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.

Q_OBE = 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 correct answer is B.

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

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