Break-even analysis (BEA) can be a useful and relatively simple planning tool. BEA calculates different price levels related to various levels of demand to determine sales needed to cover costs.
When most expenses can be accurately estimated, only two missing variables remain: profit and demand. Demand is usually tougher to estimate. By deciding that profit must at least be zero, you can then simply find the demand you must have to make the project a reasonable task.
This Fact Sheet illustrates methods in which break-even analysis can be applied to sales, profits, and costs. It also illustrates how it can be used to help make sound decisions for your business such as employing idle space or equipment, planning advertising, granting credit, and expanding production.
Uses
- Assists in making a choice between two courses of action
- Supports the planning of manufacturing and ordering
- Crucial for start-ups and launching new products/services
- Helps determine which offering are worth developing
- Tells you if an offering is worth conducting a more intensive analysis
- Serves as a substitute for estimating an unknown factor
Limitations
- Many expenses cannot be sorted into fixed or variable
- Time consuming if several products are sold
- Doesn’t account for external factors and potential market share
- Doesn’t account for funds for expansion
- Doesn’t account for marketing and branding efforts
Definitions
Variable Cost (VC): a cost that varies directly with output and changes with increases or decreases in production changes. Examples are packaging, direct materials, sales commission, hourly or billable labour and credit card processing fees.
Fixed Cost (FC): a cost that does not vary in the short term and does not change with production or sales levels. Usually FCs are basic operating expenses such as rent or a lease, advertising, utilities, salaries and insurance.
Contribution Margin (CM): the price of a product minus the associated variable costs. The CM represents the funds available to pay for fixed expenses and net profit.
- Total CM = (Price per unit x number of units) ̶ (VC per unit x number of units)
- Per Unit CM = (Price per unit) ̶ (VC per unit)
Contribution Margin Ratio (CMR): shows how the contribution margin will be affected by a change in sales
- Total CMR = Total CM / Total Sales = %
- Per Unit CMR = Per Unit CM / Price per unit = %
Net Income: the total dollar value after all expenses are paid
- Net Income = CM ̶ Fixed Costs
- Net Income = Sales Revenue ̶ Variable Costs ̶ Fixed Costs
Break-Even Point (BEP): The number of units or sales you need to make in order to cover all expenses without making a profit. To calculate the BEP you’ll need to know your fixed costs per month or year, variable costs per unit, and a price per unit. The BEP can be defined as:
- Total Sales Revenue = Total Expenses
- Profit = $0.00
- Total Contribution Margin = Total Fixed Expenses
- BEP = Fixed Costs / (Price per Unit ̶ Variable Cost per Unit) or,
- BEP = Fixed Costs / CM
Example
Consider the following information for a coffee shop for the sale of cappuccinos:
Price = $5 per medium cup cappuccino
Fixed Costs = $1500 per month (rent, utilities, salary)
Variable Cost = $2 per medium cup of cappuccino (cup, lid, napkin, beans, and water)
What is the BEP?
BEP = Fixed Costs / (Price per Unit ̶Variable Cost per Unit)
BEP = 1500 / (5 – 2) = 1500 / 3 = 500 units
What is the BEP in dollars?
$ BEP = 1500 + (2 x 500) = $2500
What is the BEP if we raise the price by $1?
BEP = 1500 / (6 ̶ 2) = 1500 / 4 = 375 units
How large is our contribution margin if we sell 600 units at $5 per unit in a month?
CM = (Price per unit x number of units) ̶ (VC per unit x number of units)
CM = (5 x 600) ̶ (2 x 600) = 3000 ̶ 1200 = $1800
What is our net income?
Net Income = CM ̶ Fixed Costs
Net Income = 1800 ̶ 1500 = $300
What percentage of our sales revenue (Contribution Margin Ratio) is available to cover the fixed costs and profit?
CMR = 1800 / (600 x 5) = 1800 / 300 = .60 = 60%
Each $1 increase in sales revenue results in a total contribution margin increase of 60 cents.
What is our BEP in sales dollars?
BEP in dollars = 1500 / .60 = $2500
We can use this information to determine sales revenue and number of units sold needed to achieve a target net income. Suppose we want to earn a $1,000 net income on cappuccinos in a month, priced at $5 per unit and has a variable cost of
$2 per unit.
How many units do we need to sell to earn a net income of $1000? First, we need to find the unit contribution margin.
- Unit CM = 5 ̶ 2 = $3
- Units Sold = (FC + Target Net income) / Unit CM
- Units Sold = (1500 + 1000) / 3 = 834 cappuccinos
What level of sales revenue do we need to earn to attain a net income of $1000? First, we need to find the contribution margin ratio:
- CMR = 3 / 5 = 60%
- Sales Revenue = (FC + Target Net income) / CMR
- Sales Revenue = (1500 + 1000) / 60% = $4167
Conclusion
Break-even analysis requires realistic costs and units that vary directly with output and change when production changes. In the long term, all costs are variable.
For many start-ups and small businesses, BEA is a useful formula for estimation and planning. However, a user should always keep in mind that there are other factors that influence the cost of goods and income levels and BEA should be used along with other management tools.
