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CAPITALCAPITALBUDGETINGBUDGETING
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PROJECTPROJECTAPPRAISALAPPRAISAL
TECHNIQUESTECHNIQUES
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RATIONALE BEHINDRATIONALE BEHIND
CAPITAL EXPENDITURECAPITAL EXPENDITUREBenefits expected over a longer period.Benefits expected over a longer period.Far reaching effects on the success or failureFar reaching effects on the success or failure
Assets once acquired can not be disposed off except at a Assets once acquired can not be disposed off except at asubstantial loss.substantial loss.
If capital assets are purchased on long term credit basis, aIf capital assets are purchased on long term credit basis, a
continuing liability is incurred over a longer period.continuing liability is incurred over a longer period.
If earnings are not increased commensurate with theIf earnings are not increased commensurate with thepurchase of the additional capital assets, the ability of thepurchase of the additional capital assets, the ability of theenterprise to discharge its financial obligations may beenterprise to discharge its financial obligations may beaffected adversely.affected adversely.
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Expansion of capital facilities by means of theExpansion of capital facilities by means of theissue of shares may dilute holding in the companyissue of shares may dilute holding in the companyand if not carefully planned and controlled, it canand if not carefully planned and controlled, it canresult in the loss of control by the management.result in the loss of control by the management.
It influences longIt influences long- -term prospects and futureterm prospects and futureearning capacity of the firm.earning capacity of the firm.
In this context the forecasting and budgeting of In this context the forecasting and budgeting of capital expenditure becomes a vital part of policycapital expenditure becomes a vital part of policymaking and management function.making and management function.
RATIONALE BEHINDRATIONALE BEHIND
CAPITAL EXPENDITURECAPITAL EXPENDITURE
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CONCEPT OF CAPITALCONCEPT OF CAPITAL
BUDGETINGBUDGETINGLong term planning of expenditure whose returns stretchLong term planning of expenditure whose returns stretchthemselves over a future periodthemselves over a future period
A process of deciding whether or not to commit A process of deciding whether or not to commitresources to a project, whose benefits would be spreadresources to a project, whose benefits would be spreadover several time periods.over several time periods.
It considers proposed capital outlay and its financing.It considers proposed capital outlay and its financing.
The exercise involved in capital budgeting is to coThe exercise involved in capital budgeting is to co- -relaterelatethe benefits to costs in some reasonable manner whichthe benefits to costs in some reasonable manner whichwould be consistent with the profitwould be consistent with the profit maximisingmaximising objectivesobjectivesof the business.of the business.
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It is a managerial decision, since it involves moreIt is a managerial decision, since it involves moreextended estimation and prediction of things to comeextended estimation and prediction of things to comerequiring high order of intellectual ability.requiring high order of intellectual ability.The economic justification for a capital expenditureThe economic justification for a capital expenditure
programmeprogramme requires a long term estimates of profits,requires a long term estimates of profits,which in turn involves projection of sales and cost of which in turn involves projection of sales and cost of operation over a period of yearsoperation over a period of yearsIt includes searching for new and more profitableIt includes searching for new and more profitableinvestment proposals, investigation, engineering andinvestment proposals, investigation, engineering and
marketing considerations to predict the consequences of marketing considerations to predict the consequences of accepting the investment and making economic analysisaccepting the investment and making economic analysisto determine the profit potential of each investmentto determine the profit potential of each investmentproposal.proposal.
A Screening process. A Screening process.
CONCEPT OF CAPITALCONCEPT OF CAPITAL
BUDGETINGBUDGETING
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ASPECTS OF CAPITALASPECTS OF CAPITAL
BUDGETINGBUDGETINGIt ranks various proposals by measuring their profitabilityIt ranks various proposals by measuring their profitability
( before considering cost of capital ) in descending order.( before considering cost of capital ) in descending order.
The company has to decide minimum desired rate of The company has to decide minimum desired rate of
return or cutreturn or cut- -off rate ( average cost of capital + return for off rate ( average cost of capital + return for
risk ) to decide about the acceptance or rejection.risk ) to decide about the acceptance or rejection.
Volume of investment to be made.Volume of investment to be made.
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TYPE OF INVESTMENTTYPE OF INVESTMENT
PROPOSALSPROPOSALSCost reduction proposalsCost reduction proposals by replacement of machinery and equipmentby replacement of machinery and equipment
plant replant re- -arrangement programmesarrangement programmes mechanisation of processmechanisation of process Provision of facilities to manufactureP rovision of facilities to manufacture
components currently purchasedcomponents currently purchased
Income maintaining proposalsIncome maintaining proposals Replacement of worn out equipmentReplacement of worn out equipment
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Income Increasing proposalsIncome Increasing proposals Additions and extensions to plant and machinery for having Additions and extensions to plant and machinery for having
additional volume of existing productionadditional volume of existing production
Installation of new plant and machinery for taking up a new productInstallation of new plant and machinery for taking up a new productor product linesor product lines
Research and Development proposalResearch and Development proposal
Summary of ProposalsSummary of Proposals Replacement proposalReplacement proposal
Expansion proposalExpansion proposal
New product Line or Diversification proposalNew product Line or Diversification proposal
Strategic Investment proposalStrategic Investment proposal
Contractual Investment proposalContractual Investment proposal
TYPE OF INVESTMENTTYPE OF INVESTMENT
PROPOSALSPROPOSALS
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FA T R AFFE TINFA T R AFFE TINCAPITAL INVESTMENTCAPITAL INVESTMENT
DECISIONSDECISIONS1 .1 . Amount of investment Amount of investment
2.2. Operating cash inflowsOperating cash inflows
3.3. Choice of horizonsChoice of horizons
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1. AMOUNT OF1. AMOUNT OF
INVESTMENTSINVESTMENTSCovers amount of funds committed to projectCovers amount of funds committed to project - - Cost of purchase of land, building, plant etc.Cost of purchase of land, building, plant etc.
Increase in level of working capitalIncrease in level of working capital
Salvages value from old assets (in case of replacement) or writeSalvages value from old assets (in case of replacement) or writeoff of assets not fully depreciated.off of assets not fully depreciated.
Cost of installation and other incidental costsCost of installation and other incidental costs
Opportunity cost of using existing resourcesOpportunity cost of using existing resources
Tax impact on sale of old assetsTax impact on sale of old assets
Residue / Terminal / Salvage value of capital expenditureResidue / Terminal / Salvage value of capital expenditure RealisableRealisable value of working capital at the end of economic lifevalue of working capital at the end of economic life
Deferred InvestmentDeferred Investment
Capital subsidyCapital subsidy
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2 . OPERATING CASH FLOWS2 . OPERATING CASH FLOWS
Cash ReceiptsCash Receipts
Cash DisbursementsCash Disbursements
Timing of cash receipts and disbursementsTiming of cash receipts and disbursements
Range of estimatesRange of estimates - - highest and lowesthighest and lowest
estimates considering the uncertaintiesestimates considering the uncertainties
After tax and without tax proceeds After tax and without tax proceeds
Absolute and relative cash Flows Absolute and relative cash Flows
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3. CHOICE OF HORIZONS3. CHOICE OF HORIZONSSelection of the time period is important for the decisionSelection of the time period is important for the decisionmakers for evaluating benefits and costs. The mostmakers for evaluating benefits and costs. The mostpractical way of resolving the horizon problems is to let thepractical way of resolving the horizon problems is to let thediscount rate take care of it. In fact, many companiesdiscount rate take care of it. In fact, many companiesimpose a shorter limit of benefits and costs, considered for impose a shorter limit of benefits and costs, considered for many type of projects.many type of projects.
Life of the project may be divided intoLife of the project may be divided into - - Physical lifeP hysical life
Economical lifeEconomical life
The relevant period in Investment Analysis is economic lifeThe relevant period in Investment Analysis is economic lifeas investment are made for the economic benefits.as investment are made for the economic benefits.
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METHODS OF RANKINGMETHODS OF RANKINGThere are several techniques for evaluation and rankingThere are several techniques for evaluation and rankingof the capital investment proposals. In case of all theseof the capital investment proposals. In case of all thesemethods the main emphasis is the return which will bemethods the main emphasis is the return which will be
derived on the capital investment in the project.derived on the capital investment in the project.Fundamental Principles :Fundamental Principles : BIGGER THE BETTER PRINCIPLEBIGGER THE BETTER PRINCIPLE , which means that, other , which means that, other
things being equal, bigger benefits are preferable to small ones.things being equal, bigger benefits are preferable to small ones.
BIRD IN HAND PRINCIPLEBIRD IN HAND PRINCIPLE , which means that other things, which means that other thingsbeing equal, early benefits are preferable to latter benefits.being equal, early benefits are preferable to latter benefits.
Mean has to be found for considering both of them in a singleMean has to be found for considering both of them in a singleyardstick.yardstick.
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P ayback period refers to the period in which the projectP ayback period refers to the period in which the projectwill generate the necessary cash to recoup the initialwill generate the necessary cash to recoup the initialinvestmentinvestment
Initial InvestmentInitial InvestmentPayback Period =Payback Period = Annual Cash inflowsAnnual Cash inflows
Annual cash inflows = Estimated cash inflows resulting Annual cash inflows = Estimated cash inflows resultingfrom the proposed investment ( i.e. net income on accountfrom the proposed investment ( i.e. net income on accountof investment before depreciation but after taxation )of investment before depreciation but after taxation )
In case of uneven cash inflows , by calculating cumulativeIn case of uneven cash inflows , by calculating cumulativecash in Flows, the paycash in Flows, the pay- -back period can be calculated.back period can be calculated.
1. PAYBACK PERIOD1. PAYBACK PERIOD
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ccept or reject criterion :ccept or reject criterion :
A project whose actual pay A project whose actual pay- -back period is more than what has beenback period is more than what has been
predetermined by the management will be straight way rejected. Thepredetermined by the management will be straight way rejected. The
fixation of maximum acceptable payfixation of maximum acceptable pay- -back period is generally done by takingback period is generally done by takinginto account the reciprocal of the cost of capital ( i.e. maximum acceptableinto account the reciprocal of the cost of capital ( i.e. maximum acceptable
paypay--back period = 100 divided by desired rate of return )back period = 100 divided by desired rate of return )
The payback period can also be used in case of mutually exclusiveThe payback period can also be used in case of mutually exclusive
projects. The projects are then arranged in ascending order according toprojects. The projects are then arranged in ascending order according to
the length of their pay back periods.the length of their pay back periods.
PAYBACK PERIODPAYBACK PERIOD
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2 . ACCOUNTING OR AVERAGE2 . ACCOUNTING OR AVERAGERATE OF RETURN ( ARR )RATE OF RETURN ( ARR )
According to this method, the capital investment According to this method, the capital investmentproposals are judged on the basis of their relativeproposals are judged on the basis of their relativeprofitability. For this purpose, capital employed andprofitability. For this purpose, capital employed andexpected income are determined according to commonlyexpected income are determined according to commonly
accepted accounting principles and practices over theaccepted accounting principles and practices over theentire economic life of the project and then the averageentire economic life of the project and then the averageyield is calculated. Such a rate is termed as Accountingyield is calculated. Such a rate is termed as Accountingrate of return. It may be calculated, according to either of rate of return. It may be calculated, according to either of the following formulathe following formula
i. Average annual net earnings
riginal Investmentx 100
ii. Annual average net earnings
Average Investmentx 100
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A UNTIN RA UNTIN RAVERAGE RATE OFAVERAGE RATE OF
RETURN ( ARR )RETURN ( ARR )The term Average annual net earnings is the average of theThe term Average annual net earnings is the average of theearnings (after depreciation and tax) over the whole of the economicearnings (after depreciation and tax) over the whole of the economic
life. One may calculate " Average annual net earnings " before tax.life. One may calculate " Average annual net earnings " before tax.
Such rate is known as preSuch rate is known as pre - - tax accounting rate of return.tax accounting rate of return.The amount of Average Investment is calculatedThe amount of Average Investment is calculatedas followsas follows - -
! LNMOQP
Original Investment - Scrap Value+ Additional Net Working Capital + Scrap Value
2
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Accept / Reject CriterionAccept / Reject Criterion - -
Any project expected to give a return below minimum Any project expected to give a return below minimum
desired rate of return will be straight way rejected. Indesired rate of return will be straight way rejected. In
case of several project, where a choice has to be made,case of several project, where a choice has to be made,
the different projects may be ranked in the descendingthe different projects may be ranked in the descending
order on the basis of their rate of return.order on the basis of their rate of return.
A UNTIN RA UNTIN RAVERAGE RATE OFAVERAGE RATE OF
RETURN ( ARR )RETURN ( ARR )
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3. DISCOUNTED CASH FLOWS3. DISCOUNTED CASH FLOWS(DCF) METHOD(DCF) METHOD
An investment is essential outlay of funds in anticipation of An investment is essential outlay of funds in anticipation of
future returns, the presence of time as a factor infuture returns, the presence of time as a factor in
investment is fundamental rather than incidental to theinvestment is fundamental rather than incidental to the
purpose of evaluation of investments. Time is alwayspurpose of evaluation of investments. Time is always
crucial for the investor, so that a sum received today iscrucial for the investor, so that a sum received today is
worth more than the same sum to be received tomorrow.worth more than the same sum to be received tomorrow.
Thus in evaluating investment projects, it is important toThus in evaluating investment projects, it is important toconsider the timings of return on investments.consider the timings of return on investments.
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Assumptions of Discounting Table :Assumptions of Discounting Table :1 .1 . Opportunity for investment is available at any time for Opportunity for investment is available at any time for
any amount.any amount.
2.2. Interest will accrue at the same rate.Interest will accrue at the same rate.3.3. Interest will be received at the end of the year.Interest will be received at the end of the year.4.4. Interest will be reinvested at the same opportunity rateInterest will be reinvested at the same opportunity rate5.5. P rice level remains the sameP rice level remains the same
DCF methods for evaluating capital expenditureDCF methods for evaluating capital expenditureproposals are of two typesproposals are of two types - -ii.. Net P resent ValueNet P resent Value Method ( NP V )Method ( NP V )
ii.ii. Internal Rate of Return Method ( I RR )Internal Rate of Return Method ( I RR )
DCF METHODDCF METHOD
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A.A. Net Present Value Method :Net Present Value Method :The net present value is the difference between presentThe net present value is the difference between presentvalue of benefits and present value of costs. If the netvalue of benefits and present value of costs. If the netpresent value is positive the conclusion ispresent value is positive the conclusion is favourablefavourable toto
the decision to go ahead with the project but if it isthe decision to go ahead with the project but if it isnegative, the project is rejected. The analyst who uses thisnegative, the project is rejected. The analyst who uses thismethod feels that it gives desired indication with the leastmethod feels that it gives desired indication with the leastconfusion.confusion.Accept/Reject CriterionAccept/Reject Criterion ::
WhereWhere NP VNP V >> Zero accept the proposalZero accept the proposalNP VNP V == Zero accept the proposalZero accept the proposalNP VNP V
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B. Profitability Index / Desirability Factor :B. Profitability Index / Desirability Factor :If the present value method is used, the present value of If the present value method is used, the present value of the earnings of one project can not be compared directlythe earnings of one project can not be compared directlywith the present value of earnings of another, unless thewith the present value of earnings of another, unless theinvestments are of the same size. In order to compareinvestments are of the same size. In order to compareproposals of different size, the Flows to investment mustproposals of different size, the Flows to investment mustbe related. This is done by dividing the present value of be related. This is done by dividing the present value of earnings by the amount of investment, to give a ratio i.e.earnings by the amount of investment, to give a ratio i.e.
called the profitability index / ratio or desirability factor.called the profitability index / ratio or desirability factor.Pr ofitablity Index =
Discounted Cash inflowDiscounted Cash outflow
OR
Profitability Ratio =Discounted Cash inflow
Discounted Cash outflowx 100
DCF METHODDCF METHOD ProfitabilityProfitability
IndexIndex
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H igher the index number, the better theH igher the index number, the better the
project. This is called benefit cost ratio.project. This is called benefit cost ratio.
Accept / Reject CriterionAccept / Reject Criterion - -
WhereWhere P IP I >> 1 accept the proposal1 accept the proposal
P IP I == 1 accept the proposal1 accept the proposalP IP I
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C.C. INTERNAL RATE OF RETURN ( IRR ) :INTERNAL RATE OF RETURN ( IRR ) :In the net present value method, the required earningsIn the net present value method, the required earningsrate is selected in advance. There is an alternative methodrate is selected in advance. There is an alternative methodwhich finds the earnings rate at which the present value of which finds the earnings rate at which the present value of the earnings equals the amount of the investment. Thisthe earnings equals the amount of the investment. Thisrate is called the timerate is called the time - - adjusted rate of return, D CF rate of adjusted rate of return, D CF rate of return, internal rate of return, yield rate, marginal efficiencyreturn, internal rate of return, yield rate, marginal efficiencyof capital etc. I RR is the rate which brings the sum of theof capital etc. I RR is the rate which brings the sum of the
future cash Flows to the same level as the originalfuture cash Flows to the same level as the originalinvestment. Thus I RR is the rate of return at which theinvestment. Thus I RR is the rate of return at which thesum of discounted cash inflows equals the sum of sum of discounted cash inflows equals the sum of discounted cash outflows.discounted cash outflows.
DCF METHODDCF METHOD - - IRRIRR
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Accept / Reject Criterion :Accept / Reject Criterion :WhereWhere
IRR IRR >> CutCut --off off --rate accept the proposalrate accept the proposal
IRR IRR == CutCut --off off-- rate accept the proposalrate accept the proposalIRR IRR
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1. 1. When cash Flows are uniform :When cash Flows are uniform :
In the case of those projects which generate uniform cashIn the case of those projects which generate uniform cash
inflows, the I RR can be calculated by locating the factor ininflows, the I RR can be calculated by locating the factor in
Annuity Table II. Annuity Table II.
Steps for Calculation of IRR :Steps for Calculation of IRR :
a.a. Divide the Investment by the annual cash in Flows. The result isDivide the Investment by the annual cash in Flows. The result is
called the Factor or P aybackcalled the Factor or P aybackb.b. Go across the row of the year (equivalent to the life of the project)Go across the row of the year (equivalent to the life of the project)
of Table II and Check up the closest figure to the factor ( asof Table II and Check up the closest figure to the factor ( as
determined in step (a) above ) and ascertain the rate.determined in step (a) above ) and ascertain the rate.
DCF METHODDCF METHOD - - IRRIRR
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c.c.If IRR is greater or equal to minimum desiredIf IRR is greater or equal to minimum desired
rate of returnrate of return accept the project. If I RR isaccept the project. If I RR is
less than minimum desired rate of return rejectless than minimum desired rate of return rejectthe project.the project.
Note :Note : Alternatively I RR may be calculated Alternatively I RR may be calculated
as per method prescribed for "uneven cashas per method prescribed for "uneven cashFlows.Flows.
DCF METHOD _ IRRDCF METHOD _ IRR
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2 .2 . If Cash Flows are not the same each year :If Cash Flows are not the same each year :The I RR can be found out by trial calculations. The cashThe I RR can be found out by trial calculations. The cashFlows of project for each year and its residue value areFlows of project for each year and its residue value arelisted and various discount rates are applied to theselisted and various discount rates are applied to theseamounts until the closest rate is found that makes their amounts until the closest rate is found that makes their total present value equal to the amount of investment. Thetotal present value equal to the amount of investment. Theindication for discounting at higher or lower rate can beindication for discounting at higher or lower rate can beconsidered on the following basisconsidered on the following basis- -
V > C V > C == H igher the rate of discountingH igher the rate of discountingV < C V < C == Lesser the rate of discountingLesser the rate of discountingVV == Discounted Cash InflowsDiscounted Cash InflowsC C == Cost of the investmentCost of the investment
DCF METHODDCF METHOD - - IRRIRR
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DCF METHODDCF METHOD - - IRRIRRWith the discounting rates ( where there is positive NP VWith the discounting rates ( where there is positive NP Vi.e. Start rate and Negative NP V i.e. end rate ), I RR isi.e. Start rate and Negative NP V i.e. end rate ), I RR isobtained by interpolation as under obtained by interpolation as under - -
== Start Rate +Start Rate +
or or
== End RateEnd Rate --SurplusSurplus = Surplus at Start Rate= Surplus at Start Rate
DeficitDeficit = Deficit at End Rate= Deficit at End Rate
Under this method it is presumed that cash inflows can beUnder this method it is presumed that cash inflows can bereinvested at internal rate of return.reinvested at internal rate of return.
urplus
urplus DeficitxDifference in start
L O
Qand end rate
e tr e t
eren e n tart and end rateLNMM
OQPP
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Evaluation of capital expenditure proposal involvesEvaluation of capital expenditure proposal involvesprojects of the future. Future is always uncertain. Nobodyprojects of the future. Future is always uncertain. Nobodycan say with certainty about the quantum and frequency of can say with certainty about the quantum and frequency of the future cash Flows.the future cash Flows.
There are too many unknown and uncertain factors whichThere are too many unknown and uncertain factors whichinfluence cash Flows and therefore, it is important toinfluence cash Flows and therefore, it is important torecogniserecognise that each cash inflows or outflows is only athat each cash inflows or outflows is only aprobable figure.probable figure.It is necessary to consider risk and uncertainty whileIt is necessary to consider risk and uncertainty whilecarrying out the capital budgeting exercise. Risk andcarrying out the capital budgeting exercise. Risk andreturn have a direct relationship.return have a direct relationship.H igher the return from the project, higher would be the riskH igher the return from the project, higher would be the risknormally and vice versa. It is, therefore, necessary that thenormally and vice versa. It is, therefore, necessary that thecapital budgeting exercise should attempt tocapital budgeting exercise should attempt to optimiseoptimiseboth, the return and risk factors.both, the return and risk factors.
RISK AND UNCERTAINITYRISK AND UNCERTAINITY
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RISK ANDRISK ANDRETURNRETURN
ANALYSISANALYSIS
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INTRODU CTIONINTRODU CTIONRisk and Return are closely related.Risk and Return are closely related.
P roject with potentiality of high profit may also increaseP roject with potentiality of high profit may also increaseperceived risk of the firm.perceived risk of the firm.
The trade off between risk and return will have bearingThe trade off between risk and return will have bearingon investors perception before and after accepting aon investors perception before and after accepting aspecific proposal.specific proposal.
If a proposal makes a firm more risky the investors willIf a proposal makes a firm more risky the investors willalso expect higher return.also expect higher return.
It is necessary to incorporate risk analysis in the analysisIt is necessary to incorporate risk analysis in the analysisof Capital Budgeting.of Capital Budgeting.
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DIAGR AM OF RISKDIAGR AM OF RISK AND RE TURN AND RE TURN
Risk ReturnPositive Relationship
High Risk Higher ExpectedReturn
Low Risk Lower Expected
ReturnHigher Risk has potentiality of Higher Returns, which will inturn will maximise the Wealth of the shareholders.Look towards risk as an opportunity.
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DES CR IP TION OF RISKDES CR IP TION OF RISK
What is Risk?What is Risk?
The estimation of future returns is done on theThe estimation of future returns is done on the
basis of various assumptions such as salesbasis of various assumptions such as salesvolume, sales price, cost, competition etc.volume, sales price, cost, competition etc.
Each of the factor in turn, depends on other Each of the factor in turn, depends on other
variables like state of economy, rate of variables like state of economy, rate of inflation and so on.inflation and so on.
The actual return will vary from theThe actual return will vary from the
estimates.This is technically referred as risk.estimates.This is technically referred as risk.
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DES CR IP TION OF RISKDES CR IP TION OF RISK
Risk with reference to Capital Budgeting:Risk with reference to Capital Budgeting:
The variability in the actual returns from aThe variability in the actual returns from aproject over its working life, in relation toproject over its working life, in relation to
estimated return as forecasted at the timeestimated return as forecasted at the time
of initial Capital Budgeting decision.of initial Capital Budgeting decision.
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DES CR IP TION OF RISKDES CR IP TION OF RISK
Decision situations :Decision situations :
Can be broken up into 3 parts.Can be broken up into 3 parts.
1 .1 .RiskRisk
2.2.UncertaintyUncertainty
3.3.CertaintyCertainty
TheThe R iskR isk situation is one in which probability of situation is one in which probability of
occurrence of a particular events are known.occurrence of a particular events are known.
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DES CR IP TION OF RISKDES CR IP TION OF RISK
TheThe UncertaintyUncertainty situation is one in whichsituation is one in which
probability of occurrence of a particular eventsprobability of occurrence of a particular events
are less known with greater variability asare less known with greater variability ascompared to risk.compared to risk.
TheThe CertaintyCertainty situation is one in which probabilitysituation is one in which probability
of occurrence of a particular events are knownof occurrence of a particular events are known
with greater degree of accuracy as compared towith greater degree of accuracy as compared to
risk and uncertainty.risk and uncertainty.
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DES CR IP TION OF RISKDES CR IP TION OF RISK
Risk and Uncertainty:Risk and Uncertainty:
Risk refers to set of unique outcomes for Risk refers to set of unique outcomes for
given event whichgiven event which can be assignedcan be assigned
probabilitiesprobabilities , while uncertainty refers to, while uncertainty refers to
outcomes of a given event which areoutcomes of a given event which are tootoounsure to be assigned probabilities.unsure to be assigned probabilities.
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RISK A ND RE TURN SU MM ARY RISK A ND RE TURN SU MM ARY FO R ACCEP TABILITY OF AFO R ACCEP TABILITY OF A
PR OJ EC T.PR OJ EC T.SituationSituation R iskR isk ReturnReturn Acceptability Acceptability
II H ighH igh H ighH igh Not RecommendedNot Recommended
IIII LowLow LowLow Not RecommendedNot Recommended
IIIIII H ighH igh LowLow Never acceptableNever acceptable
IVIV LowLowH
ighH
igh RecommendedRecommended
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ME ASU REMEN T OF RISKME ASU REMEN T OF RISK
Risk with reference to Capital Budgeting,Risk with reference to Capital Budgeting,
results fromresults from Variation between EstimatedVariation between Estimated
and Actual Returns.and Actual Returns.
Greater the variability between the twoGreater the variability between the two
more risky the project.more risky the project.
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ME ASU REMEN T OF RISKME ASU REMEN T OF RISKExample:Example:
P rojectP roject NP V(Rs.)NP V(Rs.) P robabilityP robability
XX 32 032 0 1 .01 .0
YY 400400
00
0 .80 .80 .20 .2
B oth the projects have equal expected NPV i.e. Rs.320.However the risk profile of project Y is greater than project
X , Hence Project Y is risky.Project X with lesser risk is expected to have same returnsas of Project Y, hence Project X is the better choice.
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1 . H ILLER S MOD EL 1 . H ILLER S MOD EL RiskR isk
EvaluationEvaluationH iller argues that uncertainty or riskH iller argues that uncertainty or riskassociated with a capital expenditureassociated with a capital expenditure
proposal isproposal is shown by Standard Deviation of shown by Standard Deviation of expected cash flows.expected cash flows.SituationSituation StandardStandard
DeviationDeviation Appraisal of Appraisal of
R iskR isk
II LowLow Lesser riskLesser risk
IIII H ighH igh H igher riskH igher risk
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H OW DO ES H ILLER S MOD EL H OW DO ES H ILLER S MOD EL
WO RKS?WO RKS?Working out Standard Deviation of the Various ranges of Working out Standard Deviation of the Various ranges of
Cash flows will help in the process of Cash flows will help in the process of taking cognizancetaking cognizance
of uncertaintyof uncertainty involved with future projects.involved with future projects.
H iller takes into account the mean of present value of H iller takes into account the mean of present value of
the cash flows and thethe cash flows and the Standard deviationStandard deviation of such cashof such cashflows, which may be determined as follows.flows, which may be determined as follows.
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STA NDARD D EVIATIO NSTA NDARD D EVIATIO NStandard deviation is a measure thatStandard deviation is a measure that indicates the degreeindicates the degreeof uncertainty (or dispersion)of uncertainty (or dispersion) of cash flows and is oneof cash flows and is oneprecise measure of risk.precise measure of risk.
Standard deviation is Square root of the Mean of theStandard deviation is Square root of the Mean of theSquared deviation.Squared deviation.
Deviation is the difference between the Value of OutcomeDeviation is the difference between the Value of Outcomeand the expected mean of value of all outcomes.and the expected mean of value of all outcomes.
Further to calculate the value of standard deviation weightsFurther to calculate the value of standard deviation weightsare provided to each deviation by its probability of are provided to each deviation by its probability of occurrence.occurrence.
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EXAMPLE OF STA NDARDEXAMPLE OF STA NDARDDEVIATIO NDEVIATIO N
Year
PV of Expected
Cashflows
DeviationfromMean
DeviationSquare
PV of Expected
Cashflows
DeviationfromMean
DeviationSquare
1 1,000 00) 0,000 1,000 00) 0,000
1,200 00) 90,000 1,100 00) 160,000 3 1,400 100) 10,000 1,250 250) 62,500 4 1,600 100 10,000 1,450 50) 2,500 5 1,800 00 90,000 1,900 400 160,000 6 2,000 500 250,000 2,300 800 640,000
Total 9,000 0 700,000 9,000 - 1, 75,000Mean 1,500 - 116,667 1,500 - 1 ,500
34 461
Project X Project Y
Standard Deviation
Return for both project is the same. Project Y is having higher StandardDeviation (Higher risk).Thus Project Y is more risky than Project X.Hence Project X is a better Choice.
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EXAMPLE OF STA NDARDEXAMPLE OF STA NDARDDEVIATIO N WITH DIFF EREN TDEVIATIO N WITH DIFF EREN T
ME ANSME ANSIf the sizes of the projects outlay differ, StandardIf the sizes of the projects outlay differ, Standarddeviation will be misleading therefore decisiondeviation will be misleading therefore decision
maker should make use of the Coefficient of maker should make use of the Coefficient of variation to judge the riskiness of the project.variation to judge the riskiness of the project.
CoCo--efficient of Variation (v)efficient of Variation (v)
Standard DeviationStandard Deviation
Mean of Expected Cash FlowsMean of Expected Cash Flows
=
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2. D EC ISIO N M AKING WIT H 2. D EC ISIO N M AKING WIT H TH E H ELP OF COTH E H ELP OF CO--EFFI CIEN TEFFI CIEN T
OF VA RIATIO NOF VA RIATIO N
CoCo--efficient of Variation is better measureefficient of Variation is better measurethan Standard deviation because it adjuststhan Standard deviation because it adjuststhe size(Quantum) of cash flows.the size(Quantum) of cash flows.
SituationSituation CoCo--efficient of efficient of VariationVariation
Appraisal of Appraisal of R iskR isk
II LowLow Lesser riskLesser riskIIII H ighH igh H igher riskH igher risk
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3 S i i i A l i3 S i i i A l i
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3. Sensitivity Analysis3. Sensitivity Analysis A P recise Measure of A P recise Measure of
Evaluating R iskEvaluating R iskSensitivity analysis provides information as to how theSensitivity analysis provides information as to how thesensitive estimate project parameters make variations insensitive estimate project parameters make variations inproject output results.project output results.Sensitivity analysis takes care of estimation errors bySensitivity analysis takes care of estimation errors by
finding out possible outcomes in evaluating the a project.finding out possible outcomes in evaluating the a project.Sensitivity analysis provides decision maker insight intoSensitivity analysis provides decision maker insight intovariability of the outcomes.variability of the outcomes.Sensitivity analysis provides different cash flowSensitivity analysis provides different cash flow
estimates under three assumptions.estimates under three assumptions.1 .1 . the worst ( Most pessimistic)the worst ( Most pessimistic)2.2. the expected ( Most likely)the expected ( Most likely)3.3. the best ( Most optimistic)the best ( Most optimistic)
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No.No. Sensitive P roject parametersSensitive P roject parameters
11 P roject CostP roject Cost
22 P roject LifeP roject Life33 Expected Cash FlowExpected Cash Flow
Capacity UtilisationCapacity Utilisation
Selling P riceSelling P riceRaw Material costRaw Material costOther Variable CostOther Variable Cost
44 P roject capacityP roject capacity
SENSITIVITY PARAMETERS
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ExampleExampleThe capital investment outlay of a projectThe capital investment outlay of a projectconsists of Rs. 100 lakhs for P lant andconsists of Rs. 100 lakhs for P lant andMachinery and Rs.4 0 lakhs for WorkingMachinery and Rs.4 0 lakhs for WorkingCapital.Capital.Other details are summarised below.Other details are summarised below.
1120
60
F ixed overheads excluding epreciation Rs.lakhs 15Rate of depreciation on plant and machinery % on W 25
405
12
Applicable tax rateTime hori on YearsPost tax cut off rate %
alvage value of plant and machinery Equal to W at theend of year 5
S ales Lakh units p.a for years 1-5S elling price per unitariable cost per unit Rs
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Required
1 . Indicate the financial viability of project by calculatingNP V.
2. Determine the sensitivity of the projects NP V under
each of the following conditions.a. Decrease in selling price by 10%
b. Increase in variable cost by 5 %
c. Increase in variable cost by 10%
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Year Ref.Cash flowRs.Lakhs D.F. @12%
Discountedcash flowsRs. Lakhs
0 A -100.00 1.00 -100.00B -40.00 1.00 -40.00
1 C 37.00 0.89 32.932 C 34.50 0.80 27.603 C 32.63 0.71 23.164 C 31.22 0.64 19.985 C 30.16 0.57 17.19
B 40.00 0.57 22.80D 23.73 0.57 13.53
17.19
A=Ca pital costB= orkin g Ca pitalC= Opeartional cash inflowD= Sal va ge Value
Calculation of NPV
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Year WDVRs.Lakhs
Depreciation@25%Rs.Lakhs
1 100.00 25.002 75.00 18.753 56.25 14.064 42.19 10.555 31.64 7.91
WDV 23.73
Depreciation on plant and Machinery
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Year
Contr ibu [email protected]/ unit(For 1 lakhunits)Rs.Lakhs
F ixedoverheads(ex ludingDep.) Rs.Lakhs
Deprec iat ionRs.Lakhs
PBTRs. Lakhs
Ta x Rs. Lakhs
Operat iona l cashinf lowRs.Lakhs
1 60 15 25.00 20.00 8.00 37.002 60 15 18.75 26.25 10.50 34.503 60 15 14.06 30.94 12.38 32.634 60 15 10.55 34.45 13.78 31.225 60 15 7.91 37.09 14.84 30.16
Operat iona l Cash inf low
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Sr. No. Change CalculationRevised
NPV Result
1Decrease in sellingPrice by 10 %
(1 X - 12) X
(1-. 4 0) X3.61 - 8.80
NegativeNPV
2Increase in Variablecost by 5 %
(1 X -3) X(1-. 4 0) X3.61 10.70
StillpositiveNPV
3Increase in Variablecost by 10 %
(1 X- 6) X(1-. 4 0) X3.61 4 .20
StillpositiveNPV
Sensitivity Analysis
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4. ASSIG NING PR OBABI LITY4. ASSIG NING PR OBABI LITYSensitivity Analysis provides more than oneSensitivity Analysis provides more than one
estimate of future return of a project. It is thereforeestimate of future return of a project. It is therefore
superior to single figure forecast as it gives moresuperior to single figure forecast as it gives more
precise ideas regarding variability of the returns.precise ideas regarding variability of the returns.
But, it has a limitation in that it does not discloseBut, it has a limitation in that it does not disclose
chances of these occurrences of these variations.chances of these occurrences of these variations.Remedy is to provide more accurate forecast byRemedy is to provide more accurate forecast by
considering probability of occurrences.considering probability of occurrences.
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ASSIG NING PR OBABI LITY ASSIG NING PR OBABI LITYThe Concept of probability is helpful as it indicates theThe Concept of probability is helpful as it indicates thepercentage chance of occurrence of each possible cashpercentage chance of occurrence of each possible cashflow.flow.
The quantification of variability of returns involves twoThe quantification of variability of returns involves twosteps.steps.
1 .1 . Depending upon chance of occurrences of a particular cashDepending upon chance of occurrences of a particular cashflow estimate, probabilities are assigned.flow estimate, probabilities are assigned.
Assignment of probabilities can be objective (large number of Assignment of probabilities can be objective (large number of observations under independent and identical situations andobservations under independent and identical situations andpast experience) and subjective (personal probabilitypast experience) and subjective (personal probabilityassignment).assignment).
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ASSIG NING PR OBABI LITY ASSIG NING PR OBABI LITY
2.2. To estimate the expected return on the project theTo estimate the expected return on the project the
returns are expressed in terms of expected monetaryreturns are expressed in terms of expected monetary
values. The expected value of a project is a weightedvalues. The expected value of a project is a weightedaverage return, where the weights are probabilitiesaverage return, where the weights are probabilities
assigned to the various expected cash flows.assigned to the various expected cash flows.
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EXAMPLE EXAMPLE A new project Cost Rs. , 000 A new project Cost Rs. , 000 lakhslakhs. The. Thefollowing information is available regardingfollowing information is available regardingthe cash flows generated, and their the cash flows generated, and their
probability for X YZ Ltd. What is expectedprobability for X YZ Ltd. What is expectedreturn on the project? Assume 10% discountreturn on the project? Assume 10% discountrate and calculate present value of expectedrate and calculate present value of expectedmonetary values.monetary values.
Cash flowsRs. Lakhs P robability
Cash flowsRs. Lakhs P robability
Cash flowsRs. Lakhs P robability
000 0 . 0 00 0 . 000 0 . 0300 0 . 0 800 0 . 0 3 00 0 .30
3 00 0 . 0 3300 0 . 3800 0 .30
Year 1 Year 3Year
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PR OBABI LITY DIST RIBUTIO N PR OBABI LITY DIST RIBUTIO N
APPR OACH
APPR OACH
In earlier slides we have seen the concept of In earlier slides we have seen the concept of
probability for incorporating risk in evaluatingprobability for incorporating risk in evaluating
capital budgeting proposals.capital budgeting proposals.
The application of this theory inThe application of this theory in analysinganalysing riskrisk
depends upon thedepends upon the behaviour behaviour of cash flows.of cash flows.
From theFrom the behaviouralbehavioural point of view cash flowspoint of view cash flowsareare
1 .1 . Independent cash flowsIndependent cash flows
2.2. Dependent cash flowsDependent cash flows
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Independent cash flows signifies thatIndependent cash flows signifies that
future cash flows are not affected by cashfuture cash flows are not affected by cash
flows of the preceding or following years.flows of the preceding or following years.Dependent cash flow depend upon theDependent cash flow depend upon the
cash flow of previous periods.cash flow of previous periods.
PR OBABI LITY DIST RIBUTIO N PR OBABI LITY DIST RIBUTIO N
APPR OACH APPR OACH
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By assigning probabilities to expectedBy assigning probabilities to expected
cash flows, NP V is found out by applyingcash flows, NP V is found out by applying
appropriate discount rate. This isappropriate discount rate. This is estimateestimate
of return.of return.
Risk is measured by finding out StandardRisk is measured by finding out Standard
deviation of the project under deviation of the project under
PR OBABI LITY DIST RIBUTIO N PR OBABI LITY DIST RIBUTIO N
APPR OACH
APPR OACH
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EXAMPLE
A new project Cost Rs. 000 lakhs The followinginformation is available regarding the cash flowsgenerated, and their probability for X YZ Ltd. What isexpected return on the project? Assume 10% discount
rate and calculate present value of expected monetaryvalues.
Cash flowsRs. Lakhs Probability
Cash flowsRs. Lakhs Probability
Cash flowsRs. Lakhs Probability
000 0 . 0 00 0 . 000 0 . 000 0 . 0 00 0 . 0 00 0 . 000 0 . 0 00 0 . 00 0 . 0
Year 1 Year Year
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B y comparing the return and Risk with other similar project, aproject having minimum risk and maximum return is selected.
Year Cash Flow Probability Expected Mo Deviation Deviation2
Deviation2 xProbabilit
y
DoubleDiscountin
g Factor
Discount
ed ValueRs. Rs. Rs.1 2000 0.20 400.00 -600.00 360000 72000
2300 0.40 920.00 -300.00 90000 36000
3200 0.40 1280.00 600.00 360000 144000
T otal 7500 1.00 2600.00 -300.00 810000 252000 0.82 206640Mean 2500 2600.00
2 2500 0.25 625.00 -350.00 122500 30625
2800 0.50 1400.00 -50.00 2500 1250
3300 0.25 825.00 450.00 202500 50625T otal 8600 1.00 2850.00 50.00 327500 82500 0.68 56100Mean 2867 2850.00
3 3000 0.40 1200.00 -360.00 129600 51840
3400 0.30 1020.00 40.00 1600 480
3800 0.30 1140.00 440.00 193600 58080
T otal 10200 1.00 3360.00 120.00 324800 110400 0.56 61824Mean 3400 3360.00
T otal 324564
570Standard Deviation of the project
Standard Deviation
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5. RISK ADJUST ED DIS COU NT5. RISK ADJUST ED DIS COU NT
R AT E (R AD) A PPR OACH
R AT E (R AD) A PPR OACH
R AD approach is simplest and most widely usedR AD approach is simplest and most widely usedmethod for incorporating risk into capital budgetingmethod for incorporating risk into capital budgeting
decision .decision .
Under this approach the amount of risk inherent inUnder this approach the amount of risk inherent in
a project is incorporated in discount rate employeda project is incorporated in discount rate employed
in the present value calculations.in the present value calculations.
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R isk inherentR isk inherentin a projectin a project
Discount Rate to beDiscount Rate to beappliedapplied
SaySay
Very R iskyVery R iskyH
igher discount rateH
igher discount rate 25%
25%
R iskyR isky H igh discount rateH igh discount rate 2 0%20%
SafeSafe Low discount rateLow discount rate 1 %1 %
RAD APPROACH
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R AD A PPR OACHR AD A PPR OACH
The risk adjusted discount rate representsThe risk adjusted discount rate represents
different risk in different class of investment.different risk in different class of investment.
The use of single rate discount the different riskThe use of single rate discount the different risk
of various projects would be logicallyof various projects would be logically
inconsistent with the firms goal of shareholdersinconsistent with the firms goal of shareholderswealthwealth maximisationmaximisation. .
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R AD A PPR OACHR AD A PPR OACH
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R AD A PPR OACH R AD A PPR OACH Accept or Reject criteria: Accept or Reject criteria: NPV Method :NP V Method :
NP V P ositiveNP V P ositive Acceptable Acceptable
NP V NegativeNP V Negative RejectReject
IRR method :IRR method :IRR AcceptableIRR AcceptableIRR IRR
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EXAMPLEEXAMPLE A textile company is considering two mutually A textile company is considering two mutuallyexclusive investment proposals. Their expectedexclusive investment proposals. Their expectedcash flow streams ( CFAT) are given as follows.cash flow streams ( CFAT) are given as follows.
ear P roposal X P roposalRs . Thousand Rs . Thousand
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The company employs the risk adjusted method of The company employs the risk adjusted method of evaluating risky projects and selects theevaluating risky projects and selects theappropriate P roject. Required rate of return are asappropriate P roject. Required rate of return are asfollows.follows.
P roject pay ackRequired rateof return
ess than year to yearsto yearsver years
Which proposal should be acceptable to the company?
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6. CER TAINTY EQUIVA LENT6. CER TAINTY EQUIVA LENT APPR OACH (CE A) APPR OACH (CE A)
CE A is an alternative to the risk adjustedCE A is an alternative to the risk adjusted
rate method, which overcome therate method, which overcome the
weaknesses of the latter method. Under weaknesses of the latter method. Under
CE A approach the riskiness of the projectCE A approach the riskiness of the project
is taken into consideration by adjusting theis taken into consideration by adjusting the
expected cash flows, while under R ADexpected cash flows, while under R AD
approach the discount rate is adjusted.approach the discount rate is adjusted.
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ST EP S I NVOLVED IN CE AST EP S I NVOLVED IN CE A1 .1 . Modify the expected cash flows to adjustModify the expected cash flows to adjust
the risk. The risk adjustment factor isthe risk. The risk adjustment factor isexpected in terms of Certainty Equivalentexpected in terms of Certainty Equivalentcoco--efficient.efficient.Co-efficient =
Risk less cash flow
Risky Cash flowThe co-efficient is fractional number between 0 and 1.There is inverse relationship between degree of risk andvalue of co-efficient.
Degree of RiskDegree of Risk Value of CoValue of Co--efficientefficientH igh RiskH igh Risk Lower coLower co- -efficientefficientLower RiskLower Risk H igher coH igher co- -efficientefficient
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ST EP S I NVOLVED IN CE AST EP S I NVOLVED IN CE A
2.2. Calculate present values of cash flowsCalculate present values of cash flows
by applying Risk free discounting rate or by applying Risk free discounting rate or
the rate which appropriately reflects thethe rate which appropriately reflects thetime value of money.time value of money.
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ST EP S I NVOLVED IN CE AST EP S I NVOLVED IN CE A3.3. Accept or Reject criteria: Accept or Reject criteria:
NPV Method :NP V Method :NP V P ositiveNP V P ositive Acceptable Acceptable
NP V NegativeNP V Negative RejectReject
IRR method :IRR method :IRR AcceptableIRR AcceptableIRR IRR
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EXAMPLEEXAMPLE A company employs certainty A company employs certainty- -equivalent of riskyequivalent of riskyinvestments. The capital budgeting department of theinvestments. The capital budgeting department of thecompany has developed the following information regardingcompany has developed the following information regardinga new project:a new project:
e a r
E x p e c t e d
A T
e r t a i n t y -
e q u i v a l e n ts . T h o u s a n d
- ......
The firm,s cost of equity capital is Rs.18% , its cost of debt is9% and the riskless rate of interest in the market on theGovernment securities is 6%. Should the project beaccepted?
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7.DEC ISIO N TREE 7.DEC ISIO N TREE
APPR OACH
(DT) APPR OACH
(DT)DT is another useful alternative for evaluatingDT is another useful alternative for evaluatingrisky investment proposals.risky investment proposals.
The outstanding feature of this approach is thatThe outstanding feature of this approach is that
it takes into account the impact of allit takes into account the impact of all
probabilistic estimates of potential outcomes.probabilistic estimates of potential outcomes.
The DT approach is especially useful for projectsThe DT approach is especially useful for projects
require decisions in sequential parts.require decisions in sequential parts.
DEC ISIO N TREE A P ICTO RIALDEC ISIO N TREE A P ICTO RIAL
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DEC ISIO N TREE A P ICTO RIAL DEC ISIO N TREE A P ICTO RIAL PRE S EN TATIO NPRE S EN TATIO N
A decision is a pictorial representation in tree A decision is a pictorial representation in tree
form which indicates probability andform which indicates probability and
interrelationship of all possible outcomes.interrelationship of all possible outcomes.
The format of the investment decisions has anThe format of the investment decisions has an
appearance of a tree with branches.appearance of a tree with branches.
Decision tree shows the sequential cash flowsDecision tree shows the sequential cash flows
and the NP V of different projects under differentand the NP V of different projects under different
circumstances.circumstances.
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EXAMPLE 1EXAMPLE 1
Investment proposal of X Ltd. requires an outlayInvestment proposal of X Ltd. requires an outlayof Rs. 2, 00 ,000 at present (t = 0 ). The investmentof Rs. 2, 00 ,000 at present (t = 0 ). The investmentproposal is expected to have 2 years economicproposal is expected to have 2 years economiclife with no salvage value. In year 1 , following arelife with no salvage value. In year 1 , following arethe cash flows and probabilities.the cash flows and probabilities.
ash Flow P robability0000 0 .110000 0 .1 0000 0 .
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In year 2, the CFAT possibilities depend on the CFAT thatIn year 2, the CFAT possibilities depend on the CFAT thatoccurs in year 1 . That is the CFAT for the year 2 areoccurs in year 1 . That is the CFAT for the year 2 areconditional on CFAT for the year 1 . Accordingly theconditional on CFAT for the year 1 . Accordingly theprobabilities assigned with the CFAT of the year 2 areprobabilities assigned with the CFAT of the year 2 areconditional probabilities. The estimated conditional CFAT andconditional probabilities. The estimated conditional CFAT andtheir associated conditional probabilities are as follows:their associated conditional probabilities are as follows:
CFAT2 robability CFAT2 robability CFAT2 robability.2 1 . 1 .1
1 . 1 . 2 .1 .2 1 . 2 . 1
If CFAT1 s. If CFAT2 s. 11 If CFAT s. 1
Recommend whether project should be accepted or notusing decision tree approach. Assume Discount rate of 12 % .
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Year 1 Path Expected NPV
Ti e 0 Probab ilities CFAT Probab ilities CFAT @ 12%Rs. Rs. Rs. Rs.
0.2 40000 1 -9 80* 0.0 -5800.8
0.3 80000 0. 100000 2 -488 0 0.18 -8 94.8
0.2 150000 3 -9010 0.0 540.
0.3 130000 4 1840 0.12 220.8
Cash Out lays 0.4 110000 0.4 150000 5 1 80 0.1 2844.8
Rs. 200000 0.3 1 0000 25 50 0.12 3090
0.1 1 0000 14 0 0.03 1844.10.3 150000 0.8 200000 8 93350 0.24 22404
0.1 240000 9 125230 0.03 3 5 .91.00 19024
Joi t Probab ilityExpected
NPV
Year 2
DECISION TREE PRESENTATION
For NPV calculations, refer next slide
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Time 0 Path Expected NPVCFAT Probabilities CFAT Probabilities @ 12%Rs. Rs. Rs. Rs.
200000 80000 0.3 40000 0.2 1 -96680 0.06 -5800.8200000 80000 0.3 100000 0.6 2 -48860 0.18 -8794.8
200000 80000 0.3 150000 0.2 3 -9010 0.06 -540.6200000 110000 0.4 130000 0.3 4 1840 0.12 220.8200000 110000 0.4 150000 0.4 5 17780 0.16 2844.8200000 110000 0.4 160000 0.3 6 25750 0.12 3090200000 150000 0.3 160000 0.1 7 61470 0.03 1844.1200000 150000 0.3 200000 0.8 8 93350 0.24 22404200000 150000 0.3 240000 0.1 9 125230 0.03 3756.9
1.00 19024.40
JointProbability
ExpectedNPV
Year 1 Year 2
Since NPV is positive project is recommended for adoption.
SPREADSHEET PRESENTATION
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A Company has the following estimates of the present A Company has the following estimates of the present
values of the future cash flows after taxes associated withvalues of the future cash flows after taxes associated with
the investment proposal, concerned with expanding thethe investment proposal, concerned with expanding the
plant capacity. It intends to use a decisionplant capacity. It intends to use a decision- -tree approach totree approach to
get clear picture of the possible outcomes of thisget clear picture of the possible outcomes of this
investment. The plant expansion is expected to cost Rs.investment. The plant expansion is expected to cost Rs.
3, 00 ,000 . The respective P Vs of future CFAT and3, 00 ,000 . The respective P Vs of future CFAT andprobabilities are as follows:probabilities are as follows:
EXAMPLE 2
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Withexpansion
Withoutexpansion
Probabailities
Rs. Rs.300000 200000 0.2500000 200000 0.4900000 350000 0.4
PV of uture CFAT
Advise the company regarding the financial feasibility of theproject.
8 H ER TZS MOD EL8 H ER TZS MOD EL
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8. H ER TZS MOD EL 8. H ER TZS MOD EL US E SIMUL ATIO N TEC H NIQUE US E SIMUL ATIO N TEC H NIQUE
H ertz has suggested that simulation technique which isH ertz has suggested that simulation technique which isflexible tool of Operational Research may be used inflexible tool of Operational Research may be used inCapital Budgeting decisions.Capital Budgeting decisions.
H e argues that planning problems of a firm are so complexH e argues that planning problems of a firm are so complexthat they cannot be described by mathematicalthat they cannot be described by mathematicalmodel. Evenmodel. Even while using mathematical model we makewhile using mathematical model we makecertain assumptions because of which solution is notcertain assumptions because of which solution is not
reliable for practical purposes.reliable for practical purposes.In most of the solutions due to uncertainties involved,In most of the solutions due to uncertainties involved,satisfactory mathematical model cannot be built.satisfactory mathematical model cannot be built.
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DIS COU NTED CAS H FLOW VDIS COU NTED CAS H FLOW V
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DIS COU NTED C AS H FLOW VDIS COU NTED C AS H FLOW VH
ER TZS MOD ELH
ER TZS MOD ELDCF ModelDCF Model H ertz ModelH ertz ModelMathematical ModelMathematical Model Statistical ModelStatistical Model
Commonly followedCommonly followedTechniqueTechnique Operational ResearchOperational ResearchExpert aided techniqueExpert aided technique
DCF model wouldDCF model wouldmerely consider merely consider expected value of eachexpected value of eachinput variable.input variable.
H ertz proposes thatH ertz proposes thatdistribution be describeddistribution be describedfor each variable.for each variable.
Less flexibleLess flexibleH
ighly flexibleH
ighly flexible
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H OW H ER TZ MOD EL WO RKS?H OW H ER TZ MOD EL WO RKS?H aving derived Mean, Standard DeviationH aving derived Mean, Standard Deviation
and Shape (Graph) of Distribution of Eachand Shape (Graph) of Distribution of Each
variables the simulation experiment may bevariables the simulation experiment may beperformed by considering different levels of performed by considering different levels of
these factors.these factors.
e.g.e.g.
In theIn the first runfirst run H igh Operating Cost with lowH igh Operating Cost with low
Market Share etc ma be used for com utinMarket Share etc ma be used for com utin
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H OW H ER TZ MOD EL WO RKS?H OW H ER TZ MOD EL WO RKS?
In the next run it may be a moderateIn the next run it may be a moderate
operating cost with a large market size mayoperating cost with a large market size may
be used for computing NP V.be used for computing NP V.
Similarly it may be a moderate operating costSimilarly it may be a moderate operating cost
with a low market size may be used for with a low market size may be used for
computing NP V.computing NP V.
And so on ..... large number of runs And so on ..... large number of runs
(iterations) may be made which would cover (iterations) may be made which would cover
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SIMUL ATIO NSIMUL ATIO N
It is statistical technique which applies toIt is statistical technique which applies to
predetermined probability distributions andpredetermined probability distributions and
random numbers to estimate risky outcomes.random numbers to estimate risky outcomes.
A simulation is akin to sensitivity analysis. The A simulation is akin to sensitivity analysis. The
technique is more comprehensive thantechnique is more comprehensive than
Sensitivity analysis.Sensitivity analysis.
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SIMUL ATIO NSIMUL ATIO N
Instead of showing the impact on the NP V for change inInstead of showing the impact on the NP V for change in
one key variable (Say change in selling price, change inone key variable (Say change in selling price, change in
variable cost) in Sensitivity analysis, Simulation enablesvariable cost) in Sensitivity analysis, Simulation enables
the distribution of probable values( NP V) for change in allthe distribution of probable values( NP V) for change in all
the key variables in one iteration/run only.the key variables in one iteration/run only.
The technique provides more information and better The technique provides more information and better
understanding about the risk associated with theunderstanding about the risk associated with the
investment decision.investment decision.
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SIMUL ATIO NSIMUL ATIO N
To be effective Simulation requiresTo be effective Simulation requires
sophisticated Computing package, as itsophisticated Computing package, as it
enables to try out large number of enables to try out large number of
outcomes with much ease.outcomes with much ease.
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EXAMPLEEXAMPLEThe production of certain commodity and theThe production of certain commodity and thecorresponding probabilities are as follows.corresponding probabilities are as follows.
Simulate the production on next 10 days and find out theaverage daily production.
aily Productionin nitsProbability . . . . . .
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SO LUTIO NSO LUTIO N
We decide the schedule of Random Numbers, where theWe decide the schedule of Random Numbers, where thenumber of number of Random Numbers in schedule isnumber of number of Random Numbers in schedule isproportional to the probability.proportional to the probability.
r o d u c t i o nin U n it s ro b a b il i t y
R a n d o mN u m b e rs
.
.
.
.
.
.
S c h e d u le o f R a n d o m N u m b e rs
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SO LUTIO NSO LUTIO NWe now consider any set of randomlyWe now consider any set of randomlyselected 10 two digit numbers, to decide theselected 10 two digit numbers, to decide thedaily production.daily production.
a ya n d o m
n u m b e r a i l y
p r o d u c t i o n1 1 1 0
7 1 00 1 0
7 1
1 1
1 1 1 0
7 7 1
7 1 0
9 1 1
1 0 79 1
1 1
1 1 .
To t a l r o d u c t i o ne r a g e a i l y
p r o d u c t i o n
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