2025年CFA《公司金融》强化训练

2025年CFA《公司金融》强化训练考试时间：______分钟总分：______分姓名：______Instructions:Pleaseanswerallquestionsbasedontheinformationprovided.Showallnecessarycalculationsforquantitativequestions.1.Acompanyisexpectedtogeneratefreecashflowsof$50millionnextyear,whichareexpectedtogrowataconstantrateof5%peryearindefinitely.Ifthecompany'sweightedaveragecostofcapital(WACC)is10%,whatisthevalueofthecompany'soperations(VU)usingthefreecashflowtothefirm(FCFF)approach?2.Youareanalyzingaprojectthatrequiresaninitialinvestmentof$1million.Theprojectisexpectedtogeneratecashinflowsof$400,000attheendofthefirstyear,$500,000attheendofthesecondyear,and$600,000attheendofthethirdyear.Iftheproject'sinternalrateofreturn(IRR)is12%,whatisthenetpresentvalue(NPV)oftheprojectifthediscountrateis10%?3.Acompanyhasadebt-to-equityratioof0.5.Ifthecostofdebtis6%andthecostofequityis12%,whatisthecompany'sweightedaveragecostofcapital(WACC)ifthecorporatetaxrateis30%?4.Acompanyisconsideringissuingnewdebttofundaproject.Theprojectisexpectedtogenerateannualcashflowsof$100,000for5years.Ifthecompany'scurrentdebt-to-equityratiois1.0,andthenewdebtissuancewouldincreasethedebt-to-equityratioto1.5,howwouldtheModigliani-Millertheoremwithtaxessuggesttheimpactonthecompany'sequitycostofcapital(rE)andoverallcostofcapital(WACC),assumingthecompanymaintainsthesamelevelofoperatingrisk?5.Astockhasanexpectedreturnof15%andastandarddeviationof20%.Therisk-freerateis5%.AccordingtotheCapitalAssetPricingModel(CAPM),whatisthestock'sbeta?6.Acompanyisconsideringacapitalbudgetingprojectwithaninitialinvestmentof$200,000.Theprojectisexpectedtogenerateannualcashinflowsof$60,000for5years.Thecompany'srequiredrateofreturnis10%.Whatistheproject'sprofitabilityindex(PI)?7.Acompanyhasthefollowinginventorylevels:*Beginninginventory:100units*Purchases:200units*Endinginventory:150unitsIfthecostofgoodssold(COGS)is$1,000,whatistheinventoryturnoverratio?8.Acompanyhasacashbalanceof$100,000atthebeginningofthemonth.Thecompanyexpectstoreceive$200,000incashduringthemonthandmakepaymentsof$150,000.Thecompany'sminimumcashbalancerequirementis$50,000.Whatisthecompany'sexpectedcashbalanceattheendofthemonth?9.Acompanyisconsideringofferingcredittermsof2/10,net30toitscustomers.Whatistheeffectiveannualcostoftradecreditifcustomersdonottakethediscountandpayonthe30thday?10.Acompany'sstockiscurrentlytradingat$50pershare.Thecompany'smanagementisconsideringastocksplit.Ifthecompanyimplementsa2-for-1stocksplit,whatwillbethenewstockprice?11.Acompanyhasacurrentstockpriceof$100pershareandadividendyieldof2%.Ifthecompany'sdividendgrowthrateisexpectedtobe5%peryearindefinitely,whatisthecompany'sexpectedtotalreturn?12.Acompanyisevaluatingacapitalbudgetingprojectwithaninitialinvestmentof$100,000.Theprojectisexpectedtogenerateannualcashinflowsof$30,000for4years.Thecompany'srequiredrateofreturnis10%.Whatistheproject'smodifiedinternalrateofreturn(MIRR)?13.Acompanyhasabondoutstandingwithafacevalueof$1,000,acouponrateof8%,andamaturityof5years.Ifthebond'syieldtomaturity(YTM)is10%,whatisthebond'scurrentprice?14.Acompanyisconsideringissuingequitytofinanceanewproject.Howwouldthisactionaffectthecompany'sdebt-to-equityratioandthecostofequity,accordingtotheModigliani-Millertheoremwithouttaxes?15.Acompanyisevaluatingtwomutuallyexclusiveprojects.ProjectAhasanNPVof$100,000andapaybackperiodof3years.ProjectBhasanNPVof$80,000andapaybackperiodof2years.BasedontheNPVandpaybackperiodcriteria,whichprojectshouldthecompanychoose?16.Acompanyhasacurrentassets-to-currentliabilitiesratioof2.0.Ifthecompany'scurrentliabilitiesare$500,000,whatisthecompany'scurrentassets?17.Acompanyisconsideringacapitalbudgetingprojectwithaninitialinvestmentof$100,000.Theprojectisexpectedtogenerateannualcashinflowsof$40,000for5years.Thecompany'srequiredrateofreturnis10%.Whatistheproject'sdiscountedpaybackperiod?18.Acompanyhasabondoutstandingwithafacevalueof$1,000,acouponrateof9%,andamaturityof10years.Ifthebond'syieldtomaturity(YTM)is8%,whatisthebond'sduration?19.Acompanyisconsideringacapitalbudgetingprojectwithaninitialinvestmentof$200,000.Theprojectisexpectedtogeneratecashflowsof$60,000attheendofthefirstyear,$70,000attheendofthesecondyear,and$80,000attheendofthethirdyear.Iftheproject'sinternalrateofreturn(IRR)is12%,whatistheproject'snetpresentvalue(NPV)ifthediscountrateis10%?20.Acompanyhasadebt-to-equityratioof0.8.Ifthecostofdebtis5%andthecostofequityis15%,whatisthecompany'sweightedaveragecostofcapital(WACC)ifthecorporatetaxrateis25%?试卷答案1.VU=$50million/(0.10-0.05)=$1,000million解析：使用永续增长模型计算公司运营价值。自由现金流预期为$50million，增长率为5%，贴现率为WACC10%。2.NPV=-$1,000,000+$400,000/(1.10)^1+$500,000/(1.10)^2+$600,000/(1.10)^3=$93,946.75解析：首先计算在IRR12%下的项目现金流现值，然后将现值与初始投资$1million相减得到NPV。3.WACC=(0.5/(0.5+1))*0.06*(1-0.30)+(1/(0.5+1))*0.12=0.096+0.08=0.176or17.6%解析：使用加权平均资本成本公式，债务权重为0.5/(0.5+1)，权益权重为1/(0.5+1)，债务成本为6%，权益成本为12%，税率为30%。4.rEwouldincrease,WACCwoulddecrease.解析：根据Modigliani-Miller定理（含税），增加财务杠杆会导致权益成本rE上升，因为财务风险增加。但由于税盾效应（Debt*TaxRate），WACC可能会下降，只要rE的增加幅度不足以抵消税盾效应。5.Beta=(0.15-0.05)/(0.20)^2=0.10/0.04=2.5解析：使用CAPM公式rearrangedtosolveforbeta:Beta=(ExpectedReturn-Risk-FreeRate)/VarianceofMarketReturn.6.PI=[($60,000/$100,000)*(1.10^-1+1.10^-2+1.10^-3+1.10^-4+1.10^-5)]/1=[0.6*3.79079]/1=2.27447or2.27解析：计算未来五年现金流的现值，然后除以初始投资$100,000。7.COGS/AverageInventory=$1,000/[(100+150)/2]=$1,000/125=8.0解析：计算平均库存[(BeginningInventory+EndingInventory)/2]，然后用COGS除以平均库存得到库存周转率。8.EndingCashBalance=$100,000+$200,000-$150,000=$150,000解析：将期初现金余额与当月预期收入相加，再减去当月预期支出。9.EffectiveAnnualCost=(DiscountPercentage/(100-DiscountPercentage))*(365/(PaymentPeriodinDays-DiscountPeriodinDays))=(2%/98%)*(365/(30-10))=0.020408*(365/20)=0.3728or37.3%解析：使用贸易信贷有效成本公式，折扣率为2%，折扣期为10天，付款期为30天。10.NewStockPrice=$50/2=$25解析：股票分割后，股数翻倍，市值不变，因此股价需要减半。11.TotalReturn=DividendYield+GrowthRate=2%+5%=7%解析：总回报等于股息收益率加上预期股息增长率。12.MIRR=[(-$100,000*(1+0.10)^4/($30,000/(1.10)^1+$30,000/(1.10)^2+$30,000/(1.10)^3+$30,000/(1.10)^4))]^(1/4)=10.61%解析：首先计算各年现金流的未来值（使用10%的再投资利率），然后将初始投资的现值与未来值相除，取四次方根。13.BondPrice=$80*PVIFA(10%,5)+$1,000*PVIF(10%,5)=$80*3.79079+$1,000*0.62092=$303.2632+$620.92=$924.18解析：使用债券定价公式，计算每年票息的现值（使用PVIFA）和到期面值的现值（使用PVIF），然后将两者相加。14.Equityissuancewoulddecreasethedebt-to-equityratioandaccordingtoModigliani-Millerwithouttaxes,increasethecostofequity(rE)duetoincreasedfinancialleverage.解析：发行新股会增加权益，从而降低债务权益比。根据无税MM定理，更高的财务杠杆会导致更高的权益成本rE。15.ChooseProjectAbasedonNPV,butfurtheranalysisisneededaspaybackperiodisnottheprimarycriterionformutuallyexclusiveprojects.解析：在互斥项目中，NPV是主要的决策标准。项目A的NPV($100,000)高于项目B($80,000)，因此应选择项目A。但Payback期不是最佳标准。16.CurrentAssets=CurrentRatio*CurrentLiabilities=2.0*$500,000=$1,000,000解析：使用流动比率公式，将流动比率2.0乘以流动负债$500,000。17.DiscountedCashFlows:$40,000/(1.10)^1=$36,363.64;$40,000/(1.10)^2=$33,057.85;$40,000/(1.10)^3=$30,052.59;$40,000/(1.10)^4=$27,320.55;$40,000/(1.10)^5=$24,836.86.CumulativePVasofendofYear3=$36,363.64+$33,057.85+$30,052.59=$99,474.08.CumulativePVasofendofYear4=$99,474.08+$27,320.55=$126,794.63.DiscountedPaybackPeriod=3+($100,000-$99,474.08)