《公司金融》期末复习试题及答案

第五章

16.计算报酬率再看看我们在本章开头所讨论的TMCC证券：

a.基于24099美元的价格，TMCC所付的借款利率是多少？

b.在2020年3月28日，该证券的价格是38260美元。如果一个投资者在发行之初以24099

美元买得，并在这一天卖出，那么她所赚取的年报酬率是多少？

c.如果一个投资者在2020年3月28日买入该证券，并一直持有至到期，那么她所赚取的年

报酬率是多少？

Toanswerthisquestion,wecanuseeithertheFVorthePVformula.Bothwillgivethesameanswer

sincetheyaretheinverseofeachother.WewillusetheFVfbrmula.thatis:

FV=PV(1+r)f

Solvingforrweget:

r=(FV/PV)1/f-1

a.PV=$100.000/(1+r)30=$24.099

r=($100,000/$24.O99)1/30-1=.0486or4.86%

b.PV=$38.260/(I+r)12=S24.099

r=($38,260/S24.099)1712-1=.0393or3.93%

c.PV=$100,000/(I+r)18=$38,260

r=(S100,000/$38"260)""-1=.0548or5.48%

17.计算现值假定你仍然希望拥有一辆价值170000美元的法拉利(见第9题)。如果你相

信你的共同基金可以达到12%的年报酬率，而且你想在9年后，当你满30岁时购买这辆汽车，

那么，现在你必须投资多少钱？

TofindthePVofalumpsum.weuse:

PV=FV/(l+z/

PV=S170.000/(1.12)9=$61.303.70

18.计算终值你刚将第一笔4000美元存入你的个人退休金账户。假定你可以赚取11%的报

酬，而且不再追加任何存款，那么，45年后你的账户将有多少钱？如果你在10年后才存进

这笔钱呢？(这个建议是一项投资策略吗？)

TofindtheFVofalumpsum.weuse:

FV=PV(1+r)f

FV=$4,000(1.11)45=$438,120.97

FV=$4,000(1.11)35=$154.299.40

Betterstartearly!

20.计算期数你预计将在2年后毕业时收到10000美元。你计划以10%的利率将这笔钱再投

资，直到你拥有

75000美元。请问，从现在开始，你还要等多长时间？

Toanswerthisquestion,wecanuseeithertheFVorthePVformula.Bothwillgivethesameanswer

sincetheyaretheinverseofeachother.WewillusetheFVfbnnula.thatis:

FV=PV(1+r)r

Solvingfort,weget:

/=ln(FV/PV)/hi(l+7•)

t=ln($75,000/$10,000)/In(l.ll)=19.31

So.themoneymustbeinvestedfor19.31years.However,youwillnotreceivethemoneyfbr

anothertwoyears.Fromnow.you'llwait:

2years+19.31years=21.31years

第六章

58.计算年金值你在考虑购买一辆新车，你既可以租这辆车，也可能用一笔3年期贷款购买

它。你想买的这辆车价值32000美元。经纪商有一项特别的租赁安排，你今天付99美元，

并在接下来的3年中每个月支付450美元。如果你购买这辆车，你将要在接下来的3年中以7%

的APR按月还款。你相信你能在3年后以23000美元的价格把这辆车卖出去。你是应该购买

这辆车，还是应该租赁？要想使购买和租赁没有什么区别，你在3年后转卖这辆车的价格应

该是多少？

答案：租赁付款的PV=14672.91美元购买的PV=13345.18美元保本点转卖价格=21363.01美元

Toanswertinsquestion,weshouldfindthePVofbothoptions,andcomparethem.Sinceweare

purchasingthecar.thelowestPVisthebestoption.ThePVofdieleasmgissimplytliePVofthelease

payments,plustheS99.Tlieinterestratewewouldusefbrtheleasingoptionisthesameastheinterestrate

oftheloan.ThePVofleasingis:

PV=$99+S45O{1-[1/(1+.07/12)1叼}/(.07/12)=$14,672.91

TliePVofpurchasingthecaiisthecurrentpriceofthecarminusthePVoftheresaleprice.ThePVofdie

resalepriceis:

PV=$23.000/[1+(.O7/12)]1X3>=$18,654.82

ThePVofthedecisiontopiuchaseis:

$32,000-18,654.82=S13345.18

Inthiscase,itischeapertobuythecarthanleasingitsincethePVofthepurchasecashflowsislower.To

findthebreakevenresaleprice,weneedtofindtheresalepacetliatmakesthePVofthetwooptionsthe

same.Inotherwords,thePVofthedecisiontobuyshouldbe:

$32,000-PVofresaleprice=$14,672.91

PVofresaleprice=$17.327.09

TheresalepricethatwouldmakethePVoftheleaseversusbuydecisionistheFVoftinsvalue,so:

Breakevenresaleprice=$17,327.09(1+(.O7/12)]n(3)=$21363.01

66.计算年金付款额这是一个典型的退休问题。使用时间线可以帮助你了解这个问题。今天，

你的朋友正在庆祝她的35岁生日。她想开始为她预期在65岁退休而储蓄。她希望在退休后的20

年间，每年生日时都能从储蓄账户中提取105000美元。第1次提款将在她66岁生日时。你的朋

友想把钱放在当地的信用合作社，年利率是7%。她想在每次生日时都存入一笔等额的钱，作为

她的退休基金。

a.如果她从36岁生日开始存款，一直到65岁(最后一笔存款的时间是65岁生日)，那么，她每

年必须存入多少钱，才能实现她的退休计划？

b.假定你的朋友刚继承了一大笔遗产。她决定不再每年存入等额的钱，而要在35岁生日时存入

一大笔钱，以实现她的退休计划。她应该存入多少钱？

c.假定你朋友的老板愿意每年贡献1500美元到这个储蓄账户中，当做公司分红计划的一部分。

此外，你的朋友预期在她55岁生日时，可从一家家庭基金领到150000美元，她也将把这笔钱存

入退休金账户中。现在，她每年应该存入多少钱，才能满足她退休时所需要的提款？

Herewearesolvingatwo-steptimevalueofmoneyproblem.Eachquestionasksforadifferentpossible

cashflowtoftmdthesameretirementplan.EachsavingspossibilityhasthesameFV.tliatis.thePVofthe

retiiementspendingwhenyoiirfriendisreadytoretue.Tlieamountneededwhenyoiirfiiendisreadyto

retii-eis:

PVA=S1O5,OOO{[1-(1/1.O7)20]/.07}=$1,112,371.50

Tliisamountisthesamefbralltliieepartsoftliisquestion.

a.Ifyotu,fiiendmakesequalannualdepositsintotheaccount,tliisisanannuitywiththeFVAequaltothe

amountneededinretuemeiit.Tlierequiredsavingseachyearwillbe:

FVA=$1412,371.50=C[(1.0730-1)/.07]

C=Sil,776.01

b.Hereweneedtofindalumpsumsavingsainoimt.UsingtheFVfbralumpsumequation,weget:

FV=$1.112,371.50=PV(107)30

PV=$146,129.04

c.Inthisproblem,wehaveakunpsiunsavingsinadditiontoanannualdeposit.Sincewealreadyknow

thevalueneededatretirement,wecansubtiactthevalueofthehunpsumsavmgsatretirementtofind

outhowmuchyourfriendisshort.Doingsogivesus:

FVoftrustfonddeposit=$150.000(1O7)10=S295.072.70

So,theamountyourfiiendstillneedsatretiiementis:

FV=$1,112,371.50-295,072.70=$817,298.80

UsingtheFVAequation,andsolvingfbrthepayment,weget:

S817,298.80=C[(1.0730-l)/.07]

C=33.652.25

Thisisthetotalannualcontnbution.butyourfiiend*semployerwillcontnbute$1,500peryear,soyour

friendmustcontiibute:

Friend'scontnbution=S8,652.25-1.500=$7,152.25

69.计算“气球款”你刚刚安排了一笔750000美元的抵押贷款，作为购置一块土地的资

金。这个抵押贷款的利率是&1%APR,要求在今后的30年中逐月付款。然而，8年后有一笔

气球款，意味着到时必须还清所有贷款。这笔气球款有多大？

Tliemonthlypaymentswithaballoonpaymentloanarecalculatedassumingalongeramoitization

schedule,intliiscase,30years.Tliepaymentsbasedona30-yearrepaymentschedulewouldbe:

PVA=S750,000=C({1-[1/(1+081/12)]360}/(.081/12))

C=$5,555.61

Now.attime=8.weueedtofindtliePVofthepaymentswhichhavenotbeenmade.Theballoonpayment

willbe:

PVA=S5,555.61({1-[1/(1+.O81/12)]12(22)}/(.081/12))

PVA=S683,700.32

74.增长年金的计算40年后你将退休，希望到时拥有200万美元。你的薪水按年支付，今年年底可得40000

美元，以后每年按跳的速度增长。对于所投资的资金，你每年可获得11%的收益。假设储蓄占薪水的比例保

持恒定，那么每年应将多少比例的工资用于储蓄？

答案：6.48%

Weneedtofindthehunpsumpaymentintotheretiiementaccount.Tliepresentvalueofthedesired

amoimtatretirementis:

PV=FV/(1+r)r

PV=S2,000,000/(1+.Il)40

PV=$30,768.82

Thisisthevaluetoday.Sincethesavmgsareinthefbnnofagrowingannuity,wecanusethegrowing

annuityequationandsolveforthepayment.Domgso,weget:

PV=C{[1-((1+g)/(l+r))r]/(r-g)}仙

$30,768.82=C{[1-((1+.03)7(1+11))]/(11-03))

C=$2,591.56

Thisistheamountyouneedtosavenextyear.So.thepercentageofyoursalaryis:

Percentageofsalary=S2,591.56S40.000

Percentageofsalary=.0648or6.48%

Notethattinsisthepercentageofyoursalaryyoumustsaveeachyear.Sinceyoursalaryisincreasingat3

percent,andthesavingsaieincreasmgat3percent,thepercentageofsalaiywillremainconstant.

第七章

21.应计利息你购买了一支利息率为6.8%的债券，它的干净价格为1073美元。如果下一个半年付息日预计

在2个月以后，账单价格是多少？

Accnieclinterestisthecouponpaymentforthepenodtimesthefiactionofthepenodthathaspassed

sincetlielastcouponpayment.Sinceweliaveaseniiaimualcouponbond,thecouponpaymentper

sixmonthsisone-halfoftheamnialcouponpayment.Tlierearetwomonthsuntilthenextcoupon

paymeitsofbwmonthshavepassedsincethelastcouponpayment.Theaccmedinterestfbrthe

bondis:

Accniedinterest=$68/2义4/6=S22.67

Andwecalculatethedirtypriceas:

Dirtyprice=Cleanpace+Accniedinterest=$1.073+22.67=Sl.095.67

22.求出债券到期期限River公司有一支利息率为8%的债券，每年付息一次，YTM为7.2吼这支债券的当期

收益率为7.55%。这支债券还剩下多少年到期？

Tofindthenumberofyearstomaturityforthebond,weneedtofindtliepaceofthebond.Sincewe

alreadyhavethecouponrate,wecanusethebondpriceequation,andsolvefbrthemunberofyears

tomaturity.Wearegiventheciinentyieldofthebond,sowecancalculatethepriceas:

Cunentyield=.0755=$80R)

Po=S8O/.O755=S1,059.60

Nowtliatwehavethepaceofdiebond,thebondpriceequationis:

P=$1,059.60=S80[(l-(1/1.072/)/.072]+$1,000/1072’

Wecansolvethisequationfortasfollows:

$1,059.60(1.0727=Sl.lll.11(1.0727-Lill.11+1,000

111.11=51.51(1.0727

2.1570=1.072’

f=log2.1570/log1.072=11.06«11years

Tliebondhas11yeaistomaturity.

29.债券报酬率的影响因素P债券是票面利率为12%的溢价债券，D债券则是票面利率为6%的折价债券。二者

都是每年付息一次，YTM为9%,5年后到期。P债券的当期收益率为多少？D债券呢？若利率维持不变，则下

一年P债券的资本利得收益率为多少？D债券呢？解释你的答案，并说明这两种收益率之间的相互关系。

Tofindthecapitalgamsyieldandthecurrentyield,weneedtofindthepaceofthebond.The

ciineiitpriceofBondPandthepaceofBondPmoneyearis:

P:Po=$12O(PYIFA7^5)+S1.OOO(P\TF7<JK5)=SI,116.69

Pi=$120(PVIFA7^4)+S1.000(PVIF7%,4)=Sl,097.19

Cun'entyield=S120/$1,116.69=.1075or10.75%

Thecapitalgainsyieldis:

Capitalgainsyield=(Newprice-Onginalprice)Originalprice

Capitalgainsyield=($1,097.19-1,111.69)/SL116.69=-.0175or-1.75%

TheciuxentpriceofBondDandthepriceofBondDilloneyearis:

D:Po=$60(PVIFA7*.,5)+$1.000(PVIF^5)=$883.31

Pi=$60(PVIFA^4)+$1.000(PVIF^4)=$902.81

Ciurentyield=S60/,$883,81=.0679or6.79%

Capitalgainsyield=($902.81-883.31)/S883.31=+.0221or+2.21%

Allelseheldconstant,premiumbondspayhighcurrentincomewhilehavingpricedepreciationas

maturitynears;discountbondsdonotpayliighcurrentincomebuthavepriceappreciationas

maturityLMS.Foreitherbond,thetotalretiunisstill9%,buttillsrenunisdistributeddifferently

betweencunentincomeandcapitalgains.

31.债券估价TheMckeegan公司有两种不同债券流通在外。M债券的面值为20000美元，20年后到期，前6

年不付利息，接下来的8年每半年付1100美元，最后6年则每半年付1400美元。N债券的面值也是20000

美元，20年后到期，但是，它在债券存在期间内都不付利息。如果这两种债券的必要报酬率都是7乐每半

年复利一次，那么M债券现在的价格是多少？N债券呢？

Tliepriceofanybond(orfinancialmstniment)isthePVofthefiinirecashflows.EventhoughBond

Mmakesdifferentcouponspayments,tofindthepriceofthebond,wejustfindthePVofthecash

flows.TliePVofthecashflowsfbrBondMis:

PM=$L1OO(PVIFA3.5%516)(PVIF3.5%】2)+$1.4OO(PVTFA3.5%,12)(PVIF3.5%,28)+S20.000(PVIF3.5%,40)

PM=$19,018.78

Noticethatfbrthecouponpaymentsof$1.400.wefbtuidthePVAfbrthecouponpayments,and

thendiscountedthelumpsumbacktotoday.

BondNisazerocouponbondwitha$20.000pai'value,therefore,thepriceoftliebondisthePVof

thepai\or:

PN=$20,000(PVIF3.5%,40)=$5951.45

第八章

10.股票估值大南瓜农场刚刚发放了每股3.50美元的股利。预计公司股利今后每年均以

5%增长。投资者对最初三年的要求回报率是14%,之后三年的要求回报率是12%,其他时

间的要求回报率是10%。计算公司股票的现价？

Thisstockliasaconstantgrowthrateofdividends,buttherequiredrenimchangestwice.Tofindthevalue

ofthestocktoday,wewillbeginbyfindingthepriceofthestockatYear6.whenboththedividendgrowth

rateandtherequiredrenimarestableforever.ThepriceofthestockinYear6willbethedividendinYear

7.dividedbytherequiredretumminusthegrowthrateindixidends.So:

7

P6=Ds(1+^)/(R-g)=Do(1+g)/(A-g)=$3.50(1.05)7/(.10_.05)=$98.50

NowwecanfindthepriceofthestockinYear3.Weneedtofindthepriceheresincetherequiredreturn

changesatthattime.ThepriceofthestockinYear3isthePVofthedividendsinYears4.5,and6.plus

thePVofthestockpriceinYear6.ThepriceofthestockinYear3is:

45233

P3=$3.50(1.05)/1.12+$3.50(1.05)/1.12+$3.50(1.05//1.12+$98.50/1.12

P3=S80.81

Finally,wecanfindthepriceofthestocktoday.ThepricetodaywillbethePVofthedividendsinYears

1,2.and3.plusthePVofthestockiiiYear3.Hiepriceofthestocktodayis:

333

Po=53.50(1.05)/1.14+$3.50(1.05)2/(口号+$3.5O(l.O5)/(1.14)+$80.81/(1.14)

Po=S63.47

20.两阶段股利增长模型ThirstyCactus公司刚支付了每股L25美元的股利。根据预测，

今后8年公司股利将按每年28%的比例增长，之后则将永远按6%恒定增长。如果要求回报

率为13%,那么股票的现价应为多少？

Wecanusethetwo-stagedividendgrowthmodelforthisproblem,whichis:

TT

Po=[D0(l+gi)/(R-g1)]{l-[(1+g”(l+R)]}+[d+g»(l+R)][D0(1+g2)/(R-&)]

Po=[51.25(1.28)/(.13-,28)][1-(1.28/1.13)8]+[(1.28)/(1.13)]8[$1.25(1.06)/(.13-.06)]

Po=S69.55

22.资本利得和收益考虑4种不同股票，它们的必要报酬率都是19%,而且最近一次刚刚派

发的股利都是每股4.50美元。W、X、Y股票预期维持的固定股利增长率分别是10%、0%和

一5%。Z股票则预期在未来2年内每年增长20%,此后维持12%的稳定增长率。这4种股票

的股利收益率分别是多少？这4种股票的预期资本利得收益率分别是多少？就你所求出的

这些股票的报酬率之间的关系展开讨论。

Weareaskedtofindthedividendyieldandcapitalgainsyieldfbreachofthestocks.Allofthestockshave

a15percentrequiredrenmi.whichisthesumofthedividendyieldandthecapitalgainsyield.Tofindthe

componentsofthetotalretiini.weneedtofindthestockpricefbreachstock.Usingthisstockpriceandthe

dividend,wecancalculatethedividendyield.Thecapitalgainsyieldfbrthestockwillbethetotalretuni

(requiredreturn)minusthedividendyield.

W:Po=Do(l+g)/(K-g)=54.50(1.10)/(.19-.10)=$55.00

Dividendyield=D-P。=$4.50(1.1O)/$55.OO=.09or9%

Capitalgainsyield=.19-.09=.10or10%

X:Po=D0(l+g)/(R-g)=$4.50/(.19-0)=$23.68

Dividendyield=DJP。=$4.50/$23.68=.19or19%

Capitalgainsyield=.19-.19=0%

Y:Po=D0(l+g)/(R—g)=$4.50(1-.05)/(.19+.05)=$17.81

Dividendyield=DJP。=$4.50(0.95)/$17.81=.24or24%

Capitalgainsyield=.19-.24=-.05or-5%

Z:P2=D2(1+g)/(R-g)=Do(l+g/)2(l+g»/(R-g2)=$4.50(1.20)2(1.12)/(.19-.12)=$103.68

Po=$4.50(1.20)/(1.19)+$4.50(1.20)2/(1.19)2+$103.68/(1.19)2=$82.33

Dividendyield=D,/Po=$4.50(1.20)/596.10=.066or6.6%

Capitalgainsyield=.19-.066=.124or12.4%

Inallcases,therequiiedretumis19%.buttheretuniisdistributeddifteientlybetweenciinentincomeaud

capitalgains.Highgrowthstockshaveanappreciablecapitalgainscomponentbutarelativelysmall

cuneutincomeyield;conversely,matme.negative-growthstocksproxideahiglicunentincomebutalso

pricedepreciationovertime.

24,非稳定增长Storic。公司刚派发每股2.45美元的股利。下一年公司将增加20%的股利，

然后，每一年的股利增长率将减少5%,直到行业平均值5%。此后，该公司就要无限期地维

持稳定增长率。如果Storic。的必要报酬率为11%,目前该股票每股股价应为多少？

Herewehaveastockwithsupemonnalgiowth.butthedividendgiowthchangeseveiyyearfbrthefirst

fbiu,years.WecanfindthepriceofthestockinYear3sincethedividendgrowthrateisconstantafterthe

thirddividend.ThepriceofthestockinYear3willbethedividendinYear4.dividedbytherequiied

returnminustheconstantdixidendgrowthrate.So.thepriceinYear3willbe:

P3=S2.45(1.20)(1.15)(1.10)(1.05)/(.11-.05)=S65.08

ThepriceofthestocktodaywillbethePVofthefirsttlueedividends,plusthePVofthestockpricein

Year3,so:

Po=S2.45(1.2O)/(l.11)+$2.45(1.20)(1.15)/1.112+$2.45(1.20)(1.15)(1.10)/1.113+$65.08/1.113

Po=S55.70

第九章

17.比较投资准绳考虑下列两个互斥项目:

（金额单位：美元）

年份现金流量（A）现金流量（B）

0-300000-40000

12000019000

25000012000

35000018000

439000010500

不管你选择哪一个项目，你都要求你的投资有15%的报酬率。

a.如果采用回收期准绳，你应该选哪一项投资？为什么？

b.如果采用贴现回收期准绳，你应该选哪一项投资？为什么？

c.如果采用NPV准绳，你应该选哪一项投资？为什么？

d.如果采用IRR准绳，你应该选哪一项投资？为什么？

e.如果采用获利能力指数准绳，你应该选哪一项投资？为什么？

f.根据从a到e的答案，你最终会选哪一项投资？为什么？

a.Thepaybackperiodforeachprojectis:

A:3+(SI80.000/5390,000)=3.46years

B:2+(S9,000/$18.000)=2.50years

ThepaybackcriterionimpliesacceptingprojectB.becauseitpaysbacksoonerthanprojectA.

b.Thediscountedpaybackforeachprojectis:

A:$20,000/1.15+S50.000/1.152+$50,000/1.153=$88,074.30

$390,000/1.154=$222.983.77

Discountedpayback=3+($390,000-88.074.30)6222,983.77=3.95years

B:$19.000/1.15+S12.000/1.152+$18.000/1.153=$37,430.76

$10.500/1.15$=$6.003.41

Discountedpayback=3+($40.000-37.430.76)/56.003.41=3.43years

ThediscountedpaybackcriterionimpliesacceptingprojectBbecauseitpaysbacksoonerthanA.

c.TheNPVforeachprojectis:

A:NPV=-$300,000+$20.000/1.15+$50,000/1,152+$50.000/1.153+S390.000/1.154

NPV=$11,058.07

B:NPV=-540,000+$19.000/1.15+$12.000/1,152+$18.000/1.153+$10.500/1.154

NPV=$3,434.16

NPVcriteriouimpliesweacceptprojectAbecauseprojectAhasahigherNPVthanprojectB.

d.TheIRRfbreachprojectis:

A:S300.000=$20.000/(l-IRR)+S50.000/(l-IRR)2+$5O.OOO/(1+IRR)3+S390.000/(l+IRR)4

Usingaspreadsheet,financialcalculator,ortrialanderrortofindtherootoftheequation,wefiud

that:

IRR=16.20%

B:S40.000=S19.000/(l+IRR)+$12.000/(l+IRR)2+S18.000/(l+IRR)3+$10,500/(l+IRR)4

Usingaspreadsheet,financialcalculator,ortrialandeuortofindtherootoftheequation,wefind

that:

IRR=19.50%

IRRdecisionmleimpliesweacceptprojectBbecauseIRRforBisgreaterthanIRRforA.

e.Theprofitabilityindexforeachprojectis:

A:PI=($20,000/1.15+$50,000/1.152+$50,000/1.153+S390.000/1.154)/$300.000=1.037

B:PI=($19.000/1.15+S12.000/1.152+$18.000/1.153+S10.500/1.154)/$40.000=1.086

ProfitabilityindexcriterionimpliesacceptprojectBbecauseitsPIisgreaterthanprojectA's.

f.Inthisinstance,theNPVcriteriaimpliesthatyoushouldacceptprojectA.whileprofitabilityindex,

paybackperiod,discomitedpayback,andIRRimplythatyoushouldacceptprojectB.Thefinal

decisionshouldbebasedontheNPVsinceitdoesnothavetherankingproblemassociatedwiththe

othercapitalbudgetingteclmiques.Therefore,youshouldacceptprojectA.

19.修正内部收益率法SlowRide公司采用以下现金流资料来评估某个项目：

（金额单位：美元）

年份现金流

0-16000

16100

27800

38400

（续）

年份现金流

46500

5-5100

公司所有项目采用10%的利率，运用全部三种方法计算项目的修正内部收益率。

TheMIRRfortheprojectwithallthreeapproachesis:

Discountingapproach:

Inthediscoiuitingapproach,wefindthevalueofallcashoutflowstotime0.whileanycashinflows

remamatthetimeatwhichtheyoccur.So,thediscountmgthecashoutflowstotime0,wefind:

Time0cashflow=-S16.000-S5,100/1.105

Time0cashflow=-$19,166.70

So,theMIRRusingthediscountmgapproachis:

234

0=-$19,166.70+S6J00/(l+MIRR)+$7,800/(l+MIRR)+S8,400/(l+MIRR)+6.500/(l+MIRR)

Usingaspreadsheet,financialcalculator,ortrialanderrortofindtherootoftheequation,wefindthat:

MIRR=18.18%

Reinvestmentapproach:

Inthereimrestnientapproacliwefindthefimuevalueofallcashexcepttheinitialcashflowattheend

oftheproject.So.reinvestingthecashflowstotime5.wefind:

Time5cashflow=$6,100(1.IO^H-$7,800(1.103)+$8.400(1.102)+$6.500(1.10)-55,100

Tune5cashflow=$31,526.81

So,theMIRRusingthediscountingapproachis:

0=-SI6.000+S31,526.81/(1-MIRR)5

$31,526.81/$16,000=(1+MIRR)5

MIRR=($31,526.81/516.000严-1

MIRR=1453or14.53%

Combinationapproach:

Inthecombinationapproacli.wefindthevalueofallcashoutflowsattime0.andthevalueofallcash

inflowsattheendoftheproject.So.thevalueofthecashflowsis:

Tune0cashflow=-SI6.000-S5J00/1.105

Tune0cashflow=-$19,166.70

Time5cashflow=SS.lOOCl.lO4)+$7,800(1.103)+S8.400(1.102)+$6.500(1.10)

Time5cashflow=$36,626.81

So.theMIRRusingthediscountingapproacliis:

0=-$19,166.70+S36.626.81/(1+MIRR)5

536,626.81/S19.166.70=(1+MIRR)5

MIRR=($36,626.81/S19J66.70)11

MIRR=.1383or13.83%

22.现金流量直觉一个项目的初始成本为I,必要报酬率为R,每年支付C,共N年。

a.用I和N来表示C,使得项目的回收期正好等于它的年限。

b.用I、N和R来表示C,使得在NPV决策法则下，这是个有利可图的项目。

C.用I、N和R来表示C,使得项目的成本效益比率等于2。

a.Tohaveapaybackequaltotheproject'slife,givenCisaconstantcashflowforNyears:

C=LN

b.TohaveapositiveNPV.I<C(PV7FA^«.y).Thus.C>I/(PVIFA^®

c.Benefits=C(PVIFAR%@=2xcosts=21

C=2I/(PVIFA^.y)

26.内部收益率法的问题某项目的现金流情况如下：

(金额单位：美元)

年份现金流

058000

1-34000

2-45000

该项目的内部收益率是多少？如果要求回报率为12%,公司应接受该项目吗？该项目的净现

值是多少？如果要求回报率为0%,该项目的净现值是多少？如果要求回报率为24%,该项目

的净现值是多少？这之间有什么关系？回答问题时，不妨绘制NPV图。

TheIRRoftheprojectis:

$58,000=$34.000/(1-IRR)+S45.000/(l+IRR)2

Usingaspreadsheet,financialcalculator,ortrialandeiTortofindtherootoftheequation,wefindtliat:

IRR=22.14%

Atailinterestrateof12percent,theNPVis:

NPV=$58,000-$34.000112-345,0001122

NPV=-$8,230.87

Atailinterestrateofzeropercent,wecanaddcashflows,sotheNPVis:

NPV=$58,000-S34.000-S45.000

NPV=-$21,000.00

Andatanmteiestrateof24percent,theNPVis:

NPV=$58,000-S34,000/1.24-S45.000/1.242

NPV=+$1,314.26

Tliecashflowsfortheprojectareunconventional.Smcetlieinitialcashflowispositiveandtlie

remainmgcashflowsarenegative,thedecisionrulefbrIRRininvalidinthiscase.TheNPVprofileis

upwardslopmg.mdicatingthattheprojectismorevaluablewhentheinterestrateincreases.

第一早

根据TacoSwell公司的下列资料，解答第25和26题（假设税率为34%）。

（单位：美元）

2008年2009年

销售收入72338085

折旧10381085

产品销售成本24872942

其他费用591515

利息485579

现金37924041

应收账款50215892

短期应付票据732717

长期债务1270015435

固定资产净值3180533921

应付账款39844025

存货89279555

股利8821011

25.编制该公司2008年和2009年的财务报表o

BalancesheetasofDec.3L2008

CashS3.792AccountspayableS3.984

Accoimtsreceivable5.021Notespayable732

Inventory8,927Cunentliabilities$4,716

Cunentassets$17.740

Long-termdebt$12.700

Netfixedassets$31.805Owners'equity32,129

Totalassets$49.545Totalliab.&equity$49.545

BalancesheetasofDec.31.2009

Cash$4,041Accountspayable$4,025

Accountsreceivable5.892Notespayable717

Inventoiy9.555CunentliabilitiesS4.742

Currentassets$19.488

Long-tenndebt$15.435

Netfixedassets$33,921Owners'equity33.232

Totalassets$53.409Totalliab.&equity$53,409

2008IncomeStatement2009IncomeStatement

Sales$7.233.00Sales$8,085.00

COGS2,487.00COGS2.942.00

Otherexpenses591.00Otherexpenses515.00

DepreciationL038.00Depreciation1,085.00

EBITS3.117.00EBIT$3,543.00

Interest485.00Interest579.00

EBT$2.632.00EBT$2.964.00

Taxes(34%)894.88Taxes(34%)