Ch_12

Chapter - 12

Risk Analysis in Capital Budgeting

2Financial Management, Ninth Edition © I M PandeyVikas Publishing House Pvt. Ltd.

Chapter 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 risk analysis in capital budgeting.

Focus on the need and mechanics of sensitivity analysis and scenario 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 capital budgeting decisions.


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 is likely to occur in the future returns from the investment.

Three broad categories of the events influencing the investment forecasts: General economic conditions Industry factors Company factors


Techniques for Risk Analysis 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


Probability A typical forecast is single figure for a period. This is

referred to as “best estimate” or “most likely” 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. It is 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 probability–a probability distribution.

Probability may be described as a measure of someone’s opinion about the likelihood that an event will occur.


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 of belief of a person rather than the objective evidence of a large number of trials are called personal or subjective probabilities.


Expected Net Present Value Once the probability

assignments have been made to the future cash flows the next step is to find out the expected net present value.

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

= 0

ENPV = (1 )

n

tt

ENCF

k

ENCF = NCF × t jt jtP


Variance or Standard Deviation Simply stated,

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.

2 2

=1

(NCF) = (NCF – ENCF)n

j jj

P


Coefficient of Variation Relative Measure of Risk It is defined as the standard deviation of the

probability distribution divided by its expected value:

Expected valueCofficient of variation = CV =

Standard deviation


Coefficient of Variation The coefficient of variation is a useful

measure of risk when we are comparing the projects which have (i) same standard deviations but different expected

values, or (ii) different standard deviations but same

expected values, or (iii) different standard deviations and different

expected values.


Risk Analysis in Practice Most companies in India account for risk while evaluating their capital expenditure

decisions. The following factors are considered to influence the riskiness of investment projects:

price of raw material and other inputs price of product product demand government policies technological changes project life inflation

Out of these factors, four factors thought to be contributing most to the project riskiness are: selling price, product demand, technical changes and government policies.

The most commonly used methods of risk analysis in practice are: sensitivity analysis conservative forecasts

Sensitivity analysis allows to see the impact of the change in the behaviour of critical variables on the project profitability. Conservative forecasts include using short payback or higher discount rate for discounting cash flows.

Except a very few companies most companies do not use the statistical and other sophisticated techniques for analysing risk in investment decisions.


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.


Risk-Adjusted Discount Rate 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 investor’s attitude towards risk.

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

= 0

NCFNPV =

(1 )

nt

tt k

f rk = k + k


Evaluation of Risk-adjusted Discount Rate The following are the advantages of risk-adjusted discount

rate method: It is simple and can be easily understood. It has a great deal of intuitive appeal for risk-averse businessman. It incorporates an attitude (risk-aversion) towards uncertainty.

This approach, however, suffers from the following limitations: There is no easy way of deriving a risk-adjusted discount rate. As

discussed earlier, CAPM provides for a basis of calculating the risk-adjusted discount rate. Its use has yet to pick up in practice.

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

It is based on the assumption that investors are risk-averse. Though it is generally true, there exists a category of risk seekers who do not demand premium for assuming risks; they are willing to pay a premium to take risks.


Certainty—Equivalent Reduce the forecasts of

cash flows to some conservative levels.

The certainty—equivalent coefficient assumes a value between 0 and 1, and varies inversely with risk.

Decision-maker subjectively or objectively establishes the coefficients.

The certainty—equivalent coefficient can be determined as a relationship between the certain cash flows and the risky cash flows.

= 0

NCFNPV =

(1 )f

nt t

tt k

*NCF Certain net cash flow =

NCF Risky net cash flowt

tt


Evaluation of Certainty—Equivalent This method suffers from many dangers in a

large enterprise: First, the forecaster, expecting the reduction that

will be made in his forecasts, may inflate them in anticipation.

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

Third, by focusing explicit attention only on the gloomy outcomes, chances are increased for passing by some good investments.


Risk-adjusted Discount Rate Vs. Certainty–Equivalent The certainty—equivalent approach recognises risk in

capital budgeting analysis by adjusting estimated cash flows and employs 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 that the certainty—equivalent approach is theoretically a superior technique.

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


Sensitivity Analysis Sensitivity analysis is a way of analysing change in

the project’s NPV (or IRR) for a given change in one of the variables.

The following three steps are involved in the use of sensitivity analysis: Identification of all those variables, which have an influence

on the project’s NPV (or IRR). Definition of the underlying (mathematical) relationship

between the variables. Analysis of the impact of the change in each of the variables

on the project’s NPV. The decision maker, while performing sensitivity

analysis, computes the project’s NPV (or IRR) for each forecast under three assumptions: (a) pessimistic, (b) expected, and (c) optimistic.


DCF Break-even Analysis Sensitivity analysis is a variation of the break-even

analysis. What shall be the consequences if volume or price or

cost changes (Sensitivity analysis)? You can ask this question differently: How much lower can the sales volume become before the project becomes unprofitable? What you are asking for is the break-even point.

DCF break-even point is different from the accounting break-even point. The accounting break-even point is estimated as fixed costs divided by the contribution ratio. It does not account for the opportunity cost of capital, and fixed costs include both cash plus non-cash costs (such as depreciation).


Pros and Cons of Sensitivity Analysis

Sensitivity analysis has the following advantages: It compels the decision-maker to identify the variables, which affect

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

It indicates the critical variables for which additional information may be obtained. The decision-maker can consider actions, which may help in strengthening the ‘weak spots’ in the project.

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

It has the following limitations: It does not provide clear-cut results. The terms ‘optimistic’ and

‘pessimistic’ could mean different things to different persons in an organisation. Thus, the range of values suggested may be inconsistent.

It fails to focus on the interrelationship between variables. For example, sale volume may be related to price and cost. A price cut may lead to high sales and low operating cost.


Scenario Analysis One way to examine the risk of investment is

to analyse the impact of alternative combinations of variables, called scenarios, on the project’s NPV (or IRR).

The decision-maker can develop some plausible scenarios for this purpose. For instance, we can consider three scenarios: pessimistic, optimistic and expected.


Simulation Analysis The Monte Carlo simulation or simply the

simulation analysis considers the interactions among variables and probabilities of the change in variables. It computes the probability distribution of NPV. The simulation analysis involves the following steps: First, you should identify variables that influence cash

inflows and outflows. Second, specify the formulae that relate variables. Third, indicate the probability distribution for each variable. Fourth, develop a computer programme that randomly

selects one value from the probability distribution of each variable and uses these values to calculate the project’s NPV.


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.


Decision Trees for Sequential Investment Decisions Investment expenditures are not an

isolated period commitments, but as links in a chain of present and future commitments. An analytical technique to handle the sequential decisions is to employ decision trees.

Steps in Decision Tree Approach Define investment Identify decision alternatives Draw a decision tree

decision points chance events

Analyse data


Usefulness of Decision Tree Approach The merits of the decision tree approach are:

It clearly brings out the implicit assumptions and calculations for all to see, question and revise.

It allows a decision maker to visualise assumptions and alternatives in graphic form, which is usually much easier to understand than the more abstract, analytical form.

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

complicated as the decision maker decides to include more alternatives and more variables and to look farther and farther in time.

It is complicated even further if the analysis is extended to include interdependent alternatives and variables that are dependent upon one another.


Utility Theory and Capital Budgeting

Utility theory aims at incorporation of decision-maker’s risk preference explicitly into the decision procedure.

As regards the attitude of individual investors towards risk, they can be classified in three categories: Risk-averse Risk-neutral Risk-seeking

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


Let us assume that the owner of a firm is considering an investment project, which has 60 per cent of probability of yielding a net present value of Rs 10 lakh and 40 per cent probability of a loss of net present value of Rs 10 lakh.

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

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

ENPV = 10 × 0.6 + (–10) × 0.4 = Rs 2 lakh


Benefits and Limitations of Utility Theory It suffers from a few advantages:

First, the risk preferences of the decision-maker are directly incorporated 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 a

utility function. Second, even if the owner’s or a dominant shareholder’s

utility function be used as a guide, the derived utility function at a point of time is valid only for that one point of time.

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

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Ch_12