公司理財(cái)課后練習(xí)答案.docx

1、第4章P8&26Thecashflowsforthisproblemoccurmonthly,andtheinterestrategivenistheEAR.Sincethecashflowsoccurmonthly,wemustgettheeffectivemonthlyrate.OnewaytodothisistofindtheAPRbasedonmonthlycompounding,andthendivideby12.So,thepre-retirementAPRis:EAR=.11=1+(APR/12)12-1;APR=12(1.11)1/,2-1=10.48%Andthepo

2、st-retirementAPRis:EAR=.08=l+(APR/12)12-1;APR=12(1.08),/,2-1=7.72%First,wewillcalculatehowmuchheneedsatretirement.TheamountneededatretirementisthePVofthemonthlyspendingplusthePVoftheinheritance.ThePVofthesetwocashflowsis:PVA=$20,00011/(1+.0772/12)12(2。)/(.0772/12)=$2,441,554.61PV=$1,000,000/(1+.08)2

3、°=$214,548.21So,atretirement,heneeds:$2,441,554.61+214,548.21=$2,656.102.81Hew川besaving$1,900permonthforthenext10yearsuntilhepurchasesthecabin.Thevalueofhissavingsafter10yearswillbe:FVA=$l,900(1+(.1048/12)so)1/(.1048/12)=$400,121.62Afterhepurchasesthecabin,theamounthewillhaveleftis:$400,121.62-

4、320,000二$80,121.62Hestillhas20yearsuntilretirement.Whenheisreadytoretire,thisamountwillhavegrownto:FV=$80,121.62l+(.1048/12)go)=$646,965.50第13章P280：11,12,13,14,18,1911. Withtheinformationgiven,wecanfindthecostofequityusingthedividendgrowthmodel.Usingthismodel,thecostofequityis:Re=$2.40(1.055)/$52+.0

5、55=.1037or10.37%WehavetheinformationavailabletocalculatethecostofequityusingtheCAPMandthedividendgrowthmodel.UsingtheCAPM,wefind:Re=.05+0.85(.08)=.1180or11.80%Andusingthedividendgrowthmodel,thecostofequityisRe=$l.60(l.06)/$37+.06=.1058or10.58%Bothestimatesofthecostofequityseemreasonable.Ifweremember

6、thehistoricalreturnonlargecapitalizationstocks,theestimatefromtheCAPMmodelisaboutthesameasthehistoricalaverage,andtheestimatefromthedividendgrowthmodelisaboutonepercentlowerthanthehistoricalaverage,sowecannotdefinitivelysayoneoftheestimatesisincorrect.Giventhis,wewouldusetheaverageofthetwo,so:Re=(.1

7、180+.1058)/2=.1119or11.19%a.ThepretaxcostofdebtistheYTMofthecompany'sbonds,so:Po=$1,080=$35(PVIFAr%*)+$1,000(PVIFr%,46)R=3.167%YTM=2x3.167%=6.33%b. Theaftertaxcostofdebtis:Rd=.0633(1-.35)=.0412or4.12%c. Theaftertaxrateismorerelevantbecausethatistheactualcosttothecompany.12. Usingtheequationtocal

8、culatetheWACC,wefind:WACC=.70(.15)+.30(.08)(l-.35)=.1206or12.06%a.Heshouldlookattheweightedaverageflotationcost,notjustthedebtcost.b.Theweightedaverageflotationcostistheweightedaverageoftheflotationcostsfordebtandequity,so:fT=.05(.75/1.75)+.08(1/1.75)=.0671or6.71%c.Thetotalcostoftheequipmentincludin

9、gflotationcostsis:Amountraised(l-.0671)=$20,000,000Amountraised=$20,000,000/(1-.0671)=$21,439,510Evenifthespecificfundsareactuallybeingraisedcompletelyfromdebt,theflotationcosts,andhencetrueinvestmentcost,shouldbevaluedasifthefirm'stargetcapitalstructureisused.18. Usingthedebt-equityratiotocalcu

10、latetheWACC,wefind:WACC=(.65/1.65)(.055)+(1/1.65)(.15)=.1126or11.26%Sincetheprojectisriskierthanthecompany,weneedtoadjusttheprojectdiscountratefortheadditionalrisk.Usingthesubjectiveriskfactorgiven,wefind:Projectdiscountrate=11.26%+2.00%=13.26%WewouldaccepttheprojectiftheNPVispositive.TheNPVisthePVo

11、fthecashoutflowsplusthePVofthecashinflows.Sincewehavethecosts,wejustneedtofindthePVofinflows.Thecashinflowsareagrowingperpetuity.Ifyouremember,theequationforthePVofagrowingperpetuityisthesameasthedividendgrowthequation,so:PVoffutureCF=$3,500,000/(.1326-.05)=$42,385,321Theprojectshouldonlybeundertake

12、nifitscostislessthan$42,385,321sincecostslessthanthisamountwillresultinapositiveNPV.第15章P322：2,4,6,12,15,16,212.Thedifferencesbetweenpreferredstockanddebtare:a. Thedividendsonpreferredstockcannotbedeductedasinterestexpensewhendeterminingtaxablecorporateincome.Fromtheindividualinvestor'spointofvi

13、ew,preferreddividendsareordinaryincomefortaxpurposes.Forcorporateinvestors,70%oftheamounttheyreceiveasdividendsfrompreferredstockareexemptfromincometaxes.b. Incaseofliquidation(atbankruptcy),preferredstockisjuniortodebtandseniortocommonstock.c. Thereisnolegalobligationforfirmstopayoutpreferreddivide

14、ndsasopposedtotheobligatedpaymentofinterestonbonds.Therefore,firmscannotbeforcedintodefaultifapreferredstockdividendisnotpaidinagivenyear.Preferreddividendscanbecumulativeornon-cumulative,andtheycanalsobedeferredindefinitely(ofcourse,indefinitelydeferringthedividendsmighthaveanundesirableeffectonthe

15、marketvalueofthestock).4.Thereturnonnon-convertiblepreferredstockislowerthanthereturnoncorporatebondsfortworeasons:1)Corporateinvestorsreceive70percenttaxdeductibilityondividendsiftheyholdthestock.Therefore,theyarewillingtopaymoreforthestock;thatlowersitsreturn.2)Issuingcorporationsarewillingandable

16、toofferhigherreturnsondebtsincetheinterestonthedebtreducestheirtaxliabilities.Preferreddividendsarepaidoutofnetincome,hencetheyprovidenotaxshield.Corporateinvestorsaretheprimaryholdersofpreferredstocksince,unlikeindividualinvestors,theycandeduct70percentofthedividendwhencomputingtheirtaxliabilities.

17、Therefore,theyarewillingtoacceptthelowerreturnthatthestockgenerates.6.Therearetwobenefits.First,thecompanycantakeadvantageofinterestratedeclinesbycallinginanissueandreplacingitwithalowercouponissue.Second,acompanymightwishtoeliminateacovenantforsomereason.Callingtheissuedoesthis.Thecosttothecompanyi

18、sahighercoupon.Aputprovisionisdesirablefromaninvestor'sstandpoint,soithelpsthecompanybyreducingthecouponrateonthebond.Thecosttothecompanyisthatitmayhavetobuybackthebondatanunattractiveprice.12.Whenacompanyhasdualclassstock,thedifferenceintheshareclassesarethevotingrights.Dualshareclassesallowmin

19、orityshareholderstoretaincontrolofthecompanyeventhoughtheydonotownamajorityofthetotalsharesoutstanding.Often,dualsharecompanieswerestartedbyafamily,takenpublic,butthefounderswanttoretaincontrolofthecompany.16.Ifthecompanyusesstraightvoting,theboardofdirectorsiselectedoneatatime.Youwillneedtoownone-h

20、alfoftheshares,plusoneshare,inordertoguaranteeenoughvotestowintheelection.So,thenumberofsharesneededtoguaranteeelectionunderstraightvotingwillbe:Sharesneeded=(600,000shares/2)+1Sharesneeded=300,001Andthetotalcosttoyouwillbethesharesneededtimesthepricepershare,or:Totalcost=300,001x$39Totalcost=$11,70

21、0,039Ifthecompanyusescumulativevoting,theboardofdirectorsareallelectedatonce.Youwillneed1/(N+1)percentofthestock(plusoneshare)toguaranteeelection,whereTVisthenumberofseatsupfbrelection.So,thepercentageofthecompany'sstockyouneedis:Percentofstockneeded=1/(N+1)Percentofstockneeded=1/(7+1)Percentofs

22、tockneeded=.1250or12.50%So,thenumberofsharesyouneedtopurchaseis:Numberofsharestopurchase=(600,000x.1250)+1Numberofsharestopurchase=75,001Andthetotalcosttoyouwillbethesharesneededtimesthepricepershare,or:Totalcost=75,001x$39Totalcost=$2,925,039第16章P342：11、12、13、14、1511-13seeexcela.UnderPlanI,theunlev

23、eredcompany,netincomeisthesameasEBITwithnocorporatetax.TheEPSunderthiscapitalizationwillbe:EPS=$750,000/240,000sharesEPS=$3.13UnderPlanII,theleveredcompany,EBITwillbereducedbytheinterestpayment.Theinterestpaymentistheamountofdebttimestheinterestrate,so:NI=$750,000-10($3,l00,000)NI=$440,000AndtheEPSw

24、illbe:EPS=$440,000/160,000sharesEPS=$2.75PlanIhasthehigherEPSwhenEBITis$750,000.b. UnderPlanI,thenetincomeis$1,500,000andtheEPSis:EPS=$1,500,000/240,000sharesEPS=$6.25UnderPlanII,thenetincomeis:NI=$1,500,000.10($3,100,000)NI=$1,190,000AndtheEPSis:EPS=$1,190,000/160,000sharesEPS=$7.44PlanIIhasthehigh

25、erEPSwhenEBITis$1,500,000.c. TofindthebreakevenEBITfortwodifferentcapitalstructures,wesimplysettheequationsforEPSequaltoeachotherandsolveforEBIT.ThebreakevenEBITis:EBIT/240,000=EBIT-.10($3,100,000)/160,000EBIT=$930,00014. Wecanfindthepricepersharebydividingtheamountofdebtusedtorepurchasesharesbythen

26、umberofsharesrepurchased.Doingso,wefindthesharepriceis:Samevalue:240000*Shareprice=160000*Shareprice+3100000Shareprice=$3,100,000/(240,000-160,000)Shareprice=$38.75pershareThevalueofthecompanyundertheall-equityplanis:V =$38.75(240,000shares)=$9,300,000Andthevalueofthecompanyundertheleveredplanis:V =

27、$38.75(160,000shares)+$3,100,000debt=$9,300,000第17章P368：1818.a.Ifthecompanydecidestoretireallofitsdebt,itwillbecomeanunleveredfirm.Thevalueofanall-equityfirmisthepresentvalueoftheaftertaxcashflowtoequityholders,whichwillbe:Vu=(EBIT)(1-fc)/RoVu=($1,300,000)(1-.35)/.20Vu=$4,225,000b. Sincetherearenoba

28、nkruptcycosts,thevalueofthecompanyasaleveredfirmis:Vl=Vu+1(1-?c)/(1-?b)xBVL=$4,225,000+1-(1一.35)/(1-.25)x$2,500,000*=$4,558,333.33Thebankruptcycostswouldnotaffectthevalueoftheunleveredfirmsinceitcouldneverbeforcedintobankruptcy.So,thevalueoftheleveredfirmwithbankruptcywouldbe:Vl=Vu4-(l-(l-fc)/(l-?B)

29、xB_C(B)Vl=($4,225,000+1(1.35)/(I-.25)x$2,500,000)-$400,000VL=$4,158,333.33Thecompanyshouldchoosetheall-equityplanwiththisbankruptcycost.第18章P382：15a.Ifthecompanywerefinancedentirelybyequity,thevalueofthefirmwouldbeequaltothepresentvalueofitsunleveredafter-taxearnings,discountedatitsunleveredcostofca

30、pital.First,weneedtofindthecompany'sunleveredcashflows,whichare:SalesVariablecostsEBTTaxNetincome$28,900,00017,340,000$11,560,0004,624,000$6,936,000So,thevalueoftheunleveredcompanyis:Vu=$6,936,000/.17Vu=$40,800,000b. AccordingtoModigliani-MillerPropositionIIwithcorporatetaxes,thevalueofleveredeq

31、uityis:Rs=R()+(B/S)(R()Rb)(1tc)Rs=.17+(.35)(.17-.09)(1-.40)Rs=.1868or18.68%c. Inaworldwithcorporatetaxes,afirm'sweightedaveragecostofcapitalequals:Rwacc=B/(B+S)(l-tc)RB+S/(B+S)RsSoweneedthedebt-valueandequity-valueratiosforthecompany.Thedebt-equityratioforthecompanyis:B/S=0.35B=0.35SSubstituting

32、thisinthedebt-valueratio,weget:B/V=.35S/(.35S+S)B/V=.35/1.35B/V=.26Andtheequity-valueratioisoneminusthedebt-valueratio,or:S/V=1-.26S/V=.74So,usingthecapitalstructureweights,thecompany'sWACCis:Rwacc=B/(B+S)(l-tc)RB+S/(B+S)RsRwacc=.26(1-.40)(.09)+.74(.1868)Rwacc=.1524or15.24%Wecanusetheweightedave

33、ragecostofcapitaltodiscountthefirm'sunleveredaftertaxearningstovaluethecompany.Doingso,wefind:VL=$6,936,000/.1524Vl=$45,520,661.16Nowwecanusethedebt-valueratioandequity-valueratiotofindthevalueofdebtandequity,whichare:B=VL(Debt-value)B=$45,520,661.16(.26)B=$11,801,652.89S=VtCEquity-value)S=$45,5

34、20,661.16(.74)S=$33,719,008.26d. Inordertovalueafirm'sequityusingtheflow-to-equityapproach,wecandiscountthecashflowsavailabletoequityholdersatthecostofthefirm'sleveredequity.First,weneedtocalculatetheleveredcashflowsavailabletoshareholders,whichare:SalesVariablecostsEBITInterestEBTTaxNetinco

35、me$28,900,00017,340,000$11,560,0001,062,149(=11,801,652.89*9%)$10,497,8514,199,140$6,298,711So,thevalueofequitywiththeflow-to-equitymethodis:S=Cashflowsavailabletoequityholders/RsS=$6,298,711/.1868S=$33,719,008.26第19章：P409.4040.a.Letxbetheordinaryincometaxrate.Theindividualreceivesanafter-taxdividen

36、dof:Aftertaxdividend=$1,000(1-x)whichsheinvestsinTreasurybonds.TheTreasurybondwillgenerateaftertaxcashflowstotheinvestorof:AftertaxcashflowfromTreasurybonds=$1,000(1-x)l+.08(1-x)Ifthefirminveststhemoney,itsproceedsare:Firmproceeds=$l,000l+.08(1-.35)Andtheproceedstotheinvestorwhenthefirmpaysadividend

37、willbe:Proceedsiffirminvestsfirst=(1-x)$l,000l+.08(1-.35)Tobeindifferent,theinvestor'sproceedsmustbethesamewhethersheinveststheafter-taxdividendorreceivestheproceedsfromthefirm'sinvestmentandpaystaxesonthatamount.Tofindtherateatwhichtheinvestorwouldbeindifferent,wecansetthetwoequationsequal,

38、andsolveforx.Doingso,wefind:$1,000(1-x)l+.08(1-x)=(1-x)($l,000l+.08(1-.35)1+.08(1-x)=l+.08(1-.35)x=.35or35%Notethatthisargumentdoesnotdependuponthelengthoftimetheinvestmentisheld.b. Yes,thisisareasonableanswer.Sheisonlyindifferentiftheafter-taxproceedsfromthe$1,000investmentinidenticalsecuritiesarei

39、dentical.Thatoccursonlywhenthetaxratesareidentical.c. Sincebothinvestorswillreceivethesamepre-taxreturn,youwouldexpectthesameanswerasinparta.Yet,becausethecompanyenjoysataxbenefitfrominvestinginstock(70percentofincomefromstockisexemptfromcorporatetaxes),thetaxrateonordinaryincomewhichinducesindiffer

40、ence,ismuchlower.Again,setthetwoequationsequalandsolveforx:$1,000(1-x)l+.12(1-x)=(1-x)($1,0001+.12.7O+(1-.70)(1-.35)1+.12(1-x)=1+12.70+(l-.70)(1-35)%=.1050or10.50%Itisacompellingargument,buttherearelegalconstraints,whichdeterfirmsfrominvestinglargesumsinstockofothercompanies.So,whenheisreadytoretire

41、,basedonhiscurrentsavings,hewillbeshort:$2,656,102.81一645,965.50=$2,010,137.31ThisamountistheFVofthemonthlysavingshemustmakebetweenyears10and30.So,findingtheannuitypaymentusingtheFVAequation,wefindhismonthlysavingswillneedtobe:FVA=$2,010,137.31=C1+(.1048/12)12(20)-1/(.1048/12)$2,486.12第5章P109,24a.Th

42、eprofitabilityindexisthePVofthefuturecashflowsdividedbytheinitialinvestment.Theprofitabilityindexforeachprojectis:PIa=$140,000/1.12+$140,000/1.122/$200,000=1.18PIb=$260,000/1.12+$260,000/1.122/$400,000=1.10Pic=$150,000/1.12+$120,000/1.122/$200,000=1.15b. TheNPVofeachprojectis:NPVa=-$200,000+$140,000

43、/1.12+$140,000/1.122NPVa=$36,607.14NPVb=-$400,000+$260,000/1.124-$260,000/1.122NPVb=$39,413.27NPVC=-$200,000+$150,000/1.12+$120,000/1.122NPVc=$29,591.84c. AcceptprojectsA,B,andC.Sincetheprojectsareindependent,acceptallthreeprojectsbecausetherespectiveprofitabilityindexofeachisgreaterthanone.d. BNPV或

44、增量PIe.e.AB第6章P128J3題Wewillusethebottom-upapproachtocalculatetheoperatingcashflowforeachyear.Wealsomustbesuretoincludethenetworkingcapitalcashflowseachyear.So,thenetincomeandtotalcashfloweachyearwillbe:Year1Year2Year3Year4Sales$8,500$9,000$9,500$7,000Costs1,9002,0002,2001,700Depreciation4,0004,0004,0

45、004,000EBT$2,600$3,000$3,300$1,300Tax8841,0201,122442Netincome$1,716$1,980$2,178$858OCF$5,716$5,980$6,178$4,858Capitalspending-$16,000NWC-200-250-300-200950Incrementalcashflow$16,200$5,466$5,680$5,978$5,808TheNPVfortheprojectis:NPV=-$16,200+$5,466/1.12+$5,680/1.122+$5,978/1.123+$5,808/1.124NPV=$1,15

46、4.53第7章P147J7題WeneedtocalculatetheNPVofeachoption,andchoosetheoptionwiththehighestNPV.So,theNPVofgoingdirectlytomarketis:NPV=Csuccess(Prob,ofSuccess)NPV=$1,500,000(0.50)NPV=$750,000TheNPVofthefocusgroupis:NPV=Co+Csuccess(Prob,ofSuccess)NPV=-$135,000+$1,500,000(0.65)NPV=$840,000AndtheNPVofusingthecon

47、sultingfirmis:NPV=Co+Csuccess(Prob,ofSuccess)NPV=-$400,000+$1,500,000(0.85)NPV=$875,000ThefirmshouldusetheconsultingfirmsincethatoptionhasthehighestNPV.第8章P171,25題Thepriceofanybond(orfinancialinstrument)isthePVofthefuturecashflows.EventhoughBondMmakesdifferentcouponspayments,tofindthepriceofthebond,

48、wejustfindthePVofthecashflows.ThePVofthecashflowsforBondMis:Pm=$800(PVIFA4%,i6)(PVIF4%,i2)+$1,000(PVIFA4%,i2)(PVIF4%,28)+$2O,OOO(PVIF4%,4o)Pm=$13,117.88Noticethatforthecouponpaymentsof$800,wefoundthePVAforthecouponpayments,andthendiscountedthelumpsumbacktotoday.BondNisazerocouponbondwitha$20,000parv

49、alue;therefore,thepriceofthebondisthePVofthepar,or:Pn=$2O,OOO(PVIF4%,4o)=$4,165.78第9章P191,7題Hereweneedtofindthedividendnextyearforastockexperiencingdifferentialgrowth.Weknowthestockprice,thedividendgrowthrates,andtherequiredreturn,butnotthedividend.First,weneedtorealizethatthedividendinYear3isthecur

50、rentdividendtimestheFVIF.ThedividendinYear3willbe:D3=Do(1.30)3AndthedividendinYear4willbethedividendinYear3timesoneplusthegrowthrate,or:D4=Do(1.30)3(1.18)Thestockbeginsconstantgrowthafterthe4thdividendispaid,sowecanfindthepriceofthestockinYear4asthedividendinYear5,dividedbytherequiredreturnminustheg

51、rowthrate.TheequationforthepriceofthestockinYear4is:P4=D4(l+g)/(R-g)NowwecansubstitutethepreviousdividendinYear4intothisequationasfollows:P4=Do(l+g/)3(l+g2)(l+g3)/(&-g3)P4=D()(1.30)3(1.18)(1.08)/(.13-.08)=56.00D()Whenwesolvethisequation,wefindthatthestockpriceinYear4is56.00timesaslargeasthedivid

52、endtoday.Nowweneedtofindtheequationforthestockpricetoday.ThestockpricetodayisthePVofthedividendsinYears1,2,3,and4,plusthePVoftheYear4price.So:Po=Do(1.30)/1.13+Do(1.30)2/1.132+Do(1.3O)3/1.133+Do(1.3O)3(1.18)/1.134+56.OODo/1.134WecanfactoroutDointheequation,andcombinethelasttwoterms.Doingso,weget:Po=$

53、65.00二Do1.30/1.13+1.302/1.132+1.303/1.133+(1.30)3(1.18)+56.00/1.134)Reducingtheequationevenfurtherbysolvingallofthetermsinthebraces,weget:$65=$39.86D0Do=$65.00/$39.86=$1.63Thisisthedividendtoday,sotheprojecteddividendforthenextyearwillbe:Di=$1.63(1.30)=$2.12第10章P212,15-1715. a.Tofindtheaveragereturn

54、,wesumallthereturnsanddividebythenumberofreturns,so:Arithmeticaveragereturn=(.34+.16+.19-.21+.08)/5Arithmeticaveragereturn=.1120or11.20%b. Usingtheequationtocalculatevariance,wefind:Variance=l/4(,34-.112)2+(.16-.112)2+(.19-.112)2+(-.21-.112)2+(.08-.112)2Variance=0.041270So,thestandarddeviationis:Sta

55、ndarddeviation=(0.041270)"Standarddeviation=0.2032or20.32%16. a.Tocalculatetheaveragerealreturn,wecanusetheaveragereturnoftheassetandtheaverageinflationrateintheFisherequation.Doingso,wefind:(1+R)=(1+r)(l+h)r=(1.1120/1.042)-1r=.0672or6.72%h.Theaverageriskpremiumissimplytheaveragereturnoftheasse

56、t,minustheaveragerealrisk-freerate,so,theaverageriskpremiumforthisassetwouldbe:RP=R-RfRP=.1120-.0510RP=.0610or6.10%Wecanfindtheaveragerealrisk-freerateusingtheFisherequation.Theaveragerealrisk-freeratewas:(1+R)=(1+r)(l+h)rf=(1.051/1.042)-1rf=.0086or0.86%Andtocalculatetheaveragerealriskpremium,wecans

57、ubtracttheaveragerisk-freeratefromtheaveragerealreturn.So,theaveragerealriskpremiumwas:rp=r-rf=6.72%-0.86%rp=5.85%Applythefive-yearholding-periodreturnformulatocalculatethetotalreturnofthestockoverthefive-yearperiod,wefind:5-yearholding-periodreturn=(1+Ri)(l+R?)(l+Ra)(l+RQ(1+R5)一15-yearholding-periodreturn=(+.1843)(1+.1682)(1+.0683)(1+.3219)(1-.1987)-15-yearholding-periodreturn=0.5655or56.55%22.Tocalculatethearithmeticandgeometricaveragereturns,wemustfirstcalculatethereturnforeachyear.Thereturnforeachyearis:Ri=($55.83-49.62+0.68)/$49.62=.1389or13.89%