1. Risk Analysis in Capital Budgeting

2. Nature of Risk Risk exists because of the inability of the decision-maker to make perfect forecasts. the risk associated with an investment may be defined as –the variability that is likely to occur in the future returns from the investment.

3. Nature of Risk Three broad categories of the events influencing the investment forecasts: –General economic conditions –Industry factors –Company factors

4. 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

5. Probability Probability may be described as a measure of someone’s opinion about the likelihood that an event will occur. A typical forecast is single figure for a period. This is referred to as “best estimate” or “most likely” forecast:

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

7. 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.

8. 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.

9. 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.

10. Coefficient of Variation It is defined as the standard deviation of the probability distribution divided by its expected value:

11. Risk Analysis in Practice Companies in India account for risk while evaluating their capital expenditure decisions. The following factors are considered –price of raw material and other inputs –price of product –product demand –government policies –technological changes –project life –inflation

12. Risk Analysis in Practice The most commonly used methods of risk analysis in practice are: –sensitivity analysis –conservative forecasts Sensitivity analysis 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.

13. Payback This method 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 recovery of capital. –Favouring short term projects over what may be riskier, longer term projects.

14. 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.

15. 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.

16. Evaluation of Risk-adjusted Discount Rate This approach suffers from the following limitations: –There is no easy way of deriving a 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.

17. Certainty—Equivalent Reduce the forecasts of cash flows to some conservative levels. The certainty— equivalent coefficient can be determined as a relationship between the certain cash flows and the risky cash flows.

18. Evaluation of Certainty— Equivalent This method suffers from many dangers – forecasts have to pass through several layers of management, the effect may make it ultra-conservative. –by focusing explicit attention only on the gloomy outcomes, chances are increased for passing by some good investments.

19. Risk-adjusted Discount Rate Vs. Certainty–Equivalent The certainty—equivalent approach recognises risk in capital budgeting analysis by adjusting estimated cash flows the risk-adjusted discount rate adjusts for risk by adjusting the discount rate.

20. 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.

21. Sensitivity Analysis 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.

22. Sensitivity Analysis The decision maker, while performing sensitivity analysis, computes the project’s NPV (or IRR) for each forecast under three assumptions: –pessimistic, –expected, and –optimistic.

23. 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.

24. Decision Trees for Sequential Investment Decisions Steps in Decision Tree Approach –Define investment –Identify decision alternatives –Draw a decision tree decision points chance events –Analyse data

25. 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.

26. Usefulness of Decision Tree Approach The demerits of the decision tree approach are: –The decision tree diagrams can become more and more complicated to include more alternatives and more variables –It is complicated even further if the analysis is extended to include interdependent alternatives and variables that are dependent upon one another.