公司理财罗斯习题集

课堂练习1Considertwosecuritiesthatpayrisk-freecashflowsoverthenexttwoyearsandthathavethecurrentmarketpricesshownhere:a.Whatistheno-arbitragepriceofasecuritythatpayscashflowsof$100inoneyearand$100intwoyears?b.Whatistheno-arbitragepriceofasecuritythatpayscashflowsof$100inoneyearand$500intwoyears?c.Supposeasecuritywithcashflowsof$50inoneyearand$100intwoyearsistradingforapriceof$130.Whatarbitrageopportunityisavailable?课堂练习2•某公司如果不从事任何新的项目，则其每年预期盈利为1亿美元。该公司面临这样一个投资机会：在今天立即投资1500万美元并在一年后投资500万美元，两年后，这一新的投资每年将为公司带来1000万美元的盈利。假设该公司有2000万股普通股票，贴现率为15%，求：•当公司不从事任何新的投资项目时每股股票的价格是多少？•投资项目的价值是多少？•如果公司进行该投资项目，每股股票的价格是多少？课堂练习3某公司如果不从事新的投资项目，它每年的每股盈利为4元，在此情形下，公司把所有的盈利当作股利分发出去（假设第一笔股利刚好在一年后收到）。在另一种情形中，假设距今三年后的每一年，公司将其盈利的25%投资于新的项目，每一个投资项目将在一年后获得40%的收益率（直至永远）。设贴现率为14%，分别求公司在不从事新的投资项目和从事新的投资项目时的股票价格。课堂练习4某公司市盈率为12，股利支付比率40%，股价为32美元。如果股利支付比率变为60%，股价为多少？课堂练习5•Pricesofzero-coupon,default-freesecuritieswithfacevaluesof$1000aresummarizedinthefollowingtable:Supposeyouobservethatathree-year,default-freesecuritywithanannualcouponrateof10%andafacevalueof$1000hasapricetodayof$1183.50.Isthereanarbitrageopportunity?Ifso,showspecificallyhowyouwouldtakeadvantageofthisopportunity.Ifnot,whynot?练习1解答a.ThissecurityhasthesamecashflowsasaportfolioofoneshareofB1andoneshareofB2.Therefore,itsno-arbitragepriceis94+85=$179.b.ThissecurityhasthesamecashflowsasaportfolioofoneshareofB1andfivesharesofB2.Therefore,itsno-arbitragepriceis94+5×85=$519c.Thereisanarbitrageopportunitybecausetheno-arbitragepriceshouldbe$132(94/2+85).Oneshouldbuytwosharesofthesecurityat$130/shareandselloneshareofB1andtwosharesofB2.Totalprofitwouldbe$4(94+85×2–130×2).练习2解答•（1）摇钱树的价值：PV=C1/r=$100,000,000/0.15=$666,666,666.67•每股股票价格=$666,666,666.67/20,000,000=$33.33•（2）NPVGO=C0+C1+[C2/r]/(1+r)T•=-$15,000,000-$5,000,000/1.15+[$10,000,000/0.15]/(1.15)•=$38,623,188.41•（3）每股股票价格=（1）+NPVGO/(股数)•=$33.33+$38,623,188.41/20,000,000•=$35.26练习3解答P=Div/r=4/0.14=28.57g=(0.25)(0.4)=0.1NPVGO=[(Investment+Return/r)/(r–g)]/(1+r)2=[(-1+0.40/.14)/(0.14–0.1)]/(1.14)2=35.73P=PV(EPS)+NPVGO=28.57+35.73=64.30练习4解答•Usingdividendmodel,priceofastockcanbewrittenasP=D/(k–g)–OritcanbewrittenasP=E*PO/(k–g)wherePOisthedividendpayoutratioanddenotesmultiplication–Rearrangingtermsweget,P/E=PO/(k–g)–Substitutingvalues12=.4/(k–g)–→1/(k–g)=12/0.4–→1/(k–g)=30–P=E*PO/(k–g)–NowsubstitutingP=$32,PO=40%,1/(k–g)=30weget–32=E*.4*30–→E=8/3–Ifthedividendpayoutratiowere60%–P=E*PO/(k–g)–P=(8/3)*.6*30=$48练习5解答•First,figureoutifthepriceofthecouponbondisconsistentwiththezerocouponyieldsimpliedbytheothersecurities.练习5解答•Accordingtothesezerocouponyields,thepriceofthecouponbondshouldbe:Thepriceofthecouponbondistoolow,sothereisanarbitrageopportunity.Totakeadvantageofit:课堂练习6•考虑两个互斥投资项目，现金流如下：•年份项目A项目B•0-5000-100000•1350065000•2350065000课堂练习6•（1）两个项目的IRR分别是多少？•（2）仅仅根据IRR，你会选择哪个项目？•（3）你根据（2）做出决策时忽略了什么？•（4）如何克服这一问题？请计算。•（5）根据（4）的结果，你会选择哪一个项目？假设贴现率为15%。•（6）根据NPV法则，你会选择哪一个项目？假设贴现率为15%。课堂练习7课堂练习7课堂练习8课堂练习8课堂练习9课堂练习10练习6解答a.Settheproject’scashflows,discountedattheinternalrateofreturn(IRR),equaltozero.•SolvefortheIRR.•IRR(ProjectA)=C0+C1/(1+IRR)+C2/(1+IRR)2•0=-$5,000+$3,500/(1+IRR)+$3,500/(1+IRR)2•IRR=0.2569•TheIRRofprojectAis25.69%.•IRR(ProjectB)=C0+C1/(1+IRR)+C2/(1+IRR)2•0=-$100,000+$65,000/(1+IRR)+$65,000/(1+IRR)2•IRR=0.1943•TheIRRofprojectBis19.43%.练习6解答•ChooseprojectAbecauseithasahigherIRRthanprojectB.•Thedifferenceinscalewasignored.ProjectBhasasubstantiallylargerinitialinvestmentthanprojectAhas.Thus,thesimpleIRRcalculationmaynotleadtothebestdecision.练习6解答•CalculatetheincrementalIRR.TheincrementalIRRistheIRRontheincrementalinvestmentfromchoosingthelargerprojectinsteadofthesmallerproject.TheincrementalcashflowsarethedifferencesbetweenthecashflowsofprojectBandthoseofprojectA.Alwayssubtracttheprojectwiththesmallerinitialcashoutflowfromtheprojectwiththelargerinitialcashoutflow.Inthisway,theinitialincrementalcashflowwillbenegative.练习6解答•B–A：•-$95,000$61,500$61,500•Next,findtheIRRofthoseincrementalcashflows.•IRR(B–A)=C0+C1/(1+IRR)+C2/(1+IRR)2•0=-$95,000+$61,500/(1+IRR)+$61,500/(1+IRR)2•IRR=0.191练习6解答•Forinvesting-typeprojects,acceptthelargerprojectwhentheincrementalrateofreturnisgreaterthanthediscountrate.Therefore,chooseprojectBsincetheincrementalIRR(19.1%)isgreaterthanthe15percentdiscountrate.练习6解答•CalculatetheNPVofeachproject.•NPV(ProjectA)=-$5,000+$3,500/(1.15)+$3,500/(1.15)2•=$689.98•TheNPVofprojectAis$689.98.•NPV(ProjectB)=-$100,000+$65,000/(1.15)+$65,000/(1.15)2•=$5,671.08•TheNPVofprojectBis$5,671.08.•SincetheNPVofprojectB,$5,671.08,isgreaterthantheNPVofprojectA,$689.98,chooseprojectB.练习7解答练习7解答练习7解答练习7解答练习10解答•6+[1.2(16–6)]=18%0011PPPD)r(E53$P5050P618.0116+[0.5(16–6)]=11%PV=$1,000/0.11=$9,090.91PV=$1,000/0.16=$6,250Thedifference,$2,840.91,istheamountyouwilloverpayifyouerroneouslyassumethatbetais0.5ratherthan1.UsingtheSML:4=6+b(16–6)b=–2/10=–0.2课堂练习11•某公司的权益市场价值为2000万美元，债务的市场价值为1000万美元。债务的成本为每年14%，一年期国库券的收益率为8%，预期下一年市场组合的收益率为18%，该公司的贝塔为0.9，假设无税。•（1）该公司的负债-权益比是多少？•（2）该公司的加权平均资本成本是多少？•（3）假设有一个全权益的公司与该公司在其他方面都一样，全权益公司的资本成本是多少？课堂练习12•某公司负