# Break Even Point

## Definition

Break-Even Point is the level of sales that results in a state of no profit and no loss for the business.

## Formula

Break-Even Point (Units) = Total Fixed Costs ÷ Contribution Margin per unit

## Explanation

Break-Even Point is the number of sales units that cause the business to break even. Sale of 1 unit more than the break-even point will result in a profit whereas sales of 1 unit lower than the break-even Point will result in a loss for the business.

How is the Break Even Point Formula derived?

A business breaks even when its total revenue equals its total cost. We can restate the equation to formulate the break-even point formula as follows:

Total Revenue

=

Total Cost

Total Revenue

=

Total Fixed Cost + Total Variable Cost

Total Revenue - Total Variable Cost

=

Total Fixed Cost

(Selling Price per Unit x Unit Sales) - (Variable Cost per Unit x Unit Sales)

=

Total Fixed Cost

Unit Sales x (Selling Price per Unit - Variable Cost per Unit)

=

Total Fixed Cost

Unit Sales x (Contribution Margin per unit)

=

Total Fixed Cost

Unit SalesBreak-Even Point  =  Total Fixed Costs ÷ Contribution Margin per unit

## Example

Sara who is the owner of a car showroom wants to know the minimum number of cars that she needs to sell in order to avoid making a loss in her first year of business.

She has provided you with the following cost and revenue estimates.

Scenario 1 Scenario 2

Sales

50 units

100 units

Revenue

\$50,000

\$100,000

Expenses:

Rent

\$10,000

\$10,000

Salaries and wages

\$20,000

\$30,000

Depreciation

\$10,000

\$10,000

Transportation

\$5,000

\$10,000

\$10,000

\$12,000

Calculate the break even point for Sara.

Step 1 Identify Fixed Costs

Rent and depreciation are fixed costs as they do not change with a change in sales quantity.

Step 2 Identify Semi-Variable Costs

Transportation costs are completely variable as they increase proportionate to the increase in sales quantity (i.e. transportation costs double when the sales double).

Salaries and overhead costs are semi-variable because they do not increase proportionately to the increase in sales.

Step 3 Calculate fixed cost element of semi-variable costs

Fixed cost portion of salaries and overheads can be found by using the high low method.

Total Cost: 1000 units

A

\$30,000

\$12,000

Total Cost: 500 units

B

\$20,000

\$10,000

Variable Cost/unit

C = (A - B) /(100 units - 50 units)

\$200

\$40

Fixed Cost

A - C × 1000

\$10,000

\$8,000

Step 4 Calculate the total fixed costs

Fixed Cost \$

Rent

\$10,000

Salaries and wages

\$10,000

Depreciation

\$10,000

\$8,000

Total Fixed Cost

\$38,000

Step 5 Calculate sales revenue per unit

Sales revenue per unit

= Total sales revenue / unit sales

= \$100,000 / 100

= \$1,000

Step 6 Calculate variable cost per unit

Variable Cost per unit \$

Salaries

From Step 3

200

From Step 3

40

Transportation

\$5000 / 50 units

100

Total

340

Step 7 Calculate Contribution Margin Per Unit

Contribution margin per unit:

= Sales revenue – variable cost

= \$1000 – \$124

= \$660

Step 8 Calculate the break-even point

Break-Even Point  =  Total Fixed Costs ÷ Contribution Margin per unit

= \$38,000 (Step 4) ÷ \$660(Step 7)

= 58 units

Sara needs to sell at least 58 units to avoid making a loss in the first year.

## Importance

Break-Even Point is important to know on a basic business level because it tells how many units a business needs to sell in order to avoid a loss which can inform business decisions. Break-Even Point Analysis helps to analyze the risk of running into a loss by assessing the margin of safety. Such information can help users to make informed decisions involving for example forming minimum sales targets, feasibility analysis, shutdown decisions and risk analysis.