Break-even Quantity shows the level of output that the business must produce and sell at which Sales Revenue equals Total Costs (TC). At Break-even Quantity neither a profit nor a loss is made.
In order to calculate and find out Break-even Quantity, Break-even Analysis shall be undertaken. Break-even Quantity can be determined either by using the Equation Methods or the Graphical Method:
1. The Equation Methods. There are two ways to calculate and determine Break-even Quantity using two different formulae:
a.) The Equation Method 1: Sales Revenue = Total Costs (TC)
b.) The Equation Method 2: Break-even Quantity (BEQ)
2. The Graphical Method. By constructing the Break-even Chart.
The Equation Method 1: Sales Revenue = Total Costs (TC)
Break-even Quantity (BEQ) can be calculated by comparing Sales Revenue with Total Costs (TC). The company breaks-even when Sales Revenue equals to Total Costs (TC):
Sales Revenue = Total Costs (TC)
Sales Revenue is calculated as Price times the number of products sold:
Sales Revenue = Price x Quantity
And, Total Costs (TC) consist of both Fixed Costs (FC) and Variable Costs (VC):
Total Costs (TC) = Fixed Costs (FC) + Total Variable Costs (TVC)
The above formula for Sales Revenue can be further broken down into details. Hence, Break-even Quantity (BEQ) can then be calculated in the following way:
Price x Quantity = Fixed Costs (FC) + Total Variable Costs (TVC)
And, Total Variable Costs (VC) equal to Average Variable Cost (AVC) times the number of products produced and sold. So:
Price x Quantity = Fixed Costs (FC) + Average Variable Cost (AVC) x Quantity
Let’s take a look at a real-life example.
Example for the Equation Method 1: Sales Revenue = Total Costs (TC) A hamburger restaurant has Fixed Costs (FC) of USD$3,500 per month. Variable Costs (VC) are USD$10 per hamburger, and the selling price of one chicken hamburger is USD$30. Question: How many chicken hamburgers does this retailer must sell per month in order to break-even? Price x Quantity = Fixed Costs (FC) + Average Variable Cost (AVC) x Quantity USD$30 x Quantity = USD$3,500 + USD$10 x Q USD$20 x Quantity = USD$3,500 Quantity = USD$3,500 / USD$20 Quantity = 175 Break-even Quantity (BEQ) = 175 chicken hamburgers Answer: This hamburger restaurant must sell 175 chicken hamburgers per month in order to break-even. If it sells 174 chicken hamburgers, it will make a loss. If it sells 176 chicken hamburgers, it will make a profit.
The Equation Method 2: Break-even Quantity (BEQ)
There is a specific formula that can be used using the Contribution Per Unit rule:
Break-even Quantity (BEQ) = Fixed Costs (FC) / Contribution Per Unit
Contribution refers to the sum of money that remains after all Variable Costs (VC) have been taken away from the Sales Revenue. Contribution amount is available to be used towards paying Fixed Costs (FC) of production.
Contribution Per Unit means selling Price less Average Variable Cost (AVC) of producing one unit. The formula for Contribution Per Unit is therefore:
Contribution Per Unit = Price – Average Variable Cost (AVC)
Therefore, the above formula for Break-even Quantity (BEQ) can be further broken down into details. Hence, Break-even Quantity (BEQ) can then be calculated in the following way:
Break-even Quantity (BEQ) = Fixed Costs (FC) / [Price – Average Variable Cost (AVC)]
Let’s take a look at a real-life example.
Example for the Equation Method 2: Break-even Quantity (BEQ) A hamburger restaurant has Fixed Costs (FC) of USD$3,500 per month. Variable Costs (VC) are USD$10 per hamburger, and the selling price of one chicken hamburger is USD$30. Question: How many chicken hamburgers does this retailer must sell per month in order to break-even? Contribution Per Unit = Price - Average Variable Cost (AVC) Contribution Per Unit = USD$30 – USD$10 Contribution Per Unit = USD$20 Therefore: Break-even Quantity (BEQ) = Fixed Costs (FC) / Contribution Per Unit Break-even Quantity (BEQ) = USD$3,500 / USD$20 Break-even Quantity (BEQ) = 175 chicken hamburgers Answer: This hamburger restaurant must sell 175 chicken hamburgers per month in order to break-even. If it sells 174 chicken hamburgers, it will make a loss. If it sells 176 chicken hamburgers, it will make a profit.
It is worth remembering that Contribution Per Unit is not the actual Profit because Fixed Costs (FC) have not yet been accounted for. However, each chicken hamburger contributes USD$20 towards the payment of the firm’s Fixed Costs (FC) of USD$3,500.
Once Fixed Costs (FC) are covered, any further sales above 175 chicken hamburgers will contribute towards the profit of the business. In other words:
Profit = Total Contribution – Fixed Costs (FC)
Specifically, Total Contribution is simply Contribution Per Unit multiplied by the quantity of sales:
Total Contribution = Contribution Per Unit x Quantity
Or:
Total Contribution = [Price – Average Variable Cost (AVC)] x Quantity
Profit at Break-even Output is 0 as USD$20 multiplied by 175 gives Total Contribution of USD$3,500 which equals Fixed Costs (FC).
Which method of calculating Break-even Quantity (BEQ) is faster?
In summary, the Break-even Analysis shall be undertaken in order to determine Break-even Quantity. Either of the two Equation Methods can be used to calculate Break-even Quantity. The second Equation Method 2 is the quicker of the two quantitative methods of calculating Break-even Quantity though.
