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 |
|
Overheads |
$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.
| Particulars | working/calculation | Salaries | Overheads |
|---|---|---|---|
|
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 |
|
Overheads |
$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 |
|
Overheads |
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.