ACCA F2 Management Accounting - 2010 - Study text - Emile Woolf Publishing
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Chapter 3: Cost behaviour and cost estimation
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Example
A company has the following costs at three activity levels.
Activity Total cost
units $
5,000 180,000
8,000 240,000
11,000 276,000
The variable cost per unit is constant over this range of activity, but there is a step
fixed cost and total fixed costs increase by 20% when the activity level exceeds 7,500
units.
Required
Estimate the expected total cost when the activity level is 7,000 units.
Answer
There is an increase in fixed costs above 7,500 units of activity, which means that
total fixed costs and the variable cost per unit are the same for 8,000 units and 11,000
units of activity. These activity levels should be used to estimate the variable cost per
unit and total fixed costs.
(1) Steps 1 and 2: Calculate the variable cost per unit
Units
$
High: Total cost 11,000 units
= 276,000
‘In-between’ 8,000 units
= 240,000
Difference: Variable cost of 3,000 units
= 36,000
Therefore variable cost per unit = $36,000/3,000 units = $12 per unit.
(2) Steps 3 and 4: Calculate fixed costs (above 7,500 units)
Substitute in the ‘high’ equation Cost
$
Total cost of 11,000 units 276,000
Variable cost of 11,000 units (× $12 per unit)
132,000
Therefore fixed costs (above 7,500 units) 144,000
(3) Calculate fixed costs at activity levels below 7,500 units
Fixed costs increase by 20% above 7,500 units.
Fixed costs above 7,500 units are therefore 120% of fixed costs below 7,500 units.
Fixed costs below 7,500 units are therefore: $144,000 × (11/120) = $120,000.
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(Note: Make sure that you understand the adjustment here. We do not subtract 20%
from fixed costs above 7,500 units!)
(4) Using the cost analysis: Prepare a cost estimate
Cost estimate Cost
$
Fixed costs (below 7,500 units) 120,000
Variable cost (7,000 units × $12) 84,000
Estimated total costs 204,000
3.5 High/low analysis when there is a change in the variable cost per unit
High/low analysis can also be used when there is a change in the variable cost per
unit between the ‘high’ and the ‘low’ levels of activity. The same approach is needed
as for a step change in fixed costs, as described above.
The method of analysis to use depends on whether the step increase in the fixed cost
is stated as a money amount of cost, or whether it is stated as a percentage increase.
The change in unit variable cost is given as a money amount
If the increase or reduction in variable cost per unit is given as a money amount, the
total cost of the ‘high’ activity level should be adjusted by the amount of the
increase or reduction, so that total costs for the ‘high’ and ‘low’ amounts have the
same basis for total variable costs.
The high/low method can then be used in the normal way to obtain a variable cost
per unit and a fixed cost at the ‘low’ activity level.
Example
A company has the following costs at three activity levels.
Activity Total cost
units $
21,000 276,000
30,000 327,000
The fixed costs are constant over this range of activity, but variable costs per unit
fall by $0.50 above 24,000 units, but only for units above that level (i.e. not for all
units).
Required
Using high/low analysis, calculate the total cost of 28,000 units.
Chapter 3: Cost behaviour and cost estimation
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Answer
The variable cost per unit falls by $0.50 per unit, but only for units above 24,000. This
means that at the 30,000 level of activity, there are 6,000 units costing $0.50 less,
which is $3,000 in total.
To carry out high/low analysis, we therefore need to add $3,000 to total costs for the
high level of output. The variable cost per unit we calculate will be the variable cost
b
efore the $0.50 reduction.
(1) Steps 1 and 2: Calculate the variable cost per unit
Units
$
High: Adjusted total cost $(327,000 + 3,000) 30,000 units
= 330,000
Low: Total cost 21,000 units
= 276,000
Difference: Variable cost of 9,000 units
= 54,000
Therefore variable cost per unit (up to 24,000 units) = $54,000/9,000 units = $6 per
unit.
The variable cost per unit above 24,000 units is $6 - $0.50 = $5.50.
(2) Steps 3 and 4: Calculate fixed costs
Substitute in the ‘low’ equation Cost
$
Total cost of 21,000 units 276,000
Variable cost of 21,000 units (× $6 per unit) 126,000
Therefore fixed costs 150,000
(3) Using the cost analysis: Prepare a cost estimate
Cost estimate for 28,000 units Cost
$
Fixed costs 150,000
Variable cost
First 24,000 units (× $6) 144,000
Next 4,000 units (× $5.50) 22,000
Estimated total costs 316,000
The change in unit variable cost is given as a percentage amount
When the change in the variable cost per unit is given as a percentage amount, a
similar method is needed as for fixed costs. A third ‘in between’ estimate of costs
should be used, and the variable cost per unit will be the same for:
the ‘in between’ activity level and
either the ‘high’ or the ‘low’ activity level.
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High/low analysis should be applied to the two costs and activity levels for which
unit variable costs are the same, to obtain an estimate for the variable cost per unit
and the total fixed costs at these activity levels. The variable cost per unit at the third
activity level can then be calculated making a suitable adjustment for the percentage
change.
Example
A company has the following costs at three activity levels.
Activity Total cost
units $
20,000 300,000
25,000 320,000
30,000 356,000
The fixed costs are constant over this range of activity, but there is a 10% reduction
in the variable cost per unit above 24,000 units of activity. This reduction applies to
all units of activity, not just the additional units above 24,000.
Required
Estimate the expected total cost when the activity level is 22,000 units.
Answer
The variable cost per unit is the same for both 25,000 units and 30,000 units.
High/low analysis should therefore be applied to these activity levels.
(1) Calculate the variable cost per unit above 24,000 units
Units
$
High: Total cost 30,000 units
= 356,000
‘In-between’ 25,000 units = 320,000
Difference: Variable cost of 5,000 units
= 36,000
Therefore variable cost per unit = $36,000/5,000 units = $7.20 per unit.
(2) Calculate the variable cost per unit below 24,000 units
The variable cost per unit above 24,000 units is 90% of the cost below 24,000 units.
The variable cost per unit below 24,000 units is therefore (× 100/90) of the cost
above 24,000 units.
Variable cost per unit below 24,000 units = $7.20 × 100/90 = $8
Chapter 3: Cost behaviour and cost estimation
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(3) Calculate fixed costs
Substitute in the ‘low’ equation Cost
$
Total cost of 20,000 units 300,000
Variable cost of 20,000 units (× $8 per unit) 160,000
Therefore fixed costs (above 7,500 units) 140,000
(4) Using the cost analysis: Prepare a cost estimate
Cost estimate for 22,000 units Cost
$
Fixed costs 140,000
Variable cost (22,000 units × $8) 176,000
Estimated total costs 316,000
Exercise and practice multiple choice questions
Exercise
A company has recorded the following costs in the past six months:
Month Activity
Total cost
Units of
output
$
January 14,000
98,700
February 12,600
91,700
March 15,300
103,350
April 14,900
101,000
May 16,100
107,450
June 16,000
107,080
Required
Using high/low analysis, prepare an estimate of total costs in August if output is
expected to be 15,000 units.
1 A company has the following costs at two activity levels.
Activity Total cost
units $
60,000 960,000
72,000 1,104,000
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The variable cost per unit is constant over this range of activity, but there is a step
fixed cost and total fixed costs increase by $36,000 when the activity level exceeds
64,000 units.
What is the expected total cost when the activity level is 70,000 units?
A $1,050,000
B $1,080,000
C $1,086,000
D $1,116,000
(2 marks)
2 A company has the following costs at three activity levels.
Activity Total cost
units $
60,000 960,000
72,000 1,104,000
The fixed cost is constant over this range of activity, but there is a reduction in the
variable cost per unit by 10% when the activity level exceeds 15,000 units. This
reduction applies to all units.
What is the expected total cost when the activity level is 14,000 units?
A $131,800
B $132,400
C $136,000
D $138,000
(2 marks)
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Paper F2
Management accounting
CHAPTER
4
Business mathematics and
computer spreadsheets
Contents
1 Dealingwithuncertainty:expectedvalues
2 Regressionanalysis
3 Correlationandthecorrelationcoefficient
4 Spreadsheetmodels
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Dealing with uncertainty: expected values
Decision-making and risk or uncertainty
Probabilities and expected values
How are expected values used?
Limitations of the expected value technique
1 Expected values and decision-making
This chapter explains some of the mathematical techniques and computer models
that might be used to provide cost and management accounting information.
Mathematical techniques might be helpful with providing more reliable
management information. Computer modelling with spreadsheets make it possible
to use some mathematical models that might otherwise be impracticable (because of
their complexity).
1.1 Decision-making and risk or uncertainty
Estimates of costs or profit are often needed by management to make a decision.
Unfortunately, it is often impossible to predict with reasonable certainty what costs,
revenues or profits will be. This is because there is considerable uncertainty about
what might happen in the future.
Sometimes, the uncertainty arises because the information needed to make an
accurate forecast of costs or revenues is not sufficiently reliable. There isn’t
enough information to make an accurate prediction.
There is also risk in most business decisions. The outcome of a decision might be
favourable or unfavourable, depending on events and circumstances in the
future. Several different possible outcomes might result from the decision, and
managers take a risk hoping that the outcome will be favourable.
Decisions are therefore often made under conditions of uncertainty or risk. There
are some mathematical techniques that can be used to analyse risk or uncertainty in
business decisions. At this stage of your studies, you do not need to know all of
them and you do not need to know any technique in great detail.
The main technique you need to understand is the use of expected values.
One way of analysing costs and revenues when there is risk or uncertainty is to:
estimate the probability of different possible results or outcomes, and
use these estimates to calculate an expected value, and
base any decision on the expected value, or prepare a plan or budget on the basis
of the expected value.
Chapter 4: Business mathematics and computer spreadsheets
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1.2 Probabilities and expected values
Probabilities
When there is risk or uncertainty about what will happen, it might be possible to
estimate probabilities of the different possible outcomes. The total of the
probabilities of different possible outcomes is always 100% or 1.0. For example:
If it is estimated that there is an equal probability that the cost per unit of a
product will be $5 and $6, there is a 0.50 probability of $5 and a 0.50 probability
of $6.
If a company thinks it might make either a profit of $20,000 from a venture or a
loss of $15,000, and it is three times more likely that there will be a profit rather
than a loss, there is a 0.75 probability of a profit and a 0.25 probability of a loss.
Estimates of the probabilities of different outcomes might be an ‘educated guess’
based on experience and judgement. Sometimes, probabilities can be estimated
more reliably, using past experience as a guide to what is likely to happen in the
future. For instance, probabilities for different possible outcomes in the future might
be based on an analysis of historical records. An example might be an estimate of
the rate of defective output from a manufacturing process: historical records might
show that 0.5% of items produced in a manufacturing process are rejected as
defective items. This historical record might be used to asses the probability that
output will be defective in the future is 0.005 (= 0.5%) and the probability that units
of output will be free from defects is 0.995.
Expected value (EV)
An expected value (EV) is a weighted average value of different possible outcomes,
where the probability of each different possible outcome can be estimated. An
expected value can also be described as the ‘weighted average of a probability
distribution’.
An EV can be calculated using the following formula.
Expected value (EV) = ∑px
where:
∑ means ‘the sum of’
p = the probability of the outcome occurring. When there is a 50% probability
of an outcome, p = 0.50 and when the probability is 7%, p = 0.07, etc. The
total of the probabilities of all possible outcomes is 1.0 or 100%.
x = the outcome for which the probability has been estimated
When there is risk or uncertainty, and there different possible outcomes, each
possible outcome (x) has an associated probability (p). For each outcome and its
associated probability, multiply x by p. Then add up the total these values for ‘px’
that you have calculated. This gives you the expected value of the future outcome –
i.e. the weighted average expected outcome.
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Example
A cost accountant, working for a firm of builders, has been asked to estimate the cost
of building a new house, for which a customer has agreed a fixed price of $500,000.
There is some uncertainty about the costs of the labour for the job. These will not be
confirmed until after the building work begins. The cost accountant has estimated
that there is a 50% chance that the cost will be $360,000 and a 50% chance that it will
b
e $480,000.
One way of estimating the expected cost of building the house is to calculate the
expected value of cost.
Cost (= outcome) Probability
x p px
$ $
360,000 0.50 180,000
480,000 0.50 240,000
Expected value
420,000
Since the income from building the house will be $500,000, the expected value of
profit from the job is $500,000 – $420,000 = $80,000.
This EV is a weighted average probability of the profit. The actual outcome might be
$360,000 (in which case profit will be $140,000) or $480,000 (in which case profit will
be $20,000). The weighted average of possible outcomes is $80,000.
Example
The chief accountant in a company is concerned about the very high level of input
errors that the cost accountants are making when they enter transaction data into the
cost accounting system.
An investigation into a sample of transactions entered into the system during the
past two months has shown that 70% of entries were error-free, 20% had 1 error and
10% contained 2 errors. During a normal month, there are 10,000 entries into the
system.
What would be the estimate of the total number of errors in transaction entries each
month?
Answer
The estimate can be made by calculating an expected number of errors per
transaction entry. This is simply a weighted average of the number of errors per
entry. This is an expected value.