Ch 12. Risk Evaluation in Capital Budgeting

8/19/2019 Ch 12. Risk Evaluation in Capital Budgeting

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Chapter 12: Risk Evaluation inCapital Budgeting


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•Risk refers to the variability in the actual

returns vis-à-vis the estimated returns, in termsof cash os!

•Risk involved in capital budgeting can be

measured in absolute as ell as relative terms!

• "he absolute measures of risk include

sensitivity analysis, simulation and standarddeviation!

• "he coe#cient of variation is a relative

measure of risk!

Compiled by: $rof! Ra%see &oshi

'e(nition of Risk'e(nition of Risk


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)ature of Risk)ature of Risk


Risk e*ists because of the inability of thedecision+maker to make perfect forecasts!

n formal terms, the risk associated ith aninvestment may be de(ned as thevariability that is likely to occur in thefuture returns from the investment!

"hree broad categories of the eventsinuencing the investment forecasts:

General economic conditions Industry factors Company factors


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-tatistical "echni.ues for Risk-tatistical "echni.ues for Risk

/nalysis/nalysis


$robability0ariance or -tandard 'eviation

Coe#cient of 0ariation


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1! $robability1! $robability


/ typical forecast for a period! "his is referredto as best estimate or most likely forecast:

/ forecaster should not give %ust one estimate,but a range of associated probability3aprobability distribution!

Probability may be described as a measure ofsomeone4s opinion about the likelihood that anevent ill occur!


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/ssigning $robability/ssigning $robability


"he probability estimate, hich is based ona very large number of observations, isknon as an objective probability!

$robability assignments that reect thestate of belief of a person rather than theob%ective evidence of a large number oftrials are called personal or subjective

probabilities!


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E*pected )et $resent 0alueE*pected )et $resent 0alue

6nce the probability assignments havebeen made to the future cash os thene*t step is to (nd out the expectednet present value.

E*pected net present value 7 -um ofpresent values of e*pected net cashos!



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2! 0ariance or -tandard 'eviation2! 0ariance or -tandard 'eviation -imply stated,

variance measuresthe deviation aboute*pected cash oof each of thepossible cash os!

-tandard deviationis the s.uare root of

variance!/bsolute 8easure

of Risk!


2 2

=1

(NCF) = (NCF – ENCF)n

j j

j

P σ ∑


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9! Coe#cient of 0ariation9! Coe#cient of 0ariation Relative Measure of Risk

t is derived as the standard deviation of theprobability distribution divided by its

e*pected value "he coe#cient of variation is a useful

measure of risk hen e are comparing thepro%ects hich have

i; same standard deviations but di


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C6)0E)"6)/= "EC>)?@E- A6R R-

E0/=@/"6)

$ayback

Risk+/d%usted 'iscount Rate

Certainty E.uivalent

COMPILED BY: PROF. RAJSEE JOSHI


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1! $ayback1! $ayback


"his method, ansers the duration ithinhich the initial investment is recovered

"he merit of paybackts simplicity

Aocusing attention on the near term future andthereby emphasising the li.uidity of the (rm throughrecovery of capital!

Aavouring short term pro%ects over hat may be

riskier, longer term pro%ects!t ignores the time value of cash os!


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2! Risk+/d%usted 'iscount Rate2! Risk+/d%usted 'iscount Rate

Risk-adjusted discount rate, ill allo forboth time preference and risk preference and ill be a sum of the risk+free rate andthe risk+premium rate reecting theinvestor4s attitude toards risk!


= 0

NCF NPV =

(1 )

nt

t

t k +∑

f r k = k + k


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Evaluation of Risk-adjustedEvaluation of Risk-adjusted

Discount RateDiscount Rate


/dvantages : t is simple and can be easily understood! t has a great deal of intuitive appeal for risk+

averse businessman!

t incorporates an attitude risk+aversion;toards uncertainty!

=imitations: "here is no easy ay of deriving a risk+ad%usted

discount rate!t does not make any risk ad%ustment in the

numerator for the cash os that are forecastover the future years!

t is based on the assumption that investors arerisk+averse! "hough it is generally true, there

e*ists a category of risk seekers ho do notdemand premium for assuming risks they are


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3. Certainty—Euivalent3. Certainty—EuivalentReduce the forecasts of

cash os to someconservative levels!

"he certaintyDe.uivalentcoe#cient assumes a

value beteen and 1,and varies inversely ithrisk!

'ecision+makersub%ectively or

ob%ectively establishesthe coe#cients! "he certaintyDe.uivalent

coe#cient can bedetermined as a

relationship beteen thecertain cash os andCompiled by: $rof! Ra%see &oshi

=0

NCF NPV =

(1 ) f

nt t

t t k

α

+∑

* NCF Certain net cash flow =

NCF Risky net cash flow

t t

t

α =


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Evaluation of Certainty—Evaluation of Certainty—

EuivalentEuivalent


"his method su


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Risk-adjusted Discount RateRisk-adjusted Discount Rate

!s. Certainty"Euivalent!s. Certainty"Euivalent


"he certaintyDe.uivalent approach recognisesrisk in capital budgeting analysis by ad%ustingestimated cash os and employs risk+free rateto discount the ad%usted cash os!

6n the other hand, the risk+ad%usted discountrate ad%usts for risk by ad%usting the discountrate! t has been suggested that the certaintyDe.uivalent approach is theoretically a superior

techni.ue!


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#ensitivity $nalysis#ensitivity $nalysis


#ensitivity analysis is a ay of analysingchange in the pro%ect4s )$0 or RR; for a givenchange in one of the variables!

"he folloing three steps are involved in the

use of sensitivity analysis:denti(cation of all those variables, hich have aninuence on the pro%ect4s )$0 or RR;!

'e(nition of the underlying mathematical;relationship beteen the variables!

/nalysis of the impact of the change in each of the

variables on the pro%ect4s )$0! "he decision maker, hile performing

sensitivity analysis, computes the pro%ect4s )$0or RR; for each forecast under threeassumptions: a; pessimistic, b; e*pected, andc; optimistic!


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DC% &reak-even $nalysisDC% &reak-even $nalysis


-ensitivity analysis is a variation of the break+even analysis!

Fhat shall be the conse.uences if volume orprice or cost changes -ensitivity analysis;G Hou

can ask this .uestion dio muchloer can the sales volume become before thepro%ect becomes unpro(tableG Fhat you areasking for is the break+even point!

DC% break-even point is di


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#cenario $nalysis#cenario $nalysis


6ne ay to e*amine the risk of investmentis to analyse the impact of alternativecombinations of variables, calledscenarios( on the pro%ect4s )$0 or RR;!

"he decision+maker can develop someplausible scenarios for this purpose! Aorinstance, e can consider three scenarios:

pessimistic, optimistic and e*pected!


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#i)ulation $nalysis#i)ulation $nalysis


"he Monte Carlo simulation or simply thesi)ulation analysis considers the interactionsamong variables and probabilities of the changein variables! t computes the probability

distribution of )$0! "he simulation analysisinvolves the folloing steps:Airst, you should identify variables that

inuence cash inos and outos!-econd, specify the formulae that relate

variables! "hird, indicate the probability distribution for

each variable!Aourth, develop a computer programme that

randomly selects one value from theprobability distribution of each variable and


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#*ortco)in's#*ortco)in's


"he model becomes .uite comple* to use!

t does not indicate hether or not thepro%ect should be accepted!

-imulation analysis, like sensitivity orscenario analysis, considers the risk of anypro%ect in isolation of other pro%ects! i!e tdoes not make comparisons beteen to

pro%ects


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Decision +rees forDecision +rees for

#euential ,nvest)ent#euential ,nvest)ent

DecisionsDecisions


nvestment e*penditures are not an isolatedperiod commitments, but as links in a chainof present and future commitments!

/n analytical techni.ue to handle the

se.uential decisions is to employ decisiontrees!


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sefulness of Decision +reesefulness of Decision +ree

$pproac*$pproac*


"he merits of the decision tree approach are:t clearly brings out the implicit assumptions and

calculations for all to see, .uestion and revise!t allos a decision maker to visualise assumptions

and alternatives in graphic form, hich is usually

much easier to understand than the more abstract,analytical form!

"he demerits of the decision tree approach are: "he decision tree diagrams can become more and

more complicated as the decision maker decides toinclude more alternatives and more variables and tolook farther and farther in time!

t is complicated even further if the analysis ise*tended to include interdependent alternatives andvariables that are dependent upon one another!


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tility +*eory and Capitaltility +*eory and Capital

&ud'etin'&ud'etin'


@tility theory aims at incorporation ofdecision+maker4s risk preference e*plicitlyinto the decision procedure!

/s regards the attitude of individualinvestors toards risk, they can beclassi(ed in three categories:Risk-averse Risk-neutral

Risk-seeking ndividuals are generally risk averters anddemonstrate a decreasing marginal utilityfor money function!


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Exa)pleExa)ple =et us assume that the

oner of a (rm isconsidering an investmentpro%ect, hich has I percent of probability of yieldinga net present value of Rs 1

lakh and J per centprobability of a loss of netpresent value of Rs 1 lakh!

$ro%ect has a positivee*pected )$0 of Rs 2 lakh!>oever, the oner may berisk averse, and he may

consider the gain in utilityarising from the positiveoutcome positive $0 of Rs1 lakh; less than the loss inutility as a result of thenegative outcome negative

$0 of Rs 1 lakh;! "he oner may re%ect theCompiled by: $rof! Ra%see &oshi

ENPV = 10 0!" # (–10) 0!$ = Rs 2 lakh


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&enets and /i)itations of&enets and /i)itations of

tility +*eorytility +*eory


t su


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Risk $nalysis in PracticeRisk $nalysis in Practice

8ost companies in ndia account for risk hileevaluating their capital e*penditure decisions!

"he folloing factors are considered to inuencethe riskiness of investment pro%ects:price of ra material and other inputs

price of productproduct demandgovernment policiestechnological changespro%ect lifeination

6ut of these factors, four factors thought to becontributing most to the pro%ect riskiness are:selling price, product demand, technical changesand government policies!


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R- /)/=H-- ) $R/C"CE "he most commonly used methods of risk analysis in

practice are: sensitivity analysis

conservative forecasts-ensitivity analysis allos to see the impact of the

change in the behaviour of critical variables on thepro%ect pro(tability! Conservative forecasts includeusing short payback or higher discount rate fordiscounting cash os!

E*cept a very fe companies most companies do notuse the statistical and other sophisticated techni.uesfor analysing risk in investment decisions!

COMPILED BY: PROF. RAJSEE JOSHI


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"hank Hou


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Ch 12. Risk Evaluation in Capital Budgeting