4.4.3 Break-Even Analysis

Objective

Complete or amend a simple break-even chart.

What is Break-Even Analysis?

Break-even analysis is a tool used to determine the point at which total revenue equals total costs. At this point, the business is neither making a profit nor incurring a loss. It helps businesses understand the relationship between costs, revenue, and 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 in direct proportion to 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 total income generated from sales.
• Break-Even Point: The level of sales at which total revenue equals total costs.

Calculating the Break-Even Point

The break-even point can be calculated in units and in sales revenue.

Break-Even Point in Units

Formula: $$ \text{Break-Even Point (Units)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} $$

Break-Even Point in Sales Revenue

Formula: $$ \text{Break-Even Point (Sales Revenue)} = \frac{\text{Fixed Costs}}{\frac{\text{Total Revenue} - \text{Total Variable Costs}}{\text{Total Revenue}}} $$

Creating a Break-Even Chart

A break-even chart is a simple graph that shows the relationship between total costs, total revenue, and the break-even point.

The chart typically has two axes: the horizontal axis represents the quantity of units sold, and the vertical axis represents the amount of money (costs and revenue).

The break-even point is where the total cost and total revenue lines intersect.

Example: Completing a Break-Even Chart

Consider a business that sells a product for £20 each. The fixed costs are £1000 per month, and the variable cost per unit is £8.

1. Calculate the contribution margin per unit: $$ \text{Contribution Margin per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit} $$ $$ \text{Contribution Margin per Unit} = £20 - £8 = £12 $$
2. 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 a fraction of a unit, the business needs to sell 84 units to break even.

Break-Even Chart Table

Units Sold	Total Revenue (£)	Total Variable Costs (£)	Total Costs (£)	Profit/Loss (£)
0	0	0	£1000	£-1000
83	£1660	£664	£1664	£-4
84	£1680	£672	£1672	£8
100	£2000	£800	£1800	£200

Suggested diagram: A simple break-even chart showing the intersection of the total cost and total revenue lines. The break-even point is clearly marked on the chart.