risk analysis in capital budgeting decisions

8/6/2019 Risk Analysis in Capital Budgeting Decisions

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Common Techniques used forCommon Techniques used for

Investment EvaluationInvestment Evaluation Discounted Cash Flow TechniquesDiscounted Cash Flow Techniques

-- Net present valueNet present value

-- Internal Rate of ReturnInternal Rate of Return-- Profitability IndexProfitability Index

NonNon--Discounted Cash Flow TechniquesDiscounted Cash Flow Techniques

-- Payback PeriodPayback Period

-- Accounting Rate of ReturnAccounting Rate of Return


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Nature of RiskNature of Risk

Risk exists because of the inability of theRisk exists because of the inability of the

decisiondecision--maker to make perfect forecasts.maker to make perfect forecasts.

An investment is not risky if we can specify aAn investment is not risky if we can specify aunique sequence of cash flows for it.unique sequence of cash flows for it.

However there are always uncertainties aboutHowever there are always uncertainties about

cash flows which render risk to the capitalcash flows which render risk to the capital

investment proposals with regard to theirinvestment proposals with regard to their

acceptance.acceptance.


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Concept of ProbabilityConcept of Probability

The concept of probability is fundamental toThe concept of probability is fundamental to

the use of risk analysis techniques.the use of risk analysis techniques.

The probability estimate based on a very largeThe probability estimate based on a very largenumber of observations is known as annumber of observations is known as an

objective probability.objective probability.

The probability estimates that are dependentThe probability estimates that are dependent

on the state of belief of a person are calledon the state of belief of a person are called

subjective probabilities.subjective probabilities.


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Statistical Techniques for RiskStatistical Techniques for Risk

AnalysisAnalysis Expected Net Present Value (ENPV) = TheExpected Net Present Value (ENPV) = The

expected net present values can be found outexpected net present values can be found out

by multiplying the monetary values of theby multiplying the monetary values of thepossible events (cash flows) by theirpossible events (cash flows) by their

probabilities.probabilities.


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ENPV for a Single PeriodENPV for a Single Period

Calculate theCalculate the

ENCF for eachENCF for each

project and findproject and find

out which projectout which projectis preferable if theis preferable if the

initial outlay is Rs.initial outlay is Rs.

6500?6500?

EventEvent Project AProject A Project BProject B

CFCF ProbProb CFCF probprob

MM 45004500 0.20.2 1400014000 0.150.15

NN 52005200 0.10.1 1200012000 0.100.10

OO 67006700 0.40.4 70007000 0.500.50

PP 71007100 0.10.1 50005000 0.100.10

QQ 84008400 0.20.2 30003000 0.150.15


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Solution.Solution.

EventsEvents Project AProject A Project BProject B

MM CFCF ProbProb Exp.Exp.

ValueValue

CFCF ProbProb Exp.Exp.

ValueValue

NN 45004500 0.20.2 900900 1400014000 0.150.15 21002100

OO 52005200 0.10.1 520520 1200012000 0.100.10 12001200

PP 67006700 0.40.4 26802680 70007000 0.500.50 35003500

QQ 71007100 0.10.1 710710 50005000 0.100.10 500500

84008400 0.20.2 16801680 30003000 0.150.15 450450

ENCFENCF 64906490 77507750


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Expected NPV Multiple PeriodExpected NPV Multiple Period

A company hasA company hasdetermined thedetermined thefollowingfollowing

probabilities forprobabilities for

net cash flowsnet cash flowsfor three yearsfor three yearsgenerated by agenerated by a

project:project:


ENPV at 12%ENPV at 12%discount rate ifdiscount rate ifthe expectedthe expectedcash outflow iscash outflow is6000?6000?

Year1Year1 Year2Year2 Year3Year3

CFCF ProbProb CFCF ProbProb CFCF ProbProb

11001100 0.10.1 11001100 0.20.2 11001100 0.40.4

24002400 0.30.3 24002400 0.30.3 24002400 0.10.1

32003200 0.20.2 32003200 0.40.4 32003200 0.30.3

45004500 0.40.4 45004500 0.10.1 45004500 0.20.2


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Standard DeviationStandard Deviation the absolutethe absolute

measure of riskmeasure of risk Variance of NCF = (NCFVariance of NCF = (NCF11 ENCF)ENCF)

22 * Prob* Prob11 ++

(NCF(NCF22 ENCF)ENCF)22 * Prob* Prob22 + (NCF+ (NCFnn ENCF)ENCF)

22 **

ProbProbnn

Standard Deviation = Root of variance.Standard Deviation = Root of variance.

Coefficient of variation : it is the relativeCoefficient of variation : it is the relative

measure of risk.measure of risk.

CV = Standard Deviation / Expected Net CashCV = Standard Deviation / Expected Net Cash

Flow.Flow.


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Question???Question???


Variance, StandardVariance, Standard

Deviation andDeviation and

Coefficient ofCoefficient ofVariationVariation

EventEvent Project AProject A Project BProject B

CFCF ProbProb CFCF probprob

MM 45004500 0.20.2 1400014000 0.150.15

NN 52005200 0.10.1 1200012000 0.100.10

OO 67006700 0.40.4 70007000 0.500.50

PP 71007100 0.10.1 50005000 0.100.10

QQ 84008400 0.20.2 30003000 0.150.15


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Conventional Techniques of RiskConventional Techniques of Risk

AnalysisAnalysis

RiskRisk--adjusted discount rateadjusted discount rate

Certainty EquivalentCertainty Equivalent


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RiskRisk--adjusted Discount rateadjusted Discount rate

RiskRisk--adjusted discount rate method uses aadjusted discount rate method uses a

higher discount rate for more risky cash flowshigher discount rate for more risky cash flows

and lesser discount rate for less risky cashand lesser discount rate for less risky cash

flows.flows.

RiskRisk--adjusted discount rate = Riskadjusted discount rate = Risk--free rate +free rate +

Premium for the riskPremium for the risk


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An investment in a project will cost Rs.An investment in a project will cost Rs.

100000 initially and it is expected to generate100000 initially and it is expected to generate

cash flows in years one through four of Rs.cash flows in years one through four of Rs.

25000, 50000, 35000,and 20000. What is the25000, 50000, 35000,and 20000. What is the

projects NPV, assuming a 10% riskprojects NPV, assuming a 10% risk--free rate.free rate.

Also compute the riskAlso compute the risk--adjusted NPV if theadjusted NPV if the

discount rate is 15%.discount rate is 15%.


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Solution.Solution.

RiskRisk--free NPV = + 3970free NPV = + 3970

RiskRisk adjusted NPV =adjusted NPV = -- 59805980


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Certainty EquivalentCertainty Equivalent

Certainty Equivalent approach computes theCertainty Equivalent approach computes theNPV of the project by converting the riskyNPV of the project by converting the riskycash flows into equivalent riskcash flows into equivalent risk--free cash flowsfree cash flows

and discount them with riskand discount them with risk free rate.free rate. The certainty equivalent coefficient can beThe certainty equivalent coefficient can be

calculated as :calculated as : Certain net cash flow/Risky netCertain net cash flow/Risky net

cash flow.cash flow. The certainty equivalent coefficient is always aThe certainty equivalent coefficient is always a

value between 0 and 1.value between 0 and 1.


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Question????Question????

Riskless Enterprises is a fastRiskless Enterprises is a fastgrowing company that follows agrowing company that follows a

rather conservative approach to itsrather conservative approach to its

capital expenditure plans due tocapital expenditure plans due to

the inherent risks involved. Thethe inherent risks involved. The

firm normally does not takefirm normally does not take

capital expenditure that last morecapital expenditure that last more

than 5 years and follows a policythan 5 years and follows a policy

of converting the risky cash flowsof converting the risky cash flows

to their certainty equivalents byto their certainty equivalents by

assigning certainty equivalentassigning certainty equivalent

factors of 0.9, 0.8, 0.7, 0.6 and 0.5factors of 0.9, 0.8, 0.7, 0.6 and 0.5for the cash flows of Year 1 tofor the cash flows of Year 1 to

Year 5, respectively.Year 5, respectively.

The cost of capital is 15% whileThe cost of capital is 15% while

riskrisk--free return is 6%free return is 6%

YearYear ProjectProject

AA

Project BProject B

00 --250250 --250250

11 6060 100100

22 7070 120120

33 8080 100100

44 120120 2020

55 120120 4040


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Question contd..Question contd..

Which project should be undertaken based onWhich project should be undertaken based on

NPV rule?NPV rule?

Which project should be undertaken if C.E.Which project should be undertaken if C.E.approach is followed?approach is followed?

Which project would you recommend ifWhich project would you recommend if

(a) Shareholders are dominant(a) Shareholders are dominant (b) Debt holders are dominant.(b) Debt holders are dominant.


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Practice Question???Practice Question???

Delta corp. is considering anDelta corp. is considering aninvestment in one of the twoinvestment in one of the twomutually exclusive proposals;mutually exclusive proposals;Project A involves an initialProject A involves an initialoutlay of Rs. 1,70,000 and Projectoutlay of Rs. 1,70,000 and ProjectB Rs. 1,50,000. The C.EB Rs. 1,50,000. The C.EApproach is employed inApproach is employed inevaluating the risk associated withevaluating the risk associated withthe investments. The current yieldthe investments. The current yieldon the treasury bills is 5% . Theon the treasury bills is 5% . Theexpected values of cash inflowsexpected values of cash inflowswith their C.Es are follows:with their C.Es are follows:

Which Project should beWhich Project should beaccepted?accepted?

Which project is riskier? HowWhich project is riskier? Howdo you know?do you know?

YrsYrs Project AProject A Project BProject B

CashCash

FlowFlow

C.EC.E CashCash

FlowFlow

C.EC.E

11 9090 0.80.8 9090 0.90.9

22 100100 0.70.7 9090 0.80.8

33 110110 0.50.5 100100 0.60.6


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Scenario AnalysisScenario Analysis

Scenario Analysis measures the change inScenario Analysis measures the change in

NPV of the project under different scenariosNPV of the project under different scenarios

changing several variables at a time because ofchanging several variables at a time because of

interrelationship of variables amongstinterrelationship of variables amongst

themselvesthemselves


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Decision Tree AnalysisDecision Tree Analysis

A decision tree is a powerful tool of analyzingA decision tree is a powerful tool of analyzing

sequential decisions. It breaks up complexsequential decisions. It breaks up complex

decisions into smaller decisions and calculatedecisions into smaller decisions and calculate

the NPV backwards to arrive at the mostthe NPV backwards to arrive at the most

pragmatic decision based on maximization ofpragmatic decision based on maximization of

NPV.NPV.


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ABC computers is considering an optionABC computers is considering an option

to develop two models; Model A andto develop two models; Model A and

Model B of Laptops. Both the modelsModel B of Laptops. Both the models

are expected to be hot sellers for theare expected to be hot sellers for the

next two years.next two years.

The capital expenditure involved inThe capital expenditure involved in

Model A is 225 cr. while Model B costsModel A is 225 cr. while Model B costs

Rs. 250 cr.Rs. 250 cr.

Since Model A is an improvised versionSince Model A is an improvised version

of the existing laptop it offers a certainof the existing laptop it offers a certain

Cash Flow of Rs. 140 cr. and Rs. 180 cr.Cash Flow of Rs. 140 cr. and Rs. 180 cr.

for the next two years.for the next two years.

However in case of Model B ABC isHowever in case of Model B ABC is

not very sure of its Cash Flows.not very sure of its Cash Flows. It expects a cash inflow of Rs. 150 cr inIt expects a cash inflow of Rs. 150 cr in

the first year with 70% probability andthe first year with 70% probability and

under exceptional circumstances it mayunder exceptional circumstances it may

yield a cash flow of Rs. 180 cr.yield a cash flow of Rs. 180 cr.

The cash flows in the second year areThe cash flows in the second year are

dependent upon the outcome of thedependent upon the outcome of the

first year. If the firm gets normal cashfirst year. If the firm gets normal cash

inflow of 150 cr in the first year theinflow of 150 cr in the first year the

chances are 30% that it would repeatchances are 30% that it would repeat

the cash flows, 40% chances that itthe cash flows, 40% chances that it

might improve to 180 cr. And 30%might improve to 180 cr. And 30%

chances that it might do exceptionallychances that it might do exceptionally

well and it may increase to 220 cr.well and it may increase to 220 cr.

If the firm does exceptionally well inIf the firm does exceptionally well in

the first year then ,chances are itthe first year then ,chances are it

would have cash flows of eitherwould have cash flows of either

220cr, 230 cr, or 250 cr, with220cr, 230 cr, or 250 cr, with

probabilities of 50%, 30% and 20%probabilities of 50%, 30% and 20%

respectively.respectively.

Examine both proposals andExamine both proposals and

recommend the best one to ABCrecommend the best one to ABC

assuming a cost of capital of 12%assuming a cost of capital of 12%


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Solution.Solution.

Model AModel A Cash InflowCash Inflow Present value@Present value@12%12%

Ist YearIst Year 140.00140.00 125.00125.00

IInd YearIInd Year 180.00180.00 143.49143.49

Total Present Values of InflowsTotal Present Values of Inflows 268.49268.49

Less Initial InvestmentLess Initial Investment 225.00225.00

NPVNPV 43.4943.49


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Model BModel B

Year 1Year 1 Year 2Year 2

ProbabilityProbability Cash FlowCash Flow ProbabilityProbability Cash FlowCash Flow

0.70.7 150150 0.30.30.40.4

0.30.3

150150180180

220220

0.30.3 180180 0.50.5

0.30.3

0.20.2

220220

230230

250250


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Model B contd.Model B contd.

Present Value of Year 2 cash flows at the end of year 1Present Value of Year 2 cash flows at the end of year 1

ENCF = 0.3*150 + 0.4*180 + 0.3*220 = 183.ENCF = 0.3*150 + 0.4*180 + 0.3*220 = 183.

Present Value of ENCF @ 12% = 183*0.893 = 163.41Present Value of ENCF @ 12% = 183*0.893 = 163.41

ENCF = 0.5*220 + 0.3*230 + 0.2*250 = 229ENCF = 0.5*220 + 0.3*230 + 0.2*250 = 229 Present Value of ENCF @ 12% = 229*0.893 = 204.46Present Value of ENCF @ 12% = 229*0.893 = 204.46


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Model BModel B

Value of Cash FlowValue of Cash Flow YY ZZ

Cash Flow of Yr.1Cash Flow of Yr.1 150.00150.00 180.00180.00

PV of Cash Flow of YearPV of Cash Flow of Year22

163.39163.39 204.46204.46

Total Cash Flow at YearTotal Cash Flow at Year

11

313.39313.39 384.46384.46

Expected Cash Flow AtExpected Cash Flow AtPoint XPoint X

313.39 * 0.7 + 384.46*0.3 = 334.71313.39 * 0.7 + 384.46*0.3 = 334.71PV of 334.71 = 298.85PV of 334.71 = 298.85

ENPV = 298.85ENPV = 298.85 250 = 48.85250 = 48.85

risk analysis in capital budgeting decisions

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