Breakeven Quantity of Sales and Net Income

“Breakeven point” or “breakeven quantity of sales” refers to the number of units of a company’s product that is produced and sold, at which point the company’s net income becomes zero.

Computing Breakeven Quantity of Sales

At the point where a company’s net income is zero, its revenues equal its costs. A company’s costs are, however, made up of variable operating costs, fixed operating costs, and fixed financing costs.

With this in mind, if Revenue = Costs, then:

$$ PQ = VQ + F + C $$

Where:

P = Price per unit.

Q = Number of units produced and sold.

V = Variable cost per unit.

F = Fixed operating costs.

C = Fixed financing costs.

Therefore if Q_BE is the breakeven quantity of sales, then:

$$ PQ_{BE}=VQ_{BE}+F+C $$

and

$$ Q_{BE}=\cfrac{F+C}{P-V} $$

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

Example: Breakeven Quantity of Sales

Assume that a company’s product costs are represented by the figures below.

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

What is the company’s breakeven quantity of sales?

Solution

$$ Q_{BE}=\cfrac{F+C}{P-V} = \cfrac{$2,500+$1,200}{$8-$4}=925 \text{ units} $$

Determining Net Income at Various Sales Levels

Using the example above, we can also determine a company’s net income at various sales levels.

$$ \begin{array}{c|c} \textbf{Units sold} & \bf{\text{Sales }($)} & \bf{\text{Net income } ($)} \\ \hline {625} & {5,000} & {-780} \\ \hline {725} & {5,800} & {-520} \\ \hline {825} & {6,600} & {-260} \\ \hline {925} & {7,400} & {0} \\ \hline {1,025} & {8,200} & {260} \\ \hline {1,125} & {9,000} & {520} \\ \hline {1,225} & {9,800} & {780} \\ \end{array} $$

As can be seen from the table, at the breakeven quantity of sales, net income = 0; below the breakeven quantity of sales, net income < 0, and above the breakeven quantity of sales, net income > 0.

Question

A company has fixed operating costs of $5,000 and fixed financing costs of $10,000. The price per unit for one of its products is $12.00, and the variable cost per unit is $5.00. The company’s breakeven quantity of sales is closest to:

A. 2,143.

B. 1,500.

C. 963.

Solution

The correct answer is A.

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

$$ Q_{BE}=\cfrac{F+C}{P-V} = \cfrac{$5,000+$10,000}{$12.00-$5.00}=2,143 \text{ units} $$