In a multi-product business the sales volume variance can be separated into sales mix and quantity variances.

Sales volume variance = Sales mix variance + Sales quantity variance

The purpose of the sales mix and quantity variances is to show how much of the sales volume variance is due to a change in the mix of the products sold (sales mix variance) and how much is due to a change in the quantity of the products sold (sales quantity variance).

The relationship between the sales mix and quantity variances and other sales variances is shown in the diagram below.

## Actual Sales Volume at Budgeted Sales Mix

Before discussing sales mix and quantity variances it is first necessary clarify what is meant by the term ‘actual sales volume at budgeted sales mix’ and to understand how it is calculated.

### How to Calculate Budgeted Sales Mix

The budgeted mix is simply the proportion by sales volume that each product represents of the total budgeted sales volume. For example if a business sells two products and budgets sales of product A of 9,000 units and product B of 3,000 then the budgeted sales mix percentage is calculated as follows.

Product A sales mix % = Product A Sales volume / Total sales volume Product A sales mix % = 9,000 / 12,000 = 75% Product B sales mix % = Product B Sales volume / Total sales volume Product B sales mix % = 3,000 / 12,000 = 25%

The business anticipates that its sales volume will be 75% product A and 25% product B.

### How to Calculate Sales Volume at Budgeted Mix

The actual sales volume at budgeted mix is now calculated by applying these percentages to the **actual** total sales volume of the products.

For example, if the actual sales of the business are 10,000 units then the actual sales volume at budgeted sales mix is calculated as follows.

Product A % = Actual sales volume x Budgeted mix Product A % = 10,000 x 75% = 7,500 Product B % = Actual sales volume x Budgeted mix Product B % = 10,000 x 25% = 2,500

At the budgeted mix the actual sales of each product should have been 7,500 product A and 2,500 product B. Of course the actual sales mix of each product will not agree to the budgeted sales mix calculations which gives rise to the sales mix and quantity variances.

## Sales Mix Variance

The sales mix variance shows how much of the sales volume variance was due to a difference between the actual sales mix and the budgeted sales mix.

The variance is calculated by taking the difference between the actual sales volume and the **actual sales volume at the budgeted mix** and multiplying this by the budgeted price to give a monetary amount.

The sales mix variance formula is as follows.

It should be noted that the term **standard** is often used when referring to unit prices, so budgeted price in the above formula could be replaced with the term standard price.

If actual volume is greater than the actual volume at budgeted mix the sales mix formula gives a positive result and the sales mix variance is a **favorable** variance. If actual volume is lower than actual volume at budgeted mix the formula will give a negative result and the sales mix variance is said to be **unfavorable**.

## Sales Quantity Variance

The sales quantity variance shows how much of the sales volume variance was due to a difference between the actual volume sold at the budgeted mix and the budgeted volume.

The variance is calculated by taking the difference between the **actual sales volume at the budgeted mix** and the budgeted sales volume and multiplying this by the budgeted price to give a monetary amount.

The sales quantity variance formula is as follows.

If the actual volume at budgeted mix is greater than the budgeted volume the sales quantity variance formula gives a positive result and the sales quantity variance is a **favorable** variance. If actual volume at budgeted sales mix is lower than budgeted volume the formula will give a negative result and the sales quantity variance is said to be **unfavorable**.

## Summing the Sales Mix and Quantity Variances

The sales volume variance is based on the difference between the actual volume of sales and the budgeted volume of sales multiplied by the budgeted unit price.

Sales volume variance = (A - B) x BP

Where A is the actual sales volume, B is the budgeted sales volume and BP is the budgeted unit price.

Using this sales volume variance formula we can now show that the sales volume variance is equal to the sum of the sales mix and quantity variances.

If the term actual sales at budgeted mix (ABM) as discussed above is added and subtracted from this formula we get the following.

Sales volume variance = (A - B) x BP Sales volume variance = (A - ABM + ABM - B) x BP Sales volume variance = (A - ABM) x BP + (ABM - B) x BP Sales volume variance = Sales mix variance + Sales quantity variance

The sales volume variance is the sum of the sales mix and quantity variances.

## Sales Mix and Quantity Variances Example

A business provides the following information relating to its sales.

Units | Price | |
---|---|---|

Actual Product A | 8,800 | 5.20 |

Actual Product B | 2,400 | 10.10 |

Actual | 11,200 | |

Budgeted Product A | 7,000 | 5.50 |

Budgeted Product B | 3,000 | 9.50 |

Budgeted | 10,000 |

### Calculate the Budgeted Sales Mix Percentages

The budgeted sales mix percentages are calculated using the **budgeted** sales information as follows.

Product A sales mix % = Product A Sales volume / Total sales volume Product A sales mix % = 7,000 / 10,000 = 70% Product B sales mix % = Product B Sales / Total sales Product B sales mix % = 3,000 / 10,000 = 30%

### Calculate the Actual Sales at the Budgeted Sales Mix

The actual sales are 11,200 units. The actual sales at the budgeted mix are calculated as follows.

Product A % = Actual sales x Budgeted mix Product A % = 11,200 x 70% = 7,840 Product B % = Actual sales x Budgeted mix Product B % = 11,200 x 30% = 3,360

Note that this differs from the actual sales mix of 8,800 units of product A and 2,400 units of product B.

### How to Calculate Sales Mix Variance

The sales mix variance is calculated as follows.

Sales mix variance = (Actual volume - Actual volume at budgeted mix) x Budgeted price. Product A mix variance = (8,800 - 7,840) x 5.50 Product A mix variance = 960 x 5.50 = 5,280 Product B mix variance = (2,400 - 3,360) x 9.50 Product B mix variance = -960 x 9.50 = -9,120 Sales mix variance = 5,280 - 9,120 = -3,840

The calculations simply show that the sales of product A were 960 higher than anticipated by the budgeted mix and the sales of product B were 960 lower than anticipated. Since product A sells at a lower price than Product B the sales mix variance is negative and is therefore an unfavorable variance.

### How to Calculate Sales Quantity Variance

The sales quantity variance is calculated as follows.

Sales quantity variance = (Actual volume at budgeted mix - Budgeted volume) x Budgeted price Product A quantity variance = (7,840 - 7,000) x 5.50 Product A quantity variance = 840 x 5.50 = 4,620 Product B quantity variance = (3,360 - 3,000) x 9.50 Product B quantity variance = 360 x 9.50 = 3,420 Sales mix variance = 4,620 + 3,420 = 8,040

The sales quantity variance formula shows that the variance is positive and therefore a favorable variance. The actual sales at budgeted mix of product A were 840 units higher than budget and the actual sales at budgeted mix for product B were 360 units higher than budget.

### Total Sales Volume Variance Proof

As we have seen, the total sales volume variance should equal the sum of the sales mix and quantity variances.

Sales volume variance = Sales mix variance + Sales quantity variance Sales volume variance = -3,840 + 8,040 = 4,200

Using the sales volume variance formula.

Sales volume variance = (Actual volume – Budgeted volume) x Budgeted price Product A volume variance = (8,800 - 7,000) x 5.50 = 9,900 Product B volume variance = (2,400 - 3,000) x 9.50 = -5,700 Sales volume variance = 9,900 - 5,700 = 4,200

The total sales volume variance is 4,200 the same as calculated above using the sum of the sales mix and quantity variances

## Sales Mix and Quantity Variances Using Contribution and Profit

The above analysis uses the budgeted price per unit of the product to calculate the monetary value of the sales mix and quantity variances. As an alternative for absorption costing the budgeted profit per unit or for marginal costing the budgeted contribution per unit can be substituted for the budgeted price in the above formulas.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.