredfirmValueofunleveredfirmPVofinteresttaxshieldsDebtMarketvalueofthefirmVofleveredfirm=Vifall-equity-financed+PVoftaxshieldIfthereistaxValueofleveredfirmDebt/EquityWACCrdebt*(1-t)requity127IfthereistaxImplicationsforCAPM:SML:r0=rF+
U(rM-rF)Assumedebtbetaiszero(i.e.,rB=rF),andsubstitute(替代)intoProp.II:ByCAPM,rSalsosatisfiesrS=rF+
L(rM-rF)Therefore
L=
U[1+(1-T)(B/S)]
FinancialDistressandAgencyCostsofDebtCostsoffinancialdistress(财务困境带来的成本)DirectCosts-legal,administrativeandaccounting(about3%offirmvalueconditionaluponbankruptcy)直接成本包括法律、管理和会计成本,约为处于破产情况下企业价值3%。FinancialDistressandAgencyCostsofDebtPerhapsoneofthemostwell-publicizedbankruptciesinrecentyearsconcernedamunicipality,OrangeCounty,California,notacorporation.近年来最广为人知的破产案例不是企业,而是市镇,如加利福尼亚州破产Thisbankruptcyfollowedlargebond-tradinglossesinthecounty’sfinancialportfolio.
这样的破产是伴随地方政府大额的债券交易损失而产生的。TheLosAngelesTimesstated:FinancialDistressandAgencyCostsofDebtIndirectCosts-LossofSales,destructionofsupplier/employeerelationships,uncertaintyrestrictsinvestment,etc.间接成本包括销售收入的下降、上下游供应链的破坏、与员工关系的恶化、限制投资的不确定性等。Forexample,manyloyalChrysler(克莱斯勒)customersswitchedto(转向)othermanufacturerswhenChryslerskirtedinsolvencyinthe1970s.ThesebuyersquestionedwhetherpartsandservicingwouldbeavailablewereChryslertofail.
FinancialDistressandAgencyCostsofDebtSometimesthetaintofimpendingbankruptcyisenoughtodrivecustomersaway.
有时候可能导致企业发生破产的迹象也会导致客户流失。Forexample,gamblersavoidedAtlantiscasino(一家赌场)inAtlanticCityafteritbecametechnicallyinsolvent(严格按照法律来讲处于破产地位).Gamblersareasuperstitiousbunch(赌徒们是一群迷信的家伙).Manyreasoned,“Ifthecasinoitselfcannotmakemoney,howcanIexpecttomakemoneythere?”FinancialDistressandAgencyCostsofDebtAparticularlyoutrageousstoryconcernedtwounrelatedstoresbothnamedMitchellsinNewYorkCity.WhenoneMitchellsdeclaredbankruptcy,customersstayedawayfrombothstores.Intime,thesecondstorewasforcedtodeclarebankruptcyaswell.另一个让人觉得好笑的故事是关于纽约两家同名却毫不相干的商店破产的例子。当其中一家宣告破产时,两家商店顾客都严重流失,最终,另一家商店也被迫宣告破产。FinancialDistressandAgencyCostsofDebtAgencyCostsofDebt(Thinkofacombinationowner/managerhere,tryingtotakeadvantageofbondholders)ExcessiveRiskTaking(采取高风险的经营决策)Underinvestment(投资不足)–stockholderswon’tpayincapitalOverpayDividends(支付高额股息)AgencyCostofDebtExampleI:IncentivetoTakeLargeRisksSupposeafirmhasassetswithamarketvalueof$200,and$300inbookvalueofdebtoutstanding(发行在外).Thebondsmature(到期)tomorrow.Whatwouldshareholdersgetiffirmisliquidated(被清算)today?Whatwouldbondholdersget?AgencyCostofDebtExampleI:IncentivetoTakeLargeRisksSupposenowtheowner/managerofthefirmhasanopportunitytomakeonelastinvestmentwithanimmediatestochasticpayoff(即刻得到的不确定支付).Theinvestmentcosts$200andhasadiscountrateof50%(veryriskyproject).AgencyCostofDebtExampleI:IncentivetoTakeLargeRisksThepossiblepayoffsandprobabilitiesareWhatshouldtheowner/managerdotomaximizethevalueofthefirm?NPV={.9*0+.1*1000}/1.5-200=-133.33PV[Firm|AcceptProject](接受此项目后企业的价值)=200-133.33=$66.67Aftertheinvestment,themarketvalueofthefirmwillfallto$66.7.
Prob. Payoff Win 10% $1000 Lose 90% $0AgencyCostofDebtExampleI:IncentivetoTakeLargeRisksWhatwillaself-interested(自私的)owner/managerdo?Inthecurrentsituationtheowner/managerwillreceivenothingwhenthebondsmaturetomorrow.Thus,shewillprefertoundertaketheproject,asthereis10%chanceofobtaining$700=$1000-$300.AgencyCostofDebtExampleI:IncentivetoTakeLargeRisksNoprojectWithprojectExpectedCFtobondholders$200.9x0+.1x300=$30ExpectedCFtoowner/manager$0.9x0+.1x700=$70PVbonds$200<$30PVstock$0>0FirmValue$200$67AgencyCostofDebtExampleI:IncentivetoTakeLargeRisksAstory,perhapsapocryphal(虚构的),illustratesthisidea.ItseemsthatFederalExpress(联邦快递)wasnearfinancialcollapsewithinafewyearsofitsinception(开端、创始).Thefounder,FrederickSmith,took$20,000ofcorporatefundstoLasVegasindespair(绝望地).Hewonatthegamingtables,providingenoughcapitaltoallowthefirmtosurvive(生存).(如果)Hadhelost,thebankswouldsimplyhavereceived$20,000lesswhenthefirmreachedbankruptcy.AgencyCostofDebtExampleII:IncentivetoUnder-investTakethesamefirmaspreviously.Assetshaveamarketvalueof$200andthereis$300indebtoutstanding(发行在外的),whichmatures(到期)tomorrow.Thefirmhasanopportunitytoundertakeacompletelyrisklessprojectwithzerorequiredreturn(thepayoffisimmediate)thatcosts$300andhasapayoutof$350.However,thefirmcanonlymakethisinvestmentwithadditionalequitycapital.
(Nomoredebtmaybeissuedbyprovisionsofexistingloancovenantsandfederalregulators按照现存的贷款契约和联邦监管机构的相关规定不能再举债)AgencyCostofDebtExampleII:IncentivetoUnder-investWhatshouldtheowner/managerdotomaximizethevalueofthefirm?NPV=$350/1–300=$50Toundertaketheproject,theowner/managershouldprovidetheadditional$100required.AgencyCostofDebtExampleII:IncentivetoUnder-investWhatwillaself-interestedowner/managerdo?NoprojectWithprojectExpectedCFtobondholders$200$300ExpectedCFtoowner/manager$0$50PVbonds$200$300PVstock$0$50FirmValue$200$350AgencyCostofDebtExampleII:IncentivetoUnder-investSincetheequityholdershadtopay$100fortheirstake(赌注)tostartwith,theylost$50,andwillnotundertaketheprojecteventhoughithaspositiveNPV.Inotherwords,owner/managerwillnotinvestthefundsbecausebondholderswouldcapturemostofthegain.AgencyCostofDebtExampleIII:Milking(压榨)thepropertyShareholdersmayattempttocapturesomeofthefirm’svaluebypayingoutextradividendsorhighersalariestomanagementattimesoffinancialdistress(财务困境).Thisisanotherinstanceinwhichtheprotectivecovenants(inparticularlimitationofdividends)onbondscanbeimportanttothebondholders.Suchtacticsoftenviolatebondindentures.
在这种情况下,对债权人的保护性条款尤其是限制股利发放的规定显得尤为重要。但这同样也违背借款合同的一般规定。Toseehowthisworks,gotoourpreviousexample.Todaythemarketvalueofthefirmis$200,buttomorrowdebtmatures,thefirmwillgobankrupt,bondholdersseize(抓住,控制)thecompany’sassets,andshareholdersgetnothing.Somanagementcansellallofthefirm’sassets,andpayoutthecashtoexistingshareholdersthroughalargedividendbeforethefirmsgoesbankrupt.AgencyCostofDebtExampleIII:Milking(压榨)thepropertyWhobears(担负)thecosts?Atfirstitlookslikebondholders,butifbondholdersareforward-looking(有远见的),theywillanticipatethesecostsanddemandahigherreturntocompensatefor(补偿)it.Ultimately,theowner/managerpaysthesecosts.AgencyCostofDebtExampleIII:Milking(压榨)thepropertyPuttingthisalltogether,wenowhaveatheoryofoptimalcapitalstructureVL=VU+PV(taxshield)-PV(costsoffinancialdistress)“Static(静态的)”TheoryofOptimalCapitalStructure(最有资本结构)AgencyCostofDebtExampleIII:Milking(压榨)thepropertyifthereisbankruptcycost
ThePeckingOrderHypothesis
(优序融资理论)
Thisisthemainalternative(选择方案)totheoptimalcapitalstructuretheoryKeyisasymmetricinformation(信息不完全):themanagermustknowmoreaboutthefirm’sprospectsthatdoesatypicalinvestor(就像普通投资者一样).
Managerscanusetheirprivateinformationto“time(确定时间)”newequityissues:Issueequitywhenitisovervalued(高估)Donotissuewhenitisundervalued,ratherissuealow-riskbondthatthemarketwillpricecorrectly.
ThePeckingOrderHypothesis
Ifafirmissuesequity,investorswillinfer(推测)thatitisovervalued,andwouldonlypayverylowprices.Ifitissuesdebt,theywillinferitisundervalued.Thus,totheextentpossible(从某种程度上讲),allfirmsneedingtoraiseexternalcapitalshouldissuedebt,ratherthanequity.
ThePeckingOrderHypothesis
Managersalsohavesomeprivateinformationaboutthefirm’sdebt(e.g.managersknowthetrueprobabilityofdefault实际违约的可能性).Soitislikelythatmanagersalsotendtoissuedebtwhentheythinkitisovervalued.Soinvestorswillrequirehigheryields(收益率)onbondissues.However,investorfearofmispricingismuchlessfordebtthanforequity.
但是,对于债券错误定价担心的投资者相比股票较少。
ThePeckingOrderHypothesis
Thetheorysaysthatmanagerspreferthefollowingorderingoffinancing:Retainedearnings(internalcash)DebtEquity
ThePeckingOrderHypothesis
Otherreasonsforthepeckingorder:DirectcostsofissuanceAgencycosts(managersdon’tlikemonitoring)
ThePeckingOrderHypothesis
ImplicationsThereisnotargetleverage(D/Edependsonfinancingneeds)Profitablefirmsuselessdebt(moreinternalcash,don’tneeddebt)Companieslikefinancialslack(havecashavailableforprojects流动资金充裕)
ThePeckingOrderHypothesis
EmpiricalfactsRegardingCapitalStructureLowdebt/assetratios:<50%ingeneral.Pricesriseinresponsetodebtincreases,fallforequityincreases:Thisprobablyhasmoretodowithsignalingthananything.
价格变化的可能性较多与新信息的公布有关。EmpiricalfactsRegardingCapitalStructurePersistentinter-industrydifferencesLowdebtingrowthindustries(higherexpectedbankruptcycosts)Significanttangibleassetsgowithhighdebt(tangibleassetsreducecostsoffinancialdistress较多的无形资产可以使企业在举债较多时也能勉强应付,不至于陷入财务困境)Veryriskyenterpriseshavelowerdebtlevels:Notethatthisisonecasewhereitisthetotalriskofthecashflowsthatmatters,notthemarketrisk(重要的是现金流的总风险而不是市场风险)EmpiricalfactsRegardingCapitalStructureProfitablefirmsissuelessdebtThisfitsbestwithpeckingorderhypothesis–managersliketokeeptheirfreecashflowSeemstocontradict(与……相悖)optimalcapitalstructuretheory:profitablefirmsneedtaxshelter(税盾)fromdebtmore6.CapitalBudgetingwithDebtr0:theunleveredfirmorprojectdiscountrate,i.e.thecostofcapitalforanall-equityfirmrB:thecostofdebtrS=r0+(B/S)(1-TC)(r0-rB),thecost(requiredreturn)ofleveredequity,fromMMProp.IIwithtaxes(Chapter15oftheRossbook)SomethingstorememberbeforewestartWACC=wB.rB.
(1-T)+wS.rS,wherewB=B/(B+S)andwS=S/(B+S),whicharetargetratios(目标比率)UCF:aftertax,unleveredcashflows(excludesaftertaxinterestpayments)LCF:aftertax,leveredcashflows(includesaftertaxinterestpayments)UCF–LCF=(1-TC).rB.BExampleSales$500,000,cashcosts$360,000,taxrate40%,interestexpense$11,666.WhatisUCF,LCF?UCF–LCF=7,000=84,000–77,000=.6x11,666sales500,000sales500,000costs360,000costs360,000op.income140,000interest-11,666taxes@40%-56,000incomeafterinterest128,334UCF84,000taxes@40%-51,334LCF77,000ExampleCapitalBudgetingwithLeverageThecapitalstructureandcapitalbudgetingdecisionsarerelated.Aprojectofanall-equityfirmmightberejected,whilethesameprojectmightbeacceptedforaleveredbutotherwiseidentical(其他情况相同)firm.Intuition:thecostofcapitalfrequentlydecreaseswithleverage,thereforeturningsomenegativeNPVprojectsintopositiveNPVprojects.(利息有税收屏蔽作用,债务比重增加能降低资本成本,从而可能使一些项目负的NPV转正)CapitalBudgetingwithLeverageForanunleveredfirmorproject,wejustdiscountbyr0(theunleveredfirmorprojectdiscountrate)Foraleveredfirm,wehavethreechoicesWACC(加权平均资本成本法)APV(AdjustedPresentValue调整净现值法)FTE(FlowstoEquity权益现金流量法)CapitalBudgetingwithLeverageIntheory,thesethreecanbemadetogiveidenticalresults(殊途同归)Inpractice,exactreconciliation(精确的解)isoftendifficult,butthethreemethodsshouldgiveapproximately(大约,大概)thesameresultsAPVismostusefulwhenleverageischangingsubstantially(大量地,实质性地)overtimeTheothertwoworkbestwithfixedleverageratiosThismethodisprobablythemostfamiliartoyou.Discountthefirm’scashflowsbytheweightedaveragecostofcapital(WACC).Valuation:
DCFValuationI:WACC169DCFValuationI:WACCInputsDebt/equityratio(constant:itisthetargetleverageratio)CostsofleveredequityandcostofdebtTaxrateUnleveredcashflows(aftertax)ExampleI:WACCValuationConsiderthevaluationoftheSingerCompany,whichisforsalefor$475,000,andhasthefollowingcharacteristics:Cashsales:$500,000peryearfortheindefinitefuture Cashcosts:72%ofsales Corporatetaxrate(TC):34% Costofcapitalifunlevered(r0):20% InterestRate(rB):10% Targetdebttoequityratio(B/S):1/3(thusB=1,S=3,andB+S=4)
AnnualCFsifthefirmwereallequityfinanced(ignoreinterestpayments)are:Cashinflows $500,000 Cashcosts -360,000 OperatingIncome 140,000 CorporateTax(.34) -47,600 UCF
92,400ExampleI:WACCValuationThepresentvalueofSingeristhusPV=92,400/.183=504,918andtheNPVoftheacquisitionwouldbeNPV=504,918–475,000=$29,918ExampleI:WACCValuationUnderstandingWACCWhenusingWACC,thevalueofthedebttaxshieldisreflectedinthedenominator(分母discountrate),ratherthanthenumerator(分子cashflows)UnderstandingWACCWACC<r0.
Thusthevalueofaprojectwith
leverageisgreaterthanthevalueoftheprojectwithout
leverage.DCFValuationII:APVTheadjustedpresentvaluemethodbeginsbycalculatingthevalueofthefirmwithallequityfinancing.Wethenseparatelycalculatethevalueofthedebttaxshield(orothersideeffects连带效应),andaddthetwotogether.TheNPVoftheunleveredfirm(NPVU)iscalculatedbydiscountingtheunleveredcashflowsbyr0:
DCFValuationII:APVTheNPVofthefinancingsideeffects(NPVF)iscalculatedbydiscountingthedebttaxshieldsbythecostofdebt:OrforaperpetuityCostsoffinancialdistress,debtfinancingsubsidies,andissuancecostscanallbeincorporatedintothefinancingsideeffects连带效应有四种:债务融资的节税效应、发行成本、破产成本和非市场利率融资的收益。NoteThevalueofaprojectwithleverageisgreaterthanthevaluewithoutleverage(financingsideeffect).WACCmethodrequiredustogivethetargetcapitalstructure,whileAPVdoesnot.APVmethodrequiresustoforecasttheannualinterestexpense(andthustheannualdebtlevel)whileWACCdoesnot.ExampleII:APVValuationSingerCompanyexamplecontinued:
ThefirstpartoftheAPVcalculationiseasy.Recallthattheunleveredcashflows(UCF)are$92,400annually.Wecanthencalculatethepresentvalueoftheunleveredcompany(VU)byVU=92,400/0.2=462,000ExampleII:APVValuationSincethepriceforSingeris$475,000,NPVU=-475,000+462,000=-13,000.SowewouldnotpurchaseSingerifwewererequiredtomaintainanallequitycapitalstructure.ExampleII:APVValuationWenowwanttocalculatetheNPVofthetaxshieldfromthedebtfinancing(thefinancingsideeffect).Singer’sannualinterestexpensewillbeBxrB.Discountingtheresultingtaxshieldperpetuity(BxrBxTC)byrB,wearriveat:ExampleII:APVValuationWestillneedtocalculatehowmuchdebt
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