# Operating Break-even Quantity of Sales

The breakeven quantity of sales, or simply breakeven point, indicates the number of units of a company’s product that is produced and sold. At this point, a company’s net income becomes zero. Similarly, we can specify the breakeven point concerning operating profit. This is referred to as the “Operating breakeven point” or “Operating breakeven quantity of sales.”

## Calculating Operating Breakeven Quantity of Sales

At the operating breakeven quantity of sales, Revenues = Operating costs, so mathematically:

$$PQ_{OBE} = VQ_{OBE} + F$$

Where:

P = Price per unit.

QOBE = Number of units produced and sold.

V = Variable cost per unit.

F = Fixed operating costs.

Therefore, rearranging the formula, the operating breakeven quantity of sales,

$$Q_{OBE}=\cfrac {F}{P-V}$$

In other words, a company’s operating breakeven quantity of sales is equal to the company’s fixed operating costs divided by the difference between the price per unit and variable cost per unit.

#### Example: Operating Breakeven Quantity of Sales

Assume that the figures below represent a company’s product costs.

$$\begin{array}{l|r} \text{Price per unit sold} & {8.00} \\ \hline \text{Variable cost per unit} & {4.00} \\ \hline \text{Fixed cost per unit} & {2,500.00} \\ \hline \text{Fixed financing cost} & {1,200.00} \\ \end{array}$$

What is the company’s operating breakeven quantity of sales?

Solution

The operating breakeven quantity of sales:

$$Q_{OBE}=\cfrac {2,500}{8.00-4.00}=625 \text{ units}$$

### Question

A company has fixed operating costs of $7,500. The price per unit for one of its products is$13.30, and the variable cost per unit is \$7.50. The company’s operating breakeven quantity of sales is closest to:

A. 2,143.

B. 1,293.

C. 864.

Solution

The operating breakeven quantity of sales can be calculated using the following formula:

$$Q_{OBE}=\cfrac {F}{P-V} =\cfrac {7,500}{13.30-7.50}= 1,293 \text{ units}$$

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