App 2 -Variance Investigation

APPENDIX 2 -VARIANCE INVESTIGATION

Accountancy Tuition Centre (Overseas Courses) Ltd 2002 1201

OVERVIEW

Objectives

To explain planning and operational variances.

To interpret and investigate variances.

Problems Calculations Market volume

and share Advantages and

disadvantages

Interdependence Direct costs Data manipulation Fixed overheads Causation

VARIANCE INVESTIGATION

LIMITATIONS OFTRADITIONAL

VARIANCES

PLANNING ANDOPERATIONAL

VARIANCES

INVESTIGATIONMODELS

OPPORTUNITYCOST

VARIANCES

CAUSES OFVARIANCES

Minimum size Percentage rule Statistical significance Statistical control charts Cost/benefit analysis

The Examiner has stated that

Candidates will not be asked to calculate variances in the paper 3.3 examination

Prior knowledge of variance analysis from previous papers is assumed.

Candidates may be given variances in the scenario and be required to interpret them or use them for further analysis.

This section of the notes is therefore provided for reference purposes only.



1 LIMITATIONS OF TRADITIONAL VARIANCE ANALYSIS

The limitations of standard costing mentioned in the previous session are relevant here.

In addition, traditional variance analysis has the following problems:

1.1 Interdependence of variances

A variance in one department may cause a variance in another.

Eg a favourable materials price variance may be achieved by buying substandard materials.

This may cause an adverse usage variance.

If the analysis is not interpreted with care a company might hold the production manager responsible for an adverse variance caused by a buyer.

1.2 Over-emphasis on direct costs

Traditional variance analysis concentrates on labour and materials variances.

However, in service businesses and in modern manufacturing environments, a large proportion of costs may be overheads.

Traditional overhead variances eg fixed overhead expenditure, are unlikely to give sufficiently detailed information for effective control.

1.3 Manipulation of data

In a budget constrained environment managers under stress may be tempted to manipulate actual results. This may be a particular problem if performance compared to budget is linked to rewards eg bonus, promotion.

Eg in a job costing system, the manager might try to hide overspends on a particular job by transferring/dumping time to jobs under-budget.

This is dysfunctional behaviour and variance analysis becomes meaningless.

1.4 Fixed overhead volume variance

A favourable volume variance simply represents over-absorption of fixed overheads due to actual output being above budget.

A belief that this “favourable” variance is of benefit to the business may lead to stockbuilding.

Excessive stockholding will however incur costs and reduce profits.



1.5 Causation

Fails to distinguish variances caused by inaccurate standards from those caused by operational factors.

Can be improved by calculating planning and operational variances.

2 PLANNING AND OPERATIONAL VARIANCES

2.1 Problems of traditional variance analysis

Traditional variance analysis compares:

Actualperformance

vs Expectedperformance

If the actual environment differs from that which was anticipated then actual performance should be compared with a standard which reflects the changed conditions (ex post standard).

Even if the environment has not changed, with hindsight (looking back) it might be realised than an unrealistic standard was used eg ideal standard.

Actual performance should be compared with a realistic standard for control and appraisal purposes – this variance is known as the Operating Variance. The difference between the ex ante and ex post targets is known as the Planning Variance.

Planning variance – a classification of variances caused by ex ante budget allowances being changed to an ex post basis.

Operational variance – a classification of variances in which non-standard performance is defined as being that which differs from an ex post standard.



2.2 Calculations

Use the following table to separate out PLANNING and OPERATING variances.

PLANNING AND OPERATING VARIANCE TABLE

£ORIGINAL FLEXED BUDGET (EX ANTE) X

REVISED FLEXED BUDGET (EX POST) X

ACTUAL RESULT X

PLANNINGVARIANCE(UNCONTROLLABLE)

OPERATINGVARIANCE(CONTROLLABLE)

Note – the examiner sometimes calls planning variances budget revision variances.

Example 1

Standard material cost/unit : 4 kgs at £2.50 = £10Budgeted Output : 20,000 unitsActual Output : 22,000 unitsMaterials actually used : 86,000 kgs at £3

With hindsight a better standard would have been 3.75 kg per unit at £2.80 per kg.

Required:

(a) Calculate the traditional variances

(i) Price Variance(ii) Usage Variance(iii) Overall Material Variance (price + usage)

(b) Calculate planning and operating variances

(c) To gain a better assessment of performance we now analyse the operatingvariance into Price and Usage.



Solution

(a) Traditional price and usage variances

(b) Planning and operating variances

£ Original flexed budget

Planning variance

Revised flexed budget

Actual result

Operating variance

(c) Operating price and usage variances

£ Operating price variance

Operating usage variance

Total operating variance

–––––

–––––

This revised analysis still indicates inefficiency on the part of the buying department and that there could be better use of materials.

Compare this with the traditional analysis which suggested a more serious inefficiency in buying ie £43,000 adverse price variance, coupled with efficient use of materials.

The PLANNING VARIANCE can also be split into price and usage, but it is questionable whether it provides useful information or not.



Example 2

Materials budget

3.4kg/unit £2/kg

Actual

2,000 units produced 7,000kg purchased and used, costing £2.20 per kg.

Required:

(a) Calculate the traditional price and usage variance.

Solution

(a) Traditional variances

Traditional price variance =

kg Traditional usage variance 2,000 units should use Actual usage

–––––

=

–––––

Example 2 (Contd)

The purchasing manager is furious when he receives a variance report criticising him. He produces evidence to suggest the average market price during the period was £2.30.

The production manager points out that the usage standard was an ideal standard and totally unrealistic. He calculates the current standard as 3.6kg/unit.

Required:

(b) Calculate

(i) the planning variance (ii) the operating price variance (iii) the operating usage variance.



Solution

(b) Planning and operational variances £ Original flexed budget

Planning variance

Revised flexed budget

Actual result

Operational variance

£ Operational price variance Kg Operational usage variance 2,000 units should use Actual usage

––––– kg @ ––––

––––

2.3 Market volume and market share variances

The traditional sales volume variance may have two elements:

the size of the market was different from expected – a change in the external environment

the share of that market was different from budget. .



The sales volume variance can therefore by split:

Sales volumevariance

Sales volumeplanning variance

Sales volumeoperational variance

Caused byexternal factors

Caused byinternal factors

Market volumevariance

Market sharevariance

£Budgeted profit/contribution fororiginal budgeted sales X

market volumeBudgeted profit/contribution for revised variancebudget sales X(revised market volume X budget market share)

market shareBudgeted profit/contribution for varianceactual sales X



Example 3

Acme Ltd has a Sales Budget of 1,795 units at a unit contribution of £20.00. This is based on the company maintaining a 5% market share. Total sales volume for the industry was estimated to be 35,900 units.

Actual sales volumes were as follows.

ACME LTD 1,850 unitsINDUSTRY 37,500 units

Required:

Calculate for ACME Ltd

(a) the traditional sales volume variance (b) the market volume and market share variance

Solution

(a) Sales volume variance

(b) Planning and operating sales volume variances table

£ Budgeted contribution for

Original budgeted sales

Market volume variance

Budgeted contribution for Revised budgeted sales

Budgeted contribution for

Actual sales

Market share variance



2.4 Advantages and disadvantages

2.4.1 Advantages

Distinguishes between variances caused by bad planning or unavoidable factors, and those due to operating factors.

Adverse operating variances indicate processes out of control which need correcting.

Planning variances can be used to update standards to current conditions.

Motivation may improve if managers know they will only be assessed on variances under their control ie operational variances.

2.4.2 Disadvantages

Extra data requirements eg market volume.

More time consuming.

Managers may claim all adverse variances have external causes and all favourable variances internal causes ie manipulation of revised standards for personal benefit.

3 OPPORTUNITY COST VARIANCES

Opportunity cost variance analysis attempts to associate variances with their direct cause.

A typical exam question requires a sub-analysis of the sales volume variance to show the reasons for sales being different from budget.

Example 4

Holland Ltd manufactures clogs.

Standard contribution per units £10. Standard labour time is 3 hours per unit.

Budget production and sales was 1,000 units.

Actual production was 900 units. Actual sales was 800 units.

Actual labour hours paid = 3,150 hours. Idle time = 500 hours.

Required:

Analyse the sales volume variance to show the gain or loss in contribution arising from the following factors:

(a) capacity (b) productivity (c) idle time (d) stock changes.



Solution

Sales volume variance =

(a) Capacity

Hours

Actual labour capacity Budget capacity

–––––

–––––

Extras potential contribution =

(b) Productivity

Hours worked =

This should produce

Actual production =

Potential contribution gain =

(c) Idle time

Potential contribution lost =

(d) Stock changes

Lost contribution due to stock increase

=

Summary £

Capacity increase Productivity increase Idle time Stock increase

Sales volume variance

––––––

––––––



4 CAUSES OF VARIANCES

Measurementerrors

Inaccuratestandards

Random factors(normal

fluctuations)

OPERATIONALFACTORS

Improve qualityof data

Calculateplanningvariances

Process is notout of control

Process is outof control

Should weinvestigate?

No need forinvestigation

Need aninvestigation rule



5 VARIANCE INVESTIGATION MODELS

Statisticalsignificance rule

Minimum size

% rule

Statisticalcontrolcharts

Managementjudgement

Cost/benefitanalysis

VARIANCEINVESTIGATION

MODELS

Ideally, only investigate variances which are

operational correctable significant benefits of investigation > costs of investigation.

5.1 Minimum size rule

Eg investigate all variances > £5,000.

An easy and widely used rule.

However, although £5,000 compared to a standard cost of £20,000 might indicate a problem, £5,000 compared to £20m is probably insignificant.

5.2 Percentage rule

Investigate variances greater than a certain percentage of standard.

Easy and widely used.

However, it ignores the absolute size of variances.

Eg investigate variances more than 5% of budget. £6 variance on a £100 budget will be investigated but £4,800 variance on a £100,000 budget will not be investigated.

Perhaps % rule should be combined will minimum size rule eg investigate if more than 5% and more than £1,000.



5.3 Statistical significance rule

5.3.1 Steps

Observe process when operating normally.

Estimate mean and standard deviation of costs under normal operations (ie with random fluctuations).

Assume costs are normally distributed eg an adverse variance more than 1.96 standard deviations (σ) above the mean (µ) has only a 2.5% chance of occurring due to random fluctuations.

Set significance level ie acceptable probability of investigating random variances.

Calculate investigation limits.

Example 5

The expected standard cost is £800, but due to random factors actual cost may fluctuate around the mean value with a standard deviation of £50. Costs fluctuate randomly according to the normal distribution.

Management wish to set investigation limits so that there is only a 2.5% chance of investigating a variance which has arisen simply due to random fluctuations.

Required:

Determine the investigation limits which management should set.

Solution



Z = x − µ

σ

⇒ x = µ + zσ

The z-value for 1.25% is 2.24 (from normal distribution tables).

... Investigate costs in excess of

and below

5.4 Statistical control charts

The above information can be illustrated on a statistical control chart.

Warning limits and Action limits are set a given distance from the mean – typically 1 SD and 2 SD respectively.

Labourrelatedcosts

£900

£850

£800

£750

£700

x xx

xx

Upper action limit(2σ)

Upper warning limit(1σ)

STANDARD COST

Lower warning limit(1σ)

Lower action limit(2σ)

JAN FEB MAR APR MAY

Management can spot worrying trends in particular variances and so be proactive rather than reactive.



5.5 Cost/benefit analysis

Identify:

costs of investigation (I) costs of correction if process is out of control (C) benefits of investigation (B) probability that process is out of control (P).

Investigate if:

pB > I + pC

Note – process out of control = operational variance

should be corrected

– process not out of control = Variance caused by random factor/planning error/measurement error

Process does not need to be corrected

Example 6

An £8,000 adverse variance will cost £1,500 to investigate and (if required) £4,000 to correct. If the variance is not corrected, and the process remains out of control, losses of £10,000 will occur.

Required:

(a) Should the process be investigated if there is a 0.4 chance it is out of control?

(b) At what level of probability would you be indifferent between investigatingand not investigating the variance?



Solution

Decision tree

0.6

RANDOMFACTOR

DON’T INVESTIGATE

OUT OF CONTROL0.4

0.6RANDOMFACTOR

0.4 OUT OF CONTROL

£4,000

INVESTIGATE

£1,500

£0

£0

£10,000

(1) Expected cost of investigation =

Expected benefit of investigating =

Optimal decision is to investigate the variance.

(2) Let p = probability the process is out of control

Equating indifference with cost = benefit and re-arranging:

∴ pB =

= =

p =



Example 7

Tudor’s management has the following data.

Cost to investigate whether a variance can be eliminated = £810.

Cost to correct a variance which can be eliminated = £300.

Probability that a variance can be eliminated = 0.30.

It has been estimated that the present value of the cost of not correcting a variance which can be eliminated is 60% of the size of the variance.

Required:

Calculate the minimum size of variance that would justify investigation.

Solution

Let V = variance

pB > I + pC

FOCUS

You should now be able to

discuss the limitations of traditional variances

calculate and discuss the advantages and limitations of planning, operational and opportunity cost variances

identify causes and explain the investigation of variances

explain and illustrate the use of investigation models including statistical control charts and decision trees.



EXAMPLE SOLUTIONS

Solution 1 – Materials

(a) Traditional price and usage variances

Price variance (2.50 – 3.00) 86,000 = £43,000 Adv

Usage variance (22,000 × 4 – 86,000) £2.50 = £5,000 Fav

Total variance = £38,000 Adv (b) Planning and operating variances

£ Original flexed budget

22,000 × 4 × £2.50 220,000

Planning variance £11,000 Adv

Revised flexed budget 22,000 × 3.75 × £2.8 231,000

Actual result

86,000 kg × £3 258,000

Operating variance£27,000 Adv

(c) Operating price and usage variances

£ Operating price variance

(2.80 – 3.00) 86,000

17,200 Adv

Operating usage variance (22,000 × 3.75 – 86,000) £2.8

9,800

Adv

Total operating variance

––––– 27,000 –––––

Adv

Solution 2 – Materials

(a) Traditional variances

Traditional price variance = (2 – 2.20) × 7,000 = £(1,400) A

kg Traditional usage variance 2,000 units should use (2,000 × 2.4) Actual usage

6,800(7,000)

–––––(200)

kg @ £2

= £(400)

–––––A



(b) Planning and operational variances £ Original flexed budget

2,000 × 3.4kg × £2 13,600

Planning variance (2,960)

Revised flexed budget 2,000 × 3.6 kg × £2.30 16,560

Actual result

(7,000 × 2.20) 15,400

Operational variance 1,160 F

Operational price variance = (2.30 – 2.20) × 7,000 = 700F Kg Operational usage variance 2,000 units should use (2,000 × 3.6) Actual usage

7,200(7,000)

––––– 200 kg @ 2.30 £460 F ––––

£1,160 ––––

F

Solution 3 – Sales

(a) Sales volume variance

(1,850 – 1,795) £20 = £1,100 Fav

(b) Planning and operating sales volume variances table

£ Budgeted contribution for

Original budgeted sales 1,795 × £20

35,900

Market volume variance

£1,600 Fav

Budgeted contribution for Revised budgeted sales 0.05 × 37,500 × £20

37,500

Budgeted contribution for

Actual sales 1,850 × £20

37,000

Market share variance

£500 Adv



Solution 4 – Opportunity cost variances

Sales volume variance = (800 – 1,000) × 10 = £(2,000)A

(a) Capacity

Hours

Actual labour capacity Budget capacity (1,000 × 3)

3,150(3,000)

–––––150

–––––

hrs favourable

Extras potential contribution = unitper hours 3

hours 150 × £10 = £500F

(b) Productivity

Hours worked = 3,150 – 500 = 2,650 hours.

This should produce 3650,2 = 883⅓ units

Actual production = 900 units

Potential contribution gain = (900 – 883⅓) × 10 = £167F

(c) Idle time

Potential contribution lost = 3

500 × 10 = £(1,667) A

(d) Stock changes

Lost contribution due to stock increase

= 100 units × £10 = £(1,000)A

Summary £

Capacity increase Productivity increase Idle time Stock increase

500167

(1,667)(1,000)

Sales volume variance

––––––(2,000)––––––

A



Solution 5 – Statistical significance

µ

800

1.25%1.25%

σ = 50µ = 800

Z = x − µ

σ

⇒ x = µ + zσ

The z-value for 1.25% is 2.24 (from normal distribution tables).

... Investigate costs in excess of 800 + 2.24 × 50 = £912

and below 800 – 2.24 × 50 = £688

Solution 6 – Cost/benefit analysis

0.6

RANDOMFACTOR

DON’T INVESTIGATE

OUT OF CONTROL0.4

0.6RANDOMFACTOR

0.4 OUT OF CONTROL

£4,000

INVESTIGATE

£1,500

£0

£0

£10,000



(1) Expected cost of investigation = £1,500 + (0.4 × £4,000) = £3,100

Expected benefit of investigating = 0.4 × £10,000 = £4,000

Optimal decision is to investigate the variance.

(2) Let P = probability the process is out of control

∴ pB10,000p

6,000pp

= = = =

I + pC 1,500 + 4,000p 1,500 0.25

Solution 7 – Minimum variance

Let V = variance

pB > I + pC

0.3 × 0.6 × V > 810 + (0.3 × 300)

0.18V > 900 V > 5,000

App 2 -Variance Investigation

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