(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.