金融学第二版讲义大纲及课后习题答案详解第六章.docx
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金融学第二版讲义大纲及课后习题答案详解第六章
CHAPTER6
HOWTOANALYZEINVESTMENTPROJECTS
Objectives
Toshowhowtousediscountedcashflowanalysistomakeinvestmentdecisionssuchas:
«Whethertoenteranewlineofbusiness
«Whethertoinvestinequipmenttoreduceoperatingcosts
Outline
6.1TheNatureofProjectAnalysis
6.2WhereDoInvestmentIdeasComeFrom?
6.3
TheNetPresentValueInvestmentRule
6.4EstimatingaProject'sCashFlows
6.5CostofCapital
6.6
SensitivityAnalysisUsingSpreadsheets
6.7AnalyzingCost-ReducingProjects
6.8ProjectswithDifferentLives
6.9RankingMutuallyExclusiveProjects
6.10InflationandCapitalBudgeting
Summary
*Theunitofanalysisincapitalbudgetingistheinvestmentproject.Fromafinanceperspective,investmentprojectsarebestthoughtofasconsistingofaseriesofcontingentcashflowsovertime,whoseamountandtimingarepartiallyunderthecontrolofmanagement.
*Theobjectiveofcapitalbudgetingproceduresistoassurethatonlyprojectswhichincreaseshareholdervalue（oratleastdonotreduceit）areundertaken.
*Mostinvestmentprojectsrequiringcapitalexpendituresfallintothreecategories:
newproducts,costreduction,andreplacement.Ideasforinvestmentprojectscancomefromcustomersandcompetitors,orfromwithinthefirm'sownR&Dorproductiondepartments.
*Projectsareoftenevaluatedusingadiscountedcashflowprocedurewhereintheincrementalcashflows
associatedwiththeprojectareestimatedandtheirNPViscalculatedusingarisk-adjusteddiscountratewhich
shouldreflecttheriskoftheproject.
*Iftheprojecthappenstobea“min-ireplica”oftheassetscurrentlyheldbythefirm,thenmanagementshould
usethefirm'costofcapitalincomputingtheproject'neipresentvalue.However,sometimesitmaybe
necessarytouseadiscountratewhichistotallyunrelatedtothecostofcapitalofthefirm
Thecorrectcostofcapitalistheoneapplicabletofirmsinthesameindustryasthenewproject.
*Itisalwaysimportanttocheckwhethercashflowforecastshavebeenproperlyadjustedtotakeaccountof
inflationoveraproject'slife.Therearetwocorrectwaystomaketheadjustment:
1.Usethenominalcostofcapitaltodiscountnominalcashflows.
2.Usetherealcostofcapitaltodiscountrealcashflows.
SolutionstoProblemsatEndofChapter
1.Yourfirmisconsideringtwoinvestmentprojectswiththefollowingpatternsofexpectedfuturenetaftertaxcashflows:
1
$1million
$5million
2
2million
4million
3
3million
3million
4
4million
2million
5
5million
1million
Theappropriatecostofcapitalforbothprojectsis10%.
Ifbothprojectsrequireaninitialoutlayof$10million,whatwouldyourecommendandwhy?
SOLUTION:
1
$1million
909,091
$5million
4,545,454
2
2million
1,652,893
4million
3,305,785
3
3million
2,253,944
3million
2,253,944
4
4million
2,732,054
2million
1,366,027
5
5million
3,104,607
1million
620,921
TotalPV
10,652,589
12,092,132
NPV
652,589
2,092,132
ProjectBisbetterthanAbecauseithasahigherNPV,aresultofpayingcashearlier.
InvestinginCost-ReducingEquipment
2.Afirmisconsideringinvesting$10millioninequipmentwhichisexpectedtohaveausefullifeoffouryearsandisexpectedtoreducethefirm'slaborcostsby$4millionperyear.Assumethefirmpaysa40%tax
rateonaccountingprofitsandusesthestraightlinedepreciationmethod.Whatistheafter-taxcashflowfromtheinvestmentinyears1through4?
Ifthefirm'shurdlerateforthisinvestmentis15%peryear,isit
worthwhile?
WhataretheinvestmentIRR'andNPV?
SOLUTION:
Wehavetofindtheincrementalcashflowsresultingfromthisinvestment.Therearetwomethodsthatwecanusetofindtheaftertaxcashflow.
1.Findthe（incremental）netincome,thenadd（incremental）depreciation.Hence:
Annualdepreciation（usingstraight-linemethod）=$10MM/4=$2.5MM
Pretaxincomeincreasesby:
$4MM-$2.5MM=$1.5MM
Netincomeincreaseby:
1.5x（1-0.4）=$0.9MM
Addingbackdepreciation（noncashexpense）:
OCF=0.9+2.5=$3.4MM
2.Addthedepreciationtaxshieldtotheafter-taxincrementalcostsaving.Hence,theyearlyOCFfromyear1to4is:
4x（1-0.4）+2.5x0.4=$3.4MM
At15%discountrate:
ttakethepr（
NPV=-$293,073MM.TheNPVisnegative,hencetheinvestmentisnotworthwhiletaking.
IRR=13.54%.TheIRRislessthanthecostofcapital（15%）oftheproject.Again,don
InvestinginaNewProduct
3.Tax-LessSoftwareCorporationisconsideringaninvestmentof$400,000inequipmentforproducinganewtaxpreparationsoftwarepackage.Theequipmenthasanexpectedlifeof4years.Salesareexpectedtobe60,000unitsperyearatapriceof$20perunit.Fixedcostsexcludingdepreciationoftheequipmentare$200,000peryear,andvariablecostsare$12perunit.Theequipmentwillbedepreciatedover4yearsusingthestraightlinemethodwithazerosalvagevalue.Workingcapitalrequirementsareassumedtobe1/12ofannualsales.Themarketcapitalizationratefortheprojectis15%peryear,andthecorporationpaysincometaxattherateof34%.WhatistheprojectNPV?
Wh'tssthebreakevenvolume?
SOLUTION:
Salesrevenuewillbe:
$20perunitx60,000unitsperyear=$1,200,000peryear
Investmentinworkingcapital=1/12x$1,200,000=$100,000
Thetotalinvestmentis$500,000:
$400,000fortheequipmentand$100,000inworkingcapital.Depreciation=$400,000/4=$100,000peryear
Totalannualoperatingcosts=$12perunitx60,000unitsperyear+$300,000=$1,020,000peryear
Theexpectedannualnetcashflowcanbederivedusingtheformula:
CF=netincome+depreciation
=（1-taxrate）（Revenue-totaloperatingcosts）+depreciation
=.66x（$1,200,000-$1,020,000）+$100,000
二$218,800peryear
0
-500,000
1
+218,800
2
+218,800
3
+218,800
4
+318,800
Ata15%hurdlerate:
NPV=$181,845
Nowwemustfindthenumberofunitsperyear（Q）,thatcorrespondstoanoperatingcashflowofthisamount.A
littlealgebrarevealsthatthebreakevenlevelofQisunitsperyear:
CASHFLOW=NETPROFIT+DEPRECIATION
=.66（8Q-300,000）+100,000=155,106
=.66（8Q-300,000）=55,106
8Q-300,000=55,106/.66=83,493.94
Q=383,493.94=47,937unitsperyear
8
Notethatcomputingtheaccountingbreakevenquantitygives:
Breakevenquantity=fixedcosts/contributionmargin
Qb=_E
P-V
Qb=$300,000peryear=37,500unitsperyear
$8perunit
InvestinginaNewProduct
4.HealthyHopesHospitalSupplyCorporationisconsideringaninvestmentof$500,000inanewplantforproducingdisposablediapers.Theplanthasanexpectedlifeof4years.Salesareexpectedtobe600,000unitsperyearatapriceof$2perunit.Fixedcostsexcludingdepreciationoftheplantare$200,000peryear,andvariablecostsare$1.20perunit.Theplantwillbedepreciatedover4yearsusingthestraightlinemethodwithazerosalvagevalue.Thehurdleratefortheprojectis15%peryear,andthecorporationpaysincometaxattherateof34%.
Find:
a.Thelevelofsalesthatwouldgiveazeroaccountingprofit.
b.Thelevelofsalesthatwouldgivea15%after-taxaccountingrateofreturnonthe$500,000investment.
c.TheIRR,NPV,andpaybackperiod（bothconventionalanddiscounted）ifexpectedsalesare600,000unitsperyear.
d.ThelevelofsalesthatwouldgiveanNPVofzero.
SOLUTION:
Theinitialinvestmentis$500,000.
Depreciation=$500,000/4=$125,000peryear
Totalannualfixedcosts=$200,000+$125,000peryear=$325,000peryear
a.Tofindtheaccountingbreakevenquantityapplythebreakevenformula:
Breakevenquantity=fixedcosts/contributionmargin
Qb=_F
P-V
Qb=$325,000peryear=406,250unitsperyear
$.80perunit
b.Toearna15%accountingROI,theaftertaxprofit（netincome）hastobe:
.15x$500,000=$75,000
Thatmeansbefore-taxprofithastobe$75,000/.66=$113,636.
Toearnthisadditionalprofit,thenewbreakevenquantitymustincreaseby:
142,045unitsperyear（requiredprofitbeforetaxes/contributionmargin=$113,636/$.80）toatotalof548,295peryear.
c.If600,000unitsperyearcanbesold,thentheexpectedannualnetcashflowcanbederivedusingthe
formula:
CF=netincome+depreciation
=（1-taxrate）（Revenue-totaloperatingcosts）+depreciation
=.66x（$1,200,000-$720,000-$325,000）+$125,000
=$227,300peryear
4
15
?
0
227,300
PV=$648,937
4
?
-500,000
0
227,300
IRR=29.09%
?
15
-500,000
0
227,300
n=2.87years
NPV=$648,937-$500,000=$148,937
Conventionalpaybackperiod=$500,000/$227,300peryear=2.2years
d.InorderfortheNPVtobe0,whatmustthecashflowfromoperationsbe?
4
15
-500,000
0
?
PMT=$175,133
Nowwemustfindthenumberofunitsperyear（Q）,thatcorrespondstoanoperatingcashflowofthisamount.A
littlealgebrarevealsthatthebreakevenlevelofQisunitsperyear:
CASHFLOW=NETPROFIT+DEPRECIATION
=.66（.8Q-325,000）+125,000=175,133
=.66（.8Q-325,000）=50,133
.8Q-325,000=50,133/.66=75,959
Q=400,959=501,199unitsperyear
.8
ReplacementDecision
5.Pepe'sSkiShopiscontemplatingreplacingitsskibootfoaminjectionequipmentwithanewmachine.Theoldmachinehasbeencompletelydepreciatedbuthasacurrentmarketvalueof$2000.Thenewmachinewillcost$25,000andhavealifeoftenyearsandhavenovalueafterthistime.Thenewmachinewillbedepreciatedonastraight-linebasisassumingnosalvagevalue.Thenewmachinewillincreaseannualrevenuesby$10,
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