corporate finance Chap008new.docx
- 文档编号:7698198
- 上传时间:2023-01-25
- 格式:DOCX
- 页数:18
- 大小:279.20KB
corporate finance Chap008new.docx
《corporate finance Chap008new.docx》由会员分享,可在线阅读,更多相关《corporate finance Chap008new.docx(18页珍藏版)》请在冰豆网上搜索。
corporatefinanceChap008new
SolutionstoChapter8
NetPresentValueandOtherInvestmentCriteria
1.NPVA=–$200+[$80annuityfactor(11%,4periods)]
=–
NPVB=–$200+[$100annuityfactor(11%,3periods)]
=–
Bothprojectsareworthpursuing.
Esttime:
01–05
2.ChooseProjectA,theprojectwiththehigherNPV.
Esttime:
01–05
3.NPVA=–$200+[$80annuityfactor(16%,4periods)]
=–
NPVB=–$200+[$100annuityfactor(16%,3periods)]
=–
Therefore,youshouldnowchooseProjectB.
Esttime:
01–05
4.IRRA=discountrate(r),whichisthesolutiontothefollowingequation:
r=IRRA=21.86%
IRRB=discountrate(r),whichisthesolutiontothefollowingequation:
r=IRRB=23.38%
Esttime:
01–05
5.No.EventhoughprojectBhasthehigherIRR,itsNPVislowerthanthatofprojectAwhenthediscountrateislower(asinProblem1)andhigherwhenthediscountrateishigher(asinProblem3).ThisexampleshowsthattheprojectwiththehigherIRRisnotnecessarilybetter.TheIRRofeachprojectisfixed,butasthediscountrateincreases,projectBbecomesrelativelymoreattractivecomparedtoprojectA.ThisisbecauseB’scashflowscomeearlier,sothepresentvalueofthesecashflowsdecreaseslessrapidlywhenthediscountrateincreases.
Esttime:
01–05
6.Theprofitabilityindexesareasfollows:
ProjectA:
$48.20/$200=0.2410
ProjectB:
$44.37/$200=0.2219
Inthiscase,withequalinitialinvestments,boththeprofitabilityindexandNPVgiveprojectsthesameranking.Thisisanunusualcase,however,sinceitisrarefortheinitialinvestmentstobeequal.
Esttime:
01–05
7.ProjectAhasapaybackperiodof$200/$80=2.5years.
ProjectBhasapaybackperiodof2years.
Esttime:
01–05
8.No.Despiteitslongerpaybackperiod,ProjectAmaystillbethepreferredproject,forexample,whenthediscountrateis11%(asinProblems1and2).AsinProblem5,youshouldnotethatthepaybackperiodforeachprojectisfixedbuttheNPVchangesasthediscountratechanges.TheprojectwiththeshorterpaybackperiodneednothavethehigherNPV.
Esttime:
01–05
9.NPV=$3,000+[$800annuityfactor(10%,6years)]
=–
Atthe10%discountrate,theprojectisworthpursuing.
IRR=discountrate(r),whichisthesolutiontothefollowingequation:
r=IRR=15.34%
YoucansolveforIRRusingafinancialcalculatorbyenteringPV=()3,000;n=6;FV=0;PMT=800;thencomputei.
SincetheIRRis15.34%,thisisthehighestdiscountratebeforeprojectNPVturnsnegative.
Esttime:
01–05
10.Paybackperiod=$2,500/$600=4.167years
Thisislessthanthecutoff,sothefirmwouldaccepttheproject.
r=2%NPV=$2,500+[$600annuityfactor(2%,6years)]
=–
r=12%NPV=$2,500+[$600annuityfactor(12%,6years)]
=–
Ifr=2%,theprojectshouldbepursued;atr=12%,itshouldnotbe.
Esttime:
06–10
11.
Profitabilityindex=NPV/investment=0.2680
Esttime:
01–05
12.NPV=$2.2billion+[$0.3billionannuityfactor(r,15years)][$0.9billion/(1+r)15]
=–
r=5%NPV=$2.2billion+$2.681billion=$0.481billion
r=18%NPV=$2.2billion+$1.452billion=$0.748billion
Esttime:
01–05
13.IRRA=discountrate(r),whichisthesolutiontothefollowingequation:
r=IRRA=25.69%
IRRB=discountrate(r),whichisthesolutiontothefollowingequation:
r=IRRB=20.69%
TheIRRofprojectAis25.69%,andthatofBis20.69%.However,projectBhasthehigherNPVandthereforeispreferred.TheincrementalcashflowsofBoverAare$20,000attime0and+$12,000attimes1and2.TheNPVoftheincrementalcashflows(discountedat10%)is$826.45,whichispositiveandequaltothedifferenceintherespectiveprojectNPVs.
Esttime:
01–05
14.
BecausetheNPVisnegative,youshouldrejecttheoffer.YoushouldrejecttheofferdespitethefactthattheIRRexceedsthediscountrate.Thisisa“borrowing-type”projectwithpositivecashflowsfollowedbynegativecashflows.AhighIRRinthesecasesisnotattractive:
Youdon’twanttoborrowatahighinterestrate.
Esttime:
01–05
15.a.r=0%NPV=–$6,750+$4,500+$18,000=$15,750
r=50%NPV=
r=100%NPV=
b.IRR=100%,thediscountrateatwhichNPV=0.
Esttime:
01–05
16.
SincetheNPVispositive,theprojectshouldbeaccepted.
Alternatively,youcancomputetheIRRbysolvingforr,usingtrialanderror,inthefollowingequation:
IRR=20.61%
SincetheIRRoftheprojectisgreaterthantherequiredrateofreturnof12%,theprojectshouldbeaccepted.
Esttime:
01–05
17.NPV9%=–$20,000+[$4,000annuityfactor(9%,8periods)]
=–
NPV14%=–$20,000+[$4,000annuityfactor(14%,8periods)]
=–
IRR=discountrate(r),whichisthesolutiontothefollowingequation:
r=IRR=11.81%
[Usingafinancialcalculator,enterPV=()20,000;PMT=4,000;FV=0;n=8,computei.]
Theprojectwillberejectedforanydiscountrateabovethisrate.
Esttime:
06–10
18.a.Thepresentvalueofthesavingsis$1,000/r.
r=0.08PV=$12,500andNPV=–$10,000+$12,500=$2,500
r=0.10PV=$10,000andNPV=–$10,000+$10,000=$0
b.IRR=0.10=10%
Atthisdiscountrate,NPV=$0.
c.Paybackperiod=10years
Esttime:
01–05
19.a.NPVforeachofthetwoprojects,atvariousdiscountrates,istabulatedbelow.
NPVA=–$20,000+[$8,000annuityfactor(r%,3years)]
=–$20,000+
NPVB=
DiscountRate
NPVA
NPVB
0%
$4,000
$5,000
2%
3,071
3,558
4%
2,201
2,225
6%
1,384
990
8%
617
–154
10%
–105
–1,217
12%
–785
–2,205
14%
–1,427
–3,126
16%
–2,033
–3,984
18%
–2,606
–4,784
20%
–3,148
–5,532
FromtheNPVprofile,itcanbeseenthatProjectAispreferredoverProjectBifthediscountrateisabove4%.At4%andbelow,ProjectBhasthehigherNPV.
b.IRRA=discountrate(r),whichisthesolutiontothefollowingequation:
r=IRRA=9.70%
IRRB=discountrate(r),whichisthesolutiontothefollowingequation:
=0IRRB=7.72%
Usingafinancialcalculator,findIRRA=9.70%asfollows:
EnterPV=(–)20;
PMT=8;FV=0;n=3;computei.
FindIRRB=7.72%asfollows:
EnterPV=(–)20;PMT=0;FV=25;n=3;
computei.
Esttime:
06–10
20.Weknowthattheundiscountedprojectcashflowssumtotheinitialinvestmentbecausepaybackequalsprojectlife.Therefore,thediscountedcashflowsarelessthantheinitialinvestment,soNPVisnegative.
Esttime:
01–05
21.
IRRB=discountrate(r),whichisthesolutiontothefollowingequation:
=0IRR=13.07%
BecauseNPVisnegative,youshouldrejecttheproject.ThisissodespitethefactthattheIRRexceedsthediscountrate.Thisisa“borrowing-type”projectwithapositivecashflowfollowedbynegativecashflows.AhighIRRinsuchcasesisnotattractive:
Youdon’twanttoborrowatahighinterestrate.
Esttime:
01–05
22.a.
Project
Payback
A
3years
B
2years
C
3years
b.OnlyProjectBsatisfiesthe2-yearpaybackcriterion.
c.Allthreeprojectssatisfya3-yearpaybackcriterion.
d.
e.False.Paybackgivesnoweighttocashflowsafterthecutoffdate.
Esttime:
06–10
23.a.Thenetpresentvaluesoftheprojectcashflowsare:
Theinitialinvestmentforeachprojectis$2,100.
Profitabilityindex(A)=$345.58/$2,100=0.1646
Profitabilityindex(B)=$241.31/$2,100=0.1149
b.Youshouldundertakebothprojects,aseachhasapositiveprofitabilityindex.Ifcapitalrationinglimitsyourchoice,youshouldundertakeprojectAforitshigherprofitabilityindex.
Esttime:
06–10
24.a.Thelessriskyprojectsshouldhavelowerdiscountrates.
b.First,findtheprofitabilityindexofeachproject.
Project
PVof
Cashflow
Investment
NPV
ProfitabilityIndex
A
$3.79
$3
$0.79
0.26
B
$4.97
$4
$0.97
0.24
C
$6.62
$5
$1.62
0.32
D
$3.87
$3
$0.87
0.29
E
$4.11
$3
$1.11
0.37
Thenselectprojectswiththehighestprofitabilityindexuntilthe$8millionbudgetisexhausted.Therefore,chooseProjectsEandC.
c.AlltheprojectshavepositiveNPV,soallwillbechosenifthereisnocapitalrationing.
Esttime:
06–10
25.a.NPVA=–$36+[$20annuityfactor(10%,3periods)]
=–$36+
NPVB=–$50+[$25annuityfactor(10%,3periods)]
=–$50+
ThusProjectAhasthehigherNPVifthediscountrateis10%.
b.ProjectAhasthehigherprofitabilityindex,asshowninthetablebelow:
Project
PVof
CashFlow
Investment
NPV
ProfitabilityIndex
A
$49.74
$36
$13.74
0.38
B
$62.17
$50
$12.17
0.24
c.AfirmwithalimitedamountoffundsavailableshouldchooseProjectAsinceithasahigherprofitabilityindexof0.38,i.e.,ahigher“bangforthebuck.”NotethatAalsohasahigherNPVaswell.
Forafirmwithunlimitedfunds,thepossibilitiesare:
(i)Iftheprojectsareindependentprojects,thenthefirmshouldchoosebothprojects.
(ii)However,iftheprojectsaremutuallyexclusive,thenProjectBshouldbeselected.IthasthehigherNPV.
Esttime:
06–10
26.a.NPVA=
NPVB=–$100+[$49annuityfactor(2%,3periods)]
=–$100+
Ifr=2%,chooseA.
b.NPVA=
NPVB=–$100+[$49annuityfactor(12%,3periods)]
=–$100+
Ifr=12%,chooseB.
c.ThelargercashflowsofprojectAtendtocomelater,sothepresentvalueofthesecashflowsismoresensitivetoincreasesinthediscountrate.
Esttime:
06–10
27.PVofcosts=$10,000+[$20,000annuityfactor(10%,5years)]
=$10,000+
Theequivalentannualcostisthepaymentwiththesamepresentvalue.SolvethefollowingequationforC:
Usingafinancialcalculator,entern=5;i=10;
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- corporate finance Chap008new
![提示](https://static.bdocx.com/images/bang_tan.gif)