2025年CFA二级《公司金融》模拟卷

2025年CFA二级《公司金融》模拟卷考试时间：______分钟总分：______分姓名：______Question1:Acompanyisevaluatingaprojectwithaninitialinvestmentof$1,000,000.Theprojectisexpectedtogenerateannualcashflowsof$300,000forthenextfiveyears.Thecompany'srequiredrateofreturnis8%.WhatistheNetPresentValue(NPV)oftheproject?Assumecashflowsoccurattheendofeachyear.Question2:Youaregiventhefollowinginformationabouttwomutuallyexclusiveprojects:ProjectA:InitialInvestment=$500,000,IRR=14%,NPV@10%=$50,000ProjectB:InitialInvestment=$400,000,IRR=12%,NPV@10%=$30,000Ifthecompany'sweightedaveragecostofcapital(WACC)is10%,whichprojectshouldbeselectedbasedontheIRRrule?WhichprojectshouldbeselectedbasedontheNPVrule?Question3:Afirmisconsideringchangingitsworkingcapitalpolicy.Currently,itfollowsamoderatepolicywithacashconversioncycleof90days.Thefirmcanshifttoamoreaggressivepolicy,reducingitscashconversioncycleto60days.Theannualsalesare$10,000,000,andthefirm'scostofgoodssoldis80%ofsales.Whatistheestimatedreductioninworkingcapitalrequirementsduetothispolicychange,assumingthefirm'sinventoryconversionperiodandaccountspayabledeferralperiodremainunchanged?Question4:Discussthepotentialtrade-offsacompanyfaceswhenitdecidestoissuedebtinsteadofequitytofinanceanewinvestment.Inyourdiscussion,addressthetaxshieldbenefitofdebtandthecostsassociatedwithfinancialdistress.Question5:Acompanyhasadebt-equityratioof0.5.Itscostofdebtis6%(beforetax),anditscostofequityis12%.Thecorporatetaxrateis30%.Whatisthecompany'sWeightedAverageCostofCapital(WACC)?Question6:YouareanalyzingacompanyusingtheDividendDiscountModel(DDM).Thecompanyjustpaidadividendof$2pershare(D0=$2).Themarketrequiresareturnof15%(k=15%),andthecompany'sdividendsareexpectedtogrowataconstantrateof5%peryear(g=5%).Whatistheestimatedintrinsicvalueofthestocktoday(P0)?Question7:CompareandcontrasttheAdjustedPresentValue(APV)approachandtheFlow-to-Equity(FTE)approachforvaluingaprojectwithdebt.Whichapproachisgenerallyconsideredmorestraightforwardtoapply,andunderwhatcircumstancesmightoneapproachbepreferredovertheother?Question8:Acompanyisconsideringthepurchaseofanewmachine.Themachinecosts$800,000andhasanexpectedeconomiclifeof8years.Itisexpectedtogenerateannualpre-taxoperatingcashflowsof$250,000.Thecompanyusesstraight-linedepreciationfortaxpurposes,themachinehasnosalvagevalue,andthecompany'staxrateis35%.Ifthecompany'sWACCis12%,whatisthePaybackPeriod(assumingcashflowsoccurattheendofeachyear)?Question9:Explaintheconceptofrealoptionsinthecontextofcapitalbudgeting.Provideanexampleofarealoptionandhowitmightaffectacompany'sinvestmentdecision.Question10:Afirmisevaluatinganinvestmentinaforeigncountry.TherequiredreturnbasedontheCapitalAssetPricingModel(CAPM)forthisinvestmentiscalculatedasfollows:RequiredReturn=Risk-FreeRate+Beta*MarketRiskPremium.Therisk-freerateis4%,themarketriskpremiumis6%,andthecompanyestimatestheBetaoftheinvestmenttobe1.2.Whatistherequiredreturnforthisinvestment?Question11:Discussthemaincomponentsofacompany'scashconversioncycle.Howcanacompany缩短(shorten)itscashconversioncycle,andwhatarethepotentialbenefitsandrisksassociatedwithashortercycle?Question12:Twocompaniesoperateinthesameindustry.CompanyAhasahigherdebtratiothanCompanyB.CompareandcontrastthepotentialimpactsoffinancialleverageontheexpectedreturnandriskforshareholdersofCompanyAversusCompanyB.Considerboththemagnifyingeffectonreturnsandtheincreasedriskoffinancialdistress.Question13:Youaregiventhefollowingdataforacompany:MarketValueofDebt=$2,000,000MarketValueofEquity=$8,000,000CostofDebt(aftertax)=5%CostofEquity=10%DividendsperShare(D0)=$1.00ExpectedGrowthRateofDividends(g)=8%Thecompany'staxrateis25%.Calculatethecompany'sestimatedintrinsicvaluepershareusingtheDividendDiscountModel(GordonGrowthModel).Assumethemarketvalueofequityreflectstheintrinsicvalue.Question14:Aprojecthasthefollowingexpectedcashflows:Year0:-$1,500,000(InitialInvestment)Year1:$600,000Year2:$700,000Year3:$800,000Year4:$900,000Theproject'sinternalrateofreturn(IRR)is12%.Ifthecompany'sWACCis10%,shouldtheprojectbeacceptedbasedontheIRRrule?Explainyourreasoning.CalculatetheNetPresentValue(NPV)oftheprojectattheWACCof10%tosupportyourdecision.Question15:Acompanyisanalyzingacapitalbudgetingproject.Theprojectrequiresaninitialinvestmentinfixedassetsof$1,000,000,whichwillbedepreciatedstraight-linetozeroover5years.Theprojectisexpectedtogenerateannualsalesof$800,000andannualoperatingcosts(excludingdepreciation)of$500,000.Thecompany'staxrateis30%.Whatistheproject'sexpectedannualoperatingcashflowforeachofthe5years?---试卷答案Question1:NPV=-1,000,000+300,000/(1+0.08)^1+300,000/(1+0.08)^2+300,000/(1+0.08)^3+300,000/(1+0.08)^4+300,000/(1+0.08)^5NPV≈$24,960.78解析思路：计算项目的净现值（NPV），需要将未来五年的预期现金流量分别折现到当前时点，然后减去初始投资额。折现率采用公司的要求回报率8%。使用现值公式PV=CF/(1+r)^t，其中CF是现金流量，r是折现率，t是时间期数。将五年现金流的现值加总，得到总现值，再减去初始投资1,000,000美元，即为NPV。计算结果为正，表明项目预期创造价值，应予接受。Question2:BasedonIRRrule:SelectProjectA(IRR=14%>WACC=10%).BasedonNPVrule:SelectProjectA(NPV=$50,000>NPV=$30,000forProjectB).解析思路：根据内部收益率（IRR）规则，应选择IRR高于加权平均资本成本（WACC）的项目。比较两个项目的IRR与10%的WACC，ProjectA的IRR（14%）高于WACC，而ProjectB的IRR（12%）低于WACC，因此IRR规则下应选择ProjectA。根据净现值（NPV）规则，应选择NPV为正且最大的项目。比较两个项目的NPV，ProjectA的NPV（$50,000）大于ProjectB的NPV（$30,000），因此NPV规则下也应选择ProjectA。虽然两个项目互斥，且在WACC为10%时都创造了正的NPV，但理论上IRR和NPV规则有时会给出不同建议（尤其是在项目规模差异很大或现金流模式不同时）。在此例中，两者一致推荐ProjectA。注意题目明确项目互斥。Question3:ReductioninWorkingCapital=(InitialCCC*Sales)/365-(NewCCC*Sales)/365Reduction=($90,000*$10,000,000)/365-($60,000*$10,000,000)/365Reduction=$245,205.48-$164,383.56Reduction≈$80,821.92解析思路：工作资本需求与现金转换周期（CCC）成正比。计算政策变更导致的工作资本需求减少量，等于变更前的工作资本总额减去变更后的工作资本总额。工作资本总额可以通过现金转换周期乘以年销售额再除以365天来估算。变更前CCC为90天，变更后为60天，年销售额为$10,000,000。首先计算变更前的工作资本需求，再计算变更后的需求，两者相减即得到减少量。注意这里的计算是基于简化模型，假设销售额均匀分布。Question4:Trade-offs:Debtprovidesataxshieldduetothedeductibilityofinterestpaymentsbeforetax,loweringtheWACCandpotentiallyincreasingfirmvalue(Modigliani-Millerwithtaxes).However,debtincreasesfinancialleverage,magnifyingbothreturnsandrisksforshareholders.Italsointroducesthecostsoffinancialdistress(bankruptcycosts,costsassociatedwithfinancialconstraints,potentiallossofmarketshareorcustomerconfidence)andagencycosts(conflictsbetweenmanagersanddebtholdersoverrisk-taking).Theoptimalcapitalstructurebalancesthebenefitsofthetaxshieldagainstthecostsoffinancialdistressandagencyconflicts.解析思路：发行债务与发行权益融资相比，存在利弊权衡。主要利处是税盾效应：由于利息支出可以在税前扣除，减少了公司的应税收入，从而降低了税负，增加了公司价值（根据有税的MM定理）。主要弊端包括：1.财务杠杆放大效应：债务能放大股东回报（好的时候更好，坏的时候更坏），同时也放大了公司的风险。2.财务困境成本：高负债增加陷入破产或财务困境的可能性，带来直接成本（如律师费、诉讼费）和间接成本（如运营中断、供应商关系恶化、客户流失、人才流失等）。3.代理成本：债权人与股东之间可能存在利益冲突（如股东可能采取风险过高的行为损害债权人利益），需要监督成本或产生其他代理成本。公司的目标是在税盾利益和财务困境成本、代理成本之间找到平衡点，确定最优资本结构。Question5:WACC=(E/V*Re)+(D/V*Rd*(1-Tc))WhereE=MarketValueofEquity=$8,000,000V=TotalMarketValue=E+D=$8,000,000+$2,000,000=$10,000,000D=MarketValueofDebt=$2,000,000Re=CostofEquity=12%or0.12Rd=CostofDebt(aftertax)=5%or0.05Tc=CorporateTaxRate=30%or0.30WACC=($8,000,000/$10,000,000*0.12)+($2,000,000/$10,000,000*0.05*(1-0.30))WACC=(0.8*0.12)+(0.2*0.05*0.7)WACC=0.096+(0.2*0.035)WACC=0.096+0.007WACC=0.103or10.3%解析思路：计算加权平均资本成本（WACC），需要根据公司市场价值的权重，分别乘以权益成本（Re）和税后债务成本（Rd），然后加总。首先计算权益和债务在总市场价值中的比例（E/V和D/V）。权益比例E/V=$8M/$10M=0.8。债务比例D/V=$2M/$10M=0.2。然后，将权益比例乘以权益成本（12%），债务比例乘以税后债务成本（5%），并考虑税收屏蔽效应（1-Tc=1-0.3=0.7）。最后将两个结果相加得到WACC。计算结果为10.3%。Question6:P0=D0*(1+g)/(k-g)P0=$2*(1+0.05)/(0.15-0.05)P0=$2*1.05/0.10P0=$2.10/0.10P0=$21.00解析思路：使用戈登增长模型（GordonGrowthModel，一种DDM的特殊形式）估算股票内在价值。公式为P0=D0*(1+g)/(k-g)，其中P0是当前股票内在价值，D0是最近刚支付的股利，g是股利预期恒定增长率，k是投资者要求的回报率。将题目给出的数值代入公式：D0=$2,g=5%(或0.05),k=15%(或0.15)。计算得到P0=$21.00。假设市场要求回报率等于股票的必要回报率。Question7:APVmethod:Calculatesthevalueofanunleveredproject(VU)andthenaddsthepresentvalueofthetaxshield(PV(TS))fromthedebt.Formula:V=VU+PV(TS).SimplertocalculateVUassumingnodebt.Thetaxshieldiscalculatedastheproductofthedebtlevelandthecorporatetaxrate,discountedattherisk-freerateorthecostofdebt.FTEmethod:Calculatesthevalueoftheprojectfromtheperspectiveoftheequityholders,assumingthedebtstructureisfixed.Itinvolvesdiscountingtheleveredfreecashflows(FCF_L)atthecostofequity(Re).FTEcanbemorecomplexasitrequiresdeterminingtheappropriatecostofequityforeachperiodgiventhechangingleverage.APVisgenerallyconsideredmorestraightforward,especiallywhenthedebtstructureiscomplexorchangesovertime,asitseparatesthevaluecomponentscleanly.APVmightbepreferredwhendealingwithprojectswithinfirmsalreadyheavilyleveraged,asitavoidsdirectlyestimatingthecostofequityfortheleveredproject.解析思路：分析调整现值法（APV）和权益现金流法（FTE）的异同。*APV方法：首先计算无杠杆项目的价值（VU），然后加上债务带来的税盾价值的现值（PV(TS)）。公式为V=VU+PV(TS)。该方法相对简单，因为它先计算假设没有债务时的项目价值。税盾价值通常按债务乘以公司税率计算，然后以无风险利率或债务成本进行折现。*FTE方法：从债权人角度计算项目的价值，假设债务结构固定。它涉及将杠杆化自由现金流（FCF_L）以权益成本（Re）进行折现。FTE方法可能更复杂，因为它需要根据杠杆水平的变化，确定每个时期应使用的恰当权益成本。通常认为APV方法更直接简单，尤其是在债务结构复杂或随时间变化时。当评估处于高杠杆状态公司的内部项目时，APV可能更优，因为它避免了直接估计杠杆项目的权益成本。Question8:AnnualDepreciation=$800,000/8=$100,000EBT(EarningsBeforeTax)=$250,000-$100,000-$500,000=-$150,000(Loss)Tax=0.35*-$150,000=$0(Notaxduetoloss)OperatingCashFlow(OCF)=EBT+Depreciation=-$150,000+$100,000=-$50,000peryearPaybackPeriod=InitialInvestment/AnnualOCF=$800,000/|-$50,000|=$800,000/$50,000=16years解析思路：计算项目的回收期。首先计算每年的折旧额（直线法）。然后计算每年的税前利润（EBT），即销售收入减去折旧和经营成本。由于EBT为负值（亏损），当年税额为零。经营现金流（OCF）等于税后利润加上折旧。由于OCF为负值，表示每年产生的现金流出。回收期是初始投资除以每年的净现金流出量。计算结果为16年。这是一个负的回收期情况，意味着项目在整个经济寿命期内都无法收回初始投资。Question9:Realoptionsareopportunitiesembeddedincapitalbudgetingdecisionsthatallowmanagementtoadapttofutureuncertainties.Theyprovidetheright,butnottheobligation,totakecertainactions.Examplesincludetheoptiontoexpandifdemandishigherthanexpected,theoptiontoabandontheprojectiflossesareincurred,theoptiontodelayinvestmentuntilmoreinformationisavailable,ortheoptiontoswitchinputsorprocesses.Valuingrealoptionsrequirestechniqueslikedecisiontrees,binomialtrees,orMonteCarlosimulations,astheycapturethevalueofmanagerialflexibility.Theycansignificantlyaffectinvestmentdecisionsbyallowingfirmstocapturefutureupsideormitigatedownsiderisk,potentiallyleadingtoacceptanceofprojectsthatappearlessattractivebasedontraditionalNPVanalysis.解析思路：解释实物期权概念。实物期权是资本预算决策中嵌入的、允许管理层根据未来不确定性进行调整的机会。它赋予管理层采取特定行动的权利，而非义务。常见的例子包括：扩张期权（需求超出预期时）、放弃期权（亏损时）、延迟期权（获取更多信息前）、转换期权（改变投入或流程）。评估实物期权需要使用决策树、二叉树或蒙特卡洛模拟等高级技术，因为它们捕捉了管理灵活性的价值。实物期权可以显著影响投资决策，通过允许公司捕捉未来上行潜力或规避下行风险，可能导致基于传统NPV分析看似吸引力不大的项目被接受。Question10:RequiredReturn=4%+1.2*6%RequiredReturn=4%+7.2%RequiredReturn=11.2%解析思路：根据资本资产定价模型（CAPM）计算要求的回报率。CAPM公式为：要求的回报率=无风险利率+Beta*市场风险溢价。题目给出无风险利率为4%，市场风险溢价为6%，项目Beta为1.2。将数值代入公式进行计算即可得到要求的回报率为11.2%。Question11:Components:InventoryConversionPeriod(ICP),AccountsReceivableCollectionPeriod(ARCP),AccountsPayableDeferralPeriod(APDP).CCC=ICP+ARCP-APDP.ToshortentheCCC:ReduceICP(e.g.,improveinventorymanagement),reduceARCP(e.g.,tightencreditpolicy,improvecollection),increaseAPDP(e.g.,negotiatelongerpaymenttermswithsuppliers,withinreasonablelimits).Benefits:Reducestheamountofcapitaltiedupinworkingcapital,lowersfinancingcosts,improvescashflow,potentiallyenhancesprofitability.Risks:MaystrainsupplierrelationshipsifAPDPisincreasedtoomuch,maydetercustomersifcreditpolicyistightened,increasedriskofstockoutsifICPisreducedtooaggressively.解析思路：分析现金转换周期的组成部分和缩短方法。*组成部分：存货转换期（ICP）、应收账款回收期（ARCP）、应付账款递延期（APDP）。现金转换周期（CCC）的计算公式为：CCC=ICP+ARCP-APDP。*缩短方法：*缩短存货转换期（ICP）：改进库存管理，提高存货周转率。*缩短应收账款回收期（ARCP）：收紧信用政策，改进收款效率。*延长应付账款递延期（APDP）：与供应商协商更长的付款期限，但要适度。*好处：减少占用在营运资本中的资金量，降低融资成本，改善现金流，可能提升盈利能力。*风险：延长APDP可能损害供应商关系；收紧ARCP可能吓跑客户；过度缩短ICP可能导致库存短缺。Question12:CompanyA(HigherDebt):*ReturnMagnification:Higherfinancialleverage(higherdebtratio)meansreturnsonequity(ROE)aremoresensitivetochangesinearningsbeforeinterestandtaxes(EBIT).IfEBITrises,ROEincreasesmorethanproportionally.IfEBITfalls,ROEdecreasesmoresharply.*RiskMagnification:HigherleverageincreasestheriskoffinancialdistressandpotentialbankruptcyifEBITfallsbelowdebtobligations.Shareholdersbearmoreoftherisk.CompanyB(LowerDebt):*ReturnMagnification:LowerleveragemeansreturnsonequityarelesssensitivetoEBITchanges.ROEmovementsaremoremoderate.*RiskMagnification:Lowerleveragereducestheriskoffinancialdistressandbankruptcy.Shareholdersfacelessriskoflosingtheirinvestment.Insummary,CompanyAofferspotentiallyhigherreturnsforshareholdersbutalsoexposesthemtosignificantlyhigherrisk.CompanyBoffersmorestablereturnsandlowerrisk,butpotentiallylowerreturnscomparedtoCompanyA.解析思路：比较高杠杆（CompanyA）和低杠杆（CompanyB）公司对股东预期回报和风险的影响。*高杠杆公司（CompanyA）：*回报放大：财务杠杆高，意味着权益回报率（ROE）对息税前利润（EBIT）变化的敏感性更高。EBIT上升时，ROE增长幅度大于EBIT；EBIT下降时，ROE下降幅度更剧烈。*风险放大：杠杆高，陷入财务困境和破产的风险如果EBIT低于债务义务。股东承担更多风险。*低杠杆公司（CompanyB）：*回报放大：杠杆低，意味着ROE对EBIT变化的敏感性较低。ROE变动更温和。*风险放大：杠杆低，财务困境和破产风险降低。股东面临的投资损失风险较小。Question13:First,calculateWACCusingthegivendata:WACC=(E/V*Re)+(D/V*Rd*(1-Tc))E=$8,000,000,D=$2,000,000,V=$10,000,000Re=10%or0.10Rd=5%or0.05(Note:Thisisthe*after-tax*costofdebtasgivenintheproblem)Tc=25%or0.25WACC=($8M/$10M*0.10)+($2M/$10M*0.05*(1-0.25))WACC=(0.8*0.10)+(0.2*0.05*0.75)WACC=0.08+(0.2*0.0375)WACC=0.08+0.0075WACC=0.0875or8.75%Now,usetheGordonGrowthModeltofindthestockprice:P0=D0*(1+g)/(k-g)WhereD0=$1.00(given),g=8%or0.08(given),k=WACC=8.75%or0.0875(calculatedabove)P0=$1.00*(1+0.08)/(0.0875-0.08)P0=$1.00*1.08/0.0075P0=$1.08/0.0075P0=$144.00解析思路：首先，使用题目给出的数据计算加权平均资本成本（WACC），因为股利增长模型中的折现率通常使用WACC。WACC=(E/V*Re)+(D/V*Rd*(1-Tc))。代入E=$8M,D=$2M,V=$10M,Re=10%,Rd=5%(题目已给出为税后成本),Tc=25%。计算得到WACC=8.75%。其次，使用戈登增长模型（股利折现模型）计算股票内在价值P0。P0=D0*(1+g)/(k-g)，其中D0=$1.00,g=8%(0.08),k=8.75%(0.0875,即之前计算的WACC)。代入数值计算得到P0=$144.00。题目假设市场价值等于内在价值。Question14:IRRRule:CompareIRRtoWACC.ProjectIRR(12%)isgreaterthanWACC(10%).Accordingtothe