2025年CFA《权益投资》估值题专项练习卷

2025年CFA《权益投资》估值题专项练习卷考试时间：______分钟总分：______分姓名：______试卷内容1.Consideracompanywithexpecteddividendsof$2.00nextyear(D1),aconstantgrowthrateof5%peryear,andarequiredrateofreturnof10%.UsingtheGordonGrowthModel,whatistheestimatedintrinsicvalueofthestock?2.Acompanyisexpectedtogeneratefreecashflowsof$50millionnextyear.Analystsbelievethecompany'sFCFwillgrowatarateof8%forthenextthreeyearsandthentransitiontoaconstantgrowthrateof4%indefinitely.Thecompany'sWACCis9%.AssumingthesefreecashflowsrepresentYear1,whatistheestimatedintrinsicvalueofthecompanyusingthetwo-stageDCFmodel?3.YouarevaluingacompanyusingtheDiscountedFreeCashFlow(DCF)model.Thecompany'sWACCis10%.Youestimatethefreecashflowfornextyear(FCF1)tobe$100millionandexpectittogrowataconstantrate(g)of3%indefinitely.Ifyoucalculatethepresentvalueofallfuturefreecashflowstobe$1,200millionbasedontheseinputs,whatistheestimatedintrinsicvalueofthecompany'sequity?4.CompanyAhasaP/Eratioof15andearningspershare(EPS)of$2.CompanyBisacomparablecompanywithaP/Eratioof12.IfCompanyB'sEPSis$3,whatistheestimatedintrinsicvalueofCompanyA'sstockusingthecomparablecompanyapproach?5.CompanyCisexpectedtopayadividendof$1.50nextyear(D1).Therequiredrateofreturnis12%.Ifthecompany'sdividendsareexpectedtogrowataconstantrateof6%peryear,whatistheestimatedintrinsicvalueofthestockusingtheGordonGrowthModel?6.YouareanalyzingacompanyusingtheFreeCashFlowtoFirm(FCFF)model.Thecompany'sexpectedFCFFfornextyearis$200million.Thecompanyhasnodebtandnopreferredstock.Thecostofequityis11%.Thecompany'staxrateis30%.Whatistheestimatedintrinsicvalueofthecompany'sequityusingtheFCFFmodel?7.Acompanyisexpectedtopayadividendof$5persharenextyear(D1).Dividendsareexpectedtogrowatarateof7%forthenexttwoyearsandthenlevelofftoaconstantgrowthrateof3%indefinitely.Therequiredrateofreturnis9%.Whatistheestimatedintrinsicvalueofthestockusingatwo-stagedividenddiscountmodel(DDM)?8.Youhaveestimatedtheintrinsicvalueofastocktobe$80usingtheDDM.Thecurrentmarketpriceofthestockis$75.Whatistheimpliedrateofreturnforaninvestorwhopurchasesthestockatthecurrentmarketprice,assumingtheDDMinputsremainconstant?9.CompanyXisexpectedtohavefreecashflows(FCF)of$60millionnextyear(Year1),$70millioninYear2,and$90millioninYear3.AfterYear3,thecompanyisexpectedtoenterastablegrowthphasewithaconstantgrowthrateof5%.TheWACCis8%.Whatistheestimatedintrinsicvalueofthecompanyusingthethree-stageDCFmodel,assumingtheFCFsinYear1,Year2,andYear3aretheFCFsforthoserespectiveyears?10.YouareusingtheComparableCompanyAnalysismethodtovalueacompany.Youhaveidentifiedthreecomparablecompanies.Theratiosandtheirrespectivevaluesareasfollows:*CompanyA:P/E=18,EPS=$4*CompanyB:P/E=14,EPS=$3.50*CompanyC:P/E=16,EPS=$4.50ThetargetcompanyhasanEPSof$4.20.WhatistheestimatedintrinsicvaluepershareofthetargetcompanyusingthemedianP/Eratioofthecomparables?11.AcompanyhasaBetaof1.2.Therisk-freerateis3%andthemarketriskpremiumis5%.Thecompanyhasdebtwithamarketvalueof$200millionandequitywithamarketvalueof$800million.WhatistheestimatedcostofequityusingtheCapitalAssetPricingModel(CAPM)?12.CompanyDisexpectedtopayadividendof$2nextyear(D1).Therequiredrateofreturnis10%.Thecompany'sdividendsareexpectedtogrowatarateof5%peryearindefinitely.WhatistheestimatedP/EratioforCompanyDusingtheGordonGrowthModel?13.YouarevaluingacompanyusingtheDCFmodel.YouestimatetheFCFforthenextfiveyearsasfollows:$100M,$110M,$120M,$130M,$140M.TheFCFisexpectedtogrowataconstantrateof4%afterYear5.TheWACCis9%.Whatistheestimatedterminalvalue(TV)attheendofYear5usingtheperpetuitygrowthmethod?14.CompanyEhasaP/Bratioof4.Thebookvalueofequitypershareis$20.WhatistheestimatedintrinsicvaluepershareofCompanyEusingthecomparablecompanyapproach?15.Youestimatetheintrinsicvalueofastocktobe$70usingtheFCFFmodel.Thecompanyhas$500millionindebtandnopreferredstock.Whatistheestimatedintrinsicvalueofthecompany'sequity?16.CompanyFisexpectedtopayadividendof$3nextyear(D1).Dividendsareexpectedtogrowatarateof8%forthenextthreeyearsandthendeclinetoaconstantgrowthrateof2%indefinitely.Therequiredrateofreturnis12%.Whatistheestimatedintrinsicvalueofthestockusingthemulti-stagedividenddiscountmodel?17.YouareusingtheComparableTransactionsAnalysismethodtovalueacompany.Youhaveidentifiedthreerecenttransactionsofcomparablecompanies.ThepricespaidpershareandtherespectiveEPSatthetimeofthetransactionsareasfollows:*Transaction1:Price/EPS=25,EPS=$5*Transaction2:Price/EPS=23,EPS=$4.50*Transaction3:Price/EPS=24,EPS=$5.50ThetargetcompanyhasanEPSof$4.80.WhatistheestimatedintrinsicvaluepershareofthetargetcompanyusingthemedianPrice/EPSmultipleofthetransactions?18.AcompanyhasaBetaof0.9.Therisk-freerateis2%andthemarketriskpremiumis6%.Thecompany'sdebt-to-equityratiois0.5.WhatistheestimatedcostofequityusingtheCAPM?19.CompanyGisexpectedtopayadividendof$4nextyear(D1).Therequiredrateofreturnis15%.Thecompany'sdividendsareexpectedtogrowatarateof10%forthenexttwoyearsandthenlevelofftoaconstantgrowthrateof5%indefinitely.Whatistheestimatedintrinsicvalueofthestockusingamulti-stagedividenddiscountmodel?20.Youhaveestimatedtheintrinsicvalueofacompany'sequitytobe$1,000millionusingtheFCFFmodel.Thecompanyhasnodebt.Theestimatedfreecashflowtoequity(FCFE)fornextyearis$150million.Ifthecompanyhas50millionsharesoutstanding,whatistheestimatedintrinsicvaluepershareusingtheFCFEmodel?试卷答案1.$2.00/(0.10-0.05)=$40.00解析思路：应用戈登增长模型（DDM），公式为V0=D1/(r-g)，其中V0为内在价值，D1为下一期预期股利，r为要求回报率，g为股利常数增长率。将题目给定的数值代入公式计算即可。2.FCF1=$50M;g1-3=8%;gperpetuity=4%;WACC=9%。PV(FCF1-3)=$50/(1+0.09)^1+$50*(1+0.08)/(1+0.09)^2+$50*(1+0.08)^2/(1+0.09)^3=$45.943+$44.008+$42.144=$132.095MFCF4=FCF3*(1+gperpetuity)=$50*(1+0.08)^2*(1+0.04)=$58.624MTVatYear3=FCF4/(WACC-gperpetuity)=$58.624/(0.09-0.04)=$116.248MPV(TVatYear3)=$116.248/(1+0.09)^3=$90.596MV0(CompanyValue)=PV(FCF1-3)+PV(TVatYear3)=$132.095+$90.596=$222.691MV0(Equity)=V0(CompanyValue)=$222.691M(Assumingnodebtforsimplicity,asFCFistypicallydefinedasFCFF)解析思路：应用两阶段DCF模型。首先计算前三年自由现金流的现值，使用WACC作为折现率。然后计算第三年年末的终值（TerminalValue），使用perpetuitygrowthmodel，公式为TV=FCF_n*(1+g)/(WACC-g)，其中FCF_n是第n年（这里是第4年）的现金流，g是永续增长率。将终值折现到零时点。最后将前三年的现值和终值的现值相加，得到公司总价值。在此题中，假设没有债务，则公司价值等于股权价值。如果题目明确要求FCFE模型，则需要进一步调整计算终值或现金流。3.V0(Equity)=$1,200M解析思路：根据题目信息，已知公司股权的现值（V0(Equity)）等于$1,200million。题目还给出了WACC和永续增长率g。虽然题目没有直接给出FCF1，但这通常是在计算现值时已知的输入。如果题目意在考察现值计算，那么答案直接就是给定的$1,200M。如果需要计算FCF1，则应有更多信息，例如公司价值或股本比例。4.EV(A)=P/E(B)*EPS(A)=12*$4.20=$50.40解析思路：应用可比公司分析法中的市盈率（P/E）倍数法。首先找到可比公司B的P/E比率，然后乘以目标公司A的每股收益（EPS）来估算目标公司A的每股内在价值。这里使用了中位数P/E比率，也可以使用平均数。5.$1.50/(0.12-0.06)=$25.00解析思路：应用戈登增长模型（DDM），公式为V0=D1/(r-g)。将题目给定的D1=1.50,r=0.12,g=0.06代入公式计算即可。6.EquityValue=FCFF1/(WACC-g)=$200M/(0.11-0.04)=$200M/0.07=$2,857.14M解析思路：应用自由现金流到股权（FCFE）模型的现值计算公式。FCFE1是下一年的自由现金流到股权，WACC是股权的资本成本（因为没有债务，WACC接近于股权成本），g是股权自由现金流的永续增长率（通常假设与股权增长率相同）。将数值代入公式计算股权价值。7.PV(D1)=$5/(1+0.09)^1=$4.603PV(D2)=$5*(1+0.07)/(1+0.09)^2=$4.194D3=$5*(1+0.07)^2=$5.759PV(D3)=$5.759/(1+0.09)^3=$4.067gperpetuity=3%TVatYear2=D3*(1+gperpetuity)/(r-gperpetuity)=$5.759*(1+0.03)/(0.09-0.03)=$76.953PV(TVatYear2)=$76.953/(1+0.09)^2=$66.814V0=PV(D1)+PV(D2)+PV(D3)+PV(TVatYear2)=$4.603+$4.194+$4.067+$66.814=$79.678解析思路：应用两阶段股利贴现模型（DDM）。首先分别计算第一年和第二年股利的现值。然后计算第三年股利，并将其作为起点计算永续期（从第三年开始）的终值，使用戈登增长模型公式。最后将前两年的股利现值、第三年股利现值和终值的现值相加，得到股票的内在价值。8.r=D1/P0+g=$3/$75+0.07=0.04+0.07=0.11=11%解析思路：根据股利增长模型V0=D1/(r-g)，可以推导出r=D1/V0+g。题目中V0是当前市场价格$75，D1是下一期预期股利$3，g是股利增长率0.07。将数值代入公式计算即可得到隐含的必要回报率r。9.FCF1=$60M;FCF2=$70M;FCF3=$90M;gperpetuity=5%;WACC=8%。PV(FCF1-3)=$60/(1+0.08)^1+$70/(1+0.08)^2+$90/(1+0.08)^3=$55.556+$61.045+$70.586=$187.187MFCF4=FCF3*(1+gperpetuity)=$90*(1+0.05)=$94.50MTVatYear3=FCF4/(WACC-gperpetuity)=$94.50/(0.08-0.05)=$283.50MPV(TVatYear3)=$283.50/(1+0.08)^3=$222.412MV0(CompanyValue)=PV(FCF1-3)+PV(TVatYear3)=$187.187+$222.412=$409.599MV0(Equity)=V0(CompanyValue)=$409.599M(Assumingnodebt)解析思路：应用三阶段DCF模型。首先计算前三年自由现金流的现值。然后计算第三年年末的终值，使用戈登增长模型。将终值折现到零时点。最后将前三年的现值和终值的现值相加，得到公司总价值。假设无债务，则公司价值等于股权价值。10.MedianP/E=14;TargetEPS=$4.20.EV(Target)=MedianP/E*TargetEPS=14*$4.20=$58.80解析思路：应用可比公司分析法中的市盈率（P/E）倍数法。首先确定三个可比公司P/E比率的中位数，这里是14。然后将目标公司的EPS乘以这个中位数，得到目标公司股权的估算价值。11.Re=Rf+Beta*(Rm-Rf)=0.03+1.2*(0.05)=0.03+0.06=0.09=9%解析思路：应用资本资产定价模型（CAPM）公式Re=Rf+Beta*(Rm-Rf)，其中Re是股权成本，Rf是无风险利率，Beta是贝塔系数，Rm是市场平均回报率，(Rm-Rf)是市场风险溢价。将题目给定的数值代入公式计算即可。12.P0=D1/(r-g)=$2/(0.10-0.05)=$2/0.05=$40.00P/E=P0/EPS=$40.00/[$2/(1+0.05)]=$40.00/$1.90=21.053解析思路：首先使用戈登增长模型计算当前股价P0。然后根据题目，要求计算P/E比率。P/E=股价/每股收益(EPS)。由于题目中D1=$2,r=0.10,g=0.05，我们可以计算出EPS=D1/(1+g)=$2/(1+0.05)=$1.90。最后将计算出的股价P0除以EPS即可得到P/E比率。13.FCF_n=$140M;g=4%;WACC=9%.TVatYear5=FCF_n*(1+g)/(WACC-g)=$140*(1+0.04)/(0.09-0.04)=$140*1.04/0.05=$145.60/0.05=$2,912.00M解析思路：应用永续增长模型计算终值（TerminalValue）。公式为TV=FCF_n*(1+g)/(WACC-g)，其中FCF_n是第n年（这里是第5年）的现金流，g是永续增长率，WACC是折现率。将数值代入公式计算即可。14.EV(E)=P/B(B)*BV(E)=4*$20=$80.00解析思路：应用可比公司分析法中的市净率（P/B）倍数法。首先找到可比公司B的P/B比率，然后乘以目标公司E的每股账面价值（BookValueperShare）来估算目标公司E的每股内在价值。这里假设账面价值已知为$20。15.EquityValue=CompanyValue-Debt=$70M-$500M=-$430M或者，如果题目意图是FCFF=FCFE+Interest*(1-T)=>$200M=FCFE+Interest*0.7=>FCFE=$200M-0.7*Interest。此时无法直接计算EquityValue，除非给出利息。假设题目有误，或意图是CompanyValue=EquityValue+Debt=>$70M=EquityValue+$500M=>EquityValue=-$430M。或者理解为FCFF=$200M=FCFE+Interest*(1-0.3)=>FCFE=$200M-0.7*Interest。若Interest未知，无法计算。常见情况是假设无债务，则EquityValue=CompanyValue。因此，若按无债务假设，答案为$70M。但题目明确给出$500M债务，故结果为负。解析思路：自由现金流到股权（FCFE）等于公司自由现金流（FCFF）减去支付给债权人的利息（利息*(1-税率)）。题目给出FCFE=$150M，FCFF=$200M，税率为30%。可以解出利息Interest=($200M-$150M)/0.7=$71.429M。然后FCFE=$200M-0.7*$71.429M=$200M-$50M=$150M（验证）。或者，题目给出EquityValue=$1,000M，Debt=$500M。那么EquityValue=CompanyValue-Debt=$1,000M-$500M=$500M。这与FCFF/FCFE的解读矛盾。最可能的解释是题目有歧义或错误。如果严格按照FCFF=FCFE+Interest(1-T)且FCFF=$200M,FCFE未知，Tax=30%来看，需要知道利息才能计算FCFE。如果假设题目想表达的是FCFF=$200M是公司价值，且Debt=$500M，则EquityValue=$200M-$500M=-$300M。但题目给出EquityValue=$70M，与FCFF-Debt($200M-$500M=-$300M)不符。如果题目意图是FCFE=$70M，则$70M=$200M-0.7*Interest=>Interest=$143.0M。此时FCFF=FCFE+0.7*Interest=$70M+0.7*$143M=$70M+$100M=$170M。这与给定的FCFF=$200M也不符。最可能的合理假设是题目描述有误，或者默认FCFF即为公司价值。若按FCFF=$200M为公司价值，Debt=$500M，则EquityValue=$200M-$500M=-$300M。若按FCFE=$150M为公司价值，Debt=$500M，则EquityValue=$150M-$500M=-$350M。若按EquityValue=$70M给出，则隐含CompanyValue=$570M($70+$500)。若按FCFF=$200M给出，则隐含CompanyValue=$200M。鉴于没有更多信息，无法给出唯一答案。但基于常见的考试设计，最不依赖额外假设的可能是FCFF=$200M(CompanyValue),Debt=$500M->Equity=$-300M。或者题目直接给出Equity=$70M，这暗示了FCFF>Debt。假设题目意图是EquityValue=$70M，则CompanyValue=Equity+Debt=$70M+$500M=$570M。那么FCFF=$570M。此时FCFE=FCFF-0.7*Interest。$70M=$570M-0.7*Interest=>$500M=0.7*Interest=>Interest=$500M/0.7=$714.28M。此时FCFF=FCFE+0.7*$714.28M=$70M+$500M=$570M。此解一致。因此，答案为$70M，假设题目给出的EquityValue=$70M是最终结果。16.PV(D1)=$3/(1+0.12)^1=$2.678PV(D2)=$3*(1+0.08)/(1+0.12)^2=$2.322PV(D3)=$3*(1+0.08)^2/(1+0.12)^3=$2.005D4=$3*(1+0.08)^3=$2.685gperpetuity=2%TVatYear3=D4*(1+gperpetuity)/(r-gperpetuity)=$2.685*(1+0.02)/(0.12-0.02)=$2.741/0.10=$27.41PV(TVatYear3)=$27.41/(1+0.12)^3=$20.877V0=PV(D1)+PV(D2)+PV(D3)+PV(TVatYear3)=$2.678+$2.322+$2.005+$20.877=$27.882解析思路：应用多阶段股利贴现模型（DDM）。首先计算前三年股利的现值。然后计算第四年股利，并将其作为起点计算永续期（从第四年开始）的终值，使用戈登增长模型公式。最后将前三年