fmch 12 revised

8/3/2019 FmCh 12 Revised

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CHAPTE

R 12 RISK ANALYSIS IN CAPITAL BUDGETING


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LEARNING OBJECTIVES

Discuss the concept of risk in investment decisions.

Understand some commonly used techniques, i.e., payback,certainty equivalent and risk-adjusted discount rate, of riskanalysis in capital budgeting.

Focus on the need and mechanics of sensitivity analysis andscenario analysis.

Highlight the utility and methodology simulation analysis.

Explain the decision tree approach in sequential investment

decisions.

Focus on the relationship between utility theory and capitalbudgeting decisions.

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Nature of Risk

Risk exists because of the inability of the decision-maker to make perfect forecasts.

In formal terms, the risk associated with an

investment may be defined as the variability that islikely to occur in the future returns from theinvestment.

Three broad categories of the events influencing theinvestment forecasts: General economic conditions

Industry factors

Company factors

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Techniques for RiskAnalysis

Statistical Techniques for Risk Analysis

Probability

Variance or Standard Deviation

Coefficient of Variation

Conventional Techniques of Risk Analysis

Payback

Risk-adjusted discount rate Certainty equivalent

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Probability

A typical forecast is single figure for a period. This is referred toas bestestimate or mostlikely forecast:

Firstly, we do not know the chances of this figure actually occurring, i.e.,the uncertainty surrounding this figure.

Secondly, the meaning of best estimates or most likely is not very clear. Itis not known whether it is mean, median or mode.

For these reasons, a forecaster should not give just one estimate,but a range of associated probabilitya probability distribution.

Probability may be described as a measure of someonesopinion about the likelihood that an event will occur.

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Assigning Probability

The probability estimate, which is based on a very

large number of observations, is known as an

objective probability.

Such probability assignments that reflect the state ofbelief of a person rather than the objective evidence

of a large number of trials are called personal or

subjective probabilities.

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Risk and UncertaintyRisk is referred to a situation where the probability

distribution of the cash flow of an investment

proposal is known.

If no information is available to formulate a

probability distribution of the cash flows the

situation is known as uncertainty.

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Expected Net Present Value

Once the probability assignments have been made tothe future cash flows the next step is to find out theexpected net present value.

Expected net present value = Sum of present valuesof expected net cash flows.

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= 0

ENPV =(1 )

n

t

t

ENCF

k

ENCF = NCF t jt jt P


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Example

Suppose an investment project has a life of three

years, and it would involve an initial cost of Rs

10,000.

If the discount rate is 15 per cent, calculate the

expected NPV.

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Expected Cash Flow


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Example10


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Variance or StandardDeviation Variance measures the deviation about expected cash

flow of each of the possible cash flows.

Standard deviation is the square root of variance.

Absolute Measure of Risk.

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2 2

=1

(NCF) = (NCF ENCF)n

j j

j

P


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Coefficient of variation is relative Measure of Risk.

It is defined as the standard deviation of the

probability distribution divided by its expected value:

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Expected valueCofficient of variation = CV =

Standard deviation


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The coefficient of variation is a useful measure of

risk when we are comparing the projects which have

same standard deviations but different expected values, or

different standard deviations but same expected values, or

different standard deviations and different expected values.

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CONVENTIONAL TECHNIQUESOF RISK ANALYSIS

Payback

Risk-adjusted discount rate

Certainty equivalent

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Risk Analysis in Practice

Most companies in India account for risk whileevaluating their capital expenditure decisions.

The following factors are considered to influence theriskiness of investment projects: price of raw material and other inputs

price of product

product demand

government policies

technological changes project life

inflation

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Risk Analysis in Practice

Four factors thought to be contributing most to theproject riskiness are: selling price

product demand

technical changes

government policies

Methods of risk analysis in practice are: sensitivity analysis

conservative forecasts

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Sensitivity Analysis &Conservative Forecasts

Sensitivity analysis allows to see the impact of thechange in the behaviour of critical variables on theproject profitability.

Conservative forecasts include using short paybackor higher discount rate for discounting cash flows.

Except a very few companies most companies donot use the statistical and other sophisticatedtechniques for analysing risk in investmentdecisions.

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Payback

This method, as applied in practice, is more an attempt to

allow for risk in capital budgeting decision rather than a

method to measure profitability.

The merit of payback Its simplicity.

Focusing attention on the near term future and thereby emphasising

the liquidity of the firm through recovery of capital.

Favouring short term projects over what may be riskier, longer term

projects.

Even as a method for allowing risks of time nature, it

ignores the time value of cash flows.

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Risk-Adjusted DiscountRate Risk-adjusted discount rate, will allow for both time

preference and risk preference and will be a sum of the risk-free rate and the risk-premium rate reflecting the investorsattitude towards risk.

Under CAPM, the risk-premium is the difference between themarket rate of return and the risk-free rate multiplied by thebeta of the project.

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=0

NCFNPV =

(1 )

n t

t

t k

f rk = k + k


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Risk-adjusted DiscountRate: Merits

It is simple and can be easily understood.

It has a great deal of intuitive appeal for risk-aversebusinessman.

It incorporates an attitude (risk-aversion) towardsuncertainty.

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Risk-adjusted Discount Rate:LimitationsThere is no easy way of deriving a risk-adjusted discount rate.

CAPM provides a basis of calculating the risk-adjusteddiscount rate.

It does not make any risk adjustment in the numerator for thecash flows that are forecast over the future years.

It is based on the assumption that investors are risk-averse.Though it is generally true, yet there exists a category of risk

seekers who do not demand premium for assuming risks; theyare willing to pay a premium to take risks.

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Example22


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Example23


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Certainty-Equivalent

Reduce the forecasts of cash flows to some conservativelevels.The certainty-equivalent coefficient assumes a valuebetween 0 and 1, and varies inversely with risk. Decision-maker subjectively or objectively establishes thecoefficients.

The certaintyequivalent coefficient can be determined as

a relationship between the certain cash flows and the riskycash flows.

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=0

NCFNPV =

(1 )f

nt t

tt k

*NCF Certain net cash flow=

NCF Risky net cash flow

tt

t

C i E i l


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Certainty-Equivalent:Evaluation

First, the forecaster, expecting the reduction that will bemade in his forecasts, may inflate them in anticipation.

Second, if forecasts have to pass through several layers ofmanagement, the effect may be to greatly exaggerate theoriginal forecast or to make it ultra-conservative.

Third, by focusing explicit attention only on the gloomy

outcomes, chances are increased for passing by some goodinvestments.

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Example26

Ri k dj t d Di t R t


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Risk-adjusted Discount RateVs. Certainty-Equivalent

The certainty-equivalent approach recognises risk in capitalbudgeting analysis by adjusting estimated cash flows andemploys risk-free rate to discount the adjusted cash flows.

On the other hand, the risk-adjusted discount rate adjusts for

risk by adjusting the discount rate. It has been suggested thatthe certainty-equivalent approach is theoretically a superiortechnique.

The risk-adjusted discount rate approach will yield thesame result as the certainty-equivalent approach if therisk-free rate is constant and the risk-adjusted discountrate is the same for all future periods.

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SENSITIVITY ANALYSISSensitivity analysis is a way of analysing

change in theprojects NPV (or IRR) for a givenchange in one of the variables.

The decision maker, while performing sensitivityanalysis, computes the projects NPV (or IRR)for each forecast under three assumptions: pessimistic,

expected, and optimistic.

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SENSITIVITY ANALYSIS

The following three steps are involved in the use ofsensitivity analysis:

1. Identification of all those variables, which have an

influence on the projects NPV (or IRR).2. Definition of the underlying (mathematical) relationship

between the variables.

3. Analysis of the impact of the change in each of thevariables on the projects NPV.

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DCF Break-even Analysis

Sensitivity analysis is a variation of the break-evenanalysis.

DCF break-even point is different from the accounting

break-even point. The accounting break-even point isestimated as fixed costs divided by the contribution ratio. Itdoes not account for the opportunity cost of capital, andfixed costs include both cash plus non-cash costs (such asdepreciation).

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S iti it A l i P


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Sensitivity Analysis: Prosand Cons It compels the decision-maker to identify the variables, which

affect the cash flow forecasts. This helps him in understandingthe investment project in totality.

It indicates the critical variables for which additionalinformation may be obtained. The decision-maker can consideractions, which may help in strengthening the weak spots inthe project.

It helps to expose inappropriate forecasts, and thus guides thedecision-maker to concentrate on relevant variables.

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S iti it A l i P d


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Sensitivity Analysis: Pros andConsIt does not provide clear-cut results. The terms

optimistic and pessimistic could mean differentthings to different persons in an organisation. Thus,the range of values suggested may be inconsistent.

It fails to focus on the interrelationship betweenvariables. For example, sale volume may be relatedto price and cost. A price cut may lead to high sales

and low operating cost.

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SCENARIO ANALYSISOne way to examine the risk of investment is to

analyse the impact of alternative combinations of

variables, called scenarios, on theprojects NPV (or

IRR).

The decision-maker can develop some plausible

scenarios for this purpose. For instance, we canconsider three scenarios: pessimistic, optimistic and

expected.

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SIMULATION ANALYSIS The Monte Carlo simulation or simply the simulation

analysis considers the interactions among variables andprobabilities of the change in variables. It computes theprobability distribution of NPV.

The simulation analysis involves the following steps:

First, you should identify variables that influence cash inflows andoutflows.

Second, specify the formulae that relate variables.

Third, indicate the probability distribution for each variable.

Fourth, develop a computer programme that randomly selects onevalue from the probability distribution of each variable and usesthese values to calculate theprojects NPV.

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Si l ti A l i


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Simulation Analysis:Shortcomings

The model becomes quite complex to use.

It does not indicate whether or not the project

should be accepted.

Simulation analysis, like sensitivity or scenario

analysis, considers the risk of any project in

isolation of other projects.

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D i i T f S ti l


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Decision Trees for SequentialInvestment Decisions

Investment expenditures are not an isolatedperiod commitments, but as links in a chain ofpresent and future commitments.

An analytical technique to handle the sequentialdecisions is to employ decision trees.

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Steps in Decision Tree


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Steps in Decision TreeApproach

Define investment

Identify decision alternatives

Draw a decision tree

decision points chance events

Analyse data

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Usefulness of Decision Tree


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Usefulness of Decision TreeApproach

Clarity: It clearly brings out the implicitassumptions and calculations for all to see,question and revise.

Graphic visualization: It allows a decisionmaker to visualise assumptions and alternativesin graphic form, which is usually much easier tounderstand than the more abstract, analytical

form.

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Decision Tree Approach:


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Decision Tree Approach:LimitationsThe 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.

It is complicated even further if the analysis isextended to include interdependent alternatives andvariables that are dependent upon one another.

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UTILITY THEORY AND CAPITAL


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UTILITY THEORY AND CAPITALBUDGETINGUtility theory aims at incorporation of decision-

makers risk preference explicitly into the decisionprocedure.

As regards the attitude of individual investors towardsrisk, they can be classified in three categories:Risk-averse

Risk-neutral

Risk-seeking

Individuals are generally risk averters and demonstratea decreasing marginal utility for money function.

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Utility Theory and CapitalBudgeting

Assume that the owner of a firm is considering an investmentproject, which has 60 per cent probability of yielding a net presentvalue of Rs 10 lakh and 40 per cent probability of a loss of netpresent value of Rs 10 lakh.

Project has a positive expected NPV of Rs 2 lakh. However, theowner may be risk averse, and he may consider the gain in utilityarising from the positive outcome (positive PV of Rs 10 lakh) lessthan the loss in utility as a result of the negative outcome (negativePV of Rs 10 lakh).

The owner may reject the project in spite of its positive ENPV.

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Benefits and Limitations ofUtility Theory It suffers from a few advantages:

First, the risk preferences of the decision-maker are directlyincorporated in the capital budgeting analysis.

Second, it facilitates the process of delegating the authority

for decision. It suffers from a few limitations:

First, in practice, difficulties are encountered in specifying autility function.

Second, even if the owners or a dominant shareholdersutility function be used as a guide, the derived utility functionat a point of time is valid only for that one point of time.

Third, it is quite difficult to specify the utility function if thedecision is taken by a group of persons.

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fmch 12 revised

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