## Definition:

A difference between the number of units used/sold and the number of units that were anticipated to be used/sold is known as a quantity variance.

Hence, the sales quantity variance assesses the increase or decrease in budgeted profit occurring due to a variation between the actual and budgeted number of units sold.

## Formula:

There are two formulas to calculate the sales quantity variance:

(actual sale in standard mix – budgeted sales) * budgeted profit per unit/contribution margin per unit

(actual sales – budgeted sales) * weighted average profit per unit/ weighted average contribution margin per unit

Contribution margin per unit is the difference between selling price per unit and variable cost per unit and is used in marginal costing.

Profit per unit is the difference between the contribution margin per unit and fixed cost per unit and is used in absorption costing.

The actual sale in standard mix is defined as the actual volume of sales proportioned into standard ratio.

## Explanation:

A “variance” in cost accounting is defined as the difference between the budgeted or standard cost/revenue and actual cost/revenue. Its ultimate objective is to help the company analyze how costs can be minimized or reduced.

Likewise, the sales quantity variance illustrates how a change in quantity of units sold can impact the profitability of the business.

The sales quantity variance is an extension of the sales volume variance. The distinction between the two is that sales volume variance measures the effect on budgeted profit due to the difference between the volume of actual sales and budgeted sales whereas the quantity variance measures the effect on profit of the company due to a difference between the actual sales mix and the budgeted sales mix.

This only happens when the company is selling two or more products at different prices and is irrelevant in the case of one product which is when we use the sales volume variance only.

## Analysis:

A variance can be positive or negative. When the profit at standard mix is less than the budgeted profit, this means that the company has earned less than what was expected and impacts the financial statements negatively. Such a variance is referred to as an unfavorable variance.

However, when the profit at standard mix is more than the budgeted profit it is called a favorable variance since the company has earned more than what was anticipated.

## Example:

A company sells coffee tables as well as dining tables and earns a standard profit per unit of $25 and $50 on each type of table respectively.

As per the budget the company had anticipated that it would sell 100 coffee tables and 60 dining tables for the current period.

However, this is not what happened and the company ended up selling 90 coffee tables and 80 dining tables.

According to the budget, the company was supposed to sell a total of 160 units at a ratio of 100:60 for coffee tables and dining tables.

This would have earned them a total budgeted profit of $5,500 (100*25 + 60*50). On the contrary, though, the company earned a profit of $6,250 (90*25 + 80*50).

The variance of $750 (F) arises due to a difference between the budgeted and actual profit. This is the volume variance.

The actual sales were not in the same ratio of 100:60 as was expected instead it was at a ratio of 90:80.

If we sold the actual sales volume at the budgeted ratio what would the profit be? Let me calculate it for you. The actual total sales volume is 170 units.

The standard mix of these 170 units would be 106.25 units of coffee tables and 63.75 units of dining tables. This would have earned the company a profit of $5,843.75 (106.25*25 + 63.75*50).

The difference between the budgeted profit and actual profit at standard mix is $343.75 (F).

This is represented by the name of sales quantity variance. Even though both the variances are favorable but the amount differs because the actual sales were not made in the same ratio as expected.

The dining tables were sold more than the standard quantity and earn a higher profit whereas the coffee tables were sold less than the standard quantity and earn a lower profit.