Go to content

## Break Even Analysis

Break-Even Analysis is a financial tool used by businesses to determine the point at which total revenue equals total costs, resulting in neither a profit nor a loss.

It helps businesses understand the minimum level of sales needed to cover all incurred costs.

Questions to ask a business owner or manager is what's your break-even level ? At what level of sales will my company start making a profit ? When can I afford to draw a salary ? One technique for answering these questions is break-even analysis.

What's Involved ?
Basically break-even analysis involves analyzing your products costs and selling prices and applying some simple calculations to arrive at your results. The key to performing a break-even point or break-even analysis is the relationship between expenses and revenues. We need to know how expenses will change as sales increase or decrease. Some expenses will increase as sales increase (variable expenses), whereas some expenses will not change as sales increase or decrease (fixed expenses).

Definitions
Important definitions used in break-even analysis are:

Contribution Margins
The term contribution margin may be expressed as a total dollar amount, as an amount per unit, or as a percentage.
• Unit Contribution Margin is Unit Selling Price less Unit Variable Cost
• Total Contribution Margin is
Units Sold multiplied by the Unit Contribution Margin or Total Sales - Total Variable Costs
• Percentage Contribution Margin Ratio is the
Unit Contribution Margin / Unit Selling Price or (Total Sales - Total Variable Costs) / Total Sales

Variable Costs (Expenses) are costs that change directly in proportion to changes in activity (volume).
Some Examples Of Variable Cost:
• Direct Raw Materials
• Direct Labor
• Commissions
• Production Supplies
• Packaging

Fixed Costs (Expenses) are costs that remain constant (fixed) for a given time period despite wide fluctuations in activity (volume).
Some Examples Of Fixed Costs:
• Management Salaries
• Payroll Taxes
• Rent
• Depreciation
• Utilities
• Insurance
• Property Taxes
• Telephone
• Interest

Example
We'll use FleeMarket Bargains as our simple example to illustrate break-even analysis.

FleeMarket Bargains information, costs, and prices:
• Sells cartoon watches that have a cost of \$10.00 (variable cost-expense)
• All unsold watches may be returned to the supplier
• Booth rental costs \$ 100.00 for the day (fixed cost-expense)
• Selling price of the watches is \$20.00

• We will use the above information to calculate the number of watches (units) and the sales dollars we need in order for our flea market business to break even for the day.

There are three methods that can be used to calculate our break even points:
• Equation Method
• Contribution Margin Method
• Graphic Method

Break-Even Equation Method
Sales = Variable Expenses + Fixed Expenses + Profit
Let's adopt this equation and calculate the number of watches that we must sell in order to breakeven.

The basic Break-Even equation becomes:
Unit Selling Price x Number of Units Sold =(Unit Cost x Number Of Units Sold) + Fixed Costs + Profit
Let X = Number of units (watches) that need to be sold to break even
\$20.00X = \$10.00X + \$100.00 + 0
\$10.00X = \$100.00 + 0
X = (\$100.00 + 0) / \$10.00
X = 10 units (watches)

Number of Watches Needed
Break-Even Number of Watches is 10

Total Sales Dollars Needed
We can easily calculate the dollar sales necessary to break even by multiplying the sales price of the watches by the break even number of watches.
Break Even Sales Dollars = 10 (watches) x \$20.00/per watch
Break Even Sales Dollars = \$200.00

Contribution Margin Methods

Unit Contribution Margin
The Unit Contribution Margin is the difference between your product's unit selling price and its unit variable cost.
Unit Contribution Margin = Unit Sales Price - Unit Variable Cost
Unit Contribution Margin (watches) = \$20.00 - 10.00
Unit Contribution Margin = \$10.00

Units Break-Even Point = (Fixed Expenses + Desired Profit) / Unit Contribution Margin
Let X = Number of units (watches) that need to be sold to break even
X = (\$100.00 + 0 ) / \$10.00

The contribution margin method is merely a shortcut version of the Basic Break-Even Equation Method.
X = 10 units (watches)

Number of Watches Needed
Units Break-Even Number of Watches is 10

Total Sales Dollars Needed
Break-Even Sales Dollars = Number of Watches x Watch Selling Price
Break Even Sales Dollars = 10 (watches) x \$20.00/per watch
Break Even Sales Dollars = \$200.00

You can use either method to calculate break-even units and/or sales dollars. The choice is a matter of personal preference.

Calculation Including a Profit
What if you want to see how many units you need to sell to not just break-even but make a certain amount of profit ? If you want to make a profit of \$200.00 from you sale of watches at the flea market all you need to do is include your desired amount of profit in your break-even calculation.

Break-Even Point plus Profit = (Fixed Expenses + Desired Profit) / Unit Contribution Margin
X = (\$100.00 + \$200.00 ) / \$10.00
X = \$300 / \$10.00
X = 30 units (watches)

Break-Even Units plus Profit Number of Watches Needed is 30

Break-Even plus Profit Sales Dollars =  Number of Watches x  Selling Price
Break-Even plus Profit Sales Dollars = 30 x \$20.00
Break-Even plus Profit Sales Dollars = \$600.00

Let's do one more thing to check our calculation. We'll construct a simple profit and loss statement.
Sales of Watches 30 watches @\$20.00 =\$600.00
Cost of Watches 30 watches @\$10.00 = \$300.00
Booth Rental (Fixed Cost)=\$100.00
Profit=\$200.00

Sure enough, if we sell 30 watches at the flea market we'll make a profit of \$200.00.

Percentage Contribution Ratio.
You can also calculate Break-Even Sales Dollars by using your unit percentage contribution ratio.
Unit Percentage Contribution Ratio =  (Selling Price - Variable Costs) / Selling Price
Break-Even Sales Dollars = Fixed Costs / Unit Percentage Contribution Ratio

Using our example where we wanted a profit of \$200.00 on our sale of watches, we can calculate the Sales Dollars needed with another variation of the Break-Even Equation.

Unit Contribution Margin Ratio Percentage = (Selling Price - Variable Costs) / Selling Price
Unit Contribution Margin Ratio Percentage =  (\$20.00 - \$10.00) / \$20.00
Unit Contribution Margin Ratio Percentage = \$10.00 / \$20.00 = 50% Or .50

Break-Even plus Profit Sales Dollars = (Fixed Expenses + Desired Profit) / Unit Contribution Margin Ratio
Break-Even plus Profit Sales Dollars = (\$100.00 + \$200.00) / .50
Break-Even plus Profit Sales Dollars  = \$600.00

Total Dollar Amounts ?
Can you use total dollar amounts to calculate your break-even sales dollars ? Thought you'd never ask.
Sure you can.

Assumptions:
Total Sales for Period                       \$20,000.00
Total Variable Costs for Period         \$15,000.00
Total Contribution Margin                  \$ 5,000.00

Total Contribution  Margin %            25% or .25
Total Contribution / Total Sales
\$5,000.00 / \$20,000.00

Total Fixed Costs for Period              \$10,000.00

Total Break-Even Sales Dollars        \$40,000.00
Fixed Costs / Contribution Margin
\$!0,000.00 / .25

In this example, we used the total contribution margin percentage instead of the unit contribution margin percentage.

Graphical Approach
For you math guys and gals.
The graphical approach has an X-axis (horizontal) that represents Units (volume) and a Y-axis (vertical) that represents Dollars and contains lines for:
• Sales
• Variable Costs (Expenses)
• Total Costs (Expenses)

The point on the graph where the Sales and Total Cost (Expense) Lines intersect is the break-even point.
Another graph that is often used to compare how alternatives on pricing, variable costs, or fixed costs may affect net income (profit) as volume changes is called a P/V Chart or Profit-Volume Graph.

As you can see there are many methods for calculating your Break-Even Points.