2025年CFA《公司估值》歷年真題考試時(shí)間：______分鐘總分：______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.試卷答案Question1:Value=D0*(1+g)/(ke-g)=$2*(1+0.05)/(0.12-0.05)=$2.10/0.07=$30解析思路：應(yīng)用戈登增長(zhǎng)模型（GGM）公式，其中D0為最近一次股利，g為永續(xù)增長(zhǎng)率，ke為股權(quán)要求回報(bào)率。將題目給出的數(shù)值代入公式直接計(jì)算得到內(nèi)在價(jià)值。Question2:FCFF模型的關(guān)鍵假設(shè)包括：公司經(jīng)營(yíng)是可持續(xù)的；公司不發(fā)行新股；股權(quán)融資是零增長(zhǎng)；公司現(xiàn)金流是永續(xù)的；公司價(jià)值等于其自由現(xiàn)金流折現(xiàn)值；公司資本結(jié)構(gòu)是永久性的。這些假設(shè)至關(guān)重要，因?yàn)樗鼈兒?jiǎn)化了模型的數(shù)學(xué)處理，使得計(jì)算成為可能。特別是關(guān)于永續(xù)性、零新股發(fā)行和現(xiàn)金流穩(wěn)定性的假設(shè)，直接關(guān)系到WACC的確定和終值的計(jì)算。如果這些假設(shè)不成立，F(xiàn)CFF的預(yù)測(cè)和折現(xiàn)將產(chǎn)生較大偏差，影響估值結(jié)果的準(zhǔn)確性。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：這是一個(gè)兩階段DCF模型。首先，分別計(jì)算前三年（Years1-3）自由現(xiàn)金流的現(xiàn)值。然后，計(jì)算第三年年末的終值（TerminalValue），終值是基于第三年的現(xiàn)金流并考慮永續(xù)增長(zhǎng)計(jì)算的。最后，將前三年的現(xiàn)值和終值的現(xiàn)值相加，得到企業(yè)價(jià)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：計(jì)算WACC需要用到資本資產(chǎn)定價(jià)模型（CAPM）計(jì)算股權(quán)成本（ke=Rf+βe*(Rm-Rf)），以及債務(wù)成本（Rd）和稅盾效應(yīng)。題目給出了ke、βe、Rf、Rm-Rf和資本結(jié)構(gòu)數(shù)據(jù)。缺少債務(wù)成本（Rd）。WACC的計(jì)算公式為：WACC=E/V*ke+D/V*Rd*(1-T)。根據(jù)提供的權(quán)重（E/V=0.8,D/V=0.2）和假設(shè)（如Rd=Rf=3%），可以計(jì)算出數(shù)值結(jié)果。若不假設(shè)Rd，則WACC為表達(dá)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：對(duì)比兩種方法的定義、基礎(chǔ)原理和適用場(chǎng)景。CCA使用市場(chǎng)可比公司的公開指標(biāo)進(jìn)行估值，側(cè)重市場(chǎng)公允性；PTA使用近期實(shí)際并購(gòu)交易的價(jià)格和指標(biāo)，側(cè)重交易驅(qū)動(dòng)因素和支付意愿。分析各自的優(yōu)勢(shì)和局限性，以及在不同情境下的適用性。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：題目要求使用加權(quán)平均法，但未給出可比公司的市場(chǎng)價(jià)值，無法直接計(jì)算權(quán)重。注意到權(quán)重是按市場(chǎng)價(jià)值比例的，且要求使用加權(quán)平均P/E。一個(gè)可能的簡(jiǎn)化思路是假設(shè)三個(gè)可比公司的市場(chǎng)價(jià)值加起來代表了某個(gè)基準(zhǔn)，或者利用行業(yè)平均P/E作為參照。這里采用了將加權(quán)平均P/E表示為行業(yè)P/E的倍數(shù)（k）的方式。最終估值=目標(biāo)公司EPS*(行業(yè)平均P/E*k)。由于缺少具體市場(chǎng)價(jià)值數(shù)據(jù)，無法得出具體的k值和P0值，但展示了計(jì)算思路。更嚴(yán)謹(jǐn)?shù)姆椒ㄐ枰袌?chǎng)價(jià)值數(shù)據(jù)。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：闡述選擇可比公司的標(biāo)準(zhǔn)：行業(yè)、規(guī)模、增長(zhǎng)、風(fēng)險(xiǎn)、財(cái)務(wù)結(jié)構(gòu)等相似性。強(qiáng)調(diào)選擇標(biāo)準(zhǔn)的重要性，因?yàn)楣乐当稊?shù)反映了市場(chǎng)對(duì)具有相似特征公司的預(yù)期。選擇不當(dāng)會(huì)導(dǎo)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：這是一個(gè)三階段DCF模型（有時(shí)也稱為多階段模型）。首先計(jì)算前三年的自由現(xiàn)金流折現(xiàn)值。然后，計(jì)算第三年年末基于第四年及以后永續(xù)增長(zhǎng)率的終值，并將終值折現(xiàn)到第三年。最后，將前三年的現(xiàn)值和終值的現(xiàn)值相加，得到股票的內(nèi)在價(jià)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：應(yīng)用自由現(xiàn)金流到公司（FCFF）的公式：FCFF=EBIT(1-T)+折舊-資本支出-營(yíng)運(yùn)資本變動(dòng)。將題目中給出的EBIT、TaxRate、Depreciation、CapEx和ChangeinNWC數(shù)值代入公式直接計(jì)算即可。Question10:FCFFYear1(