2025年CFA二级考试《公司金融》练习卷

2025年CFA二级考试《公司金融》练习卷考试时间：______分钟总分：______分姓名：______一Acompanyisevaluatinganewprojectthatrequiresaninitialinvestmentof$1,000,000.Theprojectisexpectedtogenerateannualcashflowsof$300,000forthenextfiveyears.Thecompany'sweightedaveragecostofcapital(WACC)is8%.CalculatetheNetPresentValue(NPV)oftheprojectusingthetraditionalNPVmethod.Assumingthecompanyusesthepaybackperiodmethodforinitialscreeningwithacutoffperiodofthreeyears,shouldthisprojectbeacceptedbasedonthiscriterion?Explainyourreasoning.Considerthescenariowherethecashflowsareuncertain.Thecompanyestimatesthatthereisa30%probabilityofreceiving$350,000peryear,a50%probabilityofreceiving$300,000peryear,anda20%probabilityofreceiving$250,000peryear.CalculatetheexpectedannualcashflowandtheexpectedNPVoftheproject.二Afirmisconsideringwhethertoleaseorbuyapieceofequipment.Theequipmentcosts$500,000andhasausefullifeof5years.Thefirmcanborrowmoneyata6%interestratetopurchasetheequipment.Iftheequipmentispurchased,itwillbedepreciatedstraight-linetozeroover5years.Thefirm'staxrateis30%.Thefirmhastheoptiontoleasetheequipmentfor$120,000peryear,paidatthebeginningofeachyear.Thelesseeisresponsibleformaintenancecosts,whichareexpectedtobe$10,000peryear.Calculatetheafter-taxcostofpurchasingtheequipment.Calculatetheafter-taxcostofleasingtheequipment.Whichoptionismorefavorableforthefirm,basedonthenetadvantagetoleasing(NAL)analysis?Showallcalculations.三XYZCorporationhasacapitalstructureconsistingof40%debtand60%equity.Thecompany'sdebthasamarketvalueof$200millionandayieldtomaturityof5%.Thecompany'sequityhasabetaof1.2.Therisk-freerateis3%,andthemarketriskpremiumis5%.Calculatethecompany'sweightedaveragecostofcapital(WACC)usingtheCapitalAssetPricingModel(CAPM)fortheequitycomponent.Assumingthecompanyisconsideringaprojectwiththesameriskasitsoveralloperations,whatistherequiredrateofreturnonthisprojectbasedontheWACC?Now,supposethecompanyisevaluatinganewprojectthatisriskierthanitsexistingoperations.Theprojecthasabetaof1.8.Whatistherequiredrateofreturnforthisriskierproject?四ABCCompanyisconsideringissuingnewsharestoraise$50millionforanewinvestmentproject.Thecompany'scurrentstockpriceis$25pershare.Theunderwritingspreadforthenewissueis5%.Calculatethetotalamountofmoneythecompanywillactuallyreceivefromtheissuanceofnewshares.Thecompanycurrentlyhas10millionsharesoutstanding.Afterthenewissue,whatwillbethenewtotalnumberofsharesoutstanding?Whatwillbethenewearningspershare(EPS)ifthecompany'searningsareexpectedtoremainunchangedat$100million?Discussthepotentialimpactofthisnewissueontheexistingshareholders,consideringthedilutioneffect.Whataresomealternativefinancingmethodsthecompanycouldconsider?五Acompanyisconsideringastockdividend.Thecurrentstockpriceis$50pershare,andthecompanyhas1millionsharesoutstanding.Thecompanyproposestodeclarea10%stockdividend.Calculatethenumberofnewsharesthatwillbeissuedtoexistingshareholders.Calculatethevalueofthestockdividendpershare.Whatwillbethenewtotalnumberofsharesoutstandingafterthestockdividend?Whatwillbethenewstockpricepershare,assumingnochangeinthecompany'smarketcapitalization?Comparetheimpactofa10%stockdividendversusa10%stocksplitonthecompany'stotalequity,shareholders'equitypershare,andmarketcapitalization.Explainthemaindifferencebetweenastockdividendandastocksplitfromanaccountingperspective.六Consideracalloptionwithastrikepriceof$50andacurrentstockpriceof$55.Theoptionhasatimevalueof$3.Calculatetheintrinsicvalueofthecalloption.Calculatethepremium(price)ofthecalloption.Ifthestockpricedecreasesto$45atexpiration,whatwillbethepayofftotheholderofthecalloption?Whatwillbetheprofitorlossfortheholder,assumingtheoptionwaspurchasedforitspremium?Now,consideraputoptionwiththesamestrikepriceof$50andthesamecurrentstockpriceof$55.Theputoptionhasatimevalueof$2.Calculatetheintrinsicvalueoftheputoption.Calculatethepremium(price)oftheputoption.Ifthestockpricedecreasesto$45atexpiration,whatwillbethepayofftotheholderoftheputoption?Whatwillbetheprofitorlossfortheholder,assumingtheoptionwaspurchasedforitspremium?七Acompanyisevaluatingtwomutuallyexclusiveprojects.ProjectAhasaninitialinvestmentof$100,000andexpectedcashflowsof$40,000peryearfor4years.ProjectBhasaninitialinvestmentof$150,000andexpectedcashflowsof$60,000peryearfor4years.Thecompany'sWACCis10%.CalculatetheInternalRateofReturn(IRR)forProjectAandProjectB.WhichprojecthasthehigherIRR?CalculatetheNetPresentValue(NPV)forProjectAandProjectB.WhichprojecthasthehigherNPV?ExplainthereasonwhytheIRRmethodmightleadtoadifferentconclusionthantheNPVmethodformutuallyexclusiveprojects.WhichprojectshouldthecompanychoosebasedontheNPVcriterion?Why?八Acompanyisconsideringacapitalrationingsituationwhereithasabudgetof$500,000forthenextyear.Ithasthreepotentialprojectsunderconsideration:*ProjectX:Initialinvestment$200,000,NPV$80,000*ProjectY:Initialinvestment$150,000,NPV$60,000*ProjectZ:Initialinvestment$100,000,NPV$50,000CalculatetheNPVperdollarinvestedforeachproject.Ifthecompanymustchooseprojectswithinitsbudgetconstraint,whichcombinationofprojectsshoulditselecttomaximizethetotalNPV?Showallcalculationsandjustifyyourchoice.试卷答案一NPV=-1,000,000+300,000/1.08^1+300,000/1.08^2+300,000/1.08^3+300,000/1.08^4+300,000/1.08^5NPV=-1,000,000+277,777.78+257,201.38+237,940.82+220,505.28+203,790.35NPV=$197,215.61Paybackperiod=InitialInvestment/AnnualCashFlow=$1,000,000/$300,000=3.33years.Sincethepaybackperiod(3.33years)isgreaterthanthecutoffperiod(3years),theprojectshouldnotbeacceptedbasedonthepaybackperiodcriterion.Expectedannualcashflow=(0.30*$350,000)+(0.50*$300,000)+(0.20*$250,000)Expectedannualcashflow=$105,000+$150,000+$50,000=$305,000ExpectedNPV=-1,000,000+305,000/1.08^1+305,000/1.08^2+305,000/1.08^3+305,000/1.08^4+305,000/1.08^5ExpectedNPV=-1,000,000+$1,082,335.64ExpectedNPV=$182,335.64解析思路：第一题考察资本预算的基本方法。首先使用传统的NPV方法计算项目净现值，通过将未来现金流的现值减去初始投资得到。然后，根据给定的回收期标准（3年）判断项目是否接受，需要比较计算出的回收期与标准回收期。最后，在存在不确定性的情况下，计算期望现金流量，并基于此计算期望NPV，评估项目的预期盈利能力。二After-taxcostofdebt=Yieldtomaturity*(1-Taxrate)=5%*(1-30%)=5%*0.70=3.5%Annualdepreciation=Costofequipment/Usefullife=$500,000/5=$100,000peryearTaxshieldfromdepreciation=Annualdepreciation*Taxrate=$100,000*30%=$30,000peryearAfter-taxcostofpurchasing:Initialoutlay=$500,000Annualafter-taxcashflows=(Annualdepreciation*Taxrate)=$30,000PVoftaxshield=$30,000/1.06^1+$30,000/1.06^2+$30,000/1.06^3+$30,000/1.06^4+$30,000/1.06^5PVoftaxshield=$30,000*(PVIFA6%,5)=$30,000*4.2124=$126,372After-taxcostofpurchasing=Initialoutlay-PVoftaxshield=$500,000-$126,372=$373,628After-taxcostofleasing:Annualleasepayment=$120,000Taxshieldfromleasepayment=Annualleasepayment*Taxrate=$120,000*30%=$36,000peryearAfter-taxleasepayment=Annualleasepayment*(1-Taxrate)=$120,000*(1-30%)=$120,000*0.70=$84,000peryearPVofafter-taxleasepayments=$84,000/1.06^1+$84,000/1.06^2+$84,000/1.06^3+$84,000/1.06^4+$84,000/1.06^5PVofafter-taxleasepayments=$84,000*(PVIFA6%,5)=$84,000*4.2124=$353,816NAL=After-taxcostofpurchasing-After-taxcostofleasingNAL=$373,628-$353,816=$19,812SincetheNALispositive($19,812),leasingismorefavorableforthefirm.解析思路：第二题考察租赁决策分析。首先计算购买方案的相关税后成本，包括初始投资、折旧带来的税盾以及折旧税盾的现值。然后计算租赁方案的相关税后成本，包括税后租赁付款额及其现值。最后，通过净租赁优势（NAL）比较两种方案的优劣，NAL为购买成本减去租赁成本，若为正则租赁更优。三Equitycostofcapital(usingCAPM)=Risk-freerate+Beta*MarketriskpremiumEquitycostofcapital=3%+1.2*5%=3%+6%=9%WACC=(Weightofdebt*After-taxcostofdebt)+(Weightofequity*Costofequity)WACC=(0.40*3.5%)+(0.60*9%)WACC=1.4%+5.4%=6.8%Requiredrateofreturnforthenewproject(sameriskasoveralloperations)=WACC=6.8%Requiredrateofreturnfortheriskierproject(beta1.8)=Risk-freerate+Beta*MarketriskpremiumRequiredrateofreturn=3%+1.8*5%=3%+9%=12%解析思路：第三题考察WACC的计算和风险调整。首先使用资本资产定价模型（CAPM）计算股权成本。然后根据债务权重、税后债务成本、股权权重和股权成本计算WACC。最后，分别计算与公司整体风险相同的新项目所需的回报率（即WACC），以及风险更高（Beta为1.8）的项目所需的调整后回报率。四Grossproceeds=Amountneeded/(1-Underwritingspread)Grossproceeds=$50,000,000/(1-0.05)=$50,000,000/0.95=$52,631,578.95Amountreceivedbythecompany=Grossproceeds=$52,631,578.95(assumingproceedsarereceivednetofunderwritingspread,ascalculated)Newtotalnumberofsharesoutstanding=Originalshares+NewsharesissuedNewsharesissued=Amountreceived/Stockprice=$52,631,578.95/$25=2,105,263.16shares(approximately)Newtotalnumberofsharesoutstanding=10,000,000+2,105,263.16=12,105,263.16shares(approximately)OriginalEPS=Totalearnings/Originalshares=$100,000,000/10,000,000=$10pershareNewEPS=Totalearnings/Newtotalshares=$100,000,000/12,105,263.16=$8.26pershare(approximately)Thenewissueleadstodilutionofexistingshareholders'ownershipandEPS.Eachexistingshareholderownsasmallerportionofthecompany,andtheearningspersharedecreaseduetotheincreasednumberofsharesoutstanding.Alternativefinancingmethodsincludedebtfinancing(e.g.,bankloan,bondissuance),retainedearnings,orotherequityfinancingmethodslikearightsoffering.解析思路：第四题考察新股发行和稀释效应。首先根据所需资金和承销费率计算发行总额。然后，发行总额即为公司实际收到的金额。接着计算新发行shares的数量，并据此计算发行后的总股本。然后计算发行前后的每股收益（EPS），比较变化。最后讨论新股发行对现有股东的稀释效应，并列举其他融资方式。五Newsharesissued=10%of1,000,000=0.10*1,000,000=100,000sharesValueofstockdividendpershare=(Totalmarketvalueafterdividend-Totalmarketvaluebeforedividend)/NewsharesissuedTotalmarketvaluebeforedividend=1,000,000shares*$50=$50,000,000Assumingmarketcapitalizationremainsunchangedafterdividend:Totalmarketvalueafterdividend=$50,000,000Valueofstockdividendpershare=($50,000,000-$50,000,000)/100,000=$0Alternatively,Value=Currentstockprice*Stockdividendrate=$50*10%=$5Newtotalnumberofsharesoutstanding=Originalshares+Newshares=1,000,000+100,000=1,100,000sharesNewstockpricepershare=Totalmarketcapitalization/Newtotalshares=$50,000,000/1,100,000=$45.45(approximately)Astockdividendincreasesthenumberofsharesoutstandingandreducesthestockpriceproportionally,butthetotalmarketcapitalizationandtotalequityremainunchanged.Fromanaccountingperspective,astockdividendincreasescommonstockandadditionalpaid-incapitalaccounts,whileastocksplitincreasesthenumberofsharesandreducesparvaluepershare,butdoesnotchangetotalstockholders'equity.解析思路：第五题考察股票股利和股票分割。首先计算新发行的股票数量。然后计算每股股票股利的价值，这等于股票分割前后的总市值变化除以新发行的股票数量，或者等于当前股价乘以股利率。接着计算股利后的总股本。最后计算股利后的新股价，等于总市值除以总股本。最后比较股票股利和股票分割对财务报表的影响，强调两者的区别。六Intrinsicvalueofcalloption=Max(0,Currentstockprice-Strikeprice)=Max(0,$55-$50)=$5Premiumofcalloption=Intrinsicvalue+Timevalue=$5+$3=$8Payofftocalloptionholderatexpiration($45)=Max(0,Expirationstockprice-Strikeprice)=Max(0,$45-$50)=$0Profit/Lossforholder=Payoff-Premiumpaid=$0-$8=-$8(Loss)Intrinsicvalueofputoption=Max(0,Strikeprice-Currentstockprice)=Max(0,$50-$55)=$0Premiumofputoption=Intrinsicvalue+Timevalue=$0+$2=$2Payofftoputoptionholderatexpiration($45)=Max(0,Strikeprice-Expirationstockprice)=Max(0,$50-$45)=$5Profit/Lossforholder=Payoff-Premiumpaid=$5-$2=$3(Profit)解析思路：第六题考察期权的基本概念和计算。首先根据期权类型（看涨/看跌）和行权价与当前股价的关系计算期权的内在价值。期权价格（溢价）等于内在价值加上时间价值。然后，根据到期时的股价计算期权持有者的收益（或损失），收益（或损失）等于期权收益减去期权购买价格。七IRRforProjectA:NPV=-100,000+40,000/(1+IRR)^1+40,000/(1+IRR)^2+40,000/(1+IRR)^3+40,000/(1+IRR)^4SetNPV=0andsolveforIRR.Usingafinancialcalculatororspreadsheet,IRRA≈18.92%IRRforProjectB:NPV=-150,000+60,000/(1+IRR)^1+60,000/(1+IRR)^2+60,000/(1+IRR)^3+60,000/(1+IRR)^4SetNPV=0andsolveforIRR.Usingafinancialcalculatororspreadsheet,IRRB≈20.54%ProjectBhasthehigherIRR($20.54%vs.18.92%).NPVforProjectA:NPVA=$197,215.61(calculatedinQuestion1)NPVforProjectB:NPVB=-150,000+60,000/1.10^1+60,000/1.10^2+60,000/1.10^3+60,000/1.10^4NPVB=-150,000+54,545.45+49,586.78+45,078.90+41,322.31NPVB=$40,533.44ProjectBhasthehigherNPV($40,533.44vs.$197,215.61).TheIRRmethodmightleadtoadifferentconclusionthantheNPVmethodformutuallyexclusiveprojectsbecauseIRRassumesreinvestmentofintermediatecashflowsattheIRRitself,whichmightn