4.4.3 Break-Even Analysis

Objective: Complete or amend a simple break-even chart

Break-even analysis is a crucial tool for businesses to understand the relationship between costs, revenue, and profit. It helps determine the point at which total revenue equals total costs, meaning the business is neither making a profit nor a loss.

A break-even chart visually represents this relationship. It shows the fixed costs, variable costs, and the point where the business starts to make a profit.

Key Terms

• Fixed Costs: Costs that do not change with the level of production or sales (e.g., rent, salaries).
• Variable Costs: Costs that change directly with the level of production or sales (e.g., raw materials, direct labor).
• Total Costs: The sum of fixed costs and variable costs.
• Total Revenue: The income generated from sales.
• Break-Even Point: The level of sales at which total revenue equals total costs (i.e., no profit or loss).

Formulae

The break-even point can be calculated using the following formulae:

• Break-Even Point in Sales (in £ or other currency): $$ \text{Break-Even Point (Sales)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} $$
• Break-Even Point in Units: $$ \text{Break-Even Point (Units)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} $$

Example: Completing a Break-Even Chart

Let's consider a business that sells products for £20 each. The fixed costs are £1000 per month, and the variable cost per unit is £8.

First, we calculate the contribution margin per unit:

$$ \text{Contribution Margin per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit} $$ $$ \text{Contribution Margin per Unit} = £20 - £8 = £12 $$

Next, we calculate the break-even point in units:

$$ \text{Break-Even Point (Units)} = \frac{\text{Fixed Costs}}{\text{Contribution Margin per Unit}} $$ $$ \text{Break-Even Point (Units)} = \frac{£1000}{£12} \approx 83.33 \text{ units} $$

Since you can't sell fractions of units, the business needs to sell 84 units to break even.

Break-Even Chart

Here's a simple break-even chart illustrating this scenario:

Sales (Units)	Total Revenue (£)	Total Costs (£)	Profit/Loss (£)
0	0	£1000	-£1000
83	£1660	£1000	£660
84	£1680	£1000	£680

Suggested diagram: A chart with units on the x-axis and revenue, costs, and profit/loss on the y-axis, showing the break-even point where the revenue and cost lines intersect.

This chart shows that the business needs to sell approximately 84 units to start making a profit. Any sales above 84 units will result in a profit.