# Interpretation of Variance

## Variance

• one which departs from expectations
• one that varies from norm or standard
• disagreement
• discrepancy

A variance as we understand in the topic variance analysis in cost accounting is a value that indicates either a loss or gain. It is the gain or loss on account of the actual activity not being exactly as planned.

We learn about the different kinds of variances with respect to the various elements of cost that we deal with in cost accounting and how we calculate them.

## Analysis

• An investigation of the component parts of a whole and their relations in making up the whole
• The abstract separation of a whole into its constituent parts in order to study the parts and their relations
• synthesis

## Variance Analysis

Variance analysis involves analysing the variances in costs incurred on account of the various elements of cost by segregating the variance relating to an element of cost into various components.

## Mathematical Interpretation

The variances that we calculate in the topic variance analysis are all value variances i.e. any variance that we calculate is the difference between two values.

Variance = Value1 − Value2

The value that we consider here is the labor/labour cost which is the product of time and rate of pay.

Labour/Labor Cost = Labour/Labor Time × Rate of Pay

Thus,

Variance = (Time1 × Rate1) − (Time2 × Rate2)

## Positive/Favourable Variance

If a variance indicates a gain or benefit, it is said to be either Positive or Favourable. It is indicated by a positive sign (+) prefixed (before) the value of the variance or by the letters Fav or F or Pos suffixed (after) the value.
• +5,000
• 5,000 Fav
• 5,000 F
• 5,000 Pos

In mathematical calculations a positive variance is taken as a positive value.

If a variance indicates a loss, it is said to be either negative or Adverse or Unfavourable. It is indicated by a negative sign (−) prefixed (before) the value of the variance or by the letters UF or Unf or Adv suffixed (after) the value.
• − 1,200
• 1,200 Unf
• 1,200 Neg

In mathematical calculations a negative variance is taken as a negative value.

## Costs

With respect to costs there would be
• ### Loss

If the actual cost is greater than the standard cost there would be a loss.

The variance would be negative if Actual cost > Standard Cost.

### Gain

If the actual cost is lesser than the standard cost there would be a gain.

The variance would be positive if Actual cost < Standard Cost.

## Profits/Incomes

With respect to Profits/Incomes there would be
• ### Loss

If the actual profit/income is lesser than the standard profit/income there would be a loss.

The variance would be positive if Actual profit/income < Standard profit/income.

### Gain

If the actual profit/income is greater than the standard profit/income there would be a gain.

The variance would be positive if Actual profit/income > Standard profit/income.

# Variance Formulae - Standard − Actual (Or) Actual − Standard ?

Variance is the difference between two values. Many a times in writing the formulae for calculating variance, we get struck up with deciding whether the standard data comes first or the actual data i.e. which term forms the minuend and which forms the subtrahend.

## Minuend

• A quantity or number from which another is to be subtracted.

## Subtrahend

• A quantity or number to be subtracted from another.

## Cost Variances

In calculating cost variances standard data forms the minuend and the actual data the subtrahend.

Variance = Standard − Actual

### Illustration

When in doubt imagine a simple example generating a negative variance.
Standard cost = 2,000
Actual cost = 2,400

Since cost is more, this should give a negative variance

How do we get a negative sign?

2,400 − 2,000 or 2,000 − 2,400

Surely, it has to be 2,000 − 2,400

Thus it should be Standard Cost − Actual Cost

## Sale/Yield Variances

In calculating sales or yield variances actual data forms the minuend and the standard data the subtrahend.

Variance = Actual − Standard

### Illustration

When in doubt imagine a simple example generating a positive variance.
Standard income = 2,500
Actual income = 3,000

Since income is more, this should give a positive variance

How do we get a positive sign?

2,500 − 3,000 or 3,000 − 2,500

Surely, it has to be 3,000 − 2,500

Thus it should be Actual Income − Standard Income

The difference between the absorbed overhead and incurred overhead is what we call the under/over absorbed overhead. This under/over absorbed overhead is what we call Overhead variance or Total Overhead Cost Variance more specifically.

Overhead variance would give an idea of how much more or less cost had been incurred when the actions are compared to plans. However, it does not give a scope for pin pointing the responsibility for the variance and thereby take corrective actions.

We cannot identify whether the difference is on account of the labourers/laborers working inefficiently (in which case, the people who manage work should be held responsible) or on account of more or less expenditure being incurred (in which case the people responsible for incurrence of expenses are to be held responsible).

Therefore, the Total Overhead Cost Variance is further analysed into its constituent parts to give an idea of the overhead variances in various other angles.

# Total Overhead Variance as a Synthesis of its Constituent Variances

The analysis of the total overhead cost variance into its constituent parts gives an idea of the overhead variances in various other angles.

The possibility for this arises on account of the fact that there are three types of costs involved in overhead variances. The Budgeted overhead cost, the incurred overhead cost and the absorbed overhead cost. The concept of absorption brings in a different angle in analysing variances, more so in case of fixed overhead variances.

All the variances involving overheads which are collectively called Overhead variances and their inter relationships are depicted in the illustration below: This can be understood as the Total Overhead Cost Variance broken down into its constituent parts and the constituent parts further broken down wherever possible.

## Inter-relationships

The inter-relationships as can be interpreted from the above illustration are
1. TOHCV = VOHCV + FOHCV

Total Cost Variance

 = Variable Cost variance + Fixed Cost Variance
2. VOHCV = VOHABSV + VOHEXPV + VOHEFFV

Variable Cost Variance

 = Variable Absorption Variance + Variable Expenditure Variance + Variable Efficiency Variance
3. FOHCV = FOHEXPV + FOHVOLV

Fixed Cost Variance

 = Fixed Expenditure Variance + Fixed Volume Variance
4. FOHVV = FOHABSV + FOHCAPV + FOHCALV + FOHEFFV

Volume Variance

 = Absorption Variance + Capacity Variance + Calendar Variance + Efficiency Variance
5. TOHCV = VOHABSV + VOHEXPV + VOHEFFV + FOHEXPV + FOHVOLV

[From (1), (2), (3)]

Total Cost Variance

 = Variable Absorption Variance + Variable Expenditure Variance + Variable Efficiency Variance + Fixed Expenditure Variance + Fixed Volume Variance
6. TOHCV = VOHABSV + VOHEXPV + VOHEFFV + FOHEXPV + FOHABSPV + FOHCAPV + FOHCALV + FOHEFFV

[From (4), (5)]

Total Cost Variance

 = Variable Absorption Variance + Variable Expenditure Variance + Variable Efficiency Variance + Fixed Expenditure Variance + Fixed Absorption Variance + Fixed Capacity Variance + Fixed Calendar Variance + Fixed Efficiency Variance

These inter-relationships will be useful in problem solving for deriving the required answers as well as in checking for the correctness of answers.