CAPITAL BUDGETING

CHAPTER 12 RISK ANALYSIS IN CAPITAL BUDGETING

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 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.

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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 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

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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

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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.

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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 of belief 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 Uncertainty

Risk 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 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.

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= 0

ENPV = (1 )

n

tt

ENCF

k

ENCF = NCF × t jt jtP

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

Example10

Variance or Standard Deviation 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 jj

P

Coefficient of Variation

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

Coefficient of Variation

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 TECHNIQUES OF RISK ANALYSIS

Payback Risk-adjusted discount rate Certainty equivalent

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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

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Risk Analysis in Practice

Four factors thought to be contributing most to the project 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 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.

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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 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.

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= 0

NCFNPV =

(1 )

nt

tt k

f rk = k + k

Risk-adjusted Discount Rate: Merits

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.

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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-adjusted discount rate.

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, yet 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.

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Example22

Example23

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.

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= 0

NCFNPV =

(1 )f

nt t

tt k

*NCF Certain net cash flow =

NCF Risky net cash flowt

tt

Certainty-Equivalent: Evaluation

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.

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Example26

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.

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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 decision maker, while performing sensitivity analysis, computes the project’s 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 of sensitivity analysis:

1. Identification of all those variables, which have an influence on the project’s NPV (or IRR).

2. Definition of the underlying (mathematical) relationship between the variables.

3. Analysis of the impact of the change in each of the variables on the project’s NPV.

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DCF Break-even Analysis

Sensitivity analysis is a variation of the break-even analysis.

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).

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Sensitivity Analysis: Pros and Cons 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.

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Sensitivity Analysis: Pros and ConsIt 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.

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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.

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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.

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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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Decision Trees for Sequential Investment DecisionsInvestment 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.

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Steps in Decision Tree ApproachDefine investment Identify decision alternatives Draw a decision tree

decision points chance events

Analyse data

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Usefulness of Decision Tree Approach

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

Graphic visualization: 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.

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Decision Tree Approach: Limitations 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.

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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.

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Utility Theory and Capital Budgeting

Assume that the owner of a firm is considering an investment project, which has 60 per cent 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).

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

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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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