Using Variance And Ratios
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The calculation and interpretation of variances, which measure the performance of a business (business unit) in comparison with standard / budget, and the ensuing control action are an important aspect of the Paper C2, Information for Management syllabus. Session 14 of the Teaching Guide covers the analysis of variances (variance calculations, investigation, causes and inter-relationships). Session 15 is concerned with management control using variances and ratios. This article covers Session 15 material, specifically: •
the concept and use of control limits and control charts;
•
control actions that may be taken in response to a reported variance;
•
calculation and evaluation of control ratios.
Control limits Standards are set in advance as a basis for comparison with actual results to reveal variation from expected performance. However, standards set should not be viewed too rigidly because: •
standards may be set at different levels (i.e. basic, current, attainable or ideal1) and thus variances from standard (favourable or adverse) may be expected;
•
standards are only estimates;
•
standards reflect the average performance that is expected over a period of time.
As a consequence: •
variance limits may be established. A limit would be an allowance for a variance (adverse or favourable) that would not trigger investigation and control action unless and until exceeded;
•
cumulative (rather than single period) variances may be compared with the control limit.
The variance allowance (or control limit) tries to allow for: •
the level at which the standard has been set (e.g. basic);
•
the difficulties of establishing the standard performance;
•
normal (or random) variations around average performance (as opposed to a consistent trend), especially if the cumulative variance is used for control purposes;
•
minor operational variances that are too small to justify the cost of investigation and control action.
While the concept of a variance allowance is relatively straightforward, the setting of the limit in practice, allowing for the several factors outlined above, is difficult. A combination of experience / judgement and the application of statistics (e.g. standard deviation) may be used. Control charts Control charts are a useful way of presenting variance data over a period of time, in relation to the control limits set (whether single period or cumulative). This is illustrated in Figure 1.
Figure 1: Control charts
Control action Whether to take action will generally depend upon whether a variance identified (especially if cumulative) is outside the control limits. If outside the limit, the variance will be material and a trend is likely to have been established. Further analysis and investigation would then follow, subject to: •
whether the underlying cause is already known or whether it is likely to be controllable, i.e. lead to the possibility of control action being taken;
•
the likely cost of investigation. Judgement needs to be made as to whether likely benefits resulting from investigation will exceed the cost;
•
behavioural considerations e.g. the effect on staff motivation.
The result could be: •
more informed performance management;
•
corrective action;
•
a change to the standard / budget;
•
no action / no change to target.
Control ratios Any business, to be successful, will need to obtain the right resources at minimum cost and use these resources efficiently to produce the desired outputs. This is the essence of the 3 Es (Economy, Efficiency and Effectiveness). The setting of standards and comparison of actual with standard / budgeted performance can be an important part of the measurement of economy, efficiency and effectiveness. Variance analysis, in the form of monetary values, measures the impact on profit of differences between actual and standard / budget. Control ratios measure performance against standard / budget in relative (%) terms. There are three key control ratios: capacity (resource input), efficiency (productivity of resource usage) and activity (output volume).
The basis of performance measurement via these control ratios is the concept of the standard hour (the amount of work achievable, at standard efficiency levels in an hour1). The standard hour provides a common basis for the measurement of work done, typically in a production (factory) environment. Actual hours worked on a variety of tasks can be compared with budgeted hours, and with the output achieved measured in standard hours. The capacity ratio typically measures the utilisation of labour resource in terms of total hours worked in comparison with those budgeted. The usual formula for the calculation of the capacity ratio is: Actual hours worked x 100% Budgeted hours A capacity ratio of 100% would mean that budgeted hours were worked. A ratio of <100% would indicate hours worked < budget and a ratio >100% would indicate hours worked > budget. The efficiency ratio measures how well the labour resource has been used in comparison with the standard set. The formula for the calculation of the efficiency ratio is: Standard hours of output x 100% Actual hours worked An efficiency ratio of 100% would mean that the productivity of labour was exactly on standard. An efficiency ratio <100% would indicate productivity < standard and an efficiency ratio >100% would indicate productivity > standard. The activity (also called volume or production volume) ratio typically measures the output achieved compared with budget. The usual formula for the calculation of the activity ratio is: Standard hours of output x 100% Budgeted hours An activity ratio of 100% would mean that output was on budget. A ratio of <100% would indicate output < budget and a ratio >100% would indicate output > budget. The activity ratio is a function of the resources utilised (capacity ratio) and how well they are used (efficiency ratio) and thus the ratio can be expressed as: Activity = Capacity x Efficiency Standard hours of output Budgeted hours = Actual hours worked Budgeted hours x Standard hours of output Actual hours worked The June 2001 and December 2001 Paper C2 examinations included questions featuring the calculation and evaluation of control ratios. These two questions are used in the following examples. Example 1 Question 4 in the June 2001 examination required the calculation of control ratios, but in a nonproduction setting (i.e. a firm of accountants). It should be noted that the capacity and activity ratios were used differently to the typical production environment formulae described above.
Candidates were required to apply their knowledge and understanding of control ratios. Clear instructions were given as to the meaning and basis for calculation of each of the ratios. Question A firm of accountants uses the standard hours worked by professional staff on client business as the basis for client charging, and for cost control. The standard hours for each client job are established in advance, based on the expected amount of time required for each task. Some of the hours worked by professional staff are not on client business and are thus not chargeable. Target control ratios are: Activity 96.9% Efficiency 102.0% Capacity 95.0% The activity ratio measures the standard hours of work by professional staff on client business, as a proportion of the total hours worked by the professional staff. The efficiency ratio measures the relationship between the standard and the actual professional staff hours spent on client business. The capacity ratio measures the actual professional staff hours spent on client business as a proportion of their total hours worked. During a period, the actual hours worked by professional staff totalled 3,630 of which 3,471 hours were spent on client business. The standard hours for the work totalled 3,502. Required: a. Calculate appropriate control ratios for the period (each to one decimal place of a percent). b. Prepare a brief report for the firm’s senior partners that: i. interprets the control ratios calculated in (a) above; ii. identifies possible causes of any variation from target. c. Describe the factors that should be considered before a decision is made to investigate a variation from target. Comment As can be seen from the question, the fact that some of the hours worked by professional staff are not on client business, and thus not chargeable, means that target ratios set for capacity and activity (as defined in this particular example) are below 100%. The target activity ratio is higher than the target capacity ratio because an efficiency ratio >100% is expected: Activity = Capacity x Efficiency 0.969 = 0.95 x 1.02 Thus 100% is not expected for any of the control ratios and thus some variances from 100% would be regarded as normal i.e. allowed for. Control limits could be established around the target levels set (although not indicated in this example). Answer a. Control ratios:
Activity ratio = (3,502 ¸ 3,630) x 100% = 96.5% Capacity ratio = (3,471 ¸ 3,630) x 100% = 95.6% Efficiency ratio = (3,502 ¸ 3,471) x 100% = 100.9%
b. Report:
To: Senior partners From: A N Accountant Date: X / X / XX Subject: Control ratios for Period X Set out below is a summary of performance (as measured by the activity, efficiency and activity ratios) for Period X, and a description of the possible causes of variation from target (currently under investigation). Control ratios: The proportion of the total hours worked by professional staff in the period, that were charged to clients, was 96.5%. This was 0.4 percentage points below target. A greater proportion of hours than target were actually spent on client business (at 95.6% a favourable capacity variance of 0.6 percentage points). However, below target efficiency (despite being above 100% it was nevertheless 1.1 percentage points below the target of 102.0%) meant that the work achieved was not converted into sufficient chargeable output. The link between activity, capacity and efficiency ratios is as follows: Activity (0.965) = Capacity (0.956) x Efficiency (1.009) Reasons for variation: Possible reasons for the favourable capacity variance versus target are improved scheduling of client business and reduced training requirements in the period. The adverse efficiency variance may have resulted from a greater proportion of less experienced junior staff hours, problems with particular jobs and / or a rather demanding target. c) Factors affecting investigation: A number of factors should be considered before deciding whether to investigate a variation from target: •
Whether control limits have been set and whether the variance lies outside the control limit. Small variations are always likely to occur (in £ and / or % of standard / target) especially in a single period.
•
Whether the variance is controllable. Variations may result from uncontrollable external factors or from central decisions (e.g. a pay award). Such variations may call for a change in the standard / target for the future, not an investigation into the past.
•
Whether a trend has been established. Variations from standard / target are more likely to justify investigation if they are repeated over several periods. Fluctuation either side of target may simply be an inevitable consequence of fluctuating business conditions.
•
Whether expected benefits are likely to exceed the cost of investigation, including the effect on staff motivation / morale. All of the above factors will have a bearing on whether the potential benefit from investigation of a variance is likely to outweigh the cost. However, there may also be other factors to consider (e.g. past experience, nature of the expense item, responsibility area) which are likely to influence the net outcome of an investigation.
Example 2 Question 2(b) in the December 2001 examination focused on the efficiency ratio in a situation where standards were set at different levels (i.e. basic, attainable and ideal) and used for different
purposes. Candidates were required to apply their knowledge and understanding of control ratios flexibly. Question A company uses basic, attainable and ideal standards within its performance management system. Attainable standards are used, within each period, as the basis for monitoring and controlling short term performance. Both basic and ideal standards are used to measure longerterm efficiency improvements. The attainable standard time for one of the operations in the company’s factory is currently set at 1.2 direct labour hours per hundred units of output. The basic and ideal standards for the operation, per direct labour hour, are set at 75 units and 90 units of output respectively. During the period just ended, 163,085 units were manufactured in 1,930 direct labour hours. The standard direct labour rate is £7.50 per hour. Required: Calculate for the operation described above: i. the direct labour efficiency variance (£) and the efficiency ratio (%) for the period; ii. the % improvement achieved to date, based on the actual performance in the most recent period compared with the basic standard; iii. the further % improvement possible, based on a comparison of the ideal and the attainable standards. Comment Attainable standards are used in the above example as the basis for monitoring and controlling short-term performance. In the absence of any information to the contrary, a ratio of 100% (actual hours versus attainable standard) is presumably the target. If attainable hours are seen as difficult to achieve, a target of slightly less than 100% could be set with control limits. Basic and ideal standards may, at the same time, be set and used but with a different purpose (as seen in this example) viz. to measure longer-term changes in efficiency. to measure longer-term changes in efficiency. Answer Standard hours of output = 163,085 units x 1.2 direct labour hours per unit 100 = 1,957 standard direct labour hours i Efficiency variance (£) = (1,957 std hrs - 1,930 actual hrs) x £7.50 per hr = £203 favourable Efficiency ratio (%) = (1,957 std hrs ¸ 1,930 actual hrs) x 100% = 101.4% ii Improvement achieved: Most recent period = 163,085 units ¸ 1,930 hours
= 84.5 units per direct labour hour Achievement (actual versus basic standard) = [(84.5 ¸ 75) - 1] x 100% = 12.7% improvement achieved iii Improvement possible: Attainable standard = 100 units ¸ 1.2 hours = 83.3 units per direct labour hour Potential (ideal versus attainable standard) = [(90 ¸ 83.3) - 1] x 100% = 8.0% further improvement possible
the concept and use of control limits and control charts;
•
control actions that may be taken in response to a reported variance;
•
calculation and evaluation of control ratios.
Control limits Standards are set in advance as a basis for comparison with actual results to reveal variation from expected performance. However, standards set should not be viewed too rigidly because: •
standards may be set at different levels (i.e. basic, current, attainable or ideal1) and thus variances from standard (favourable or adverse) may be expected;
•
standards are only estimates;
•
standards reflect the average performance that is expected over a period of time.
As a consequence: •
variance limits may be established. A limit would be an allowance for a variance (adverse or favourable) that would not trigger investigation and control action unless and until exceeded;
•
cumulative (rather than single period) variances may be compared with the control limit.
The variance allowance (or control limit) tries to allow for: •
the level at which the standard has been set (e.g. basic);
•
the difficulties of establishing the standard performance;
•
normal (or random) variations around average performance (as opposed to a consistent trend), especially if the cumulative variance is used for control purposes;
•
minor operational variances that are too small to justify the cost of investigation and control action.
While the concept of a variance allowance is relatively straightforward, the setting of the limit in practice, allowing for the several factors outlined above, is difficult. A combination of experience / judgement and the application of statistics (e.g. standard deviation) may be used. Control charts Control charts are a useful way of presenting variance data over a period of time, in relation to the control limits set (whether single period or cumulative). This is illustrated in Figure 1.
Figure 1: Control charts
Control action Whether to take action will generally depend upon whether a variance identified (especially if cumulative) is outside the control limits. If outside the limit, the variance will be material and a trend is likely to have been established. Further analysis and investigation would then follow, subject to: •
whether the underlying cause is already known or whether it is likely to be controllable, i.e. lead to the possibility of control action being taken;
•
the likely cost of investigation. Judgement needs to be made as to whether likely benefits resulting from investigation will exceed the cost;
•
behavioural considerations e.g. the effect on staff motivation.
The result could be: •
more informed performance management;
•
corrective action;
•
a change to the standard / budget;
•
no action / no change to target.
Control ratios Any business, to be successful, will need to obtain the right resources at minimum cost and use these resources efficiently to produce the desired outputs. This is the essence of the 3 Es (Economy, Efficiency and Effectiveness). The setting of standards and comparison of actual with standard / budgeted performance can be an important part of the measurement of economy, efficiency and effectiveness. Variance analysis, in the form of monetary values, measures the impact on profit of differences between actual and standard / budget. Control ratios measure performance against standard / budget in relative (%) terms. There are three key control ratios: capacity (resource input), efficiency (productivity of resource usage) and activity (output volume).
The basis of performance measurement via these control ratios is the concept of the standard hour (the amount of work achievable, at standard efficiency levels in an hour1). The standard hour provides a common basis for the measurement of work done, typically in a production (factory) environment. Actual hours worked on a variety of tasks can be compared with budgeted hours, and with the output achieved measured in standard hours. The capacity ratio typically measures the utilisation of labour resource in terms of total hours worked in comparison with those budgeted. The usual formula for the calculation of the capacity ratio is: Actual hours worked x 100% Budgeted hours A capacity ratio of 100% would mean that budgeted hours were worked. A ratio of <100% would indicate hours worked < budget and a ratio >100% would indicate hours worked > budget. The efficiency ratio measures how well the labour resource has been used in comparison with the standard set. The formula for the calculation of the efficiency ratio is: Standard hours of output x 100% Actual hours worked An efficiency ratio of 100% would mean that the productivity of labour was exactly on standard. An efficiency ratio <100% would indicate productivity < standard and an efficiency ratio >100% would indicate productivity > standard. The activity (also called volume or production volume) ratio typically measures the output achieved compared with budget. The usual formula for the calculation of the activity ratio is: Standard hours of output x 100% Budgeted hours An activity ratio of 100% would mean that output was on budget. A ratio of <100% would indicate output < budget and a ratio >100% would indicate output > budget. The activity ratio is a function of the resources utilised (capacity ratio) and how well they are used (efficiency ratio) and thus the ratio can be expressed as: Activity = Capacity x Efficiency Standard hours of output Budgeted hours = Actual hours worked Budgeted hours x Standard hours of output Actual hours worked The June 2001 and December 2001 Paper C2 examinations included questions featuring the calculation and evaluation of control ratios. These two questions are used in the following examples. Example 1 Question 4 in the June 2001 examination required the calculation of control ratios, but in a nonproduction setting (i.e. a firm of accountants). It should be noted that the capacity and activity ratios were used differently to the typical production environment formulae described above.
Candidates were required to apply their knowledge and understanding of control ratios. Clear instructions were given as to the meaning and basis for calculation of each of the ratios. Question A firm of accountants uses the standard hours worked by professional staff on client business as the basis for client charging, and for cost control. The standard hours for each client job are established in advance, based on the expected amount of time required for each task. Some of the hours worked by professional staff are not on client business and are thus not chargeable. Target control ratios are: Activity 96.9% Efficiency 102.0% Capacity 95.0% The activity ratio measures the standard hours of work by professional staff on client business, as a proportion of the total hours worked by the professional staff. The efficiency ratio measures the relationship between the standard and the actual professional staff hours spent on client business. The capacity ratio measures the actual professional staff hours spent on client business as a proportion of their total hours worked. During a period, the actual hours worked by professional staff totalled 3,630 of which 3,471 hours were spent on client business. The standard hours for the work totalled 3,502. Required: a. Calculate appropriate control ratios for the period (each to one decimal place of a percent). b. Prepare a brief report for the firm’s senior partners that: i. interprets the control ratios calculated in (a) above; ii. identifies possible causes of any variation from target. c. Describe the factors that should be considered before a decision is made to investigate a variation from target. Comment As can be seen from the question, the fact that some of the hours worked by professional staff are not on client business, and thus not chargeable, means that target ratios set for capacity and activity (as defined in this particular example) are below 100%. The target activity ratio is higher than the target capacity ratio because an efficiency ratio >100% is expected: Activity = Capacity x Efficiency 0.969 = 0.95 x 1.02 Thus 100% is not expected for any of the control ratios and thus some variances from 100% would be regarded as normal i.e. allowed for. Control limits could be established around the target levels set (although not indicated in this example). Answer a. Control ratios:
Activity ratio = (3,502 ¸ 3,630) x 100% = 96.5% Capacity ratio = (3,471 ¸ 3,630) x 100% = 95.6% Efficiency ratio = (3,502 ¸ 3,471) x 100% = 100.9%
b. Report:
To: Senior partners From: A N Accountant Date: X / X / XX Subject: Control ratios for Period X Set out below is a summary of performance (as measured by the activity, efficiency and activity ratios) for Period X, and a description of the possible causes of variation from target (currently under investigation). Control ratios: The proportion of the total hours worked by professional staff in the period, that were charged to clients, was 96.5%. This was 0.4 percentage points below target. A greater proportion of hours than target were actually spent on client business (at 95.6% a favourable capacity variance of 0.6 percentage points). However, below target efficiency (despite being above 100% it was nevertheless 1.1 percentage points below the target of 102.0%) meant that the work achieved was not converted into sufficient chargeable output. The link between activity, capacity and efficiency ratios is as follows: Activity (0.965) = Capacity (0.956) x Efficiency (1.009) Reasons for variation: Possible reasons for the favourable capacity variance versus target are improved scheduling of client business and reduced training requirements in the period. The adverse efficiency variance may have resulted from a greater proportion of less experienced junior staff hours, problems with particular jobs and / or a rather demanding target. c) Factors affecting investigation: A number of factors should be considered before deciding whether to investigate a variation from target: •
Whether control limits have been set and whether the variance lies outside the control limit. Small variations are always likely to occur (in £ and / or % of standard / target) especially in a single period.
•
Whether the variance is controllable. Variations may result from uncontrollable external factors or from central decisions (e.g. a pay award). Such variations may call for a change in the standard / target for the future, not an investigation into the past.
•
Whether a trend has been established. Variations from standard / target are more likely to justify investigation if they are repeated over several periods. Fluctuation either side of target may simply be an inevitable consequence of fluctuating business conditions.
•
Whether expected benefits are likely to exceed the cost of investigation, including the effect on staff motivation / morale. All of the above factors will have a bearing on whether the potential benefit from investigation of a variance is likely to outweigh the cost. However, there may also be other factors to consider (e.g. past experience, nature of the expense item, responsibility area) which are likely to influence the net outcome of an investigation.
Example 2 Question 2(b) in the December 2001 examination focused on the efficiency ratio in a situation where standards were set at different levels (i.e. basic, attainable and ideal) and used for different
purposes. Candidates were required to apply their knowledge and understanding of control ratios flexibly. Question A company uses basic, attainable and ideal standards within its performance management system. Attainable standards are used, within each period, as the basis for monitoring and controlling short term performance. Both basic and ideal standards are used to measure longerterm efficiency improvements. The attainable standard time for one of the operations in the company’s factory is currently set at 1.2 direct labour hours per hundred units of output. The basic and ideal standards for the operation, per direct labour hour, are set at 75 units and 90 units of output respectively. During the period just ended, 163,085 units were manufactured in 1,930 direct labour hours. The standard direct labour rate is £7.50 per hour. Required: Calculate for the operation described above: i. the direct labour efficiency variance (£) and the efficiency ratio (%) for the period; ii. the % improvement achieved to date, based on the actual performance in the most recent period compared with the basic standard; iii. the further % improvement possible, based on a comparison of the ideal and the attainable standards. Comment Attainable standards are used in the above example as the basis for monitoring and controlling short-term performance. In the absence of any information to the contrary, a ratio of 100% (actual hours versus attainable standard) is presumably the target. If attainable hours are seen as difficult to achieve, a target of slightly less than 100% could be set with control limits. Basic and ideal standards may, at the same time, be set and used but with a different purpose (as seen in this example) viz. to measure longer-term changes in efficiency. to measure longer-term changes in efficiency. Answer Standard hours of output = 163,085 units x 1.2 direct labour hours per unit 100 = 1,957 standard direct labour hours i Efficiency variance (£) = (1,957 std hrs - 1,930 actual hrs) x £7.50 per hr = £203 favourable Efficiency ratio (%) = (1,957 std hrs ¸ 1,930 actual hrs) x 100% = 101.4% ii Improvement achieved: Most recent period = 163,085 units ¸ 1,930 hours
= 84.5 units per direct labour hour Achievement (actual versus basic standard) = [(84.5 ¸ 75) - 1] x 100% = 12.7% improvement achieved iii Improvement possible: Attainable standard = 100 units ¸ 1.2 hours = 83.3 units per direct labour hour Potential (ideal versus attainable standard) = [(90 ¸ 83.3) - 1] x 100% = 8.0% further improvement possible
