module 2 capital budgeting.pdf financial management

Capital budegeting calicut university

1. Investment Decisions/Capital
Budgeting

2. Capital Budgeting
•Capitalbudgetingistheprocessofmakinginvestment
decisionrelatingtocapitalexpenditure.
•Acapitalexpendituremaybedefinedasanexpenditurethe
benefitsofwhichareexpectedtobereceivedoverperiodoftime
exceedingoneyear.
•Capitalexpenditureisincurredinonepointoftimewhereas
benefitsofexpenditurearerealisedindifferentperiodsoftime
infuture.

3. Meaning
❑CapitalBudgetingistheprocessofallocatingtheresourcesof
theorganisationinthelongterminvestmentprojectstogenerate
profit.
❑Itistheprocessofidentifying,analysingandselecting
investmentprojectswhosereturnsareexpectedoveraseriesof
yearsinfuture.
Eg:AcompanymakesadecisiontoinvestinanewprojectofRs
100croreexpectingRs20croreextraprofitperyearfor10years.

4. Features of Capital Budgeting
1.Funds are invested for long term activities.
2.It involves huge outlays.
3.Current funds are exchanged for future benefits
4.The benefits are expected over a number of years in
future.
5.It involves a high degree of risk.
6.They are not easily reversible.
7.Gestationperiod(i.e.Periodbetweentheinitialoutlay
andanticipatedreturn)islong.

5. Need and importance of capital budgeting
CapitalBudgetingisconcernedwithheavyexpendituredecisions.
Thebenefitsofsuchexpenditureisexpectedtobederivedfrom
manyyearsinfuture.
Importance
1.Hugeinvestment
2.Irreversibledecisionorreversibleatsubstantialloss
3.Longtermimplication:
4.Hugerisk:
5.Growth

6. 6.Ithasimpactonfirm’scompetitivestrength
7.Mostdifficultdecision:Capitalbudgetingdecisionsarevery
difficulttomakedueto:
a)uncertaintyoffuture
b)decisionsarebasedonestimateaboutfutureyears’cashflows
c)Morerisk
d)Thebenefitsandcostareaffectedbyeconomic,politicalandtechnologicalforces
8.LongTermCommitmentoffunds
9.NationalImportance:Itdeterminesemployment,economic
activitiesandeconomicgrowth.

7. Limitations of Capital Budgeting Decisions
1.Thebenefitsarereceivedinfuture.Theseareuncertain.
Thereforeanelementofriskisinvolved.
2.Somefactorsaffectinginvestmentproposalscannotbeexpressed
inmoneyvalue.Eg:employeesmorale,skill,etc.
3.Itisverydifficulttoestimatetheperiodforwhichinvestmentis
made.
4.Itisverydifficulttoestimatetherateofreturnandcostofcapital.
5.Ifthecapitalbudgetingdecisionsgowrong,itmaycreateserious
consequencesonthefirm’sliquidity,profitability,etc.

8. Types of Investment Decisions
1.Expansionanddiversification:Acompanymay
addcapacitytoitsexistingproductlinestoexpand
existingoperations.Similarlyafirmmayexpand
itsactivitiesinanewbusiness.
2.Replacementandmodernisation:Themain
objectiveofmodernisationandreplacementisto
improveoperatingefficiencyandreducecosts.

9. Steps in Capital Budgeting/Capital Budgeting Process
Itisa6stepcomplexprocess
1.Projectidentification/generation:Itinvolvescontinuoussearchforcompatible
investmentopportunities.
2.Projectscreening:Eachprojectisthensubjecttoapreliminaryscreeningprocess
inordertoassesswhetheritistechnicallyfeasible,resourcesrequiredare
availableandtheexpectedreturnsareadequatetocompensatetherisksinvolved.
3.Projectevaluation:Afterscreening,thenextstepistoevaluateprofitabilityof
eachproposal.
Thisinvolvestwosteps:
a)estimationofcostsandbenefitsintermsofcashflows,and
b)selectinganappropriatecriteriontojudgethedesirabilityofthe
project.
Therearemanymethodswhichmaybeusedforthispurposesuchaspayback
method,netpresentvaluemethod,Internalrateofreturn,etc.

10. 4.Projectselection:Nextstepistoselectandapprovethebest
proposal.
5.Projectexecutionandimplementation:Theselectedprojectis
implementednext.Thismeansthattheproposalinpaperbecomes
areality.
6.Performancereview:Theprojectsimplementedmustbereviewed
atregularintervalstowatchtheprogressandtakecorrective
action,ifrequired.

11. Estimation of cash flows
•Foracapitalbudgetingdecision,itisnecessarytoestimatecash
outflowsandcashinflows.
•Cashoutflowmeansinvestment.Itisknownascost.
•Cashinflowmeansbenefits.
•Thus,cashflowincludescostandbenefits.
•Onthebasisofthecost-benefitanalysis,theprofitableprojectis
selected.So,costandbenefits(orcashflows)arerequiredtobe
estimatedfirst.
•Estimationoffuturecashflowsofaprojectisoneofthemost
importantstepsincapitalbudgetingtoestimatetheprofitabilityof
theprojects.

12. Considerations in determining cash flows
1.Cashflowsoraccountingprofit:Theoretically,thesetwocriteriaare
availabletoexpressbenefits.
2.Incrementalcashflows:Forcapitalbudgetingdecisiononlyincremental
cashflowistobeconsidered.Incrementalcashflowsarethosecash
flowswhicharedirectlyaffectedbytheinvestmentdecision.
3.Timevalueofmoneyandinflationshouldbeconsidered.
4.Effectofchangeinworkingcapitalshouldbeconsidered.
5.Effectoftax:Cashflowsaftertaxshouldbeconsidered.
6.Effectofdepreciationshouldalsobeconsidered.
7.Proceedingfromsaleofassetsshouldbetreatedascashinflow,ifthe
newassetsispurchasedtoreplaceanexistingasset.
8.Effectofoverheadcostsandotherindirectexpensesshouldbe
consideredonlyiftheychangewhentheprojectisaccepted.

13. Types of cash flows
There are three types of cash flows:
1.Initialcashflow(Initialinvestment):Itistheinvestmentrequired
inthebeginninganewproject.Inthecaseofreplacement
projects,thescrapvalueshouldbedeductedfromthecostof
newasset.
2.Netannualcashinflowsoroperatingcashflows:Theinitial
investmentisexpectedgenerateaseriesofcashinflowsfromthe
project.Thesecashinflowsarecallednetannualcashinflows.
Thismayoccurbytwomeans(a)additionalrevenue(b)cash
savingoperations.Theannualcashflowsshouldbeadjustedfor
taxes,depreciation,etc.
3.Terminalcashinflows:Itisthecashinflowsfortheterminalyear
oftheproject.Itincludesscrapvalueandworkingcapitalwhich
wasinvestedinthebeginningbutnotrequiredfurtherasthe
projectisterminated.

14. Otherinformationrequiredforcapitalbudgetingdecision
Apart from cash flows, the following information is required for
capital budgeting decision
1.RequiredRateofreturn:Aninvestmentproposalisaccepted
whenthereturnestimatedismorethantherequiredrateof
return.Itisalsocalledcostofcapitaorcutoffrateorhurdle
rate
2.Otherinformation:Economiclifeoftheproject,availablefund
andriskofobsolescence.

15. Investment appraisal methods/Techniques of capital budgeting
•Investmentappraisal(Projectappraisal)istheassessmentofa
projecttoknowwhetheritisworthwhiletoinvestmoneyinit.
Itisatooltoexamineastowhetheritwouldbemostrealistic,
reliableandreasonabletoinvestresourcesintheproject.
Techniquesofcapitalbudgetingcanbeclassifiedintotwobroad
categories:
1.TraditionalMethodsorNon-discountedcashflowTechniques
2.ModernMethodsorDiscountedCashFlowTechniques.

16. Techniques of capital budgeting
1.TraditionalMethodsorNon-discountedcashflowTechniques
a)UrgencyMethod
b)PaybackMethod(Profitaftertaxandbeforedepreciationis
considered)
c)AccountingRateofReturnMethod(Accountingprofitisconsidered)
2.ModernMethodsorDiscountedcashflowTechniques.
a)DiscountedPayBackMethod
b)NetPresentValueMethod
c)BenefitCostRatio(ProfitabilityIndex)
d)InternalRateofReturn
e)NetTerminalValueMethod.

17. Traditional Methods or Non-discounted Cash flow
Techniques
TraditionalMethodsdonottakeintoconsiderationthetimevalue
ofmoney.
a)UrgencyMethod:Thismethodisusedtojustifytheacceptance
ofcapitalprojectsonthebasisofemergencyrequirementor
undercrisisconditions.Urgencyordegreeofnecessityplaysan
importantroleandtheprojectthatcannotbepostponedis
undertakenfirst.Mosturgentprojectistakenupfirst.
Itisaverysimpletechnique.Themaindemeritsofthismethod
are:itisnotbasedonscientificanalysisandselectionofthe
projectisnotmadeonthebaseofeconomicalconsideration.

18. b) Pay Back Period Method
Paybackperiodisthenumberofyearsrequiredtorecoverthe
costoftheinvestment.
Thismethodmeasurestheperiodoftimerequiredtorecover
theoriginalcostofaprojectfromtheadditionalearningsofthe
project.
Underthismethod,variousinvestmentsarerankedaccording
tothelengthoftheirpaybackperiod.Theinvestmentwitha
shorterpaybackperiodispreferredtotheonewhichhaslonger
paybackperiod.

19. 1.When annual cash inflows are equal:
Payback period=Original cost of the project(initial cash outlay) ÷annual net
cash inflow
Eg: If a project involves a cash outlay or Rs 500000 and generates cash inflow
of Rs 100,000 for 7 years, pay back period will be:
Payback period: Rs 500,000 ÷Rs 100,000= 5 years
2. When annual cash inflows are not equal
Here,Paybackperiodiscalculatedbycumulatingthenetcashinflowsuntil
theoriginalinvestmentisrecovered.Itisascertainedbycumulatingcash
inflowstillthetimewhenthecumulativecashinflowsbecomeequalto
initialinvestment.
Eg:1)IfthecostoftheprojectisRs100,000andthenetcashflowsare:1
st
year-
10000,2
nd
year-15000,3
rd
year–25000,4
th
year-30000,5
th
year20000,6
th
year-
50000
10000+15000+25000+30000+20000=100000
5years
How to determine Pay Back Period

20. Suitability of Payback method
Paybackmethodisappropriateinthefollowingcases:
1.Whenthecostoftheprojectiscomparativelysmall.
2.Whentheprojectislikelytobecompletedinshortperiod.
3.Whenonlylimitedfundsareavailable.
4.Whenthecashearningcapacityofthecompanyislow.
5.Whenthereisachanceofobsolescenceduetotechnological
development
ImportantNote:Underpaybackperiodmethodcashinflowmeans
operatingprofitbeforedepreciationbutaftertax.
DecisionRule:Theshorterthepaybackperiodthebettertheproject.

21. Advantages
1.Itissimpletounderstandandeasytoapply
2.Itishelpfultobusinesswhichlacktheappropriateskillsnecessaryfor
moresophisticatedtechniques.
3.Itisveryimportantforcashforecasting,budgetingandcashflow
analysis
4.Thismethodcanbeusedprofitablyforshorttermcapitalprojects
whichstartyieldingreturnsintheinitialyears.
5.Incaseofcapitalrationing,acompanyiscompelledtoinvestin
projectshavingshortestpaybackperiod.Insuchcases,thismethod
canbeused.
6.Thismethodismostsuitablewhentheprojectisveryuncertain.
7.Itdoesnotinvolveassumptionsaboutfutureinterestrates.
8.Ithelpstominimisethepossibilityoflossesthroughobsolescence.
9.Itisusefultofirmswhenexperiencingliquidityconstraints.

22. Disadvantages of traditional payback approach
1.Itignoresthetimevalueofmoneyandcostofcapital.
2.Itcompletelyignorescashinflowsafterthepaybackperiod.
3.Itfailstoconsiderthewholelifetimeofaproject.
4.Itdoesnotmeasuretherateofreturn.
5.Itdoesnotmeasureprofitabilityofprojects.Itinsistsonlyon
recoveryofthecostoftheproject.
6.Itdoesnotconsiderthesalvagevalueofaninvestment.
7.Thismethodmakesnoattempttomeasureapercentagereturn
onthecapitalinvestedandisoftenusedinconjunctionwith
othermethods.

23. Modern Pay Back Period Methods
Followingaresomeofthemostpopularimprovementsto
traditionalpaybackperiodconcept.
a)Postpaybackprofitabilitymethod
b)Postpaybackperiodmethod
c)Paybackreciprocals

24. a)Post pay back profitability method
•Underthismethod,entirecashinflowsgeneratedfromaproject
duringitsworkinglifearetakenintoaccount.Itiscalculatedas
under:
Postpaybackprofitability=Totalcashinflowsinlife-initialcost
Ifcostofvariousprojectsdifferssubstantially,postpayback
profitabilityindexmaybecalculatedtorelativeprofitabilityofthe
projectsasbelow:

25. b)Postbackprofitability
Postbackprofitability=Totalcashflowsinlife-initialcost
ProjectA:
(8X20000)-100000=60000
ProjectB:
[(3x3000)+(5x1000)]-100000=40000

26. b)Post pay back period method
•Thismethodtakesintoaccountthe
periodbeyondaproject’spayback
period.
•Thismethodisalsoknownas‘surplus
lifeoverpaybackmethod.
•Underthismethod,theprojectwith
longerpostpaybackperiodispreferred.

27. c) Payback reciprocals
•Thepaybackreciprocalisacrudeestimateoftherateofreturnfora
projectorinvestment.
•Thepaybackreciprocaliscomputedbydividingthedigit"1"bya
project'spaybackperiodexpressedinyears.
•Itisanapproximationoftheannualrateofreturnonaninvestment.
•Forexample,ifaproject'spaybackperiodis4years,thepayback
reciprocalis1dividedby4=0.25=25%.
Theformulaforcomputingpaybackreciprocalisasfollows.

28. c)Accounting rate of return Method.
•Thismethodtakesintoaccounttheearningsfrom
theinvestmentoveritswholelife.
•Itisbasedonaccountingprofitandnotoncash
flows.Thatis,annualearningsafterdepreciation
andtaxesareusedtocalculateARR.
•Thismethodisalsoknownasunadjustedrateof
returnmethod.
•Inthismethod,mostoftenthefollowingtwoformulaeareapplied:
1. AverageRateofReturnonaverageinvestmentmethod
2. AverageRateofReturnonNetinvestmentmethod.

29. AverageRateofReturnonaverageinvestmentmethod
•Underthismethodaverageannualprofit(aftertax)is
expressedaspercentageofaverageinvestment.
•ARRisfoundoutbydividingaverageincomebythe
averageinvestment.Theformulaeis:

30. AverageRateofReturnonaverageinvestmentmethod
•Ifadditionalworkingcapitalisneeded
forsmoothrunningoftheproject,it
shouldbeaddedtotheaboveaverage
investmentforfindingouttheeffective
averageinvestment.

31. AverageRateofReturnonNetinvestmentmethod.
The following formulae is also used fro finding out ARR.
OfthevariousARRondifferentalternativeproposals,theonehaving
highestrateofreturnistakentobethebestinvestmentproposal.
Ofthemutuallyexclusiveprojects,theprojectwithhighestARRis
selected.
IfonlyoneprojectisunderconsiderationandARRismorethan
targetedrateorreturn,theprojectisaccepted.Otherwise,rejected.

32. Iftwoormoreprojectsarecompared:
•ProjecthavinghighestARRistakentobe
thebestinvestmentproposal.
Ifonlyoneprojectisunderconsideration:
•IfARRismorethantargetedrateorreturn,
theprojectisaccepted.Otherwise,rejected.
Evaluation of Projects by using ARR

33. Advantages of ARR
1.Simplicity:Itissimpletounderstandandeasytoapply
2.EntireLifecovered:Ittakesintoconsiderationearningsoverthe
entirelifeoftheproject
3.AccountingProfitability:Itconsidersprofitabilityoftheinvestment
4.Comparisonofprojects:Projectsofdifferentcharactercanbe
comparedquicklybyuseofranking.
5.Accountingdata:Rateofreturncanbereadilycalculatedwiththe
helpofaccountingdata.Itisnotconcernedwithcashflowsbut
ratherbaseduponprofitswhicharereportedinannualaccounts
andsenttoshareholders

34. Disadvantages of ARR
1.Time value ignored: It does not take into account time value of money.
2.Nodifferentiationininvestment:Itdoesnotdifferentiatethesizeofthe
investmentrequiredforeachproject.Competinginvestmentproposals
withthesameARRmayrequiredifferentamountofinvestment
3.Cash flow ignored: It is based upon accounting profit instead of cash
flow.
4.It ignores possibility of profit re-investment:It ignores the fact that
profit can be reinvested.
5.Itconsideraveragerateofreturnonly:Itconsidertheaveragerateof
returnbutnotthedeviationsinreturnoverthelifeoftheproject.

35. Discounted Cashflow techniques (Time
adjusted cash flow techniques)
•Payback and ARR does not consider the time
value of money
•But in fact, the value of money received in future
is not equivalent to the value of money invested
today.
•This limitation can be overcome by using
discounted cashflow techniques which consider
time value of money.

36. Features of Discounted cash flow technique:
1.Itconsidertimevalueofmoney
2.Cashflowsareusedinsteadofaccounting
profit
3.Interestfactorisconsidered
4.Entirecashflowsofaprojectthroughoutthe
lifeareconsidered.

37. a)DiscountedPayBackMethod
b)NetPresentValueMethod
c)BenefitCostRatio/Profitability
IndexMethod
d)InternalRateofReturn
e)NetTerminalValueMethod
2.ModernMethodsorDiscountedCashFlowTechniques.

38. a)Discounted Pay Back Method
•Inthismodifiedmethod,cashflowsarefirstconvertedinto
theirpresentvaluesbyapplyingsuitablediscountingfactors
andthenaddedtoascertaintheperiodoftimerequiredto
recovertheinitialoutlayontheproject.
Qn
•InvestmentRs80000,discountrate10%,Cashflowsare
17600,20400,23200,26000&31,600
•Calculatediscountedpaybackperiod

39. b)Net Present Value Method
•Underthismethod,allfuturecashinflowsandcash
outflowsarediscountedtopresentvaluesbyusing
firm’scostofcapitalorapredeterminedrate.
•Thenthepresentvaluesofcashoutflowsisdeducted
fromthesumofpresentvalueofcashinflows.The
balanceamountistheNetPresentValue(NPV).
•NPV=
PresentvalueofCashInflows–Present
valueofcashoutflows

40. b)Net Present Value Method
•NPVmaybeeitherpositiveorzeroornegative.
•PositiveNPVindicatesthattheactualrateofreturnismore
thanthediscountrate(costofcapitalorpredeterminedrate
ordesiredrate).WhenNPVispositiveorzero,theproposal
shouldbeaccepted.
•NegativeNPVindicatesthattheactualrateofreturnisless
thanthediscountrate(costofcapitalorpredeterminedrate).
WhenNPVisnegative,theproposalshouldberejected.
•Iftwoormoreprojectsarecompared,projecthavingthe
maximumpositiveNPVisselected.

41. Steps to be followed under NPV method.
1.Determinationofanappropriaterateofreturn/discountrate:
Itshouldbetheminimumrequiredrateofreturncalledcutoff
rateordiscountrate.Thediscountrateshouldbeeitherthe
actualrateofinterestonlongtermloansoritshouldbethe
opportunitycostofcapitaloftheinvestor.
2.ComputationofPresentValueofcashinflows(profitbefore
depreciationandaftertax)withthehelpofdiscountrate
3.ComputationofPresentValueoftotalinvestmentoutlay(cash
outflows)withthehelpofdiscountrate.Ifthetotalinvestment
istobemadeintheinitialyear,thepresentvalueshallbethe
sameasthecostofinvestment.

42. Steps to be followed under NPV method.
4.Calculatethenetpresentvalueofeachproject
bysubtractingthepresentvalueofcashinflows
fromthevalueofcashoutflowsforeachproject.
5.Decision
•IftheNPViszeroorpositive,theproposalmaybe
accepted,otherwisetheproposalshouldbe
rejected.
•Toselectmutuallyexclusiveprojects,theproject
havingthemaximumpositivenetpresentvalue
shouldberejected.

43. Treatmentofworkingcapitalrequirementoftheproject
•Ifadditionalworkingcapitalisrequiredfortheprojectinthe
beginning,itshouldbeaddedtotheinitialinvestment.Ifit
isrequiredsubsequently(eg:3
rd
year)aftercommencement
oftheproject,itspresentvalueshouldbeworkedout.Then
thepresentvalueisaddedtotheinitialinvestment.
•Thistreatmentisdonebecauseweassumethatfunds
initiallytiedupinworkingcapital(additionalworking
capital)wouldbereleasedonlyinthelastyearwhenthe
investmentisterminated.

44. Advantages of the NPV Method
1.It recognises the time value of money.
2.Itissuitabletobeappliedinasituationwithuniformoruneven
cashflowsorcashflowsatdifferentperiodsoftime.
3.Ittakesintoaccounttheearningsovertheentirelifeoftheproject
4.Ittakesintoconsiderationtheobjectiveofmaximumprofitability
5.NPVofdifferentprojectscanbeadded.Eg:ProjectA’sNPVisRs20
lakh,ProjectB’sNPVisisRs12lakh.Ifbothprojectsareselected,
NPVwillbeequaltoRs32lakh.

45. Disadvantages of NPV Method
1.Difficulttooperate:Ascomparedtothetraditionalmethods,the
NPVmethodismoredifficulttounderstandandoperate.
2.Itmaynotgivegoodresultswhilecomparingprojectswith
unequallives.Thisisbecausetheprojecthavinghighernetpresent
valuebutrealisedinalongerlifespanmaynotbeasdesirableasa
projecthavingsomethinglesserNPVachievedinamuchshorter
spanoflifeoftheasset.
3.Itmaynotgivegoodresultswhilecomparingprojectswithunequal
investmentoffunds.
4.Itisnoteasytodetermineanappropriatediscountrate.

46. Benefit Cost Ratio(Profitability Index Method)
•Twoprojectshavingdifferentinvestmentoutlaycannotbecomparedby
NPVMethodbecauseitindicatestheNPVinabsoluteterms.
•Forexample,ProjectXandProjectYarehavinginitialinvestmentofRs
50000andRs100,000respectively.TheirNPVisasunder:
•AccordingtotheabsolutefigureofNPV,Yappearsbetter.InfactX,an
investmentofRs50000providesanNPVofRs10000whereasY,an
investmentof100000(twiceofX)providesanNPVofRs12000only.
•Insuchasituation,profitabilityindexmethodshouldbeappliedasitisa
relativemeasureofacceptabilityofprojects
Project X Project Y
Present Valueof investment (Cost)50000 100000
Present Value of cash inflows(benefits)60000 112000
10000 12000

47. Benefit Cost Ratio(Profitability Index Method)..contd
•Itistheratioofpresentvalueofcashinflowstothepresentvalueof
cashoutflows.
•Itistheratioofpresentvalueofbenefitstocost.
•Itisparticularlyusefultocomparetheprojectshavingdifferent
investmentoutlays.
•Itiscomputedasfollows:
•ItcanbealsoexpressedasNetPresentValueIndexasbelow.

48. Decision Rule
•If Profitability Index is more than 1, it can be accepted.
•If Profitability Index is less than 1, it should be rejected
•In the case of mutually exclusive projects, the project with higher
Profitability Index is to be selected.
•Higher the profitability Index, better is the project.

49. Internal Rate of Return (IRR) Method
•InternalRateofReturnistherateofreturn
(discountrate)atwhichthepresentvalueof
cashinflowsisequaltothepresentvalueof
cashoutflows.
•Inotherwords,itisthediscountrateatwhich
NPViszero.
•ItisfirstintroducedbyJoelDean.

50. Internal Rate of Return (IRR) Method
•Inordertofindouttherateofreturnofa
project,estimatednetcashinflowsofeach
yeararediscountedatvariousratestillarate
isobtainedatwhichthepresentvalueof
cashinflowisequaltotheinitialinvestment.
•Itisalsocalledtimeadjustedrateofreturn.

51. CalculationofIRR
a)Whencashflowsareequal:
Itcanbeexplainedwiththehelpofanexample.
ProjectcostRs6000,expectedcashinflowofRs2000,life5years
Step1:Firstofallaroughapproximationmaybemadewithreferenceto
PresentValueAnnuityFactor.Thisiscalculatedbythefollowingformula.
Here,PVAFis6000÷2000=3

52. •Step2:SearchforthevalueofPVAFinthePVAFTable(TableII)forthe
givennumberofyears.IfPVAFisfoundinthetableII,the
correspondingratewillbetheIRR.
Ifnotfound,searchforthevaluenearesttoPVofAnnuityFactorin
thegivenyearrowofPVAFTable(TableII).Therategiveninthe
columnofthenearestPVFactorwillbetheapproximateIRR.
Inthegivenexample,thePVAFfor5yearsnearestto3is2.991and
3.127.Correspondingdiscountratesare20%and18%.Hence,theIRR
fallsbetween18%and20%.Since,thevalue2.991isnearerto3,IRR
willbeapproximate20%.

53. Step3:InordertomakeapreciseestimationoftheIRR,findoutthe
presentvaluesoftheprojectforboththeserates.Itiscalculatedas
follows:
PVat18%=2000X3.127=6254
PositiveNPV=6254-6000=254
PVat20%=2000X2.991=5982
NegativeNPV=5982-6000=-18

54. •Step4:FindouttheexactIRRbyinterpolation.Theinterpolation
shouldbemadebetweentwoclosestdiscountrateshavingapositive
NPVandanegativeNPV.Theinterpolationformulaisasfollows.
=18+1.88=19.88%

55. b) When cash flows are unequal
Whencashflowsareunequal,IRRiscalculatedbyTrialandError
Method.Inthismethod,presentvaluesofcashinflowsarecomputed
atdifferentrates.Inthelast,therateatwhichthetotalPVofcash
inflowsisequaltothecostoftheprojectistreatedastheIRR.
Step1:Calculateaveragecashinflowandestablishfirsttrialrate:Itis
difficulttodecidetherateatwhichthetrialshouldbecommenced.
However,thefirsttrialratecanbecalculatedonthebasisofaverage
annualcashinflow.Togetthefirsttrialrate,thefollowingformulacan
beused.
PresentValueFactor=InitialInvestment÷Averageannualcashinflows

56. SearchforthevaluenearesttoPVofAnnuityFactorinthegivenyearrow
ofPresentValueAnnuityFactorTable(TableII).Therategiveninthe
columnofthenearestPVFactorwillbethefirsttrialrate.Thereafter,the
presentvalueofcashinflowsofalltheyearswillbecomputedatthisrate
usingPVFTableforalumpsum(TableI)
Investment 8000
First year 2000
Second year 3000
Third year 7000
Avg:12000/3=4000
PVAF=8000/4000=2 Search 2 in table 2 against 3 year row. Trial rate 12%

57. StepII:Thetotalofthepresentvalueofcashinflowsforallyears
calculatedbyfirsttrialratewillbecomparedwiththecostofthe
project.
IftheNPVatthefirstratecomespositive,ahigherrateshouldbetried.
IftheNPVcomesnegatives,alowerrateshouldbetried.Thisexercise
isdonetilltheNPVcomestozero.Sincethisistedious,interpolation
shouldbeappliedasshownbelow:

58. Step 3. Computation of actual IRR: Application of interpolation.

59. Advantages of IRR
1.Thismethodconsidersallthecashflowsovertheentirelifeofthe
project.
2.Ittakesintoaccounttimevalueofmoney
3.IRRgivestruepictureoftheprofitabilityoftheproject
4.Itisconsistentwiththeshareholderwealthmaximisationobjective.
Whenever,IRRisgreaterthanopportunitycostofcapital,the
shareholders’wealthwillbeenhances.

60. Disadvantages
1.TheIRRmethodisdifficulttounderstandanduseinpractice
becauseitinvolvestediousandcomplicatedcalculation.
2.Thismethoddoesnotconsiderimportantfactorslikeproject
duration,futurecosts,orthesizeoftheproject.
3.ValueadditivityprincipledoesnotholdgoodwhenIRRmethodis
used.Eg:ProjectA’sIRRis20%,ProjectB’sIRRis12%.Ifboth
projectsareselected,IRRwillnotbeequalto20+12.
4.Itdoesnottakeintoaccountliquidityissuesoftheorganisation.
5.Itdoesnotgivethedetailsofabsolutereturnbutgivespercentage
return.

61. Net Terminal Value Method
Thismethodisbasedontheassumptionthateachannualcashinflow
(profitaftertaxbutbeforedepreciation)isreceivedattheendofthe
yearandisreinvestedinanotherassetatacertainrateofreturnfrom
themomentitisreceivedtilltheterminationoftheproject.
Then,thetotalcompoundedsumisdiscountedathediscountfactor
ofthelastyear(costofcapital)andpresentvalueisfoundout.This
presentvalueiscomparedwithcostoftheproject.Theexcessofthe
presentvalueoverthecostoftheprojectistheNetTerminalValue.
Hence,inNTVmethodbothcompoundinganddiscountingtechnique
areused

62. Future Value of 1 Table

63. Decision Criterion
WhenNTVispositiveorzero,theproposalshouldbeacceptedinthe
caseofindependentprojects.
WhenNTVisnegative,theproposalshouldberejectedinthecaseof
independentprojects..
Toselectbetweenmutuallyexclusiveprojects(whereonlyoneprojectis
tobeselected),projectsshouldberankedinorderofNTV.ie.Thefirst
preferenceshouldbegiventotheprojecthavingthemaximum
positiveNTV

64. Risk Analysis in Capital Budgeting
•Riskinaninvestmentreferstothevariabilitythatislikely
toariseinfuturebetweentheestimatedreturnsandthe
actualreturnsfromtheinvestmentproposal
•Itisveryessentialtomakeriskanalysisofinvestment
proposalsbeforethemanagementgoesaheadwiththe
project.
•Acceptabilityofprojectsmainlydependsupontheir
returnsandrisk.
•Generally,returnand riskarepositively
correlated(movinginsamedirection).

65. •Afirmshouldconsiderriskwhileestimating
therequiredrateofreturnonaproject.
Beforeinvestingfundsinaproject,itis
necessarytoconsidertheriskandreturn
associatedwithallthealternative
investmentoptions.
•Theprocessofcomparingtheriskand
returnstoselectthemostprofitable
investmentproposalisknownasrisk-return
analysis.

66. Methods of Risk analysis
1.Risk Adjusted Discount Rate
2.Certainty equivalent method

67. 1.Risk Adjusted Discount Rate
Generally, if there is more risk in an investment
proposal, a higher rate of return will be expected.
UnderthisRiskAdjustedDiscountRateTechnique,
someadjustmentwillbemadeindiscountrate.
Thisisdoneaccordingtothedegreeofrisk
associatedwiththeproject.Ifriskishighthe
discountrateisraised(addingriskpremiumto
discountrate).

68. 1.Risk Adjusted Discount Rate
Eg:IftheManagementdesiresarateof
returnof12%.Iftheprojectismorerisky,a
riskpremium,say,3%maybeaddedtothe
12%toprovideforrisk.Thusriskadjusted
discountrateis15%.Thismeansthatcash
flowswillbediscountedby15%.

69. •Eg:Iftherearetwoprojectsandoneproject
ishavingmoreriskthantheotherone,
higherriskpremiummayaddedtoriskfree
rateinthecaseofriskierprojectandlower
riskpremiummaybeaddedtoriskfreerate
intheothercase
•Riskadjusteddiscountrateisequaltorisk
freerateofreturn+riskpremiumfor
investmentinariskyproject.

70. •DecisionRule:Theriskadjustedrate
ofdiscountcanbeusedbothinNPV
andIRR.IfNPVisused,theproject
withhigherNPVwillbeselected.
•InthecaseofIRR,theprojectwith
theIRRgreaterthantherisk
adjustedrateofreturnareselected.

71. 2. Certainty Equivalent method.
•Underthismethod,theriskinvolvedintheprojectis
takenintoconsiderationbyadjustingtheexpectedcash
flows.
•cashflowsarereducedtoacertainlevelbyusinga
CertaintyEquivalentcoefficient’.Itistheratioofriskfree
cashflowtoriskycashflow.Itisascertainedasunder:
Riskfreecashflow/Riskycashflow.
Itwillbelessthan1

72. Steps
1.CalculateCertaintyEquivalentcoefficient’.Itis
theratioofriskfreecashflowtoriskycashflow.
Itisascertainedasunder:
Riskfreecashflow/Riskycashflow.
2.CalculateRiskadjustedcashflowforeachyear
bymultiplyingcashflowwithCertaintyEquivalent
Coefficient.

73. Steps
3.Findthepresentvalueofriskadjustedcash
flowforeachyear
4.Obtainthetotalofpresentvalueofallyears
5.FindtheNPVoftheproject
6.Takingthedecision.(Projectwithhigher
positiveNPVwillbeselected.