This calculator helps you determine the crucial point where your total revenue equals your total costs (fixed and variable), resulting in zero profit. Simply enter any three of the four variables to solve for the missing one.
Break-Even Point (BEP) Calculator
Break-Even Point Formula: calculate fixed variable costs linear relationship
Q = F / (P – V)
Where P – V is the Contribution Margin per unit (CM).
Variables Used in Calculation:
- Total Fixed Costs (F): Costs that do not change with the volume of production or sales (e.g., rent, insurance).
- Selling Price per Unit (P): The price at which one unit of the product or service is sold.
- Variable Cost per Unit (V): Costs that fluctuate directly with the volume of production (e.g., raw materials, direct labor).
- Break-Even Quantity (Q): The number of units that must be sold to cover all costs.
What is fixed variable costs linear relationship?
The relationship between fixed and variable costs is linear in the context of Cost-Volume-Profit (CVP) analysis. The Break-Even Point (BEP) is a specific application of this linear model. It defines the production level where total revenue is exactly equal to total costs, meaning a business neither makes a profit nor incurs a loss. Understanding this point is vital for pricing decisions, budget planning, and determining the minimum viable sales target.
Total costs are calculated as: $\text{Total Cost} = \text{Fixed Costs} + (\text{Variable Cost per Unit} \times \text{Quantity})$. Because fixed costs are constant and variable costs change proportionally with quantity, the relationship is a straight line. The higher the selling price relative to the variable cost (the higher the Contribution Margin), the steeper the revenue line, and the faster the break-even point is reached.
How to Calculate Break-Even Point (Example)
Assume a company has Fixed Costs of $60,000, a Selling Price of $150, and a Variable Cost of $90.
- Identify the Variables: $F = 60,000, P = 150, V = 90$.
- Calculate the Contribution Margin (CM): $\text{CM} = P – V = \$150 – \$90 = \$60$.
- Apply the BEP Formula: $Q = F / \text{CM}$.
- Solve for Q: $Q = \$60,000 / \$60 = 1,000$ units.
- Conclusion: The company must sell 1,000 units to cover all costs.
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Frequently Asked Questions (FAQ)
What is the difference between fixed and variable costs?
Fixed costs remain constant regardless of production volume (e.g., rent, depreciation), while variable costs change in direct proportion to volume (e.g., raw materials, commissions). Understanding this distinction is key to CVP analysis.
Why is the Contribution Margin important in BEP?
The Contribution Margin ($P-V$) represents the revenue left over after covering variable costs. This margin is what “contributes” to covering the fixed costs. Once fixed costs are covered, the Contribution Margin becomes profit.
What happens to the BEP if the Selling Price increases?
If the fixed costs and variable costs remain constant, increasing the selling price (P) will increase the Contribution Margin (P-V), resulting in a lower Break-Even Point (Q). You need to sell fewer units to break even.
Can a negative number of units be a break-even point?
No. The quantity (Q) must be a non-negative number. If the selling price (P) is less than the variable cost (V), the contribution margin is negative, leading to an illogical or unattainable break-even point under normal operations, which this calculator will flag as an error.