1 Paper F9 Financial Management Cai Ji-fu Accounting School

2 Project appraisal and risk Chapter 10

3 Topic list Risk and uncertainty Sensitivity analysis Probability analysis Other risk adjustment techniques

4 Exam guide Risk and uncertainty are increasingly examinable in financial management exams and sensitivity calculations are particularly important. You need to be able to explain these techniques as well as be confident and competent with the calculations.

5 1 Risk and uncertainty Fast forward The distinction between risk and uncertainty is that risk is quantifiable, whilst uncertainty is not. Risk can be a situation where there are several possible outcomes and, on the basis of past relevant experience, probability can be assigned to the various outcomes that could prevail. Uncertainty can be a situation where there are several possible outcomes but there is little past relevant experience to enable the probability of the possible outcomes to be predicted. There are a wide range of techniques for incorporating risk into project appraisal.

6 Risk and uncertainty Distinction between the terms risk and uncertainty risk  Several possible outcomes  On basis of past relevant experience, assign probability to outcomes Uncertainty  Several possible outcomes  Little past experience, thus difficult to assign probability to outcomes

7 Risk and uncertaint y Risk may be incorporated into an appraisal by the use of: Sensitivity analysis Probability analysis Expected values and variance, or standard deviation of returns analysis Simulation Adjusted payback Risk adjusted discount rate

8 2 Sensitivity analysis Fast forward Sensitivity analysis assesses how responsive the project’s NPV is to change in the variables used to calculate that NPV. One particular to sensitivity analysis, the certainty-equivalent approach, involves the conversion of the expected cash flows of the project to riskless equivalent amounts.

9 2 Sensitivity analysis Key term Sensitivity analysis is one method of analyzing the surrounding a capital expenditure project and enable an assessment to be made of how responsive the project’s NPV is to changes in the variables that are used to calculate that NPV. Sensitivity analysis is a modeling and risk assessment procedure in which changes are made to significant variables in order to determine the effect of these changes on the planned outcome.

10 2 Sensitivity analysis The NPV could depend on a number of uncertainty independent variables Selling price Sales volume Cost of capital Initial cost Operating costs Benefits A more concise form of analysis takes each estimate in turn and assesses the percentage change required to change an investment decision.

11 2 Sensitivity analysis The formula of calculating the sensitivity of each variable: The lower the percentage, the more sensitive is NPV to that project variable as the variable would need to change by a small amount to make the project non-viable. Sensitivity to cost of capital can be determined by computing the IRR

12 2 Sensitivity analysis Weakness of this approach to sensitivity analysis The method requires that changes in each variable are isolated. However management is more interested in the combination of the effects of changes in two or more key variables. Looking at factors in isolation is unrealistic since they are often interdependent.

13 2 Sensitivity analysis Weakness of this approach to sensitivity analysis Sensitivity analysis does not examine the probability that any particular variation in costs or revenues might occur Critical factors may be those over which mangers have no control In itself it does not provides a decision rule, parameters defining acceptability must be laid down by managers

14 Sensitivity analysis Weaknesses of sensitivity analysis It assumes that changes to variable can be made independently. This is unlikely. It only identifies how far a variable needs to change, it does not look at the probability of such a change. It is not an optimizing technique. It provides information on the basis of which decisions can be made. It does not point to the correct decision directly.

15 Sensitivity analysis The certainty-equivalent approach By this method, the expected cash flows of the project are converted to riskless equivalent amount. The greater the risk of an expected cash flow, the smaller the ‘certainty-equivalent’ value (for receipt) or the larger the certainty equivalent value (for payments)

16 Sensitivity analysis Key term Certainty equivalent (CE) – the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Certainty equivalent < expected value, risk aversion is present Certainty equivalent = expected value, risk indifference is present Certainty equivalent >expected value, risk preference is present

17 3 Probability analysis Fast forward A probability analysis of expected cash flows can often be estimated and used both to calculate an expected NPV and to measure risk. The standard deviation of the NPV can be calculated to assess risk when the construction of probability distribution is complicated.

18 Probability analysis Probability distribution A set of possible values that a random variable can assume and their associated probabilities of occurrence.

19 Probability analysis The economic value of an investment is determined by: (a)the expected return on the investment (b)the variance, or standard deviation, of the return on the investment. For a given standard deviation, investors prefer higher expected returns and, for a given expected return, investors prefer lower standard deviation.

20 Probability analysis Step 1 calculate an expected value of the NPV Step 2 measure risk, for example in the following ways By calculating the worst possible outcome and its probability By calculating the probability that the project will fail to achieve a positive NPV By calculating the standard deviation of the NPV

21 Expected values An expected value is computed by multiplying the value of each possible outcome by the probability of that outcome, and summing the results. The weighted average of possible outcomes, with the weights being the probabilities of occurrence. An expected value is a ‘representative’ figures to use in project appraisals. An expected value will not in itself indicate the degree of risk involved.

22 Expected values Expected value of outcome or rate of return E(r) = expected value of outcome or rate of return r i = the ith possible outcome or rate of return P i = probability that the ith outcome or return will occur n = the number of possible outcome or rate of return

23 Example (discrete probability distributions) State of the Economy P i Investment’s Rate of Return T-Bills Corporate Bonds Stock 1 Stock 2 Deep recession Mild recession Average economy Mild boom Strong boom Expected rate of return % % 12.0% % (3.0%) % (2.0%) %

24 Graphic discrete probability distributions probability Rate of return (%) Stock 1

25 Graphic discrete probability distributions probability Rate of return (%) Stock 2

26 Normal Distribution 68.26% 0 -3σ -2σ -1σ E(r) 1σ 2σ 3σ 99.73% 95.44%

27 Normal distribution Probability Distribution $ probability 50% 5%

28 Normal distribution Probability Distribution $ probability E(r)= σ -1σ 0 1σ 2σ 95.44%

29 Risk Measurement-the standard deviation of the NPV F Variance,, is defined as follows: F Standard deviation, σ is : F Coefficient of variation, CV, is:

30 Expected value and Risk

31 ……continue Expected Rate of Return or Risk Measure Investment Alternatives T-Bills Corporate Bonds Stock 1 Stock 2 Expected rate of return[E(r)] Variance (σ 2 ) Standard deviation (SD or σ) Coefficient of variation(CV) 8.00% % % % % % % % 0.40

32 Expected values Problems with expected values An investment may be one-off, and ‘expected’ NPV may never actually occur Assigning probabilities to evens is highly subjective Expected values do not evaluate the rage of possible NPV outcomes

33 Expected values The simple expected value of decision rule is appropriate if three conditions are met or nearly met: There is a reasonable basis for making the forecasts and estimating the probability of different outcome The decision is relatively small in relation to business. Risk is then small in magnitude The decision is for a category of decisions that are often made. A technique which maximizes average payoff is then valid.

34 Expected values Key point The expected value technique is ideally suited to the sort of problem which is repetitive and involves only small amount outlays of money.

35 Expected values Advantages of expected values Recognizes that there are several possible outcomes and is, therefore, more sophisticated than single value forecasts. Enable the probability of the different outcome to be quantified. Leads directly to a simple optimizing decision rule Calculations are relatively simple.

36 Expected values Limitations of expected values By asking for a series of forecasts the whole forecasting procedure is complicated. Inaccurate forecasting is already a major weakness in project evaluation. The probabilities used are also usually very subjective. The expected value is merely a weighted average of the probability distribution, indicating the average payoff if the project is repeated is many times.

37 Expected values Limitations of expected values The expected value gives no indication of the dispersion of possible outcome about the expected value. The more widely spread out the possible results are, the more risky the investment is usually seen to be. The expected value ignores this aspect of the probability distribution. In ignoring risk, the expected value technique also ignore the investor’s attitude to risk. Some investors are more likely to take risks than others.

38 4 Simulation Fast forward Other risk adjustment techniques include the use of simulation models, adjusted payback and risk-adjusted discount rates. Simulation is a modeling technique that can incorporate many combinations of variables in producing a range of possible outcomes and their probability distribution.

39 Simulation Sensitivity analysis considered the effect of changing one variable at a time. Monte Carlo simulation allows us to consider the effect of all possible combinations of variables. Simulation allows both the expected value and the degree of dispersion to be taken into account in decision making.

40 Simulation Simulation involves the construction of a mathematical model to recreate It then possible to formulate a distribution of possible cash flows from the project from which the probability of different outcomes can be calculated.

41 Simulation the simulation process Stage1-Specify major variable Stage2-specify the relationship between variables to calculate an NPV Stage3-simulate the environment

42 Result of simulation Probability Distribution probability Expected NPV

43 Simulation Merits of simulation It includes all possible outcomes in the decision-making process It is a relatively easily understood technique It has a wide variety of applications (stock control, component replacement)

44 Simulation Drawbacks of simulation Model can become extremely complex, particularly where dependent probability are involved, and thus the time and costs involved in their construction can be more than is gained from the improved decision Probability distribution may be difficult to formulate.

45 5 Adjusted payback One way of dealing with risk to shorten the payback period required. A maximization payback period can be set to reflect the fact that the risk increases the longer the time period under consideration. The advantages of payback as an investments appraisal method mean that adjusted payback can’t be recommended as a method of adjusting for risk.

46 6 Risk-adjusted discount rates Investor want higher returns for higher risk investments. The greater the risk attached to future returns, the greater the risk premium required. Investor also prefer cash now to later and require a longer return for longer time periods. In investment appraisal, a risk-adjusted discount rate can be used for particular types or risk class of investment projects to reflect their relative risks.

47 Risk-adjusted discount rates A required return (discounted rate) that is increased relative to the firm’s overall cost of capital for projects or groups showing greater than “average” risk and decreased for projects or groups showing less than “average” risk. RAD = Rf + (Rm – Rf) × (beta) Beta represents the risk of the investment