2025年CFA《公司估值》历年真题

2025年CFA《公司估值》历年真题考试时间：______分钟总分：______分姓名：______Question1:Acompanyisexpectedtogrowitsdividendsataconstantrateof5%peryearindefinitely.Thelastdividendpaid(D0)was$2pershare.Iftherequiredrateofreturnonequity(ke)is12%,calculatetheestimatedintrinsicvalueofthestockusingtheGordonGrowthModel(GGM).Question2:DescribethekeyassumptionsunderlyingtheFreeCashFlowtoFirm(FCFF)model.ExplainwhytheseassumptionsarecriticalforthevalidityoftheFCFFvaluationapproach.Question3:YouareanalyzingacompanyprojectedtogenerateFreeCashFlowstoFirm(FCFF)of$100millionnextyear(Year1),$120millioninYear2,and$150millioninYear3.Thereafter,FCFFisexpectedtogrowataconstantrateof4%indefinitely.Thecompanyhasnodebt,andtheweightedaveragecostofcapital(WACC)is10%.Calculatetheenterprisevalue(EV)usingatwo-stagediscountedcashflow(DCF)model.Question4:Acompanyhasabetaof1.2.Therisk-freerateis3%,andthemarketriskpremiumis7%.Thecorporatetaxrateis25%.Thecompanyhasdebtwithamarketvalueof$200millionandequitywithamarketvalueof$800million.Calculatethecompany'sWeightedAverageCostofCapital(WACC).Question5:CompareandcontrastthevaluationapproachesusedintheComparableCompaniesAnalysis(Multiples)andthePrecedentTransactionsAnalysis.Underwhatcircumstancesmightoneapproachbemoreappropriatethantheother?Question6:YouarevaluingacompanyusingthePrice/Earnings(P/E)multiplemethod.Youhaveidentifiedthreecomparablecompanies.CompanyAtradesataP/Emultipleof15,CompanyBtradesataP/Emultipleof18,andCompanyCtradesataP/Emultipleof20.Thetargetcompanyhasearningspershare(EPS)expectednextyearof$5.TheindustryaverageP/Emultipleis17.Usingaweightedaverageofthecomparablemultiplesbasedonmarketcapitalization,estimatetheintrinsicvaluepershareofthetargetcompany.Assumetheweightsareproportionaltothemarketcapsofthecomparables.Question7:DescribetheprocessofselectingappropriatecomparablecompaniesforaMultiplesvaluationanalysis.Whatfactorsshouldbeconsideredwhenchoosingcomparables,andwhyaretheyimportant?Question8:AcompanyisexpectedtogenerateFreeCashFlowtoEquity(FCFE)nextyearof$3pershare.FCFEisexpectedtogrowat10%inYear2,8%inYear3,andthengrowataconstantrateof6%indefinitely.Therequiredrateofreturnonequity(ke)is12%.Calculatetheestimatedintrinsicvalueofthestockusingamulti-stageDiscountedCashFlow(DCF)model.Question9:Youaregiventhefollowingdataforacompany:-EarningsBeforeInterestandTaxes(EBIT)nextyear:$150million-InterestExpense:$30million-TaxRate:30%-Depreciation:$20million-CapitalExpenditures:$50million-ChangeinNetWorkingCapital:$10million-MarketValueofDebt:$100million-MarketValueofEquity:$400millionCalculatetheFreeCashFlowtoFirm(FCFF)fornextyear.Question10:Acompanyisconsideringanacquisition.Thetargetcompanyisexpectedtogeneratesynergiesof$20millioninthefirstyearaftertheacquisition,decreasingby$2millionperyearforthenextthreeyears.Thepost-acquisitionFCFFinYear4isexpectedtobe$120million,anditisexpectedtogrowataconstantrateof5%thereafter.TheWACCforthecombinedcompanyis9%.Calculatethepresentvalueofthesynergiesandtheterminalvalueofthetargetcompany'sFCFFatthetimeofacquisition,assumingthesynergiesarerealizedoneyearaftertheacquisition.Determinethemaximumpricetheacquiringcompanyshouldbewillingtopayforthetargetcompanytoday,basedsolelyonthesecashflowsandgrowthprospects.试卷答案Question1:Value=D0*(1+g)/(ke-g)=$2*(1+0.05)/(0.12-0.05)=$2.10/0.07=$30解析思路：应用戈登增长模型（GGM）公式，其中D0为最近一次股利，g为永续增长率，ke为股权要求回报率。将题目给出的数值代入公式直接计算得到内在价值。Question2:FCFF模型的关键假设包括：公司经营是可持续的；公司不发行新股；股权融资是零增长；公司现金流是永续的；公司价值等于其自由现金流折现值；公司资本结构是永久性的。这些假设至关重要，因为它们简化了模型的数学处理，使得计算成为可能。特别是关于永续性、零新股发行和现金流稳定性的假设，直接关系到WACC的确定和终值的计算。如果这些假设不成立，FCFF的预测和折现将产生较大偏差，影响估值结果的准确性。Question3:Year1FCFF:$100MYear2FCFF:$120MYear3FCFF:$150MGrowthrate(g):4%WACC:10%PV(Year1)=$100M/(1+0.10)^1=$90.91MPV(Year2)=$120M/(1+0.10)^2=$99.17MPV(Year3)=$150M/(1+0.10)^3=$112.69MTerminalValue(TV)atYear3=FCFFYear4/(WACC-g)=$150M*(1+0.04)/(0.10-0.04)=$156M/0.06=$2600MPV(TVatYear3)=$2600M/(1+0.10)^3=$2186.29MEV=PV(Year1)+PV(Year2)+PV(Year3)+PV(TVatYear3)EV=$90.91M+$99.17M+$112.69M+$2186.29M=$2489.06M解析思路：这是一个两阶段DCF模型。首先，分别计算前三年（Years1-3）自由现金流的现值。然后，计算第三年年末的终值（TerminalValue），终值是基于第三年的现金流并考虑永续增长计算的。最后，将前三年的现值和终值的现值相加，得到企业价值（EV）。Question4:EquityBeta(βe):1.2Risk-FreeRate(Rf):3%MarketRiskPremium(Rm-Rf):7%CorporateTaxRate(T):25%MarketValueofDebt(D):$200MMarketValueofEquity(E):$800MTotalMarketValue(V)=D+E=$1000MWeightofDebt(D/V):$200M/$1000M=0.20WeightofEquity(E/V):$800M/$1000M=0.80CostofDebt(Rd):Notdirectlygiven,butWACCformulausesRd*(1-T).WecannotcalculateanumericalWACCwithoutRd.AssumingRdisknownorcanbeestimated,theformulaisWACC=E/V*ke+D/V*Rd*(1-T).IfweassumeRd=Rf(acommonsimplificationifnotprovided),Rd=3%.WACC=0.80*12%+0.20*3%*(1-0.25)WACC=0.96%+0.20*3%*0.75WACC=0.96%+0.045=1.005%(UsingRd=3%)IfRdisnotspecified,theWACCcannotbenumericallydetermined.Theformulaandweightsarekey.解析思路：计算WACC需要用到资本资产定价模型（CAPM）计算股权成本（ke=Rf+βe*(Rm-Rf)），以及债务成本（Rd）和税盾效应。题目给出了ke、βe、Rf、Rm-Rf和资本结构数据。缺少债务成本（Rd）。WACC的计算公式为：WACC=E/V*ke+D/V*Rd*(1-T)。根据提供的权重（E/V=0.8,D/V=0.2）和假设（如Rd=Rf=3%），可以计算出数值结果。若不假设Rd，则WACC为表达式形式。Question5:ComparableCompaniesAnalysis(Multiples)involvesvaluingacompanybycomparingitsfinancialmetrics(likeP/E,P/B,EV/EBITDA)tothoseofsimilarcompaniesinthemarket.Itreliesontheprincipleofcomparabletransactionsandisoftenusedforpubliccompanies.PrecedentTransactionsAnalysisinvolvesvaluingacompanybasedonthemultiplespaidinrecentactualM&Atransactionsofsimilarcompanies.Itreflectswhatbuyersarewillingtopayinthemarketandisoftenusedforprivatecompaniesorwhenacquiringapubliccompany.Multiplesanalysisisgenerallymoreappropriatewhentherearemanyactivecomparablesinthemarket,whilePrecedentTransactionsismorerelevantwhentherearefewavailabletransactionsorwhencapturingsynergypotentialiskey,thoughitcanbelessforward-looking.解析思路：对比两种方法的定义、基础原理和适用场景。CCA使用市场可比公司的公开指标进行估值，侧重市场公允性；PTA使用近期实际并购交易的价格和指标，侧重交易驱动因素和支付意愿。分析各自的优势和局限性，以及在不同情境下的适用性。Question6:MarketCapsofComparables:CompanyA:Notgiven,assumeweightwACompanyB:Notgiven,assumeweightwBCompanyC:Notgiven,assumeweightwCTotalWeight=wA+wB+wC=1Weightsproportionaltomarketcap:wA=CapA/(CapA+CapB+CapC),wB=CapB/(CapA+CapB+CapC),wC=CapC/(CapA+CapB+CapC)IndustryAverageP/E:17TargetEPS:$5EstimatedIntrinsicValue(P0)=TargetEPS*AverageMultipleAverageMultiple=wA*15+wB*18+wC*20P0=$5*(wA*15+wB*18+wC*20)Sinceweightsareproportionaltomarketcaps,wecanusetheratiooftheaveragemultipletotheindustryaverage:AverageMultiple/IndustryAverage=(wA*15+wB*18+wC*20)/17LetAverageMultiple=17*kP0=$5*(17*k)=$85k解析思路：题目要求使用加权平均法，但未给出可比公司的市场价值，无法直接计算权重。注意到权重是按市场价值比例的，且要求使用加权平均P/E。一个可能的简化思路是假设三个可比公司的市场价值加起来代表了某个基准，或者利用行业平均P/E作为参照。这里采用了将加权平均P/E表示为行业P/E的倍数（k）的方式。最终估值=目标公司EPS*(行业平均P/E*k)。由于缺少具体市场价值数据，无法得出具体的k值和P0值，但展示了计算思路。更严谨的方法需要市场价值数据。Question7:Theprocessofselectingcomparablecompaniesinvolvesidentifyingasetofcompaniesthatoperateinthesameindustry,havesimilarbusinessmodels,size(marketcapitalizationorrevenue),growthprospects,riskprofile,andfinancialstructure.Keyfactorsincludeindustrysimilarity,scale,profitability,growth,marketposition,capitalintensity,taxrates,dividendpolicy,andcurrency.Itisimportanttochooserelevantcomparablesbecausethevaluationmultiple(e.g.,P/E)reflectsmarketexpectationsforcompanieswithsimilarcharacteristics.Usingirrelevantcomparableswillleadtodistortedvaluationmultiplesandpotentiallyincorrectvaluationconclusions.解析思路：阐述选择可比公司的标准：行业、规模、增长、风险、财务结构等相似性。强调选择标准的重要性，因为估值倍数反映了市场对具有相似特征公司的预期。选择不当会导致估值偏差。Question8:FCFEYear1:$3GrowthRateYear2(g1):10%GrowthRateYear3(g2):8%GrowthRateYear4onwards(g):6%RequiredRateofReturnonEquity(ke):12%PV(FCFEYear1)=$3/(1+0.12)^1=$2.68PV(FCFEYear2)=$3*(1+0.10)/(1+0.12)^2=$3.30/1.2544=$2.63PV(FCFEYear3)=$3*(1+0.10)*(1+0.08)/(1+0.12)^3=$3.48/1.4049=$2.47FCFEYear4=FCFEYear3*(1+g)=$3.48*1.06=$3.69TerminalValue(TV)atYear3=FCFEYear4/(ke-g)=$3.69/(0.12-0.06)=$3.69/0.06=$61.50PV(TVatYear3)=$61.50/(1+0.12)^3=$61.50/1.4049=$43.75IntrinsicValue=PV(Year1)+PV(Year2)+PV(Year3)+PV(TVatYear3)IntrinsicValue=$2.68+$2.63+$2.47+$43.75=$51.53解析思路：这是一个三阶段DCF模型（有时也称为多阶段模型）。首先计算前三年的自由现金流折现值。然后，计算第三年年末基于第四年及以后永续增长率的终值，并将终值折现到第三年。最后，将前三年的现值和终值的现值相加，得到股票的内在价值。Question9:FCFF=EBIT*(1-T)+Depreciation-CapEx-ChangeinNWCFCFF=$150M*(1-0.30)+$20M-$50M-$10MFCFF=$105M+$20M-$50M-$10MFCFF=$65M解析思路：应用自由现金流到公司（FCFF）的公式：FCFF=EBIT(1-T)+折旧-资本支出-营运资本变动。将题目中给出的EBIT、TaxRate、Depreciation、CapEx和ChangeinNWC数值代入公式直接计算即可。Question10:FCFFYear1(