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(NPV- IRR– IP)
Sequence
• Introduction• Basictermsreview• Capitalbudgetingintroduction• Capitalbudgetingtechnique• Sensitivityanalysis• Scenarioanalysis
•LetsBegin
AreviewofBasics:PresentValue,NetPresentvalueandfuturevalue• Presentvalue (PV)isthecurrentworthofafuturesumofmoneyorstreamofcashflowsgivenaspecifiedrateofreturn.Inotherwords,presentvalue,alsoknownas present discounted value,isthe value ofanexpectedincomestreamdeterminedasofthedateofvaluation
• Differencebetweenaproject’svalueanditscostisitsNPV• Futurevalue isthe value ofanassetataspecificdate.Itmeasuresthenominal future sumofmoneythatagivensumofmoneyis"worth"ataspecifiedtimeinthe future assumingacertaininterestrate,ormoregenerally,rateofreturn;itisthepresent valuemultipliedbytheaccumulationfunction.
Fewformulas
Discountfactor;1/(1+r)t
PV=C1/1+r+C2/(1+r)2 ...+Ct/(1+r)t
Presentvalue=DF2*C2NPV=Investment+PV
AreviewofBasic:Example
• aCEOofcorporationislookingtoinvest$1millioninprojectX• Heasksfromyou(FINANCIALMANAGER)whethertoinvestornot,andifyesthenwhatshouldbethegroundsYouranswermaybe:
first:forecastthecashflowsmaybegeneratedbytheprojectSecond:determinetheappropriateopportunitycostofCapital.Thatshouldreflectboth;timevalueofmoneyandRiskfactorThird: usetheopportunitycostofcapitaltodiscounttheproject'sfuturecashflowsFourth: calculateNPVbysubtractingthe1millioninvestmentfrompresentvalue:(Bothformulasaregivenbelow)
PV=C1/1+r+C2/(1+r)2 ...+Cn/(1+r)t NPV=C0 +C1/1+r+C2/(1+r)2 ...+Cn/(1+r)t
Note: InvestinProjectifitsNPVisgreaterorequaltozero
NetPresentValue
• Example:buildingcosts700,000itcanbesoldfor$ 800,000.ifthediscountrateis10%,calculate:
§ PresentValue§ NetPresentValue
PV=C1/1+r+C2/(1+r)2 ...+Cn/(1+r)n
=800,000/(1+.10)PV=RS.727273NPV=C0 +C1/1+r+C2/(1+r)2 ...+Cn/(1+r)n
=700,000-727273NPV=$ +27273
NPVStrengthsandWeaknesses
Strengths:• Cashflows
assumedtobereinvestedatthehurdlerate.
• AccountsforTVM.• Considersall
cashflows.
Weaknesses:• Maynotinclude
managerialoptionsembeddedintheproject.SeeChapter14.
NetPresentValueProfile
DiscountRate(%)03691215
IRRNPV@13%
SumofCF’s PlotNPVforeachdiscountrate.
NetP
resentValue
$000s15
10
5
0
-4
AreviewofBasic:Example…continue• CEOasks,whyGreaterNPVissoimportant?Youanswer:NPVisimportantasifthefirmdoesnotearnequalormorethanwhattheshareholdersexpectthantheymightselltheirshareinthemarket.“InvestorswouldforecastthedividendsthatProjectXpayanddiscountthosedividendsbytheexpectedrateofreturnofsecuritieshavingsimilar
risk.ӯOnlythingtoansweriswherethediscountratecomesfrom?
Itistheopportunitycostofinvestingintheprojectratherthaninthecapitalmarket.ifthefirmdoesnotearnfromtheprojectwhatitsshareholdersexpect(costofcapital)thanitshouldreturnthecashtotheshareholdersandletthemtoinvestinFinancialMarketsbypurchasingfinancialAsset
InvestmentProjectX
If10%orreturn
Cash
FinancialManager
Shareholders(Ifprojectreturnlessthan
10%)
Investment(FinancialAsset)
Firstoption:Invest
Secondoption:PaydividendtoShareholders
ShareholdersInvest
themselves
Figure1;DeisionthroughNPVifdiscountrateis10%
ImportantPointstoberememberedaboutNetPresentValue
• First:NPVrulerecognizesthata$todayisworthmorethana$tomorrow(timevalueofmoney).
• Second:NPVdependsontheforecastedcashflowsfromtheprojectandtheopportunitycostofcapital
• Third:PVmeasuresintodaysmoney,thereforeweaddthemup.• NPVdependsonCashflows,notonbookreturns.Bookreturnsaretheaccountingrecordratherthancashas:
BookrateofReturns=bookincome/bookassets
CapitalBudgeting
TheCapitalBudgetingProcessofgeneratingInvestmentProjectProposalsandestimatingProject“After-TaxIncrementalOperatingCashFlows”
TheCapitalBudgetingProcess
• Generateinvestmentproposalsconsistentwiththefirm’sstrategicobjectives.
• Estimateafter-taxincrementaloperatingcashflowsfortheinvestmentprojects.
• Evaluateprojectincrementalcashflows.
TheCapitalBudgetingProcess
• Selectprojectsbasedonavalue-maximizingacceptancecriterion.
• Reevaluateimplementedinvestmentprojectscontinuallyandperformpostauditsforcompletedprojects.
ClassificationofInvestmentProjectProposals
1.Newproductsorexpansionofexistingproducts
2.Replacementofexistingequipmentorbuildings
3.Researchanddevelopment4.Exploration5.Other(e.g.,safetyorpollutionrelated)
Paybackmethod
• Paybackperiod incapitalbudgetingreferstothe period oftimerequiredtorecoupthefundsexpendedinaninvestment,ortoreachthebreak-evenpoint.
Forexample,a$1000investmentwhichreturned$500peryearwouldhaveatwo-year paybackperiod.Thetimevalueofmoneyisnottakenintoaccount.
Paybackmethod
Cash flows
NPVat10%Paybackperiod(years)
3C2C1C0CProject
2,62435,000500500-2000A
-58201,800500-2000B
50205001,800-2000C
PaybackiscalculatedbytakingtheaccumulatedofallCFs NPViscalculatedwiththehelpofthefollowingformula
nr)+1/(nC...+2r)+1/(2Cr++1/1C+0C=NPV
DiscountedpaybackSomecompaniesdiscountthecashflowsbeforetheycomputepaybackperiod
DiscountedCashflowsRs
NPVat10%Paybackperiod(years)
C3C2C1C0Project
2,62435,000/1.13500/1.12
=413
500/1.12
=455-2000A
-58-01,800/1.12=1,488
500/1.1
=455-2000B
5020500/1.12
=413
1,800/1.1
=1,636-2000C
Whypaybackcangivemisleadinganswers
• Paybackruleignoresallcashflowsafterthecutoffdate.• Itsrulegivesequalweighttoallcashflowsbeforethecutoffdate• Companiesstillfrequentlyuseitbecauseitisthesimplestwaytocommunicatetheidea.
• Everyonecanunderstandit• Managerlikeitasittellshortspanperiod;goodfortheirpromotion
PBPStrengthsandWeaknesses
Strengths:• Easytouseand
understand• Canbeusedasa
measureofliquidity
• Easiertoforecast STthanLTflows
Weaknesses:• Doesnotaccount
forTVM• Doesnotconsider
cashflowsbeyondthePBP
•
InternalRateofReturn(IRR)
IRR isthediscountratethatequatesthepresentvalueofthefuturenetcashflowsfromaninvestmentprojectwiththeproject’sinitial
cashoutflow.
tCF2CF1CFt)IRR+1(2)IRR+1(1)IRR+1(
+...++ICO=
ExampleProjectData
Afinancialmanagerisevaluatinganewprojectforherfirm.Shehasdeterminedthattheafter-taxcashflowsfortheprojectwillbe$10,000;$12,000;$15,000;$10,000;and$7,000,respectively,foreachoftheYears1through5.Theinitialcashoutlaywillbe$40,000.
IndependentProject
• Independent -- Aprojectwhoseacceptance(orrejection)doesnotpreventtheacceptanceofotherprojectsunderconsideration.
◆For this project, assume that it is independent of any other potential projects.
$15,000$10,000$7,000
IRRSolution
$10,000$12,0002)IRR+1(1)IRR+1(
Findtheinterestrate(IRR)thatcausesthediscountedcashflowstoequal$40,000.
+ +
++$40,000 =
5)IRR+1(4)IRR+1(3)IRR+1(
IRRSolution(Try10%)
$40,000 = $10,000(PVIF10%,1)+$12,000(PVIF10%,2)+$15,000(PVIF10%,3)+$10,000(PVIF10%,4)+ $
7,000(PVIF10%,5)$40,000 = $10,000(.909)+$12,000(.826)+
$15,000(.751)+$10,000(.683)+$7,000(.621)
$40,000 = $9,090+$9,912+$11,265+$6,830+$4,347
= $41,444 [Rateistoolow!!]
IRRSolution(Try15%)
$40,000 = $10,000(PVIF15%,1)+$12,000(PVIF15%,2)+$15,000(PVIF15%,3)+$10,000(PVIF15%,4)+ $
7,000(PVIF15%,5)$40,000 = $10,000(.870)+$12,000(.756)+
$15,000(.658)+$10,000(.572)+$7,000(.497)
$40,000 = $8,700+$9,072+$9,870+$5,720+$3,479
= $36,841 [Rateistoohigh!!]
.10 $41,444.05 IRR $40,000 $4,603
.15 $36,841
($1,444)(0.05)$4,603
IRRSolution(Interpolate)
$1,444X
X =
X =.0157
IRR =.10+.0157 = .1157or11.57%
IRRAcceptanceCriterion
No!Thefirmwillreceive11.57% foreachdollarinvestedinthisprojectatacostof
13%.[IRR <HurdleRate]
Themanagementofacompany hasdeterminedthatthehurdlerateis13%for
projectsofthistype.Shouldthisprojectbeaccepted?
IRRsontheCalculator
Wewillusethecashflowregistrytosolve
theIRRforthisproblemquicklyand
accurately!
ActualIRRSolutionUsingYourFinancialCalculator
StepsintheProcessStep1: Press CF keyStep2: Press 2nd CLRWork keysStep3:ForCF0 Press-40000 Enter¯ keysStep4:ForC01 Press 10000 Enter¯ keysStep5:ForF01 Press 1 Enter¯ keysStep6:ForC02 Press 12000 Enter¯ keysStep7:ForF02 Press 1 Enter¯ keysStep8:ForC03 Press 15000 Enter¯ keysStep9:ForF03 Press 1 Enter¯ keys
ActualIRRSolutionUsingYourFinancialCalculator
StepsintheProcess(PartII)Step10:ForC04 Press 10000 Enter¯ keysStep11:ForF04 Press 1 Enter¯ keysStep12:ForC05 Press 7000 Enter¯ keysStep13:ForF05 Press 1 Enter¯ keysStep14: Press ¯ ¯ keysStep15: Press IRR keyStep16: Press CPT key
Result: InternalRateofReturn =11.47%
IRRStrengthsandWeaknesses
Strengths:• Accountsfor
TVM• Considersall
cashflows• Less
subjectivity
Weaknesses:• Assumesallcash
flowsreinvestedattheIRR
• DifficultieswithprojectrankingsandMultipleIRRs
NPVontheCalculator
WewillusethecashflowregistrytosolvetheNPVforthisproblemquickly
andaccurately!
Hint:Ifyouhavenot clearedthecashflowsfromyourcalculator,thenyoumayskiptoStep15.
ActualNPVSolutionUsingYourFinancialCalculator
StepsintheProcessStep1:PressCFkey
:2StepPressnd2CLRWorkkeys40000-Press0CFFor:3Stepkeys¯EnterPress01CFor:4Step10000keys¯EnterPress01FFor:5Step1keys¯EnterPress02CFor:6Step12000keys¯EnterPress02FFor:7Step1keys¯EnterPress03CFor:8Step15000keys¯EnterPress03FFor:9Step1keys¯Enter
PartII)StepsintheProcess(Press04CFor:10Step10000keys¯EnterPress04FFor:11Step1keys¯EnterPress05CFor:12Step7000keys¯EnterPress05FFor:13Step1keys¯Enter
Step14:Press¯¯keysStep15:PressNPVkey
Enter,ForI=:16Step13Enter¯keysStep17:PressCPTkeyResult:1,424.42$-=NetPresentValue
ActualNPVSolutionUsingYourFinancialCalculator
CreatingNPVProfilesUsingtheCalculator
Hint:Aslongasyoudonot“clear”thecash
flowsfromtheregistry,simplystartatStep15andenteradifferentdiscountrate.EachresultingNPVwill
providea“point”foryourNPVProfile!
ProfitabilityIndex(PI)
PIistheratioofthepresentvalueofaproject’sfuturenetcashflowstotheproject’sinitialcashoutflow.
CF1 CF2 CFn(1+k)1 (1+k)2 (1+k)n
+...++ ICOPI=
PI=1+[NPV /ICO ]
<<OR>>
PIAcceptanceCriterion
This.1.00lessthanisPITheNo!meansthattheprojectisnotprofitable.[RejectasPI <
1.00 ]
PI=$38,572/$40,000=.9643(Method#1,13-33)
Shouldthisprojectbeaccepted?
PIStrengthsandWeaknesses
:Strengths•SameasNPV•Allows
comparisonofdifferentscale
projects
:Weaknesses•SameasNPV•Providesonly
relativeprofitability•PotentialRanking
Problems
OtherProjectRelationships
• MutuallyExclusive -- Aprojectwhoseacceptanceprecludestheacceptanceofoneormorealternativeprojects.
◆ Dependent -- A project whose acceptance depends on the acceptance of one or more other projects.
PotentialProblemsUnderMutualExclusivity
A.ScaleofInvestmentB.Cash-flowPatternC.ProjectLife
Rankingofprojectproposalsmaycreatecontradictoryresults.
A.ScaleDifferences
Compareasmall(S)andalarge(L)project.
NETCASHFLOWSProjectSProjectLENDOFYEAR
0-$100-$100,000
100
2$400$156,250
ScaleDifferences
CalculatethePBP,IRR,NPV@10%,andPI@10%.Whichprojectispreferred?Why?
PINPVIRRProject
S 100% $231 3.31L25% $29,1321.29
B.CashFlowPattern
Letuscompareadecreasing cash-flow(D)projectandanincreasing cash-flow(I)project.
NETCASHFLOWSProjectD ProjectIENDOFYEAR
0-$1,200-$1,20011,000100250060031001,080
D 23% $1981.17I 17% $1981.17
CashFlowPattern
CalculatetheIRR,NPV@10%, andPI@10%.Whichprojectispreferred?
Project IRR NPV PI
C.ProjectLifeDifferences
Letuscomparealong life(X)projectandashort life(Y)project.
NETCASHFLOWSProjectXProjectYENDOFYEAR
0-$1,000-$1,00010 2,00020033,3750
X50%$1,5362.54Y 100%$8181.82
ProjectLifeDifferences
CalculatethePBP,IRR,NPV@10%,andPI@10%.Whichprojectispreferred?Why?
Project IRR NPV PI
AnotherWaytoLookatThings
1. Adjustcashflowstoacommonterminalyearifproject“Y”willNOT bereplaced.CompoundProjectY,Year1@10%for2years.
Year0123CF-$1,000 $0$0$2,420
Results: IRR*=34.26% NPV=$818*LowerIRRfromadjustedcash-flowstream.XisstillBest.
ReplacingProjects withIdenticalProjects
2. UseReplacementChainApproach(AppendixB)whenproject“Y”willbereplaced.
0123
-$1,000$2,000-1,000$2,000
-1,000$2,000
-$1,000$1,000$1,000$2,000
Results:IRR*=100%NPV* = $2,238.17
*HigherNPV,butthesameIRR. YisBest.
CapitalRationing
CapitalRationingoccurswhenaconstraint(orbudgetceiling)isplacedonthetotalsizeofcapitalexpendituresduringaparticularperiod.
Example:JulieMillermustdeterminewhatinvestmentopportunitiestoundertakeforBasketWonders(BW).Sheislimitedtoamaximumexpenditureof$32,500only forthiscapitalbudgetingperiod.
AvailableProjectsforBW
ProjectICOIRRNPVPIA$ 50018% $501.10 B5,000 25 6,5002.30 C5,000 37 5,5002.10 D7,500 20 5,0001.67 E12,500 26 5001.04 F15,000 28 21,0002.40G17,500 19 7,5001.43 H25,000 15 6,0001.24
ChoosingbyIRRsforBW
ProjectICOIRRNPVPIC$5,00037% $5,500 2.10 F15,000 28 21,000 2.40 E12,500 26 500 1.04 B5,000 25 6,5002.30
ProjectsC,F,andEhavethe threelargestIRRs.
Theresultingincrease in shareholderwealth is$27,000 witha$32,500outlay.
ChoosingbyNPVsforBW
ProjectICOIRRNPVPIF$15,00028% $21,000 2.40 G17,500 19 7,500 1.43 B5,000 25 6,5002.30ProjectsFandGhavethe two
largestNPVs.Theresultingincrease in shareholderwealth is
$28,500 witha$32,500outlay.
ChoosingbyPIsforBW
ProjectICOIRRNPVPIF $15,000 28% $21,000 2.40B 5,000 25 6,500 2.30C 5,000 37 5,500 2.10D 7,500 20 5,000 1.67G 17,500 19 7,5001.43ProjectsF,B,C,andDhavethefourlargestPIs.
Theresultingincrease in shareholderwealth is$38,000witha$32,500outlay.
SummaryofComparison
Method ProjectsAccepted ValueAddedPI F,B,C,andD$38,000NPV FandG$28,500IRR C,F,andE$27,000
PI generatesthegreatest increase inshareholderwealthwhenalimitedcapitalbudgetexistsfora
singleperiod.
Post-CompletionAudit
Post-completionAuditAformalcomparisonoftheactualcostsandbenefits
ofaprojectwithoriginalestimates.
• Identifyanyprojectweaknesses• Developapossiblesetofcorrectiveactions• ProvideappropriatefeedbackResult:Makingbetterfuturedecisions!
MultipleIRRProblem*
Two!!Thereareasmanypotential IRRsastherearesignchanges.
LetusassumethefollowingcashflowpatternforaprojectforYears0to4:
-$100+$100+$900-$1,000Howmanypotential IRRscouldthisprojecthave?
*RefertoAppendixA
Projectanalysis
• Investmentprocessstartswiththepreparationofanannualcapitalbudget.
• Projectauthorizationandproblemofbiasedforecasts• Postaudits
• Identificationofproblems• AccuracyofforecastAnysuggestion
Sensitivityanalysis
• Uncertaintymeansmorethingscanhappenthanwillhappen.• Example
AcompanyisintroducingnewscootersforcityusewithRs.15bNetinvestmentfor10years,producingNCFofRs.3Bintenyears.Staffhavepreparedtheforecastsat10%NPV.= (-15)+3/(1.1)10 =Rs.+3.43billionsProductiondepartmentestimatedcostperunitisRs.300,000and100,00scootercanbemadeintheyear.Ifcalculatedtherevenueasthefirmhas1%marketshare,itwillbe:Unitsales=newproductshareinmarket*sizeofscootermarket
37.5billions(Revenue)=100,000*375,000
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be apportioned to different sources of uncertainty in its inputs.
SensitivityanalysisPreliminarycash-flowforecastforcompany
Year1- 10(onetotenyears)Year0(zero)Description
NIL15billionInvestment
37.5NILRevenue
30NILVariablecost
3NILFixedcost
1.5NILDepreciation
3NILPretaxprofit
1.5NILTax
1.5NILNetprofit
3NILOperatingcashflow
3NILNetcashflow
1. Investmentisdepreciatedover10yearsstraightline2. Income istaxedatarateof50%
Sensitivityanalysis…
• ValueInformation• SupposethatproductiondepartmentisworriedaboutthemachinewhichwillnotworkproperlyandthefirmhastopurchaseanothermethodwhichincureperunitcostanextraRs.20,000:unitssales*additionalunitcost*(1-taxrate)Rs.1Billion =100,000*20,000*.50
ItwillreducetheNPVby:1/(1.10)10
• Limitsofsensitivityanalysis• Givingambiguousresults
Scenarioanalysis
• Scenarioanalysis isaprocessofanalyzingpossiblefutureeventsbyconsideringalternativepossibleoutcomes(sometimescalled"alternativeworlds").
• Thus,the scenarioanalysis,whichisamainmethodofprojections,doesnottrytoshowoneexactpictureofthefuture.