ACCA F5 Performance Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 10: Basic variance analysis
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Deciding whether to investigate a variance
Management responses to reported variances
Factors to consider
Interdependence between variances
Statistical control charts
Cost-benefit analysis for variance investigation
11 Deciding whether to investigate a variance
11.1 Management responses to reported variances
When a variance is reported, the manager responsible must decide whether it
should be investigated. The purpose of investigating a variance is to:
find out the cause or causes of the variance
decide whether the variance is ‘controllable’: a variance is controllable if
management control action can be taken that will affect the amount of the
variance in future periods
if the variance is controllable, to decide whether any control action should be
taken to deal with its cause.
Investigating the cause of a variance takes management time and can be costly.
Management should not spend time and money on an investigation if the expected
benefits are unlikely to exceed the costs.
The size of a reported variance can be misleading. For example, if a reported labour
efficiency variance is $4,000 adverse, this does not mean that $4,000 can be saved by
taking action to correct the cause of the adverse variance.
The reported variance is a historical variance, and any control action can only
affect the future, not what has already happened in the past.
The reported variance shows how much actual costs were higher than expected
because actual efficiency was worse than the expected standard of efficiency.
However, this does not mean that control action will enable the entity to achieve
standard efficiency in the future. For example, the standard might be an ideal
standard, which means that the reported efficiency variance will almost certainly
always be adverse.
Control action should affect all periods in the future, so the effect of taking
control action in response to a reported variance in one period could have an
effect that lasts for several periods, or even years, into the future.
11.2 Factors to consider
Before making a decision whether to investigate a variance, the following factors
should be considered:
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Size of the variance. As a general rule, the cause of a variance is more likely to
be significant when the variance is large. For example, a sales volume variance
that is $40,000 adverse will be considered more significant than a sales volume
variance of $400 adverse. The larger the variance, the greater the potential
benefit from investigation and control measures.
Favourable or adverse variance. Significant controllable favourable variances
should be investigated as well as adverse variances. However, more significance
might be given by management to adverse variances than to favourable
variances. Management might take the view that if a reported variance is
favourable, no action is needed and the variance might continue to be favourable
in future periods – and this is desirable. However, using the same logic, unless
control action is taken to correct the cause of an adverse variance, adverse
variances will continue in the future – and this is undesirable. For this reason, a
fairly small adverse variance might be investigated, but a favourable variance of
the same amount might not be investigated.
Probability that the cause of the variance will be controllable. A decision
whether or not to investigate the cause of a variance will also depend on the
expectation of management that the cause of the variance will be controllable.
For example, management might be aware that there has recently been a
significant increase in the market price of a raw material, or an increase in pay
rates for employees. If so, they might decide that reported adverse material price
and labour rate variances shouldn’t be investigated, because the main cause is
already known and it is unlikely that any control measures can be taken that will
be effective in reducing adverse price and rate variances in the future.
Costs and benefits of control action. Investigating a variance has a cost in terms
of both management time and expenditure. A variance should not be
investigated unless the expected benefits exceed the costs of investigation and
control. The benefits are the cost savings or other benefits that will be obtained
in the future if the variance is found to have a controllable cause and control
action is therefore taken.
Random variations in reported variances. Management might take the view
that a favourable or adverse variance in one month is due to random factors that
will not recur next month. A decision might therefore be taken to do nothing in
the current month about the variance, but to wait and see whether the same
variance occurs again next month. If the variance is due to random factors, it
should not happen again next month, and management can probably ignore it
without risk.
Reliability of budgets and measurement systems. Management might have a
view about whether the variance is caused by poor planning and poor
measurement systems, rather than by operational factors. If so, investigating the
variance would be a waste of time and would be unlikely to lead to any cost
savings.
11.3 Interdependence between variances
In some cases, individual variances should not be considered in isolation. The cause
of one variance might be connected to the cause of another variance. For example:
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An adverse materials usage variance might be caused by purchasing cheaper-
than-normal materials (favourable price variance). If the quality of the materials
is less than normal, higher rates of wastage or loss in production may occur.
An adverse direct labour rate variance might be caused by using experienced
workers who are more skilled but who are paid a higher rate. The employees
might do the work more efficiently and more quickly (so there would be a
favourable efficiency variance for labour and variable overheads) but there will
be an adverse rate variance.
Using unskilled workers to do a job might result in a favourable rate variance
but an adverse efficiency variance. In addition, unskilled workers may cause
higher wastage of materials, so that there may also be an adverse materials
usage variance.
A favourable sales volume variance might be the result of cutting prices (adverse
sales price variance).
Mix variances are described in the next chapter. However, there may be a
connection between the total material usage variance in production (the material
yield variance) and the mix of different materials used in production. Using a
cheaper mix of materials in production will result in a favourable mix variance,
but the consequence mat be inefficiency in material usage (an adverse yield
variance).
The possibility of interdependence between variances means that if management
decide to investigate one reported variance, they might find that they also have to
investigate or more inter-related variances, to establish the cause of the variance and
the possible benefits from control action.
11.4 Statistical control charts
Statistical control charts might be used for the assessment of variances and making a
decision whether or not to investigate a reported variance.
Control limits might be set for each variance, so that only variances that are an
unusually large amount, and exceed the control limit, should be investigated.
This could be plotted on a statistical control chart, with the control limits shown
as ‘trigger limits’ for control action. The control limit for investigating a
favourable variance could be a different size to the control limit for an adverse
variance.
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This statistical control chart shows reported variances over time. The variances
recorded on the chart could be:
The variance in each individual control period
A cumulative total of variances, for example a 12-month rolling total for the
variance. The variance should only be investigated if the cumulative total for the
past 12 months exceeds the upper or lower control limit.
11.5 Cost-benefit analysis for variance investigation
The decision about whether or not to investigate a variance might be based on an
assessment of:
the costs of investigating the variance
the probability that the cause of the variance will be a controllable factor
the costs of control action if the cause is controllable
the expected benefits from control action if the cause is controllable.
This method weighs up the expected value of the costs and the expected value of
the benefits of investigating a variance.
The ‘decision rule’ for investigating a variance can be expressed as a formula.
The variance should be investigated if:
I + pC < pB
Where:
I = the cost of investigating the variance
C = the cost of correcting the cause of the variance, if the cause is found to be
controllable
p = the probability that the cause of the variance will be controllable
B = the expected benefits from control action, if the cause of the variance is found to
be controllable
Example
An adverse material usage variance of $1,400 has been reported.
The estimated cost of investigating the cause of a material usage variance is $800.
It is also estimated that if the cause of the variance is found, after investigation, to be
controllable, the cost of taking control action would be $650.
The estimated benefits from control action, if the cause of the variance is found to be
controllable, are $2,500.
The probability that the variance will be caused by a controllable factor is 60%.
Should the variance be investigated?
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Answer
EV of costs of investigation = I + pC = $800 + 0.60 ($650) = $1,190.
EV of benefits from investigation and control = pB = 0.6 × $2,500 = $1,500.
The EV of benefits exceed the EV of costs by $310; therefore the variance should be
investigated.
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Paper F5
Performancemanagement
CHAPTER
11
Advanced variance analysis
Contents
1 Materials mix and yield variances
2 Planning and operational variances
3 Market size and market share variances
4 Behavioural aspects of standard costing
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Materials mix and yield variances
Definition of materials mix and yield variances
Calculating a direct materials mix variance
Calculating a direct materials yield variance
Changing the materials mix: factors to consider
1 Materials mix and yield variances
1.1 Definition of materials mix and yield variances
When standard costing is used for products which contain two or more items of
direct material, the total materials usage variance can be analysed into a materials
mix and a materials yield variance. However, mix and yield variances have a useful
meaning only when the proportions (or ‘mix’) of the different raw materials in the
final product can be varied and so are subject to management control
The total direct materials usage variance is calculated by taking each item of
direct material in turn, and calculating a materials usage variance in the normal
way. The total direct material usage variance is the sum of the direct materials
usage variance for each of the individual materials.
The materials mix variance measures how much of this total variance is
attributable to the fact that the actual combination or mixture of materials that
was used was more expensive or less expensive than the standard mixture for
the materials.
The materials yield variance is a total usage variance for all the materials taken
together, assuming that the materials are in the standard proportions or mix. It is
calculated as a single figure, using the weighted average standard price per unit
of material for the calculation of the variance.
The mix component of the usage variance therefore indicates the effect on costs of
changing the combination (or mix or proportions) of material inputs in the
production process.
The yield component indicates the effect on costs of the total materials inputs
yielding more or less output than expected.
There is possible value for management, for control purposes, in calculating a mix
variance and a yield variance, but only if they are in a position to control the
mixture or proportions of the materials in the manufactured item.
1.2 Calculating a direct materials mix variance
There are two methods of calculating the mix variance. Both should provide exactly
the same variance. You should use the method that you find easier to understand.
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Method 1
Take the total quantity of al the materials used and calculate what the quantities
of each material in the mix should be if the total usage had been in the standard
proportions or standard mix.
Compare the actual quantities of each individual material that were used, and
the standard quantities that would have been used (the standard mix) if the total
usage had been in the standard proportions or standard mix.
For each material, take the difference between the quantity in the actual mix
used and the quantity in the standard mix. If actual usage is higher than
standard usage, the variance is adverse. If actual usage is less than standard
usage, the variance is favourable. The total mix variance in material quantities is
always zero.
Convert the mix variance for each individual material into a money value by
multiplying by the standard price per unit of the material. Add the total mix
variances for each material (money values) to obtain the total mix variance.
If the actual mix used is more expensive than the standard mix, the total mix
variance is adverse. If the actual mix used is cheaper than the standard mix, the
total mix variance is adverse.
Example
Product N is produced from three direct materials that are mixed together in a
process, materials A, B and C. The standard materials cost for product N is as
follows:
Material
Quantity
Standard price
per kilo
Standard
cost
kilos
$
$
A 1
20
20
B 1
22
22
C 8
6
48
10
90
Actual output during month 6 amounted to 200 units of product N in total. Actual
usage of each material was as follows:
Material kilos
A 160
B 180
C 1,760
2,100
Required
Calculate the direct materials mix variance for month 6.
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Answer
The total quantity used was 2,100 kilos. This total usage can be divided into a
standard mix for materials A, B and C and the standard mix and actual mix can be
compared, as follows.
Material
Actual
mix
Standard
mix
Mix variance
in quantities
Standard price
per kilo
Mix variance
in value
kilos kilos
kilos
$ $
A 160 (1) 210
50
(F) 20 1,000
(F)
B 180 (1) 210
30
(F) 22 660
(F)
C 1,760 (8) 1,680
80
(A) 6 480
(A)
2,100 2,100
0
1,180
(F)
For each individual item of material, the mix variance is favourable when the actual
mix is less than the standard mix, and the mix variance is adverse when actual
usage exceeds the standard mix.
The total mix variance is favourable in this example because the actual mix of
materials used is cheaper than the standard mix.
Method 2
Method 2 produces the same value for the mix variance.
Take the total quantity of materials used.
For each material, calculate a mix variance in quantities, the same as for method
1. However, do not decide yet whether the variance is adverse or favourable for
each material.
Next, calculate the weighted average price per unit of materials in the mix. This
is calculated as [the total direct materials cost per unit divided by the total
number of units of materials in one unit of finished product].
For each material, calculate the difference between the standard price for the
material and the weighted average standard price.
A cheap material is a material whose standard price is lower than the weighted
average standard price for materials in the mix.
An expensive material is a material whose standard price is higher than the
weighted average standard price for materials in the mix.
Next, for each material in the mix, multiply the mix variance in quantities by the
difference between its standard price and the weighted average standard price.
Decide whether the variance for each material is favourable or adverse.
− If there is more of a cheap material in the actual mix than in the standard
mix, the variance for the material is favourable.
− If there is less of a cheap material in the actual mix than in the standard mix,
the variance for the material is adverse.
− If there is more of an expensive material in the actual mix than in the
standard mix, the variance for the material is adverse.