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**Variance Analysis: Material, Labour, Overhead and Sales Variances!**

The function of standards in cost accounting is to reveal variances between standard costs which are allowed and actual costs which have been recorded. The Chartered Institute of Management Accountants (UK) defines variances as the difference between a standard cost and the comparable actual cost incurred during a period. Variance analysis can be defined as the process of computing the amount of, and isolating the cause of variances between actual costs and standard costs. Variance analysis involves two phases:

(1) Computation of individual variances, and

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(2) Determination of Cause (s) of each variance.

**We now turn to explain below the computation of material, labour and factory overhead variances: **

### I. Material Variance:

**The following variances constitute materials variances:**

**Material Cost Variance**:

Material cost variance is the difference between the actual cost of direct material used and standard cost of direct materials specified for the output achieved. This variance results from differences between quantities consumed and quantities of materials allowed for production and from differences between prices paid and prices predetermined.

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**This can be computed by using the following formula: **

Material cost variance = (AQ X AP) – (SQ X SP)

Where AQ = Actual quantity

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AP = Actual price

SQ = Standard quantity for the actual output

SP = Standard price

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The material quantity or usage variance results when actual quantities of raw materials used in production differ from standard quantities that should have been used to produce the output achieved. It is that portion of the direct materials cost variance which is due to the difference between the actual quantity used and standard quantity specified.

**As a formula, this variance is shown as: **

Materials quantity variance = (Actual Quantity – Standard Quantity) x Standard Price

A material usage variance is favourable when the total actual quantity of direct materials used is less than the total standard quantity allowed for the actual output.

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**Compute the materials usage variance from the following information: **

Standard material cost per unit Materials issued

Material A — 2 pieces @ Rs. 10=20 (Material A 2,050 pieces)

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Material B — 3 pieces @ Rs. 20 =60 (Material B 2,980 pieces)

Total = 80

Units completed 1,000

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Material usage variance = (Actual Quantity – Standard Quantity) x Standard Price

Material A = (2,050 – 2,000) x Rs. 10 = Rs. 500 (unfavourable)

Material B = (2980 – 3000) x Rs. 20 = Rs. 400 (favourable)

Total = Rs. 100 (unfavourable)

It should be noted that the standard rather than the actual price is used in computing the usage variance. Use of an actual price would have introduced a price factor into a quantity variance. Because different departments are responsible, these two factors must be kept separate.

**(a) Material Mix Variance:**

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The materials usage or quantity variance can be separated into mix variance and yield variance.

For certain products and processing operations, material mix is an important operating variable, specific grades of materials and quantity are determined before production begins. A mix variance will result when materials are not actually placed into production in the same ratio as the standard formula. For instance, if a product is produced by adding 100 kg of raw material A and 200 kg of raw material B, the standard material mix ratio is 1: 2.

Actual raw materials used must be in this 1: 2 ratio, otherwise a materials mix variance will be found. Material mix variance is usually found in industries, such as textiles, rubber and chemicals, etc. A mix variance may arise because of attempts to achieve cost savings, effective resources utilisation and when the needed raw materials quantities may not be available at the required time.

Materials mix variance is that portion of the materials quantity variance which is due to the difference between the actual composition of a mixture and the standard mixture.

**It can be computed by using the following formula: **

Material mix variance = (Standard cost of actual quantity of the actual mixture – Standard cost of actual quantity of the standard mixture)

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Or

Materials mix variance = (Actual mix – Revised standard mix of actual input) x Standard price

**Revised standard mix or proportion is calculated as follows: **

Standard mix of a particular material/Total standard quantity x Actual input

**Example:**

A product is made from two raw materials, material A and material B. One unit of finished product requires 10 kg of material.

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**The following is standard mix: **

** **

**During a period one unit of product was produced at the following costs: **

** **

Compute the materials mix variance.

**Solution: **

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Material mix variance = (Actual proportion – Revised standard proportion of actual input) x Standard price.

**(b) Materials Yield Variance: **

Materials yield variance explains the remaining portion of the total materials quantity variance. It is that portion of materials usage variance which is due to the difference between the actual yield obtained and standard yield specified (in terms of actual inputs). In other words, yield variance occurs when the output of the final product does not correspond with the output that could have been obtained by using the actual inputs. In some industries like sugar, chemicals, steel, etc. actual yield may differ from expected yield based on actual input resulting into yield variance.

The total of materials mix variance and materials yield variance equals materials quantity or usage variance. When there is no materials mix variance, the materials yield variance equals the total materials quantity variance. Accordingly, mix and yield variances explain distinct parts of the total materials usage variance and are additive.

**The formula for computing yield variance is as follows: **

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Yield Variance = (Actual yield – Standard Yield specified) x Standard cost per unit

**Example:**

Standard input = 100 kg, standard yield = 90 kg, standard cost per kg of output = Rs 200

Actual input 200 kg, actual yield 182 kg. Compute the yield variance.

** **

In this example, there is no mix variance and therefore, the materials usage variance will be equal to the materials yield variance.

The above formula uses output or loss as the basis of computing the yield variance. Yield variance can also be computed on the basis of input factors only. The fact is that loss in inputs equals loss in output. A lower yield simply means that a higher quantity of inputs have been used and the anticipated or standard output (based on actual inputs) has not been achieved.

**Yield, in such a case, is known as sub-usage variance (or revised usage variance) which can be computed by using the following formula: **

Sub-usage or revised usage variance = (Revised Standard Proportion of Actual Input – Standard quantity) x Standard Cost per unit of input

**Example:**** **

**Standard material and standard price for manufacturing one unit of a product is given below: **

** **

** **

Materials yield variance always equal sub-usage variance. The difference lies only in terms of calculation. The former considers the output or loss in output and the latter considers standard inputs and actual input used for the actual output. Mix and yield variance both provide useful information for production control, performance evaluation and review of operating efficiency.

**Materials Price Variance:**

A materials price variance occurs when raw materials are purchased at a price different from standard price. It is that portion of the direct materials which is due to the difference between actual price paid and standard price specified and cost variance multiplied by the actual quantity. Expressed as a formula,

Materials price variance = (Actual price – Standard price) x Actual quantity

Materials price variance is un-favourable when the actual price paid exceeds the predetermined standard price. It is advisable that materials price variance should be calculated for materials purchased rather than materials used. Purchase of materials is an earlier event than the use of materials.

Therefore, a variance based on quantity purchased is basically an earlier report than a variance based on quantity actually used. This is quite beneficial from the viewpoint of performance measurement and corrective action. An early report will help the management in measuring the performance so that poor performance can be corrected or good performance can be expanded at an early date.

Recognizing material price variances at the time of purchase lets the firm carry all units of the same materials at one price—the standard cost of the material, even if the firm did not purchase all units of the materials at the same price. Using one price for the same materials facilities management control and simplifies accounting work.

If a direct materials price variance is not recorded until the materials are issued to production, the direct materials are carried on the books at their actual purchase prices. Deviations of actual purchase prices from the standard price may not be known until the direct materials are issued to production.

**Example:**

**Assuming in Example 1 that material A was purchased at the rate of Rs 10 and material B was purchased at the rate of Rs 21, the material price variance will be as follows:**

Materials price variance = (Actual Price – Standard Price) x Actual Quantity

Material A = (10 – 10) x 2,050 = Zero

Material B = (21 – 20) x 2,980 = 2980 (un-favourable)

Total material price variance = Rs 2980 (un-favourable)

The total of materials usage variance and price variance is equal to materials cost variance.

### II. Labour Variances:

Direct labour variances arise when actual labour costs are different from standard labour costs. In analysis of labour costs, the emphasis is on labour rates and labour hours.

**Labour variances constitute the following:**

**Labour Cost Variance:**

Labour cost variance denotes the difference between the actual direct wages paid and the standard direct wages specified for the output achieved.

**This variance is calculated by using the following formula: **

Labour cost variance = (AH x AR) – (SH x SR)

**Where: **

AH = Actual hours

AR = Actual rate

SH = Standard hours

SR = Standard rate

1. Labour Efficiency Variance:

The calculation of labour efficiency or usage variance follows the same pattern as the computation of materials usage variance. Labour efficiency variance occurs when labour operations are more efficient or less efficient than standard performance. If actual direct labour hours required to complete a job differ from the number of standard hours specified, a labour efficiency variance results; it is the difference between actual hours expended and standard labour hours specified multiplied by the standard labour rate per hour.

**Labour efficiency variance is computed by applying the following formula: **

Labour efficiency variance = (Actual hours – Standard hours for the actual output) x Std. rate per hour.

**Assume the following data: **

Standard labour hour per unit = 5 hr

Standard labour rate per hour = Rs 30

Units completed = 1,000

Labour cost recorded = 5,050 hrs @ Rs 35

Labour efficiency variance = (5,050-5,000) x Rs 30 = Rs 1,500 (unfavourable) It may be noted that the standard labour hour rate and not the actual rate is used in computing labour efficiency variance. If quantity variances are calculated, changes in prices/rates are excluded, and when price variances are calculated, standard quantities are ignored.

(i) Labour Mix Variance:

Labour mix variance is computed in the same manner as materials mix variance. Manufacturing or completing a job requires different types or grades of workers and production will be complete if labour is mixed according to standard proportion. Standard labour mix may not be adhered to under some circumstances and substitution will have to be made. There may be changes in the wage rates of some workers; there may be a need to use more skilled or expensive types of labour, e.g., employment of men instead of women; sometimes workers and operators may be absent.

**These lead to the emergence of a labour mix variance which is calculated by using the following formula: **

Labour mix variance = (Actual labour mix – Revised standard labour mix in terms of actual total hours) x Standard rate per hour

**To take an example, suppose the following were the standard labour cost data per unit in a factory: **

** **

In a period, many class B workers were absent and it was necessary to substitute class B workers. Since the class A workers were less experienced with the job, more labour hours were used.

**The recorded costs of a unit were: **

** **

**Labour mix variance will be calculated as follows: **

Labour mix variance = (Actual proportion – Revised standard proportion of actual total hours) x standard rate per hour

**Revised standard proportion: **

**(ii) Labour Yield Variance:**

The final product cost contains not only material cost but also labour cost. Therefore, gain or loss (higher or lower output than the standard output) should take into account labour yield variance also. A lower output simply means that final output does not correspond with the production units that should have been produced from the hours expended on the inputs.

**It can be computed by applying the following formula: **

Labour yield variance = (Actual output – Standard output based on actual hours) x Av. Std. Labour Rate per unit of output.

Or

Labour yield variance = (Actual loss – Standard loss on actual hours) x Average standard labour rate per unit of output

Labour yield variance is also known as labour efficiency sub-variance which is computed in terms of inputs, i.e., standard labour hours and revised labour hours mix (in terms of actual hours).

**Labour efficiency sub-variance is computed by using the following formula: **

Labour efficiency sub-variance = (Revised standard mix – standard mix) x Standard rate

2. Labour Rate Variance:

Labour rate variance is computed in the same manner as materials price variance. When actual direct labour hour rates differ from standard rates, the result is a labour rate variance. It is that portion of the direct wages variance which is due to the difference between actual rate paid and standard rate of pay specified.

**The formula for its calculation is: **

Labour rate variance = (Actual rate – Standard rate) x Actual hours

Using data from the example given above, the labour rate variance is Rs 25,250, i.e.,

Labour rate variance = (35 – 30) x 5050 hours = 5 x 5050 = Rs 25,250 (unfavourable)

The number of actual hours worked is used in place of the number of the standard hours specified because the objective is to know the cost difference due to change in labour hour rates, and not hours worked. Favourable rate variances arise whenever actual rates are less than standard rates; unfavourable variances occur when actual rates exceed standard rates.

3. Idle Time Variance:

Idle time variance occurs when workers are not able to do the work due to some reason during the hours for which they are paid. Idle time can be divided according to causes responsible for creating idle time, e.g., idle time due to breakdown, lack of materials or power failures. Idle time variance will be equivalent to the standard labour cost of the hours during which no work has been done but for which workers have been paid for unproductive time.

Suppose, in a factory 2,000 workers were idle because of a power failure. As a result of this, a loss of production of 4,000 units of product A and 8,000 units of product B occurred. Each employee was paid his normal wage (a rate of? 20 per hour). A single standard hour is needed to manufacture four units of product A and eight units of product B.

**Idle time variance will be computed in the following manner: **

**Standard hours lost: **

Product A = 4, 000/ 4 = 1,000 hr.

Product B = 8, 000 / 8 = 1,000 hr.

Total hours lost = 2,000 hr.

Idle time variance (power failure)

2,000 hours @ Rs 20 per hour = Rs 40,000 (Adverse)

### III. Overhead Variances:

The analysis of factory overhead variances is more complex than variance analysis for direct materials and direct labour. There is no standardisation of the terms or methods used for calculating overhead variances. For this reason, it is necessary to be familiar with the different approaches which can be applied in overhead variances.

**Generally, the computation of the following overhead variances are suggested: **

** **

**(1) Total Overhead Cost Variance: **

This overall overhead variance is the difference between the actual overhead cost incurred and the standard cost of overhead for the output achieved.

**This can be computed by applying the following formula: **

(Actual overhead incurred) – (Standard hours for the actual output x Standard overhead rate per hour)

Or

(Actual overhead incurred) – (Actual output x Standard overhead rate per unit)

To illustrate the overall overhead variance, assume that the actual overhead for a department amounts to Rs 1,00,000 for the month of January and standard (or allowed) hours for work performed total 4,500 hours, while actual hours used are 5,000.

**If overhead rate is Rs 20 per hour, the overall overhead variance will be the following: **

** **

**(2) ****Variable Overhead Variance: **

It is the difference between actual variable overhead cost and standard variable overhead allowed for the actual output achieved.

**The formula for computing this variance is as follows: **

(Actual Variable Overhead Cost) – (Actual Output x Variable Overhead rate per unit)

Or

(Actual Variable Overhead Cost) – (Std. hours for actual output x Std. Variable overhead rate per hour)

**(3) ****Fixed Overhead Variance: **

This variance indicates the difference between the actual fixed overhead cost and standard fixed overhead cost allowed for the actual output.

**This variance is found by using the following formula: **

Fixed Overhead Variance = (Actual Fixed Overhead Cost – Fixed Overhead absorbed)

Or

(Actual Fixed Overhead Cost) – (Actual Output x Fixed Overhead rate per unit)

Or

(Actual fixed overhead cost) – (Std. hours for actual output x Std. fixed overhead rate per hour)

**(4) Variable Overhead Expenditure (Spending or Budget) Variance: **

This variance indicates the difference between actual variable overhead and budgeted variable overhead based on actual hours worked.

**This variance is found by using the following: **

(Actual variable overhead – Budgeted variable overhead)

**(5) ****Variable Overhead Efficiency Variance: **

This variance is like labour efficiency variance and arises when actual hours worked differ from standard hours required for good units produced. The actual quantity produced and standard quantity fixed might be different because of higher or lower efficiency of workers employed in the manufacturing of goods.

**This variance is found by using the following formula: **

(Actual hours – Standard hours for actual output) x Standard variable overhead rate per hour

**(6) ****Fixed Overhead Expenditure (Spending or Budget) Variance: **

This variance indicates the difference between actual fixed overhead and budgeted fixed overhead.

**The formula for computing this variance is as follows: **

(Actual fixed overhead – Budgeted fixed overhead)

If actual fixed overhead costs are greater than budgeted fixed costs, an unfavourable variance results because actual costs exceed the budget. Actual overhead costs seldom equal budgeted costs because property tax rates may change, insurance premiums may increase or equipment changes may affect depreciation rates. As an illustration, assume that a company completed 36,000 units (equal to 18,000 standard production hours) in 18,500 hours at the recorded fixed cost of Rs 7,51,000. The standard fixed cost rate per hour is Rs 40. Therefore,

Expenditure variance = (Actual fixed overhead costs – Budgeted fixed overhead costs)

That is, = 7,51,000 – (18,500 x 40)

= 7,51,000 – 7,40,000

= Rs 11,000 (Unfavourable)

The expenditure or budget variance provides management with information which helps in controlling costs. The budget variance is usually prepared on a departmental basis and the factors that cause the budget variances are, therefore, controllable by departmental managers.

**(7) ****Fixed Overhead Volume Variance: **

Volume variance relates to only fixed overhead. This variance arises due to the difference between the standard fixed overhead cost allowed (absorbed) for the actual output and the budgeted fixed overhead based on standard hours allowed for actual output achieved during the period. The variance shows the over-or-under-absorption of fixed overheads during a particular period. If the actual output is more than the standard output, there is over-absorption and variance is favourable. If actual output is less than the standard output, the volume variance is unfavourable.

**The formula for computing this variance is as follows: **

(Budgeted fixed overhead applied to actual output – Budgeted fixed overhead based on standard hours allowed for actual output)

Or

(Actual production – Budgeted production) x Std. fixed overhead rate per unit

**Volume variance is further sub-divided into three variances: **

**(8) ****Fixed Overhead Calendar Variance: **

It is that portion of volume variance which is due to the difference between the number of actual working days in the period to which the budget is applicable and budgeted number of days in the budget period.

If actual working days is more than the budgeted working days, the variance is favourable as work has been done on days more than budgeted or allowed and vice-versa.

**The formula is as follows: **

(No. of actual working days – No. of budgeted working days) x Std. fixed overhead rate per day. Calendar variance can be computed based on hours or output.

**Then the formulae are: **

**Hours Basis****: **

Calendar Variance = (Revised Budget Capacity hours – Budget Hours) x Std. Fixed Overhead rate per hour

If revised budgeted capacity hours are more than the budgeted hours, the variance will be favourable. In the reverse situation, the variance will be unfavourable.

**Output Basis****: **

Calendar Variance = (Revised budgeted quantity in terms of actual number of days worked – Budgeted quantity) x Standard fixed overhead rate per unit

If revised budgeted quantity is more than the budgeted quantity; the variance is favourable; if revised budgeted quantity is less, the variance will be unfavourable.

**(9) ****Fixed Overhead Efficiency Variance:**

It is that portion of volume variance which arises when actual hours of production used for actual output differ from the standard hours specified for that output. If actual hours worked are less than the standard hours, the variance is favourable and when actual hours are more than the standard hours, the variance is unfavourable.

**The formula is: **

Fixed Overhead Efficiency Variance = (Actual hours – Standard hours for actual production) x Fixed overhead rate per hour

Fixed Overhead Efficiency Variance = (Actual production – Standard production as per actual time available) x Fixed overhead rate per unit

**(10) ****Fixed Overhead Capacity Variance: **

It is that part of fixed overhead volume variance which is due to the difference between the actual capacity (in hours) worked during a given period and the budgeted capacity (expressed in hours). The formula is

Capacity Variance = (Actual Capacity Hours – Budgeted Capacity) x Standard fixed overhead rate per hour

This variance represents idle time also. If actual capacity hours are more than the budgeted capacity hours, the variance is favourable and if actual capacity hours are less than the budgeted capacity hours the variance will be unfavourable.

In case actual number of days and budgeted number of days are also given, then budgeted capacity hours will be calculated in terms of actual number of days and it will be known as revised budgeted capacity hours, i.e., budgeted hours in actual days worked.

**In this situation, the formula for calculating capacity variance will be as follows: **

Capacity Variance = (Actual Capacity hours – Revised Budgeted Capacity hours) x Standard fixed overhead rate per hr.

In the above formula, the variance will be favourable if actual capacity hours are more than the revised budgeted hours. However, if actual capacity hours are lesser than the revised budgeted hours, the variance will be adverse as lesser hours means that lesser actual hours have been worked taking the actual days utilised into account.

**Two-way, Three-way and Four-way Variance Analysis****: **

The above overhead variances are also classified as Two-way, Three-way and Four-way variance.

**The different variances under these categories are listed below: **

**(A) ****Two-way Variance Analysis: **

The two-way analysis computes two variances budget variance (sometimes called flexible budget or controllable variance) and volume variance, which means:

(i) Budget variance = Variable spending variance + Fixed spending (budget) Variance + Variable efficiency variance

(ii) Volume variance = Fixed volume variance

**(B) ****Three -Way Variance Analysis: **

The three-way analysis computes three variances spending, efficiency and volume variances. Therefore,

(i) Spending variance = Variable spending variance + Fixed spending (budget) variance

(ii) Efficiency variance = Variable efficiency variance

(iii) Volume variance = Fixed volume variance

**(C) ****Four-way Variance Analysis: **

**The four-way analysis includes:**

(i) Variable spending variance

(ii) Fixed spending (budget) variance

(iii) Variable efficiency variance

(iv) Fixed volume variance.

**Illustrative Problem 1****: **

Budgeted hours for month of March = 180 hours

Standard rate of article produced per hour = 50units

Budgeted fixed overhead = Rs 27, 000

Actual Production = 9, 2000 units

Actual hours for Production = 175 hours

Actual fixed Overhead Costs = Rs 28, 000

Calculate Overhead Cost Variances.

**Solution:**

**1. Overhead Cost Variance: **

(Actual Overhead Cost – Standard Overhead of actual output)

(Rs 28,000-9,200 units x 3)

Rs 28,000 – 27,600 = Rs 400 (unfavourable)

Standard Overhead rate per unit = Rs 27,000/(180 hrs x 50) = 27,000/9, 000 = Rs 3

**2. Overhead Expenditure Variance: **

(Actual Overhead – Budgeted Overhead)

(Rs 28,000 – 27,000) = Rs 1,000 (unfavourable)

**3. ****Overhead Volume Variance: **

(Budgeted Overhead for actual output – Budgeted fixed overhead)

(Rs 3 x 9,200 units – 2,700)

(27,600 – 27,000) = Rs 600 (favourable)

**It can be calculated in the following manner also: **

(Actual Production – Budgeted Production) x Std. rate per unit

(9,200 – 9,000) x Rs 3 = Rs 600 (favourable)

Or

(Budgeted hrs for actual production – Budgeted hours) x Std. rate per hour

( 184 hrs-180) x Rs 150

4 x 150 = Rs 600 (favourable)

For 9,000 units standard hours required = 180 hrs.

For 9,200 units standard hours (9, 200 x 180)/9, 000 = 184 hrs

**Illustrative Problem 2****: **

**From the following data, calculate overhead variances: **

** **

**Solution:**

**1. Total Overhead Cost Variance: **

Actual overhead cost – (Actual units x Std. Rate)

(Rs 3,05,000 + 4,70,000) – (16,000 x Rs 50)

Rs 7,75,000 – Rs 8,00,000 = Rs 25,000 (favourable)

Standard rate = Standard Overhead /Standard Output

**2. Variable Overheads Variance: **

Actual variable cost – (Actual units x Std. Rate)

4,70,000 – (16,000 x Rs 30)

Rs 4,70,000 – Rs 4,80,000 = Rs 10,000 (favourable)

**3. Fixed Overhead Variance: **

Actual fixed overhead cost – (Actual units x Std. Rate of fixed overhead)

3,05,000-(16,000 x 20)

3,05,000 – 3,20,000 = Rs 15,000 (favourable)

**4. Volume Variance: **

(Actual units x St. rate) – Budgeted fixed overheads

(16,000 x Rs 20) – Rs 3,00,000 = Rs 20,000 (favourable)

**5. Expenditure Variance: **

Actual fixed overheads – Budgeted fixed overheads

Rs 3,05,000 – Rs 3,00,000 = Rs 5,000 (unfavourable)

**6. Capacity Variance****: **

Std. Rate x (Revised budget units – Budgeted units)

Revised budgeted units = Budgeted units + Increase in capacity

= 15,000 + 5/100 x 15,000= 15,750 units 100

= Capacity variance

= Rs 20 (15,750 units – 15,000 units)

= Rs 20 x 750 = Rs 15,000 (favourable)

**7. Calendar Variance: **

Increase or decrease in production due to more or less working days x Std. rate per unit within 25 days, standard production with increased capacity = 15,750 units within 2 days (27 – 25),

production will be increased by = (15, 750 x 2)/25 = 1,260 units

Calendar variance = 1,260 units x Rs 20

= Rs 25,200 (favourable)

**8. Efficiency Variance: **

Std. rate x (Actual production – Std. production)

Standard production:

Budgeted production = 15,000 units

Production increased due to increase in capacity 5% = 750 units

Now budgeted production = 15,000 + 750 = 15,750 units

Production increased due to 2 more working days

Units for 2 days = (15, 750 x 2)/25 days = 1,260 units

Total units = 15,750 + 1,260

= 17,010 units

Efficiency Variance = Rs 20 (16,000 units – 17,010 units)

Rs 20 (- 1,010 units) = Rs 20,200 (unfavourable)

**Illustrative Problem 3****: **

**In department A the following data is submitted for the week ending 31st October: **

** **

** **

**Statement of fixed overhead variances of department A: **

**A. Expenditure variance: **

(Actual overhead – Budgeted overhead)

Rs 1,50,000 – Rs 1,40,000 = Rs 10,000 (Adverse)

**B. Volume variance: **

Std. fixed overhead rate per unit x (Actual output – Budgeted output)

Rs 100 (1,200 – 1,400) = Rs 20,000 (Adverse)

**C. Total overhead cost variance: **

(Actual overhead – Overhead recovered by actual output)

Rs 1,50,000 – Rs 1,20,000 = Rs 30,000 (Adverse)

**(a) ****Efficiency variance: **

Std. fixed overhead rate per unit x (Actual production – Std. production for actual hours)

Rs 100 (1200 – 32 x 35) = Rs 8000 (Favourable)

**(b) ****Capacity variance:**

Std. fixed overhead rate per hour (Actual hours – Standard hours)

Rs 3,500 (32 – 40) = Rs 28,000 (Adverse)

**Illustrative Problem 4****: **

**A Cost Accountant of a company was given the following information regarding the overheads for February, 2012: **

(a) Overheads cost variance Rs 1,400 adverse.

(b) Overheads volume variance Rs 1,000 adverse.

(c) Budgeted hours for February 2012, 1,200 hours.

(d) Budgeted overheads for February 2012, Rs 6,000.

(e) Actual rate of recovery of overheads Rs 8 per hour.

**You are required to assist him in computing the following for February, 2012: **

(1) Overheads expenditure variance.

(2) Actual overheads incurred.

(3) Actual hours for actual production.

(4) Overheads capacity variance.

(5) Overheads efficiency variance.

(6) Standard hours for actual production.

**Solution:**** **

Computation of Required Variances

(1) Overheads Expenditure Variance

= Overheads Cost Variance – Overheads Volume Variance

= Rs 1,400 (A) – Rs 1,000 (A)

= Rs 400 (A)

(2) Actual Overheads incurred

= Budgeted Overheads + Overhead Expenditure Variance

= Rs 6,000 + Rs 400 (A)

= 6,400

(3) Actual hours for actual production

Actual overheads incurred/Actual rate of recovery of overheads per hour

= Rs 6,400/8 = 800 hours

(4) Overheads Capacity Variance

= Standard Overhead x (Actual Hours – Budgeted Hours)

= 5 x (800 hours – 1,200 hours)

= Rs 2,000 (A)

= Standard Rate of Overhead = Budgeted overheads / Budgeted hours

= Rs 6, 000/1, 200 = Rs 5 per hour

(5) Overhead Efficiency Variance

= Overheads Volume variance – Overhead Capacity variance

= Rs 1,000 (A) – Rs 2,000 (F)

= Rs 1,000 (F)

(6) Standard Hours for Actual Production

Volume Variance

= Standard Overheads Rate x (Standard hours for Actual Production – Budgeted Hours) or 1,000 (A) = 5 (x- 1,200)

or 1,000 (A) = 5 x – 6,000

or -5 x = – 5,000

or x = 1,000 hours

**Illustrative Problem 5****: **

New India Company uses a standard costing system. The company prepared its budget for 2012 at 10,00,000 machine hours for the year. Total budgeted overhead costs is Rs 12,50,00,000. The variable overhead rate is Rs 100 per machine hour (Rs 200 per unit).

**Actual results for 2012 are as follows: **

** **

**Required:**

(I) Compute for the fixed overhead

(a) Budgeted amount

(b) Budgeted cost per machine hour

(c) Actual cost

(d) Volume variance

(II) Compute variable overhead spending variance and variable overhead efficiency variance.

**Solution:**

**(I) For fixed overhead****: **

**(a) Budgeted Amount: **

Total budgeted overhead = Rs 12,50,00,000

Less: Budgeted variable overhead (10,00,000 machine hrs x Rs 100 budgeted rate per machine hour) = 10,00,00,000

Budgeted fixed overhead 2,50,00,000

**(b) Budgeted (fixed) cost per machine hour: **

= Rs 2,50,00,000 budgeted amount/10,00,000 budgeted machine hours

= Rs 25 per machine hour

**(c) Actual cost (fixed): **

It is calculated through fixed overhead spending variance.

Fixed overhead spending variance = Actual cost incurred – Budgeted amount

Actual cost = Budgeted amount + Unfavourable spending variance

= 2,50,00,000+ 60,00,000 A

= Rs 3,10,00,000

Because fixed overhead spending variance is unfavourable, the amount of actual costs is higher than the budgeted amount.

**(d) Production Volume Variance: **

Budgeted variable overhead per unit = Rs 200

Budgeted variable overhead rate = Rs 100 per machine hour

Therefore budgeted machine hours allowed per unit = Rs 200/Rs 100

= 2 machine hours

**Formula****: **

Budgeted fixed overhead – Fixed overhead absorbed or allowed for actual output units

= Rs 2,50,00,000 – (Rs 25 per machine hour x 2 machine hours per unit x 4,98,000 units)

= Rs 2,50,00,000 – Rs 2,49,00,000 (absorbed fixed overhead)

= Rs 1,00,000 Adverse

Or

**Another formula****: **

(St hrs for actual production – Budgeted hrs) x St. fixed overhead rate per hr

= (2 x 4,98,000) – (10,00,000 hrs) x Rs 25

= (9,96,000 hrs – 10,00,000 hrs) x Rs 25

= Rs 1,00,000 Adverse

Or

**Another formula****: **

(Budgeted production – Actual production) x St. fixed overhead rate per unit

Standard fixed overhead rate per unit = Budgeted fixed overhead/Budgeted units

= Rs 2,50,00,000/5,00,000 units

= Rs 50 per unit

Budgeted units = 2 machine hour needed for 1 unit

In 10,00,000 machine hours, units produced will be

= 10,00,000/2 = 5,00,000 units

Now, applying the formula

(5,00,000 units – 4,98,000 units) x Rs 50

= 2,000 units x Rs 50 = Rs 1,00,000 Adverse

**(II) For Variable ****overhead **

**(a) Variable overhead spending variance****: **

(Budgeted Variable overhead cost – Actual Variable overhead)

Budgeted variable overhead cost = Actual hrs works x St. Variable overhead rate per hour

= 9,60,000 hrs x Rs 100

= Rs 9,60,00,000

Now, applying the formula

(Rs 9,60,00,000 – Rs 10,08,00,000)

= Rs 48,00,000 Adverse

Or

**Another formula****: **

(St. machine hr rate – Actual machine hr rate) x Actual hrs worked

= (Rs 100 – Rs 10, 08, 00, 000/9, 00, 000 hrs) x 9, 60, 000 hrs

= (Rs 100 – Rs 105) x 9,60,000 hrs

= Rs 48,00,000 Adverse

**(b) Variable overhead efficiency Variance****: **

(St. hours for actual output – Actual hrs) x St. Variable overhead rate per hour

= ((4,98,000 units x 2 hrs) – 9,60,000 hrs) x Rs 100

= (9,96,000 hrs – 9,60,000 hrs) x Rs 100

= 36,000 hours x Rs 100

= Rs 36,00,000 Favourable

**Note: **

The other variances, although not asked in the question, have been computed as below.

**(Ill) For Fixed overhead****: **

Calender Variance, Efficiency Variance, Capacity Variance.

**(a) Fixed overhead Calender Variance: **

= (Budgeted hrs – Revised budgeted Capacity hrs) x St. fixed overhead rate per hour

= (10,00,000 hrs – 2 hrs x 4,98,000 units) x Rs 25

= (10,00,000 hrs – 9,96,000 hrs) x Rs 25

= 4,000 hrs x 25 = Rs 1,00,000 Adverse

Variance is adverse because of lesser use of hours available.

**(b) Fixed overhead Efficiency Variance: **

(st. hr for actual production – Actual hrs) x Fixed overhead rate per hour

= (2 hrs x 4,98,000 units) – 9,60,000 hrs ) x 25

= (9,96,000 hrs – 9,60,000 hrs) x 25

= 36,000 hrs x Rs 25

= Rs 9,00,000 F

It is favourable because actual hrs are less than standard hours.

**(c) Fixed Overhead Capacity Variance****: **

(Budgeted Capacity hrs – Actual Capacity hours) x St. fixed overhead rate per hr

= (9,96,000 hrs – 9,60,000 hrs) x Rs 25

= 36,000 hrs x Rs 25

= Rs 9,00,000 Adverse

Since actual hours are less than budgeted hours, in terms of capacity utilisation, it indicates Adverse Variance

**Fixed Overhead Expenditure Variance****: **

(also known as Spending or Budget Variance)

(Budgeted fixed overhead – Actual fixed overhead)

= Rs 2,50,00,000 – Rs 3,10,00,000

= Rs 60,00,000 Adverse

This is already given in the question.

**Fixed Overhead Variance****: **

(budgeted fixed overhead cost – Actual fixed overhead cost)

Budgeted fixed overhead cost =

(i) Actual output units x St. fixed overhead rate per unit

Or

(ii) St. hours for actual output x St. fixed overhead rate per hour

**Applying the formula****: **

(i) (4,98,000 units x Rs 50 per unit) – Rs 3,10,00,000

= 2,49,00,000-3,10,00,000

= Rs 61,00,000 Adverse

Or

(ii) (9,96,000 hrs x Rs 25 per hr) – Rs 3,10,00,000

= Rs 2,49,00,000 – Rs 3,10,00,000

= Rs 61,00,000 Adverse

**Verification: **

Fixed overhead Variance = Fixed overhead expenditure variance + Fixed overhead volume variance

Rs 61,00,000 A = Rs 60,00,000 A + Rs 1,00,000 A

**Variable Overhead Variance****: **

(Budgeted variable overhead cost – Actual variable overhead cost) Budgeted variable overhead cost =

(i) Actual output units x St. variable overhead rate per unit

Or

(ii) St. hours for actual output x St. variable overhead rate per hour

**Applying the formula****: **

(i) (4,98,000 units x Rs 200 per unit) – Rs 10,08,00,000

= Rs 9,96,00,000 – Rs 10,08,00,000

= Rs 12,00,000 Adverse

Or

(ii) (9,96,000 hrs x Rs 100) – Rs 10,08,00,000

= Rs 9,96,00,000 – Rs 10,08,00,000

= Rs 12,00,000 Adverse

**Verification****: **

Variable overhead variance = Variable overhead expenditure variance + Variable overhead efficiency variance

Rs 12,00,000 A = Rs 48,00,000 A + Rs 36,00,000 F

Rs 12,00,000 A = Rs 12,00,000 A

**Total Overhead Cost Variance****: **

(Budgeted overhead cost – Actual overhead cost)

Budgeted overhead cost =

(i) Actual output units x St. overhead rate per unit

Or

(ii) St. hours for actual output x St. overhead rate per hour

**Applying the formula****: **

St. overhead rate per unit = Variable overhead rate + Fixed overhead rate = Rs 200 + Rs 50 = Rs 250

Or

St. overhead rate per hour =

= Variable overhead rate per hour + Fixed overhead rate per hour

= Rs 100 + Rs 25 = Rs 125

(i) (4,98,000 units x Rs 250) – (Rs 3,10,00,000 + Rs 10,08,00,000)

= Rs 12,45,00,000 – Rs 13,18,00,000

= Rs 73,00,000 Adverse

Or

(ii) (9,96,000 hrs x Rs 125) – (Rs 3,10,00,000 + Rs 10,08,00,000)

= Rs 12,45,00,000-Rs 13,18,00,000

= Rs 73,00,000 Adverse

**Verification****: **

Total overhead cost variance = Fixed overhead cost variance + Variable overhead cost variance

Rs 73,00,000 A = Rs 61,00,000 A + Rs 12,00,000 A

Rs 73,00,000 A = Rs 73,00,000 A

**Illustrative Problem 6**:

**The following information has been extracted from the books of Goru Enterprises which is using standard costing system: **

Actual output = 9,000 units

Direct wages paid = 1,10,000 hours at Rs 22 per hour, of which 5,000 hour, being idle time, were not recorded in production

Standard hours = 10 hours per unit

Labour efficiency variance = Rs 3,75,000 (A)

Standard variable Overhead = Rs 150 per unit

Actual variable Overhead = Rs 16,00,000

**You are required to calculate: **

(i) Idle time variance

(ii) Total variable overhead variance

(iii) Variable overhead expenditure variance

(iv) Variable overhead efficiency variance.

**Solution:**

Actual output = 9,000 units

Idle time = 5,000 hours

Production time (Actual) = 1,05,000 hours

Standard hours for actual production = 10 hours/unit x 9,000 units = 90,000 hours.

Labour efficiency variance = Rs 3,75,000 (A)

i.e. Standard rate x (Standard Production time – Actual production time) = Rs 3,75,000 (A).

SR (90,000 – 1,05,000) = – 3,75,000

SR = -3,75,000/-15,000 = Rs 25

(i) Idle time variance = 5,000 hours x 25 Rs hour = Rs 1,25,000. (A)

(ii) Standard Variable Overhead = Rs 150/unit

Standard hours = 10 hours/unit

Standard Variable Overhead rate/hour =150/10 = Rs15/hour

Total Variable Overhead variance = Standard Variable Overhead – Actual Variable Overhead

= Standard Rate x Standard hours – Actual rate x Actual hours

= (15) x (10 x 9,000) – 16,00,000

= 13,50,000 -16,00,000

Total Variable Overhead Variance = 2,50,000 (A)

(iii) Variable Overhead Expenditure Variance = (Standard Rate x Actual Hours) – (Actual Rate x Actual Hours)

= (15 x 1,05,000) – 16,00,000

= 15,75,000 – 16,00,000

= Rs 25,000 (A)

(iv) Variable Overhead Efficiency Variance = Standard Rate x (Standard Hours for actual output – Actual hours for Actual output)

= 15 (90,000 – 1,05,000)

= 15 (-15,000)

= Rs 2,25,000 (A)

**Alternative Solution****: **

Actual Output = 9,000 Units

Idle time = 5,000 hrs

Direct Wages Paid = 1,10,000 hours @ Rs 22 output of which 5,000 hours being idle, were not recorded in production.

Standard hours = 10 per unit.

Labour efficiency variance = Rs 3,75,000 (A)

Or

Standard Rate (Standard Time – Actual Time) = – 3,75,000

Or (90,000 – 1,05,000) = – 3,75,000/Standard Rate.

Or Standard Rate = Rs 25/-

(i) Idle time variance = Standard Rate x Idle time

25 x 5,000 = Rs 1,25,000 (A)

(ii) Standard Variable Overhead/unit =150

Standard Rate = 150/10 = Rs 15/hour

Standard Quantity = 10 hours

Actual Variable Overhead = 16,00,000

Standard Variable Overhead = 150 x 9,000 = 13,50,000

Actual Variable Overhead = 16,00,000

Total Variable Overhead Variance = 2,50,000 (A)

(iii) Variable Overhead expenditure Variance = Standard Variable Overhead for actual hours – Actual Variable Overhead

= (150 x 1,05,000)-16,00,000

= 15,75,000-16,00,000

= 25,000 (A)

(iv) Variable overhead efficiency variance = (Standard Variable Overhead for actual output – Standard Variable Overhead for Actual hours)

= 15 (10 hours x 90,000 units – 1,05,000)

= 15 (90,000 – 1,05,000)

= 15 (- 15,000)

= 2,25,000 (A)

**Illustrative Problem 7****: **

**The Norkhill Furniture Company has the following standard cost per unit of furniture: **

** **

**For July 2012, when 1100 units of furniture were produced, the following information is available: **

Lumber purchased: 50,000 feet at Rs 390 per 100 feet

Lumber used: 56,000 feet

Direct labour: 3,100 hours @ Rs 105

Variable overhead: Rs 1,55,000

Fixed Overhead: Rs 2,90,000

Any materials price variance is assigned to the purchasing department at the time of purchase.

**You are required to: **

(a) Prepare a flexible budget for the actual level of activity.

(b) Prepare a complete analysis of all variances, including a three-way analysis of overhead variances.

**Three-way Analysis of Overhead Variances: **

(i) Spending variance = (Actual Overhead costs – Budgeted overhead costs based on actual hours)

= 4,45,000 – (Rs 3,00,000 + 100 x 33,100 hours)

= 4,45,000- 4,55,000

= Rs 10,000 (F)

(ii) Efficiency variance

= (Budgeted overhead costs based on actual hours – Budgeted overhead costs based on Std. hours)

= (Rs 4,55,000 – (Rs 3,00,000 + Rs 50 x 3300 hrs)

= 4,55,0000 – 4,65,000

= Rs 10,000 (F)

(iii) Volume variance

= (Budgeted overhead Costs based on Std. hours in terms of actual units – Applied over head costs)

= (Rs 150 x 3300 hrs) – (Rs 150 x 3100 hrs)

= Rs 4,95,000 – 4,65,000

= Rs 30,000 (F)

**Illustrative Problem 8**:

**Jumbo Food Products Ltd. operates a system of standard costing and in respect of one of its products which is manufactured within a single cost centre, data for one week have been analysed as follows: **

** **

**The production and sales achieved resulted in no changes of stock. You are required to compute: **

(i) The actual output;

(ii) Actual profit;

(iii) Actual price per kg of material;

(iv) Actual rate per labour hour;

(v) Amount of production overhead incurred;

(vi) Amount of production overhead absorbed;

(vii) Production overhead efficiency variance;

(viii)** **Selling price variance;

(ix) Sales volume profit variance.

### IV. Sales Variances:

Sales variance is the difference between the actual value of sales achieved in a given period and budgeted value of sales. There are many reasons for the difference in actual sales and budgeted sales such as selling price, sales volume, sales mix.

**Sales variance can be calculated by using any of the following two methods:**

A. Sales variance based on turnover

B. Sales variances based on margin (i.e.,contribution margin or profit)

The first approach i.e., sales variance based on turnover, accounts for difference in actual sales and budgeted sales. The sales variances using margin approach accounts for difference in actual profit and budgeted profit. In the margin method, it is assumed that cost of production is constant, i.e., no difference is assumed between actual cost of production and standard cost of production.

The reason for this assumption is that cost variances are calculated separately to analyse the difference between actual cost and standard cost of production. Therefore, cost side of the sales variance is assumed constant under the margin method.

Sales variances computed under these two methods show different amounts of variance.

**The different sales variances under these two approaches and their formula are given below:**

**A. Sales Variances Based on Turnover:**

** **

**(i) ****Sales Value Variance: **

Also known as sales variance, this variance shows the difference between actual sales value and budgeted sales value.

**The formula is:**

Sales Value Variance = (Actual value of sales – Budgeted value of sales)

Actual sales = Actual quantity sold x Actual selling price

Budgeted sales = Standard quantity x Standard selling price

Or

Sales value variance = (Actual quantity x Actual selling price) – (Standard quantity x Standard selling price)

If actual sales are more than the budgeted sales, there is favourable variance and if actual sales are less than the budgeted sales, unfavourable variance arises.

**(ii) ****Sales Price Variance: **

This variance is due to the difference between actual selling price and standard or budgeted selling price.

**The formula is: **

Sales price variance = (Actual selling price – Budgeted selling price) x Actual quantity

If actual selling price is less than the budgeted selling price, variance is favourable and if actual selling price is more than the budgeted selling price, there will be unfavourable sales price variance.

**(iii) ****Sales Volume Variance: **

Sales volume variance arises when the actual quantity sold is different from the budgeted quantity. If actual sales quantity exceeds the budgeted sales quantity, there is a favourable sales volume variance and if actual quantity sold is less than the budgeted quantity, the variance is unfavourable.

**The formula is: **

Sales volume variance = (Actual quantity – Budgeted quantity) x Budgeted selling price

**Sales volume variance is divided into two variances: **

(i) Sales mix variance

(ii) Sales quantity variance

**(i) ****Sales Mix Variance: **

Sales mix variance is one part of overall sales volume variance. This variance shows the difference between actual mix of goods sold and budgeted mix of goods sold.

**The formula is: **

Sales Mix Variance = (Actual Mix of quantity sold – Actual quantity in standard proportion) x Standard selling price

Or

Sales Mix Variance = (Budgeted price per unit of actual mix – Budgeted price per unit of budgeted mix) x Total actual quantity.

If actual sales mix are more than the mix in standard or budgeted proportion, the variance is favourable and if actual mix sales are less than the standard mix (of actual sales), the variance is unfavourable. Similarly, if budgeted price per unit of actual mix is more than the budgeted price per unit of budgeted mix, favourable variance will arise. In the reverse situation, variance will be unfavourable.

**(ii) ****Sales Quantity Variance:**

This variance is also a part of overall volume variance. This variance shows the difference between total actual sales quantity and total budgeted sales quantity. If total actual quantity is more than the total budgeted quantity, variance will be favourable and if total actual quantity is less than the total budgeted quantity, there will be unfavourable sales quantity variance.

**The formula is: **

Sales quantity variance = (Total actual quantity – Total budgeted quantity) x Budgeted price per unit of budgeted mix

The total of sales mix variance and sales quantity variance will be equal to sales volume variance.

#### B. Sales Variance Based on Margin (i.e., Contribution Margin or Profit):

The sales variances using margin approach show the difference in actual profit and budgeted profit only whereas sales variances based on turnover show the difference between total actual sales and total budgeted sales.

**The following sales variances are calculated if margin or profit is the basis of calculation: **

Sales Variances based on Margin or Profit

**(i) Total Sales Margin Variance: **

This variance indicates the aggregate or total variance under the margin method. This variance shows the difference between actual profit and budgeted profit.

**The formula is: **

Total sales margin variance = Actual Profit – Budgeted profit

If actual profit is more than the budgeted profit, variance will be favourable and if actual profit is less than the budgeted profit, unfavourable variance will arise.

**(ii) ****Sales Margin Price Variance: **

This variance is one part of total sales margin variance and arises due to the difference between actual margin per unit and budgeted margin per unit. It is significant to note that, assuming cost of production being constant, the difference in the actual margin and budgeted margin will only be because of the difference between actual selling price and budgeted selling price. The formula for calculating sales margin price variance is

Sales Margin Price Variance = (Actual Margin per unit – Budgeted Margin per unit) x Actual quantity

If actual margin per unit is more than the budgeted margin per unit, favourable variance will be found and if actual margin is less than the budgeted margin, variance will be unfavourable.

**(iii) ****Sales Margin Volume Variance: **

This variance shows the difference between actual sales units and budgeted sales units.

**The formula is: **

Sales Margin Volume Variance = (Actual quantity – Budgeted quantity) x Budgeted Margin per unit.

If actual sales units are more than the budgeted sales units, variance will be favourable and if actual sales units are less than the budgeted sales units, unfavourable variance will arise.

**Sales margin volume variance can be calculated using another formula which is: **

Sales margin volume variance = (Standard profit on actual quantity of sales – Budgeted profit)

If standard profit exceeds budgeted profit, variance will be favourable and if standard profit is less than the budgeted profit, unfavourable variance will emerge.

**Sales margin volume variance consists of:**

(i) Sales margin mix variance and

(ii) Sales margin quantity variance.

**(i) Sales Margin Mix Variance: **

This variance shows the difference between actual mix of goods and budgeted (standard) mix of goods sold.

**The formula is: **

Sales Margin Mix Variance = (Actual sales mix – Standard proportion of actual sales mix) x Budgeted margin per unit.

If budgeted margin per unit on actual sales mix is more than the budgeted margin per unit on budgeted mix, variance will be favourable. In the reverse situation, unfavourable variance will arise.

**(ii) Sales Margin Quantity Variance: **

This variance will be found when the total actual sales quantity in standard proportion is different from the total budgeted sales quantity.

**The formula is: **

Sales Margin Quantity Variance = (Actual sales in standard proportion – Budgeted sales) x Budgeted margin per unit on budgeted mix

If actual sales (in standard proportion) are more than the budgeted sales, variance will be favourable and if actual sales are less than the budgeted sales, unfavourable variance will arise.

### Related Articles:

- Overhead Variance: Classification and Methods (With Calculations)
- Variance Analysis: Meaning, Classification and Computation