ACCA - P5 Study text - Emile Woolf INT

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Chapter 3: Decision-making with risk and uncertainty

However,anEVisjustaweightedaverageofdifferentpossibleoutcomes.TheNPV

ismorelikelytobepositivethannegative,butthereissomeriskofanegativeNPV.

Andifthemarketconditionsaregood,itwouldbemuchbettertochooseProject1.



As explained earlier, there are other ways of making a logical choice between

mutually-exclusive projects.

 Using the maximax decision rule, Project 1 would be selected because it offers

the possibility of the highest possible NPV ($60 million).

 Using the maximin decision criterion, the decision would be to choose the

project with the maximum ‘minimum NPV’.

Using the maximin approach, Project 2 should be selected because its worst

possible outcome is + $1 million, better than the other two projects. Whatever

happens,theNPVwillbeatleast$1million.



Usingtheminimaxregretdecisioncriterion,thechoiceshouldbetheprojectwhere

themaximumpossibleregr

etisminimised.Thefollowingtablesetsouttheregrets:



Project Poor (0.3) Moderate (0.5) Good (0.2)

Regret Regret Regret

Maximum

regret

$m $m $m $m

1 21 7 0 21

2 0 12 40 40

3 11 0 22 22



Forexample, if the market conditionsare moderate,wewould not regretchoosing

Project3,butifwehadchosenProject1 wewouldhaveregrettedthedecisionby$7

million(NPV22‐NPV15).



Using the minimax regret basis for decision‐making, Project 1 should be selected

becausethemaximumamountbywhichwewouldregretmakingthischoiceis$21

million.Thiswillhappenifthema

rketconditionsturnouttobepoor. 



Thereisno‘correct’basisformakingdecisionsinconditionsofriskoruncertainty.

Thereare,however,differentlogicalapproachestomakingthechoice.

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Assessing risk in decision-making

 Standard deviation of the expected return

 Sensitivity analysis

 Simulation

2 Assessing risk in decision-making

The decision rules considered so far do not measure risk mathematically. However,

when a probability distribution of possible outcomes is available, the decision-

maker can analyse the risk using a statistical or mathematical method.

The decision is then made by considering both the expected return (for example, the

EV of NPV) and the risk.

Three approaches to measuring and analysing risk are:

 calculating the standard deviation of the expected return

 sensitivity analysis

 simulation modelling.

For the purpose of the P5 examination, sensitivity analysis is probably the most

important of these three analytical rechniques.

2.1 Standard deviation of the expected return

When the possible outcomes from a decision are estimated as a probability

distribution, we can calculate both the EV of the expected return and the standard

deviation of the expected return.

Standard deviation is a statistical measurement of risk or variation. A higher

standard deviation indicates higher risk (higher potential variation above or below

the EV of return).

The formula for calculating the standard deviation of a probability distribution is:

s = S ×−×

()

prob x

()

Example

The original example will again be used.

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 profits from investing in each of the projects will depend on the state

of the market. The following estimates of net present value have been prepared:

Chapter 3: Decision-making with risk and uncertainty

State of market Diminishing Static Expanding EV of NPV

Probability 0.4 0.3 0.3

$000 $000 $000 $000

Project 1 100 200 900 370

Project 2 0 500 600 330

Project 3 180 190 200 189

Required

(a) Calculate the standard deviation of the expected NPV for each project.

(b)

Consider how the measurements of standard deviation might affect the choice

of project.

Answer

Project 1 NPV Probability

x = 370

x p

−

p(x− x )

Diminishing 100 0.4 - 270 29,160

Static 200 0.3 - 170 8,670

Expanding 900 0.3 570 84,270

122,100

s = 122,100 = (in $000s) 349.4

Project 2 NPV Probability

x = 330

x p

−

p(x− x )

Diminishing 0 0.4 - 330 43,560

Static 500 0.3 + 170 8,670

Expanding 600 0.3 + 270 21,870

74,100

s = 74,100 = (in $000s) 272.2

Project 3 NPV Probability

x¯ = 189

x p

x – x¯ p(x – x¯)

Diminishing 180 0.4 - 9 32.4

Static 190 0.3 + 1 0.3

Expanding 200 0.3 + 11 36.3

69.0

s = 69 = (in $000s) 8.3

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Summary

Project EV of NPV Standard deviation

$000 $000

Project 1 370 349.4

Project 2 330 272.2

Project 3 189 8.3

The choice between the three projects can take risk into consideration, as well as the

EV of the NPV. In this example the project with the highest EV also has the highest

risk, and the project with the lowest EV has the lowest risk.

With simple probability distributions, such as the probabilities shown in this

example, the standard deviation has no further meaning or practical value.

However, if a probability distribution showed the characteristics of a normal

distribution (or another recognised probability distribution), it would be possible to

carry out further detailed analysis of the risk using normal distribution tables.

Advantages of measuring standard deviation

There are several advantages to measuring the standard deviation of possible

outcomes.

 A standard deviation gives a numerical value to the spread of possible results

around the average or expected value.

 It gives recognition to risk in a decision, and quantifies the risk.

 It can be used for statistical analysis when it can be assumed that the probability

distribution is a normal distribution.

Disadvantages of measuring standard deviation

The meaning or significance of a standard deviation is limited when the probability

distribution is not a normal distribution or (other recognisable probability

distribution).

2.2 Sensitivity analysis

Sensitivity analysis is a method of risk or uncertainty analysis in which the effect on

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

tested. 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.

Chapter 3: Decision-making with risk and uncertainty

 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)?

The starting point for sensitivity analysis is the original plan or estimates, giving an

expected profit or value. 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

or value 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.

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.

Sensitivity analysis and strategic decision making

In the examination you may be required to do some sensitivity analysis. For

example, you may have produced an estimated future outcome of a decision or a

strategy, and this expected outcome may fail to meet the strategic objective or target.

You may therefore be required to calculate the amount by which a variable or factor

in your estimate would need to change in value before the objective or target could

be met.

With sensitivity analysis, the technique is to assume that the value of all other

factors in the forecast or estimate will remain the same, and there is only one factor

whose change in value you wish to analyse.

This may seem complex, but the following simple examples should illustrate the

technique.

Example

A company is considering a strategy of making and marketing a new product in its

existing markets. Market research has been carried out, which suggests that at a

selling price of $6 per unit, sales demand each year will be for 200,000 units.

It has also been estimated that the variable cost per unit will be $4 and attributable

annual fixed costs for the venture would be $250,000.

Required

(a) Suppose that the company has established a target minimum profit/sales ratio

of at least 15% for all products. By how much would the variable cost per unit

need to be less than the estimated amount for the product to achieve this

minimum profit/sales ratio target?

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(b) Suppose instead that the company has established a target minimum

contribution/sales ratio of at least 40% for all products. What would the

minimum selling price need to be in order to meet this target?

Answer

(a) The expected profit on the basis of the estimated figures is as follows:

Sales (200,000 × $6)

1,200,000

Variable costs (200,000 × $4)

800,000

Contribution 400,000

Fixed costs 250,000

Profit 150,000

Profit/sales ratio = 150,000/1,200,000 = 12.5%.

This is less than the minimum target of 15%.

Given no change in any of the other variables (sales price, sales volume or

fixed costs, the amount by which the variable cost per unit need to be less than

the estimated amount of $4 is calculated as follows.

Estimated annual sales 1,200,000

Minimum profit required to meet target (15%) 180,000

Current estmate of profit 150,000

Amount by which annual profit (and contribution) must increase 30,000

To increase the annual profit by $30,000, the variable cost per unit would need

to be lower by $30,000/200,000 units = $0.15 per unit. This is 3.75% less than

the current estimate, which means that the maximum variable cost per unit

should be $3.85.

Management may then wish to consider possible strategies for reducing the

variable cost per unit by $0.15.

(b) The estimated contribution/sales ratio is 33.3% ($2/$6). Given no change in

the variable cost per unit, the minimum sales price required to meet the

minimum target C/S ratio is calculated as follows:

Minimum C/S ratio = 40%.

Therefore maximum ratio of variable cost/sales = 60%.

Variable cost = $4.

Therefore minimum sales price = $4/60% = $6.67.

Chapter 3: Decision-making with risk and uncertainty

Summary: sensitivity analysis and decision-making

To carry out sensitivity analysis within a strategic planning or decision making

process, the basic technique is to:

 Calculate the expected outcome (for example, annual profit) on the basis of

current estimates

 Establish the minimum required outcome in order to meet the strategic target or

objective.

 Calculate the gap between these two – current expected outcome and target

outcome.

 Given no change in the value of any of the other variables, calculate by how

much the selected item needs to change in value in order to meet the target or

objective.

2.3 Simulation

Simulation modelling is used when a plan or budget is represented by a

mathematical model. The model will contain a large number of inter-related

variables (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).

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

set of values for each variable. It is then used to produce the expected outcome or

result again, with a different set of values for each variable. 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 that can be analysed statistically, by putting the possible outcomes into a

probability distribution.

Simulation modelling therefore leads on to further statistical analysis of risk.

One example of simulation is a mathematical model which could be approached

using the ‘Monte Carlo’ method. With Monte Carlo simulation, a probability

distribution for the possible different values for each variable is used to allocate

random numbers to each possible value. Random number allocations are given to

all the different possible values for every input variable in the model. (The random

number allocation should reflect the probability distribution).

A special computer program can be used to generate random numbers, and the

random numbers generated by the program are used to give a value to each variable

in the model. These values are then used to calculate the result or outcome that

would occur.

Repeating the simulation many times produces a probability distribution of the

possible outcomes.

Paper P5: Advanced performance management

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.

 It is useful for problems which cannot be solved analytically.

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 P5

Advanced performance management

CHAPTER

Quantitative techniques

in budgeting

Contents

1 Analysing costs into fixed and variable

2 Forecasting techniques

3 Uncertainty in budgeting

4 The learning curve

Paper P5: Advanced performance management

Analysing costs into fixed and variable

 The need to estimate fixed and variable costs

 High low method

 Linear regression analysis

1 Analysing costs into fixed and variable

1.1 The need to estimate fixed and variable costs

To prepare accurate cost budgets, it is important to understand how costs ‘behave’.

Cost behaviour refers to the way in which total costs increase as the volume of an

activity increases.

It is commonly assumed that total costs can be analysed into fixed costs and a

variable cost per unit of activity, such as a variable cost per unit of product or per

hour of service. Some overhead costs are a mixture of fixed costs and variable costs,

but these can be separated into a fixed cost portion and a variable cost portion.

To prepare reliable cost budgets or cost estimates, it may be necessary to estimate

fixed costs and variable costs.

 Direct material costs are normally 100% variable costs.

 Direct labour costs may be treated as variable costs. However, when there is a

fixed labour force, direct labour costs may be budgeted as a fixed cost.

 Overhead costs maybe treated as fixed costs. However, for an accurate analysis

of overhead costs, it may be necessary to make an estimate of fixed costs and

variable costs. These estimates are often based on an analysis of historical costs.

You should be familiar already with two techniques for estimating fixed and

variable costs:

 the high low method

 linear regression analysis.

It is unlikely that you will be expected to use either technique in your examination.

However, you might be required to comment on each technique, and its reliability

as a forecasting/budgeting technique to estimate costs.

1.2 High low method

The high low method provides an estimate of fixed and variable costs for an activity

by taking two historical costs:

 the total costs for the highest recorded volume of the activity, and

 the total costs for the lowest recorded volume of the activity.

ACCA - P5 Study text - Emile Woolf INT - 2010

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