Chapter 6 Project Appraisal and Risk
1. Objectives
1.1 Distinguish between risk and uncertainty in investment appraisal.
1.2 Define sensitivity analysis and discuss its usefulness in assisting investment decisions.
1.3 Apply sensitivity analysis to investment projects and explain the meaning of the findings.
1.4 Define and apply an expected value (EV) and discuss the usefulness of probability analysis in assisting investment decisions.
1.5 Discuss the use of simulation to take account of risk and uncertainty in investment appraisal.
2. Risk and Uncertainty
2.1 Investment appraisal faces the following problems:
(a) all decisions are based on forecasts;
(b) all forecasts are subject to uncertainty;
(c) this uncertainty needs to be reflected in the financial evaluation.
2.2 The decision maker must distinguish between:
(a) Risk – can be quantifiable and be applied to a situation where there are several possible outcomes and, on the basis of past relevant experience, probabilities can be assigned to the various outcomes that could prevail.
(b) Uncertainty – is unquantifiable and can be applied to a situation where there are several possible outcomes but there is little past experience to enable the probability of the possible outcomes to be predicted.
2.3 In investment appraisal the areas of concern are therefore the accuracy of the estimates concerning:
(a) Project life
(b) Predicted cash flows and associated probabilities
(c) Discount rate used
3. Sensitivity Analysis
3.1 Sensitivity analysis typically involves posing “what if?” questions. For example, what if demand fell by 10% compared to our original forecasts? Would the project still be viable?
3.2 In project appraisal, sensitivity analysis assesses how responsive the project’s NPV is to changes in the variables used to calculate that NPV.
3.3 The NPV could depend on a number of uncertain independent variables.
(a) Selling price
(b) Sales volume
(c) Cost of capital
(d) Initial cost
(e) Operating costs
(f) Benefits
3.4 Sensitivity analysis therefore provides an indication of why a project might fail. Management should review critical variables to assess whether or not there is a strong possibility of events occurring which will lead to a negative NPV. Management should also pay particular attention to controlling those variables to which the NPV is particularly sensitive, once the decision has been taken to accept the investment.
3.5 A simple approach to deciding which variables the NPV is particularly sensitive to is to calculate the sensitivity of each variable:
Sensitivity 
= 
NPV 
% 
PV of project variable 
3.6 The lower the percentage, the more sensitive is NPV to that project variable as the variable would need to change by a smaller amount to make the project nonviable.
3.7 
EXAMPLE 1 


ABC Co is considering a project with the following cash flows.
Cash flows arise from selling 650,000 units at $10 per unit. ABC Co has a cost of capital of 8%. Required: Measure the sensitivity of the project to changes in variables. Solution: The PVs of the cash flow are as follows.
NPV = 1,024 The project has a positive NPV and would appear to be worthwhile. The sensitivity of each project variable is as follows. (a) Initial investment (b) Sales volume (c) Selling price (d) Variable costs (e) Cost of capital. We need to calculate the IRR of the project.
IRR = 0.15 + = 18.56% The elements to which the NPV appears to be most sensitive are the selling price followed by the sales volume. Management should thus pay particular attention to these factors so that they can be carefully monitored. 
3.8 Strengths and weaknesses of sensitivity analysis
Strengths 
Weaknesses 
(a) No complicated theory to understand. 
(a) It assumes that changes to variables can be made independently, e.g. material prices will change independently of other variables. This is unlikely. If material prices went up the firm would probably increase selling price at the same time and there would be little effect on NPV. A technique called simulation (see later) allows us to change more than one variable at a time. 
4. Expected Value (EV)
4.1 When there are a number of possible outcomes for a decision and probabilities can be assigned to each, then an EV may be calculated.
4.2 
CONCEPT 

The EV is the weighted average of all possible outcomes, with the weightings based on the probability estimates. The formula for calculating an EV is: EV = 
4.3 
EXAMPLE 2 


A firm has to choose between three mutually exclusive, the outcomes of which depend on the state of the economy. The following estimates have been made:
Determine which project should be selected on the basis of expected market values. Solution: Project A
Project B
Project C
On the basis of expected values, Project A should be selected. 
4.4 
EXAMPLE 3 


ABC Co is considering an investment of $460,000 in a noncurrent asset expected to generate substantial cash inflows over the next five years. Unfortunately the annual cash flows from this investment are uncertain, but the following probability distribution has been established:
At the end of its fiveyear life, the asset is expected to sell for $40,000. The cost of capital is 5%. Should the investment be undertaken? Solution: Expected annual cash flows are:
NPV calculation:
As the ENPV is negative, the project should not be undertaken. An alternative approach would be to calculate three separate NPVs and then combine them, giving the following figures:
ENPV = 0.3 x (212,190) + 0.5 x 4,260 + 0.2 x 220,710 = (17,385) Even though the ENPV is negative these figures show that there is a 70% chance of the project giving a positive NPV. Some investors may consider the project acceptable on this basis. 
4.5 
Test your understanding 1 


A company is considering whether to invest in equipment for providing a new service to its clients. The equipment will cost $100,000 and will have a disposal value of $20,000 after four years. Estimates of sales and incremental fixed cost cash expenditures are as follows.
The company expects to achieve a contribution/sales ratio of 40% on all the services it provides. Incremental fixed costs will be $215,000 per annum. The project has a fouryear life. The company’s cost of capital is 9%. Calculate the three possible NPVs an the expected NPV. Comment on your results. 
4.6 
EXAMPLE 4 


A company is considering a project involving the outlay of $300,000 which it estimates will generate cash flows over its two year life at the probabilities shown in the following table.
Year 2
The company’s investment criterion for this type of project is 10% DCF. You are required to calculate the expected value of the project’s NPV and the probability that the NPV will be negative. Solution: Calculate expected value of the NPV.
Measure risk. 
(A) The standard deviation of the NPV
4.7 The disadvantage of using the EV of NPV approach to assess the risk of the project is that the construction of the probability distribution can become very complicated. If we were considering a project over 4 years, each year have five different forecasted cash flows, there would be 625 (54) NPVs to calculate. To avoid all of these calculations, an indication of the risk may be obtained by calculating the standard deviation of the NPV.
4.8 
EXAMPLE 5 


Frame Co is considering which of two mutually exclusive projects, A or B, to undertake. There is some uncertainty about the running costs with each project, and a probability distribution of the NPV for each project has been estimated, as follows.
You are required to decide which project should the company choose, if either. Solution: We can begin by calculating the EV of the NPV for each project.
Project A has a higher EV of NPV, but what about the risk of variation in the NPV above or below the EV? This can be measured by the standard deviation of the NPV. The standard deviation of a project’s NPVs, can be calculated as:
Although Project A has a higher EV of NPV, it also has a higher standard deviation of NPV, and so has greater risk associated with it. Which project should be selected? Clearly it depends on the attitude of the company’s management to risk. 
4.9 Advantages and limitation of expected values
Advantages 
Limitations 
(a) The technique recognises that there are several possible outcomes and is, therefore, more sophisticated than single value forecasts. 
(a) 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. 
5. Simulation (模擬)
5.1 Sensitivity analysis considered the effect of changing one variable at a time. Simulation improves on this by looking at the impact of many variables changing at the same time.
5.2 Using mathematical, it produces a distribution of the possible outcomes from the project. The probability of different outcomes can then be calculated.
5.3 
EXAMPLE 6 


The following probability estimates have been prepared for a proposed project.
The cost of capital is 12%. Assess how a simulation model might be used to assess the project’s NPV. Solution: A simulation model could be constructed by assigning a range of random number digits to each possible value for each of the uncertain variables. The random numbers must exactly match their respective probabilities. This is achieved by working upwards cumulatively from the lowest to the highest cash flow values and assigning numbers that will correspond to probability groupings as follows.
* Probability is 0.15 (15%). Random numbers are 15% of range 00 – 99. For revenue, the selection of a random number in the range 00 and 14 has a probability of 0.15. This probability represents revenue of $40,000. Numbers have been assigned to cash flows so that when numbers are selected at random, the cash flows have exactly the same probability of being selected as is indicated in their respective probability distribution above. Random numbers would be generated, for example by a computer program, and these would be used to assign values to each of the uncertain variables. For example, if random numbers 378420015689 were generated, the values assigned to the variables would be as follows.
A computer would calculate the NPV many times over using the values established in this way with more random numbers, and the results would be analysed to provide the following. (a) An expected value for the project. The decision whether to go ahead with the project would then be made on the basis of expected return and risk. 
5.4 Advantages and drawbacks of simulation
Advantages 
Drawbacks 
(a) It includes all possible outcomes in the decisionmaking process. 
(a) Models can become extremely complex and the time and costs involved in their construction can be more than is gained from the improved decisions. 
Examination Style Questions
Question 1 – NPV and Sensitivity Analysis
Betula Co has recently acquired a patent, at a cost of $1·3 million, which would allow it to manufacture and sell a product for measuring an individual’s biorhythms. The marketing department of Betula Co estimates that 300,000 units of this product can be sold during each of the next four years. The selling price of the product is $24 and variable costs are estimated to be $18 per product. Fixed costs (excluding depreciation) are estimated to be $2·2 million per year. This figure consists of $1·4 million additional fixed costs and $0·8 million existing fixed costs that are to be apportioned to the new product.
To manufacture the new product, equipment costing $1·5 million will be acquired immediately. The estimated residual value of this equipment in four years’ time is $0·5 million. The company calculates depreciation on a straightline basis.
The cost of capital of Betula Co is 9%.
Betula is currently considering whether to go ahead with the project.
Required:
(a) Calculate the net present value of the decision to go ahead with the project.
(5 marks)
(b) Undertake sensitivity analysis to show the change needed to each of the following before a zero NPV is achieved:
(i) discount rate;
(ii) initial outlay on equipment;
(iii) net annual operating cash flows;
(iv) residual value of the equipment.
(11 marks)
(c) Evaluate briefly the information produced in your answer to (a) and (b) above and state, with reasons, whether or not the project should go ahead. (4 marks)
(Total 20 marks)
Question 2 – Expected value and Working Capital Management
ZSE Co is concerned about exceeding its overdraft limit of $2 million in the next two periods. It has been experiencing considerable volatility in cash flows in recent periods because of trading difficulties experienced by its customers, who have often settled their accounts after the agreed credit period of 60 days. ZSE has also experienced an increase in bad debts due to a small number of customers going into liquidation.
The company has prepared the following forecasts of net cash flows for the next two periods, together with their associated probabilities, in an attempt to anticipate liquidity and financing problems. These probabilities have been produced by a computer model which simulates a number of possible future economic scenarios. The computer model has been built with the aid of a firm of financial consultants.
Period 1 cash flow 
Probability 
Period 2 cash flow 
Probability 
$000 

$000 

8,000 
10% 
7,000 
30% 
4,000 
60% 
3,000 
50% 
(2,000) 
30% 
(9,000) 
20% 
ZSE Co expects to be overdrawn at the start of period 1 by $500,000.
Required:
(a) Calculate the following values:
(i) the expected value of the period 1 closing balance;
(ii) the expected value of the period 2 closing balance;
(iii) the probability of a negative cash balance at the end of period 2;
(iv) the probability of exceeding the overdraft limit at the end of period 2.
Discuss whether the above analysis can assist the company in managing its cash flows. (13 marks)
(b) Identify and discuss the factors to be considered in formulating a trade receivables management policy for ZSE Co. (8 marks)
(c) Discuss whether profitability or liquidity is the primary objective of working capital management. (4 marks)
(Total 25 marks)
(ACCA F9 Financial Management June 2010 Q1)
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