ACCA paper f9 financial management study materials F9FM session07 d08

SESSION 07 – PROJECT APPRAISAL UNDER RISK OVERVIEW Objective To appraise investment projects where the outcome is not certain Definitions Sources of risk RISK AND UNCERTAINTY REDUCTION OF RISK SENSITIVITY ANALYSIS SIMULATION STATISTICAL MEASURES Definition Method Advantages Limitations Use Stages Advantages Limitations Expected values Standard deviation 0701 SESSION 07 – PROJECT APPRAISAL UNDER RISK RISK AND UNCERTAINTY 1.1 Definition 1.1.1 Risk A condition in which several possible outcomes exist, the probabilities of which can be quantified from historical data 1.1.2 Uncertainty The inability to predict possible outcomes due to a lack of historical data being available for quantification 1.2 Sources of risk in projects The major risks to the success of an investment project will be the variability of the future cash flows This could be the variability of income streams or the variability of cost cash flows or a combination of both SENSITIVITY ANALYSIS Definition The analysis of changes made to significant variables in order to determine their effect on a planned course of action The cash flows, probabilities, or cost of capital are varied until the decision changes, i.e the NPV becomes zero This will show the sensitivity of the decision to changes in those elements Therefore the estimation of IRR is an example if sensitivity analysis, in this case on the cost of capital Sensitivity analysis can also be referred to as “what if?” analysis 2.1 Method Step Calculate the NPV of the project on the basis of best estimates Step For each element of the decision (cash flows, cost of capital) calculate the change necessary for the NPV to fall to zero The sensitivity can be expressed as a % change For an individual cash flow in the computation 0702 SESSION 07 – PROJECT APPRAISAL UNDER RISK Sensitivity = NPV × 100% PV of flow considered Commentary For change in sales volume, the factor to consider is contribution This may involve combining a number of flows Example Williams has just set up a company, JPR Manufacturing Ltd, and estimates its cost of capital to be 15% His first project involves investing in $150,000 of equipment with a life of 15 years and a final scrap value of $15,000 The equipment will be used to produce 15,000 deluxe pairs of rugby boots per annum generating a contribution of $2.75 per pair He estimates that annual fixed costs will be $15,000 per annum Required: (a) Determine, on the basis of the above figures, whether the project is worthwhile (b) Calculate what percentage changes in the factors would cause your decision in (a) change (i) (ii) (iii) (iv) (v) initial investment volume fixed costs scrap value cost of capital Comment on your results Ignore tax 0703 SESSION 07 – PROJECT APPRAISAL UNDER RISK Solution (a) Time − 15 − 15 15 Initial cost Contribution Fixed costs Scrap value Cash flow $ DF @ 15% PV $ _ _ (b) The sensitivity of the decision in (a) can be calculated by expressing the NPV as a percentage of the various factors (i) Initial investment Sensitivity = (ii) Volume The PV figure of contribution is directly proportional to volume Sensitivity = (iii) Fixed costs Sensitivity = (iv) Scrap value Sensitivity = (v) Sensitivity to cost of capital This can be found by calculating the project’s IRR: Year 1-15 15 NPV 0704 Cash flow $ (150,000) 26,250 15,000 factor Present value $ _ _ SESSION 07 – PROJECT APPRAISAL UNDER RISK IRR = r1 + NPV1 (r2 − r1 ) NPV1 − NPV2 = 2.2 Advantages of sensitivity analysis It gives an idea of how sensitive the project is to changes in any of the original estimates It directs management attention to checking the quality of data for the most sensitive variables It identifies the Critical Success Factors for the project and directs project management It can be easily adapted for use in spreadsheet packages 2.3 Limitations Although it can be adapted to deal with multi-variable changes, sensitivity is normally only used to examine what happens when one variable changes and others remain constant Assumes data for all other variables is accurate Without a computer it can be time-consuming Probability of changes is not considered SIMULATION 3.1 Use of simulation Simulation is a technique which allows more than one variable to change at the same time One example of simulation is the “Monte Carlo” method Calculations will not be required in the exam, an awareness of the stages is sufficient 3.2 Stages in a Monte Carlo simulation (1) Specify the major variables (2) Specify the relationship between the variables (3) Attach probability distributions to each variable and assign random numbers to reflect the distribution (4) Simulate the environment by generating random numbers 0705 SESSION 07 – PROJECT APPRAISAL UNDER RISK (5) Record the outcome of each simulation (6) Repeat simulation many times to obtain a probability distribution of the likely outcomes 3.3 Advantages It gives more information about the possible outcomes and their relative probabilities It is useful for problems which cannot be solved analytically 3.4 Limitations It is not a technique for making a decision, only for obtaining more information about the possible outcomes It can be very time-consuming without a computer It could prove expensive in designing and running the simulation, even on a computer Simulations are only as good as the probabilities, assumptions and estimates made STATISTICAL MEASURES 4.1 Expected values The quantitative result of weighting uncertain events by the probability of their occurrence 4.1.1 Calculation Expected value = weighted arithmetic mean of possible outcomes = x p(x) ∑ Where x = value of an outcome, p(x) = probability of that outcome , ∑ = sum Example State of market Probability Project Project Project Diminishing 0.4 100 180 Static 0.3 200 500 190 Expanding 0.3 1,000 600 200 Figures represent the net present value of projects under each market state in $m Required: Determine which is the best project based on expected values 0706 SESSION 07 – PROJECT APPRAISAL UNDER RISK Solution Project Expected value = Project Expected value = Project Expected value = The best project based on expected values is 4.1.2 Advantages It reduces the information to one number for each choice The idea of an average is readily understood 4.1.3 Limitations The probabilities of the different possible outcomes may be difficult to estimate The average may not correspond to any of the possible outcomes Unless the same decision has to be made many times, the average will not be achieved; it is therefore not a valid way of making a decision in “one-off” situations The average gives no indication of the spread of possible results, i.e it ignores risk 4.2 Standard deviation A measure of variation of numerical values from a mean value A measure of spread i.e it indicates the likely level of variation from an expected value Exam questions are more likely to provide standard deviation for interpretation, rather than to require its calculation 4.2.1 Calculation σ = standard deviation = x = each observation x = mean of observations Prob (x) = probability of each observation ∑ (x − x ) prob ( x ) Note that variance = σ2 0707 SESSION 07 – PROJECT APPRAISAL UNDER RISK Example Using the information from Example 2, calculate the standard deviation for each project Solution Project Project Project 4.2.2 Advantages It gives an idea of the spread of possible results around the average It can be used in further mathematical analysis, in particularly using Normal Distributions.” 4.2.3 Limitations The calculation of standard deviation can be difficult The exact meaning is not widely understood by non-financial managers REDUCTION OF RISK Ways of reducing project risk: Setting a maximum payback period Use of a higher discount rate − therefore reducing the influence of distant cash flows Select projects with a combination of low standard deviation and acceptable average predicted outcome More effort directed to Critical Success Factors indicated by sensitivity analysis 0708 SESSION 07 – PROJECT APPRAISAL UNDER RISK Key points Exam calculations on project risk are likely to focus on sensitivity analysis i.e finding the value of key variables at which NPV = Adjusting the discount rate to reflect a project’s risk is dealt with later in the session on the Capital Asset Pricing Model (CAPM) FOCUS You should now be able to: distinguish between risk and uncertainty; evaluate the sensitivity of project NPV to changes in key variables; explain the role of simulation in generating a probability distribution for the NPV of a project; apply the probability approach to calculating expected NPV of a project and the associated standard deviation 0709 SESSION 07 – PROJECT APPRAISAL UNDER RISK EXAMPLE SOLUTIONS Solution — Sensitivity analysis (a) Time − 15 − 15 15 Initial cost Contribution Fixed costs Scrap value Cash flow $ (150,000) 41,250 (15,000) 15,000 DF @ 15% 5.847 5.847 0.123 PV $ (150,000) 241,189 (87,705) 1,845 _ 5,329 _ The project is worthwhile as NPV is positive (b) The sensitivity of the decision in (a) can be calculated by expressing the NPV as a percentage of the various factors (i) Initial investment If the initial investment rises by more than $5,329, the project would be rejected Sensitivity = 5,329 × 100 = 3.6% 150 ,000 (ii) Volume The PV figure of contribution $241,189 is directly proportional to volume If this PV is reduced by more than $5,329, the project would be rejected Sensitivity = ,329 × 100 = 2.2% 241,189 (iii) Fixed costs Sensitivity = 0710 5,329 × 100 = 6.1% 87 ,705 SESSION 07 – PROJECT APPRAISAL UNDER RISK (iv) Scrap value Sensitivity = ,329 × 100 = 289% 1,845 From the above calculations the decision to accept the project is extremely sensitive to most of the figures given in the question The project will be rejected in the event of small rises in the initial investment or fixed cost figures or falls in contribution or volume It could be seen, for instance, that the project just breaks even if fixed costs become $15,000 × 1.06 = $15,900 The scrap value is relatively irrelevant to the investment decision – we would have to pay to have the plant taken away before the project would be rejected (v) Sensitivity to cost of capital This can be found by calculating the project’s IRR, which is probably only marginally above 15% Year Cash flow $ (150,000) 26,250 15,000 1-15 15 16% factor 5.575 0.108 Present value $ (150,000) 146,344 1,620 _ NPV at 16% IRR = r1 + (2,036) _ NPV1 (r − r ) NPV1 − NPV2 = 15% + 5,329 (16% − 15%) 5,329 + 2,036 = 15.7% If the cost of capital rises from 15% to more than 15.7% the project would be rejected Solution — Expected values Project Expected value = 100 × 0.4 + 200 × 0.3 + 1,000 × 0.3 = 400 Project Expected value = × 0.4 + 500 × 0.3 + 600 × 0.3 = 330 Project Expected value = 180 × 0.4 + 190 × 0.3 + 200 × 0.3 = 189 Therefore, based on expected values, Project should be adopted 0711 SESSION 07 – PROJECT APPRAISAL UNDER RISK Solution — Standard deviation Project ( 100 − 400 ) × 0.4 + (200 − 400) × 0.3 + (1,000 − 400) × = Project ( − 330 )2 × 0.4 + (500 − 330)2 × 0.3 + (600 − 330) × 0.2 = Project 74 ,100 = 272 ( 180 − 189 ) × 0.4 + (190 − 189) × 0.3 + (200 − 189)2 × 0.3 = 0712 156,000 = 395 69 = 8.3 ... estimates It directs management attention to checking the quality of data for the most sensitive variables It identifies the Critical Success Factors for the project and directs project management It... calculation of standard deviation can be difficult The exact meaning is not widely understood by non -financial managers REDUCTION OF RISK Ways of reducing project risk: Setting a maximum payback period