# 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 material cost which is the product of quantity of material and its price.

Material Cost

= Quantity × Price

Thus,

Variance

= (QuantityMat1 × PriceMat1) − (QuantityMat2 × PriceMat2)

## 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

# Material Variances

The variance in the cost of materials i.e. the difference between the standard cost of materials for actual output and the actual cost of materials would give the variance on account of materials. We call this Material Cost Variance.

Material Cost Variance gives an idea of how much more or less the cost that has been incurred is when the actuals are compared to standards. However, it does not give a scope for pin pointing the reasons for variance and thereby take corrective actions.

We cannot identify whether the variance is on account of more or less purchase price being paid (in which case, the purchases department should be further investigated) or on account of more or less quantity of materials being used (in which case the production department should be further investigated) etc.

Therefore to enable derivation of data that would be useful, material cost variance is analysed further into its constituent parts.

# Material Cost Variance - Synthesis of Constituent Variances

The analysis of material cost variance into its constituent parts gives an idea of the material variance in various other angles. This possibility for analysis arises on account of the fact that material cost is a product of and is thereby influenced by two factors, i.e. the quantity of materials and the price of materials .

All the variances involving materials which are collectively called Material variances and their inter relationships are depicted in the illustration below:

This can be understood as Material Cost Variance being broken down into its constituent parts and the constituent parts being further broken down wherever possible.

## Inter-relationships

The inter-relationships as can be interpreted from the above illustration are
1. MCV = MPV + MUV/MQV

Cost variance

 = Price Variance + Usage/Quantity Variance
2. MUV/MQV = MMV + MYV/MSUV

Usage/Quantity variance

 = Mix variance + Yield/Sub-Usage variance
3. MCV = MPV + MMV + MYV/MSUV

Cost variance

 = Price variance + Mix variance + Yield/Sub-Usage 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.