Written by The breakeven point (BEP) is the point at which a company’s total sales revenue equals its total costs.
It is the level of sales or production volume at which a business neither incurs a profit nor a loss.
When a company reaches the break-even point, it is said to “break even” because the revenue generated from sales exactly covers all the costs incurred to produce and sell the goods or services.
Breakeven point is the point where:
- Total revenue equals total costs.
- Sales dollars value equal the sum of variable costs and fixed costs.
- Total contribution equals total fixed cost.
At the breakeven point, the total contribution margin (the difference between the total sales revenue and the total variable costs) is equal to the total fixed costs.
Once the breakeven point is reached, any additional sales beyond that point will generate a profit for the business.
Breakeven Point in Units
The breakeven point in units is the number of units a business needs to sell to cover its total costs and break even.
It is the sales units or volume where the business will not be making a profit or loss.
It is calculated by dividing the total fixed costs by the difference between sales per unit and variable cost per unit.
The formula for calculating the breakeven point in units is:
BEP in units=\(\frac{\text{Total fixed costs}}{\text{Sales per unit – Variable cost per unit}}\)
Before we go on to calculate the break-even point in units, it is important I explain some concept regarding break-even point in unit:
- Fixed Costs (FC): Fixed costs are costs that do not vary with the level of production or sales. They include rent, salaries, insurance, and other overhead expenses.
- Variable Costs per Unit (VC): Variable costs are directly associated with the production or sale of a unit of the product or service. These costs may include raw materials, direct labor, and variable overhead costs.
- Selling Price per Unit (SP): Selling price refers to the price at which the product or service is sold to customers.
Example 1
A company sells pens for 50 naira each. The variable cost per pen is 30 naira and the total fixed costs are 100,000 naira. How many pens does the company need to sell to break even?
Solution:
BEP in units=\(\frac{100,000}{50-30}\)=5,000 pens
So, the company needs to sell 5000 pens to breakeven.
Example 2
A tailor makes and sells shirts for 1,000 naira each. The variable cost per shirt is 600 naira and the total fixed costs are 20,000 naira. How many shirts does the tailor need to sell to break even?
Solution:
BEP in units=\(\frac{20,000}{1,000-600}\)=50 shirts
Therefore, the tailor needs to sell 50 shirts to breakeven..
Breakeven point in Sales Naira
The break-even point in sales Naira is the amount of sales revenue needed to cover the fixed costs and variable costs of a business.
It represents the amount of sales revenue where total revenues for a product equal total costs.
in other words, it is the point where the business has sold enough products to cover all its costs.
It can be calculated by dividing the fixed costs by the contribution margin ratio.
The contribution ratio is the ratio of the difference between the sales price per unit and the variable costs per unit to the sales price per unit.
\(\text{Break-even point in sales Naira} = \frac{\text{Fixed costs}}{\text{Contribution margin ratio}}\)
Where the contribution margin ratio is calculated as:
\(\text{Contribution margin ratio} = \frac{\text{Sales price per unit} – \text{Variable costs per unit}}{\text{Sales price per unit}}\)
Example 3
A company incurs fixed costs amounting to 100,000 Naira and variable costs of 500 Naira per unit. Determine the break-even point in Naira considering that the selling price per unit is 1,000 Naira.
Solution:
In this problem, the fixed costs are ₦100,000, the sales price per unit is ₦1,000, and the variable costs per unit are ₦500.
Before we can solve Breakeven point in sales Naira, we need to know first obtain the value of contribution margin ratio
\(\text{Contribution margin ratio} = \frac{1,000 – 500}{1,000} = 0.5\)
\(\text{Break-even point in sales Naira} = \frac{100,000}{0.5} = 200,000\)
So, the break-even point in sales Naira for this company is ₦200,000.
Example 4
Determine the Break-even point in sales naira given that the company has fixed costs of ₦1,000,000, a sales price per unit of ₦200, and variable costs per unit of ₦50.
Solution:
Here, the fixed costs are ₦1,000,000, the sales price per unit is ₦200, and the variable costs per unit are ₦50.
We need to know first obtain the value of contribution margin ratio before we can solve Breakeven point in sales Naira.
\(\text{Contribution margin ratio} = \frac{200 – 50}{200} = 0.75\)
\(\text{Break-even point in sales Naira} = \frac{1,000,000}{0.75} = 1,333,333.33\)
So, the break-even point in sales Naira for this company is ₦1,333,333.33.
Conclusion
To conclude, the break-even is the point where the total revenue equals total cost so that the firm is neither making profit nor loss.
The sales volume or units where the firm is neither making a profit nor loss is called the breakeven point in sales units or volume while the sales revenue at the breakeven point is called breakeven point in sales naira/dollar.
