ACCA F5 Performance Management - 2010 - Study text

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Chapter 6: Decision making with risk and uncertainty

An advantage of sensitivity analysis is that if a spreadsheet model is used for

analysing the original plan or decision, sensitivity analysis can be carried out

quickly and easily, by changing one value at a time in the spreadsheet model. For

example, cash budgets on a spreadsheet are used extensively with ‘what-if analysis’

to analyse the possible future cash position in a business.

3.3 Identifying the key variables with sensitivity analysis

Sensitivity analysis can be used to calculate by how much the value of an item (or

‘variable’) must change before the expected profit or outcome becomes

unacceptable. For example, sensitivity analysis can be used to estimate by how

much expected sales volume would have to fall short of the estimate before a

product became unprofitable.

By applying sensitivity analysis to each variable, it should be possible to identify

those that are the most critical, where an error in the estimate could have a large

impact on the actual outcome.

Example

A company is considering launching a new product in the market. Profit estimates

are as follows:

$ $

Sales (10,000 units)

200,000

Variable costs:

Materials 120,000

Labour 20,000

140,000

Contribution

60,000

Fixed costs (all directly attributable)

50,000

Profit

10,000

The estimates of sales volume, sales price, variable costs and fixed costs are

uncertain.

Sensitivity analysis can be used to calculate the extent to which the profitability of

the product depends on the accuracy of the estimates. We can calculate by how

much each of these variables would have to be ‘worse’ than estimated before the

product became loss-making.

Profit can fall by $10,000 before the product ceases to be profitable. Profit would fall

by $10,000 if:

 sales volume is $10,000/$60,000 = 16.7% less than expected: this is because each

1% fall in sales volume will reduce contribution by 1%

 the sales price is $10,000/$200,000 = 5% less than expected

 material costs are $10,000/$120,000 = 8.3% more than expected

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 labour costs are $10,000/$20,000 = 50% more than expected

 fixed costs are $10,000/$50,000 = 20% more than expected.

The product would cease to be profitable if a combination of variables turned out

worse than expected. In the example above, for instance, the product would cease to

be profitable if fixed costs were 10% more than expected and sales volume was also

8.3% less than expected.

Management can use sensitivity analysis to decide whether they have sufficient

confidence in the estimates so that they can go ahead with their planned decision

(for example, a decision to launch a new product), or whether the uncertainty is so

great that it would be too risky to go ahead.

Assessing the uncertainty is a matter of judgement.

Chapter 6: Decision making with risk and uncertainty

Maximax, maximin and minimax regret

 Worst, most likely and best possible outcomes

 Constructing a pay-off table or profit table

 Maximax, maximin and minimax regret decision rules

4 Maximax, maximin and minimax regret

4.1 Worst, most likely and best possible outcomes

When a choice has to be made between two or more mutually exclusive options, the

choice might be affected by the different possible outcomes that might occur with

each option.

For example, a book publisher might need to decide how many copies of a new

book to print. He might be considering three options – to print 1,000 copies, 5,000

copies or 10,000 copies. The most profitable choice of print quantity will depend on

the sales demand for the book, which is uncertain. Sales demand might depend on

the publicity that the book receives from book reviewers. The decision about the

print quantity must be taken before it is known what the publicity and expected

sales for the book will be.

The choice between two or more alternative courses of action might be based on the

worst, most likely or best expected outcomes from each course of action. A pay-off

table can be produced which records all possible profit values from the different

courses of action.

In the example above, a pay-off table (also called a profit table) might be

constructed as follows:

Course of action

Adverse publicity.

Bad book reviews

Reasonable

publicity

Good publicity.

Excellent reviews

Estimated sales

1,000

Estimated sales

5,000

Estimated sales

10,000

Profit/loss

Print 1,000 copies -+ $2,000

+ $2,000

Print 5,000 copies - $8,000

+ $10,000

Print 10,000 copies - $12,000

+ $1,000

+ $35,000

This pay-off table or profit table can then be analysed, and a choice can be made

between the different decision options under consideration.

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4.2 Constructing a pay-off table or profit table

A pay-off table can be constructed as follows.

 One side of the table (rows or columns) should list the different mutually

exclusive options, from which a choice will be made

 The other side of the table should list the different possible results or outcomes

that might occur.

 For each option and possible outcome, the value of the expected outcome (for

example, the expected profit) should be entered in the appropriate box.

Example

A shopkeeper must decide how many boxes of apples to buy each day. A box of

apples earns contribution of $40 and costs $25. Demand is uncertain and could vary

from 30 boxes to 10 boxes. The most likely demand is considered to be 20 boxes.

Any apples that are purchased but not sold will be thrown away at the end of the

day.

The shopkeeper has decided that he will buy 10 boxes, 20 boxes or 30 boxes each

day, and these are the only three options he wants to consider.

Required: Construct a pay-off table and suggest how many boxes of apples the

greengrocer should buy each day.

In the pay-off table below:

 the different decision options are rows in the table

 the different possible outcomes (daily sales demand) are shown in the columns.

For each decision option, we can calculate the daily profit for each possible volume

of sales demand.

Course of action

Demand

10 boxes

Demand

20 boxes

Demand

30 boxes

$ $

Buy 10 boxes 150

150 150

Buy 20 boxes (100)

300 300

Buy 30 boxes (350)

50 450

Entries in the pay-off table are calculated as follows:

Buy 10 boxes - Sell 10 boxes Revenue 10 × $40 = $400, costs 10 × $25 = $250,

profit = $400 – $250 = $150.

- The shopkeeper cannot meet the demand of 20 or 30 boxes, so if

sales demand is more than 10 boxes per day, sales will be just 10

boxes.

The profit/contribution per day is $150, regardless of actual sales

demand.

Chapter 6: Decision making with risk and uncertainty

Buy 20 boxes - Daily purchase costs = 20 × $25 = $500.

- Sell 10 boxes Revenue 10 × $40 = $400, costs $500, loss =

$400 – $500 = $(100).

- Sell 20 boxes Revenue 20 × $40 = $800, costs $500, profit =

$800 – $500 = $300.

- If demand is 30 boxes, but the shopkeeper buys just 20 boxes,

profit per day will also be $300, and sales demand for 10 boxes

will not be met.

Buy 30 boxes - Daily purchase costs = 30 × $25 = $750.

- Sell 10 boxes Revenue 10 × $40 = $400, costs = $750, loss =

$400 – $750 = $(350).

- Sell 20 boxes Revenue 20 × $40 = $800, costs = $750, profit =

$800 – $750 = $50.

- Sell 30 boxes Revenue 30 × $40 = $1,200, costs = $750, profit

= $1,200 – $750 = $450.

The pay-off table or profit table does not identify the ‘best’ option. It simply shows

what the outcome will be for each decision option, given different possible

circumstances that might actually occur.

Management need to use their judgement, given this information, to decide which

option to select. The course of action chosen by the company will depend on the

attitude to risk of its decision-maker.

2.3 Maximax, maximin and minimax regret decision rules

Choosing between mutually-exclusive courses of action can be stated as ‘decision

rules’. A decision rule is simply the basis or ‘rule’ which a decision-maker uses to

select between mutually exclusive options.

As suggested earlier in this chapter, the choice between different options might be

based on an assessment of probabilities, and the preferred option might be the one

that offers the highest expected value of profit. Alternatively, simulation or

sensitivity analysis may be used to compare expected profits with the risk or

uncertainty, and a choice between the different options based on an assessment of

risk and return.

The choice between mutually exclusive options might also be based on any of the

following decision rules:

 Maximax rule

 Maximin rule

 Minimax regret rule

To use any of these decision rules, it is helpful to construct a pay-off table.

Maximax decision rule

This is a decision rule based on the view that the decision-maker should select the

course of action with the best possible pay-off, such as the highest possible profit.

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This approach is based on the view that the decision-maker should seek the highest

return, assuming that events turn out in the best way possible. The maximax

decision rule can be described as a decision rule for the ‘risk seeker’.

Maximin decision rule

This decision rule is based on the view that the decision-maker will select the course

of action with the highest expected return under the worst possible conditions. The

choice is based on trying to maximise the minimum possible profit.

The decision maker therefore looks at the profit that will occur if the worst possible

outcome happens, and will choose the option that offers the highest profit under

these conditions.

This decision rule might be associated with a risk-averse decision maker.

Minimax regret decision rule

This decision rule is based on the concept of ‘regret’.

‘Regret’ is the difference between the profit that will be earned by choosing one

option choice, and the profit that would have been earned if the most profitable

option had been selected, given a particular outcome.

For example suppose that a company has to choose between options 1, 2 and 3, and

the profit from each option depends on whether sales demand is weak, average or

strong. For each option (1, 2 and 3) and each possible outcome (weak, average or

strong sales demand), there is ‘regret’. This is the amount by which the profit earned

by choosing the option would be worse than ‘the best possible profit’ from choosing

either of the other two options, given the nature of the sales demand.

‘Regret’ could be defined as the opportunity cost of having made the wrong

decision, given the actual conditions that apply in the future.

The decision rule is to select the option with the lowest possible ‘regret’.

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

the state of the market, but the state of the market will not be known until after the

choice of project has been made. The following estimates of annual profit have been

prepared:

State of market Declining

Static

Expanding

$000

Project 1 (100)

120

950

Project 2 50

500

600

Project 3 180

190

200

Chapter 6: Decision making with risk and uncertainty

Which project would be selected if the decision is based on:

(a) the maximax decision rule

(b) the maximin decision rule

Answer

Maximax decision rule

The decision should be to select the option that offers the prospect of the highest

profit. This is Project 1 where the annual profit would be $950,000 if there is an

expanding market.

It does not matter that this project would make a loss of $100,000 if the market turns

out to be in decline. The decision rule is to select the option offering the best

possible return.

Maximin decision rule

This decision rule is based on the returns that would be obtained if the worst

possible outcome occurs. The worst outcome is a declining market. If the market

turns out to be in decline, the most profitable option would be Project 3, for which

the profit would be $180,000.

Minimax regret decision rule

To apply the minimax regret decision rule, we must first prepare a pay-off table

showing the regret the decision-maker would have choosing Project 1, Project 2 or

Project 3, and the actual market conditions turn out declining, static or expanding.

The regret with each course of action is shown in the pay-off table below.

State of market Diminishing

Static

Expanding

Maximum regret

$000

Project 1 280

380

Project 2 130

350

Project 3 0

310

750

For example, suppose that the market turns out to be in decline. The most profitable

option would be Project 3, for which the profit would be $180,000.

 If Project 1 is selected and the market is in decline the regret will be $280,000,

which is the difference between the loss that would be made from Project 1 and

the profit that would have been made if the best option (Project 3) had been

selected.

 If Project 2 is selected and the market is in decline the regret will be $130,000,

which is the difference between the profit that would be made from Project 2

and the profit that would have been made if the best option (Project 3) had been

selected.

 If Project 3 is selected, there would be no regret, because the best option would

have been chosen, given that the market is in decline.

Paper F5: Performance management

Similarly, suppose that the market turns out to be static. The most profitable option

would be Project 2, for which the profit would be $500,000.

 If Project 1 is selected and the market is static the regret will be $380,000, which

is the difference between the profit that would be made from Project 1 and the

profit that would have been made if the best option (Project 2) had been selected.

 If Project 3 is selected and the market is static the regret will be $310,000, which

is the difference between the profit that would be made from Project 3 and the

profit that would have been made if the best option (Project 2) had been selected.

 If Project 2 is selected, there would be no regret, because the best option would

have been chosen, given that the market is static.

The regrets can be calculated in the same way on the assumption that the market is

expanding.

A table of ‘regrets’, once completed, shows the amount of the regret for each

possible course of action (projects 1, 2 or 3), given each possible outcome (declining,

static or expanding market).

The right-hand column of the table shows the maximum regret for each option. This

is the maximum amount of regret that will be experienced by selecting that option.

The minimax regret decision option rule is to select the option where the maximum

regret is the lowest. In this example, this is Project 2, for which the maximum regret

is $350,000.

Conclusion

The maximax, maximin and minimax regret decision rules provide a logical basis

for making a choice between mutually exclusive options, where the future

conditions are uncertain and there are no probability estimates of what the future

conditions might be.

The main disadvantage of choosing between mutually-exclusive courses of action

on the basis of the worst, most likely or best possible outcome is that the choice

ignores the likelihood or probability of the worst, most likely or best outcomes

actually happening.

If probability estimates had been available in the previous example for future

market conditions (declining, static or expanding market), a different decision rule

such as the expected value rule might be more appropriate – because it takes the

probabilities of the different outcomes into consideration.

Paper F5

Performancemanagement

CHAPTER

Budgeting

Contents

1 Objectives of budgeting

2 Preparing a budget

3 Budgetary systems

4 Fixed and flexed budgets

5 Behavioural aspects of budgeting

Paper F5: Performance management

Objectives of budgeting

 Objectives of budgeting and budgetary control

 Budgeting: co-ordination of corporate and divisional objectives

1 Objectives of budgeting

1.1 Objectives of budgeting and budgetary control

A business entity should plan over the long-term, medium-term and short-term.

 Long-term planning, or strategic planning, focuses on how to achieve the

entity’s long-term objectives. Strategic objectives might be expressed in general

terms, such as the objective of growth in returns to company shareholders.

Detailed strategic plans may also be formulated for a planning period of five or

ten years (a ‘five-year plan’ or ‘ten-year plan’).

 Medium-term or tactical planning focuses on the next year or two. Medium-term

plans need to be consistent with longer-term strategic plans, but they are

prepared in greater detail.

 Short-term or operational planning covers daily. Weekly or monthly planning at

an operational level. These plans need to be consistent with medium-term plans

and with the entity’s operating standards and policies.

Strategic planning, medium-term planning and operational planning can be seen as

a planning hierarchy, each with its own performance targets.

Budgets are medium-term plans for the business, expressed in financial terms. A

typical budget is prepared annually and covers the next financial year.

Budgeting can be described as planning at the ‘tactical’ management level. As

annual plans, they must be consistent with the longer-term strategic plans of the

organisation. They can also provide a useful benchmark for setting shorter-term

operational targets, such as monthly sales volumes and output volumes, efficiency

targets, capacity utilisation targets, and so on.

Purposes of budgeting

Budgets have several purposes.

 They provide a link between long-term plans into more detailed short-term

operational plans. They are the middle link in the performance hierarchy of the

planning system. They help to ensure that detailed planning is linked to the

long-term objectives of the entity.

 They should co-ordinate the actions of all the different parts of the entity – so

that all parts of the entity work towards the same goals. (This is known as ‘goal

congruence’ and is considered in more detail later.)

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

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