ACCA F5 Performance Management - 2010 - Study text

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Paper F5

Performancemanagement

CHAPTER

Decision-making with risk

and uncertainty

Contents

1 Risk and uncertainty

2 Using probabilities: expected values and

simulation

3 Sensitivity analysis

4 Maximax, maximin and minimax regret

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Risk and uncertainty

 The nature of risk and uncertainty

 Reducing uncertainty

 Dealing with risk and uncertainty in decision-making

 Risk preference

1 Risk and uncertainty

1.1 The nature of risk and uncertainty

A lot of decision-making in business involves some risk or uncertainty. Decisions

might be based on what the decision-maker thinks will happen, but there is some

possibility that the actual outcome will be different – possibly better or possibly

worse than expected.

 Uncertainty occurs when there is insufficient information about what will

happen, or what will probably happen, in the future. It is therefore likely that

estimates of future values (estimates of future sales, future costs, and so on) will

be inaccurate.

 Risk occurs when the future outcome from a decision could be any of several

different possibilities. However, it might be possible to assess with reasonable

accuracy the probability of each possible outcome. When there are reliable

estimates of the probability for each possible outcome, risk can be assessed or

analysed statistically.

1.2 Reducing uncertainty

Uncertainty occurs when there is a lack of reliable information. It can therefore be

reduced by obtaining more information on which some reliance can be placed.

However, it is doubtful whether uncertainty can be eliminated altogether.

There is often uncertainty about the likely volume of sales demand for a product.

 For established products, it might be possible to estimate future sales by taking

historical sales figures, and making adjustments for sales growth or decline, and

planned changes is the sales price.

 For new products, however, estimating sales demand can be very difficult

because there is no benchmark on which to base the estimate.

Uncertainty about future sales demand for a product can be reduced through the

use of market research or focus groups.

Market research is research into a particular market, such as the market for a

product, for the purpose of obtaining information about the market – such as

attitudes and buying intentions of customers in the market.

 Market research might be carried out, for example, to test the attitudes of target

customers to a prototype of a new product.

Chapter 6: Decision making with risk and uncertainty

 In some cases, market research might attempt to obtain an estimate of the likely

sales demand for a product.

A focus group is a group of participants who are invited to give their views,

opinions and ideas about a product or market to a market research team. The

members of a focus group will be selected so as to represent a target audience or

target market, and the information provided by the group will therefore be

representative of the views of the target market as a whole.

By analysing data obtained from market research surveys or focus groups, an entity

might expect to obtain more reliable estimates of the likely sales demand for a

product.

1.3 Dealing with risk and uncertainty in decision-making

When there is uncertainty or risk in a business decision, management should

consider both:

 the expected incremental costs, revenues and profits, and also

 the risk or uncertainty.

There are several different ways of allowing for risk and uncertainty in decision-

making. The approach taken by management will depend to a large extent on their

attitude to risk. In other words, to what extent will a management decision be

affected by the risk or uncertainty in the situation?

Risk cannot be removed from a decision, because risk exists in the situation itself. A

decision-maker can try to analyse the risk, and must make a decision on the basis of

whether the risk is justified or acceptable.

1.4 Risk preference

Risk preference describes the attitude of a decision-maker towards risk. Decision-

makers might be described as risk averse, risk-seeking or possibly risk neutral.

 A risk averse decision maker considers risk in making a decision, and will not

select a course of action that is more risky unless the expected return is higher

and so justifies the extra risk. A risk-averse decision maker does not try to avoid

risk as much as possible; however he might want a substantially higher expected

return to make any extra risk worth taking.

 A risk neutral decision maker ignores risk entirely in making a decision. The

decision of a risk neutral decision maker is to select the course of action with the

highest expected return, regardless of risk.

 A risk-seeking decision maker also considers risk in making a decision. A risk

seeker, unlike a risk-averse decision-maker, will take extra risks in the hope of

earning a higher return.

It is often assumed that managers are risk averse, and so will not select a course of

action that has higher risk unless it offers a higher expected return sufficient to

justify the risk that is taken.

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Using probabilities: expected values and simulation

 Expected values

 Simulation

2 Using probabilities: expected values and simulation

2.1 Expected values

One technique for comparing risk and return of different decision options is the use

of expected values.

Expected values can be used to analyse information where risk can be assessed in

terms of probabilities of different outcomes. Where probabilities are assigned to

different outcomes, we can evaluate the worth of a decision as the expected value or

weighted average of these outcomes.

Expected value (EV) = weighted average of possible outcomes.

The weighted average value is calculated by applying the probability of each

possible outcome to the value of the outcome.

EV = ∑px

Where

p = the probability of each outcome and

x = the value of each outcome

An EV is a measurement of weighted average value.

A decision might be based on selecting the course of action that offers the highest

EV of profit, or the lowest EV of cost. In other words, the ‘decision rule’ is to select

the course of action with the highest EV of profit or the lowest EV of cost.

The main advantage of using EVs to make a decision is that it takes into

consideration the probability or likelihood of each different possible outcome, as

well as its value (profit or cost)

Example

A business entity has to decide which of three projects to select for investment. The

three projects are mutually exclusive, and only one of them can be selected. The

projects do not involve any initial capital expenditures.

Chapter 6: Decision making with risk and uncertainty

The expected annual profits from investing in each of the projects will depend on

the state of the market. The following estimates of annual profits (operational cash

flows) have been prepared:

State of market Declining

Static

Expanding

Probability 0.4

0.3

$000

Project 1 100

200

900

Project 2 0

500

600

Project 3 180

190

200

(Note: This type of table is called a ‘pay-off table’ or a ‘pay-off matrix’. It shows all

the possible ‘pay-offs’ or results – NPV, profit and so on – from different possible

decisions or strategies).

Required

Identify which project would be selected if the decision is to choose the project with

the highest expected value of annual profit.

Answer

For each project we can calculate the EV of annual profits.

State of market Probability Project 1 Project 2 Project 3

Profit

EV of

profit

Profit

EV of

profit

Profit EV of

profit

$000

$000 $000 $000

Declining 0.4 100

0 180 72

Static 0.3 200

500

150 190 57

Expanding 0.3 900

270

600

180 200 60

370

330 189

Based on expected values, project 1 should be selected because it has the highest EV

of annual profit.

Advantages of using expected values

Using EVs to make a decision has some advantages.

 An EV is a weighted average value, that is based on all the different possible

outcomes and the probability that each will occur.

 It recognises the risk in decisions, based on the probabilities of different possible

results or outcomes.

 It expresses risk in a single figure, which makes it easy to compare different

options and reach a decision.

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Disadvantages of using expected values

Using EVs to make a decision also has some serious disadvantages.

 The probabilities of the different possible outcomes may be difficult to estimate.

If the probabilities are unreliable, expected values will also be unreliable.

 The EV is unlikely to be an actual outcome that could occur. In the example

above, the EVs for projects 1, 2 and 3 ($370,000, $330,000 and $189,000

respectively) are not expected to occur. They are simply weighted average

values.

 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 about the future

when the outcome will happen only once.

 An EV is an average value. It gives no indication of the range or spread of

possible outcomes. It is therefore an inadequate measurement of risk.

 Expected values might be used by a risk-averse decision-maker, but would not

be used by a risk-seeking decision-maker.

Example

Expected values should be reliable for decision-making when:

 Probabilities can be estimated with reasonable accuracy, and

 The outcome from the decision will happen may times, and will not be a ‘one-off’

event.

The following example illustrates this.

A company manufactures Product K. At the moment, when customers complain

that there is one or more defects in the product they have bought, the company

repairs the product, at its own cost. Management is now considering a new policy,

whereby the company will accept no liability at all for any defects in the product,

but will reduce the sales price by $6 per unit.

The estimates of defects in each product, and the costs of repairing each defect, have

been estimated from historical records as follows.

Number of defects

per product

Probability

Cost of repairing

one defect

Probability

0 0.99 20 0.2

1 0.07 30 0.5

2 0.02 40 0.3

3 0.01

The company makes and sells 10,000 units of Product K each month.

Would it be cheaper to continue repairing faulty products, or would it be more

profitable to reduce the sales price by $6 per unit for all units of the product?

Chapter 6: Decision making with risk and uncertainty

Answer

We can calculate the EV of repair costs each month.

Number of

defects per

product

Probability

EV of

defects

per

product

Cost of

repairing

one defect

Probability

EV of cost

of repair per

defect

$ $

0 0.99 0.00 20 0.2 4.0

1 0.07 0.07 30 0.5 15.0

2 0.02 0.04 40 0.3 12.0

3 0.01 0.03 31.0

0.14

The EV of the cost of repairs per unit produced is therefore 0.14 × $31 = $4.34.

The average total cost per month of repairs, given production and sales of 10,000

units, is therefore 10,000 × $4.34 = $43,400.

This is less than the cost of reducing the sales price by $6 ($60,000 per month).

On the basis of cost and profit, the decision should therefore be to continue

repairing defects, because this will be less costly by $16,600 per month.

Analysing the expected value

In this example, the estimate of monthly repair costs using an EV is likely to be very

reliable, since the probabilities are based on historical records and the outcome

happens many times over (10,000 times each month).

The EV is simply a weighted average cost that reflects the following probability

distribution of possible outcomes. A slightly simplified probability distribution is as

follows.

Defects

per

product

Probability

Cost of

repair

Probability

Joint

probability

Total cost

of repairs

EV of

repair

cost

$ $ $

0 0.99 0 1.00 0.990 0.0 0.00

1 0.07 20 0.20 0.014 20.0 0.28

30 0.50 0.035 30.0 1.05

40 0.30 0.021 40.0 0.84

2 0.02 20 0.20 0.004 40.0 0.16

30 0.50 0.010 60.0 0.60

40 0.30 0.006 80.0 0.48

3 0.01 20 0.20 0.002 60.0 0.12

30 0.50 0.005 90.0 0.45

40 0.30 0.003 120.0 0.36

EV of repair cost per unit 4.34

Paper F5: Performance management

The EV of cost represents a wide range of possible outcomes, from a 99% probability

of $0 repair costs to a 0.3% probability of costs of $120.

3.2 Simulation

Simulation modelling can be used to assess probabilities when:

 there are many different variables in the situation, each with different probable

outcomes

 the relationship between these variables might be complex

 extensive information is required about risk (and the range of different possible

outcomes), not just the weighted average (EV) or the most likely outcome.

This method of risk assessment might be used, for example, with a complex model

such as a financial risk model or an economic model. In business modelling,

simulation is probably most closely associated with Monte Carlo simulation

modelling

The nature of Monte Carlo simulation modelling

A simulation model will contain a large number of inter-related variables (for

example sales volumes of each product, sales prices of each product, availability of

constraining resources, resources per unit of product, costs of materials and labour,

and so on).

For each variable, there are estimated probabilities of different possible values.

These probabilities are used to assign a range of random numbers to each variable.

(The random number allocation should reflect the probability distribution).

For example, suppose that in a very simple simulation model, there are four

variables: sales volume, sales price, unit variable cost and fixed costs, and that the

value of each of these variables is independent of the other three variables. (For

example the expected sales volume is independent of the sales price, variable cost

and fixed costs.) The possible values for each variable and their associated

probability, and the assignment of a range of random numbers, might be as follows.

Sales volume Variable cost per unit

Units Probability

Random

number

range

$ Probability

Random

number

range

10,000 20% 00 – 19 2 10% 00 – 09

20,000 50% 20 – 69 3 30% 10 – 39

30,000 30% 70 – 99 4 40% 40 – 79

5 20% 80 – 99

Sales price per unit

$14 15% 00 – 14

Fixed costs

$15 40% 15 – 54 $200,000

85% 00 – 84

$16 35% 55 – 89 $220,000

10% 85 – 94

$17 10% 90 – 99 $240,000

5% 95 – 99

Chapter 6: Decision making with risk and uncertainty

The model is then used to calculate the value of the outcome or result, for a given

set of values for each variable. This simple model can be used to calculate the

expected profit, given a combination of sales volume, sales price, variable cost and

fixed costs.

The values for each variable are determined by generating random numbers f or

each variable. For example if the random numbers 14, 85, 63, 27 are generated for

this model, the selected values might be 10,000 units of sale, $16 as the sale price, $4

as the unit variable cost and $200,000 as fixed costs – giving a loss of $80,000.

The model is then used to produce the expected outcome or result again, with a

different set of values for each variable, obtained by generating another set of

random numbers. The model is used to prepare a large number of different possible

outcomes, each time with different combinations of values for all the variables.

As a result, the model will produce a range of many different possible results or

outcomes – in this simple example a range of possible annual profit figures.

Repeating the simulation many times produces a probability distribution of the

possible outcomes and this probability distribution can be analysed statistically.

Simulation modelling therefore leads on to further statistical analysis of the risk in a

given situation.

Advantage of the Monte Carlo method

The advantages of Monte Carlo simulation modelling are as follows:

 It gives more information about the possible outcomes and their relative

probabilities, so that the risk in a situation or decision (for example the

probability distribution of different possible outcomes) can be analysed

statistically and in depth.

 It is useful for complex decision problems, where the use of expected values for

decision-making would be inappropriate and simplistic.

Limitation of the Monte Carlo method

It is not a technique for making a decision, only for getting more information about

the risk and the probability of different possible outcomes.

Paper F5: Performance management

Sensitivity analysis

 The nature of sensitivity analysis

 Carrying out sensitivity analysis

 Identifying the key variables with senstivity analysis

3 Sensitivity analysis

3.1 The nature of sensitivity analysis

Sensitivity analysis is a method of uncertainty analysis which tests the effect on the

expected outcome of changes in the values of key ‘variables’ or key factors. For

example, in budget planning, the effect on budgeted profit might be tested for

changes in the budgeted sales volume, or the budgeted rate of inflation, or budgeted

materials costs, and so on.

There are several ways of using sensitivity analysis.

 We can estimate by how much an item of cost or revenue would need to differ

from their estimated values before the decision would change.

 We can estimate whether a decision would change if estimated sales were x%

lower than estimated, or estimated costs were y% higher than estimated. (This is

called ‘what if…?’ analysis: for example: ‘What if sales volume is 5% below the

expected amount)?

When estimates are uncertain, sensitivity analysis is useful for assessing what

would happen if the estimates prove to be wrong. For example, if management

consider that their estimates of sales volume might be inaccurate by up to 20%,

sensitivity analysis could be used to assess what the profit (or loss) would be if

sales volume is 20% less than estimated.

Sensitivity analysis is therefore a common sense approach to assessing the

uncertainty in a situation.

3.2 Carrying out sensitivity analysis

The starting point for sensitivity analysis is the original plan or estimate. For

example this might be a plan which estimates the expected profit in a budget, or the

expected profit from a particular project or transaction.

Key variables are identified (such as sales price, sales volume material cost, labour

cost, completion time, and so on). The value of the selected key variable is then

altered by a percentage amount (typically a reasonable estimate of possible

variations in the value of this variable) and the expected profit is re-calculated.

In this way, the sensitivity of a decision or plan to changes in the value of the key

items or key factors can be measured.

ACCA F5 Performance Management - 2010 - Study text - Emile Woolf Publishing

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