Break-even charts are essential tools that help businesses visualise costs, revenues, and profitability to make informed decisions about pricing, output, and investment.
Key Break-even Concepts
Before constructing or interpreting a break-even chart, it is important to understand the key financial concepts that underpin it. These concepts help a business determine how many units it needs to sell in order to cover its costs and begin to make a profit.
Break-even Output
Break-even output refers to the level of output or sales at which a business neither makes a profit nor incurs a loss. It is the point at which total revenue equals total costs (which include both fixed and variable costs).
Definition: The number of units that must be sold for total revenue to match total costs.
Why it matters: Knowing the break-even output helps businesses set realistic sales targets and pricing strategies.
Formula:
Break-even output = Fixed costs ÷ Contribution per unit
If a company’s fixed costs are £10,000 and the contribution per unit is £20, then:
Break-even output = 10,000 ÷ 20 = 500 units
This means the business must sell 500 units before it begins to make a profit.
Margin of Safety
The margin of safety shows how much output or sales can fall before the business starts making a loss. It represents the difference between the actual output and the break-even output.
Definition: The number of units by which actual sales exceed the break-even level.
Importance: A higher margin of safety means the business has more room for error or demand fluctuations.
Formula:
Margin of safety = Actual output – Break-even output
For example, if a business sells 700 units and the break-even point is 500 units, the margin of safety is:
Margin of safety = 700 – 500 = 200 units
This means the business can afford to sell 200 fewer units before it starts to make a loss.
Contribution per Unit
Contribution per unit refers to the amount of money each unit sold contributes towards covering fixed costs and eventually generating profit.
Definition: The difference between the selling price per unit and the variable cost per unit.
Formula:
Contribution per unit = Selling price – Variable cost per unit
If a product sells for £50 and costs £30 to produce (variable cost), then:
Contribution per unit = 50 – 30 = £20
This £20 contributes to covering fixed costs, and after those are covered, it becomes profit.
Total Contribution
Total contribution is the sum of contributions from all units sold. It is used to determine whether fixed costs are covered and to calculate overall profit.
Formula:
Total contribution = Contribution per unit × Output
If 600 units are sold and the contribution per unit is £20, then:
Total contribution = 20 × 600 = £12,000
If fixed costs are £10,000, then the profit is:
Profit = Total contribution – Fixed costs = 12,000 – 10,000 = £2,000
Drawing Break-even Charts
A break-even chart is a graphical representation of costs and revenue at various levels of output. It helps visualise when a business starts to make a profit and the level of output required to achieve that.
Step-by-step Guide to Drawing a Break-even Chart
Draw axes:
Horizontal axis (X-axis): Represents output (number of units produced/sold).
Vertical axis (Y-axis): Represents financial values (£), including costs and revenue.
Plot the fixed costs line:
This is a horizontal line because fixed costs remain constant regardless of output.
Plot the total costs line:
Starts from the point where fixed costs meet the Y-axis.
It slopes upwards because total costs increase with output due to variable costs.
Formula: Total cost = Fixed costs + (Variable cost per unit × Output)
Plot the total revenue line:
Starts from the origin (0,0), since if no products are sold, no revenue is earned.
It rises at a constant rate based on the selling price per unit.
Formula: Total revenue = Selling price × Output
Label the break-even point:
The point where the total revenue and total cost lines intersect.
At this point, revenue equals total costs, meaning there is neither profit nor loss.
Shade areas of profit and loss:
The area above the total cost line and below the revenue line (to the right of break-even) indicates profit.
The area where costs exceed revenue (to the left of break-even) represents loss.
Indicate the margin of safety:
If actual output is known, mark it on the X-axis.
The distance between actual output and break-even output is the margin of safety.
Interpreting Break-even Charts
Once constructed, a break-even chart provides a number of insights for managers and decision-makers.
Uses of Break-even Charts
Identify the break-even output: Helps businesses know the minimum output needed to avoid a loss.
Evaluate profitability: Allows assessment of how much output is needed to achieve a desired level of profit.
Assist in pricing decisions: If break-even is too high, businesses may consider raising prices or reducing costs.
Assess risk: A narrow margin of safety signals higher risk if sales fall unexpectedly.
Features to Interpret
Gradient of total cost line: Steeper slopes suggest higher variable costs.
Steepness of revenue line: A steeper line means a higher selling price per unit.
Distance between lines: The gap between revenue and total costs shows the level of profit at a given output.
Effects of Changes in Price, Costs, and Output
Break-even charts can be redrawn to show the impact of changes in business conditions. This allows businesses to evaluate new scenarios and prepare for potential challenges.
1. Changes in Selling Price
Increasing selling price:
Raises the revenue per unit.
The total revenue line becomes steeper.
Break-even output decreases (fewer units needed to cover costs).
Larger margin of safety (assuming sales remain constant).
Decreasing selling price:
Reduces revenue per unit.
The total revenue line flattens.
Break-even output increases (more units needed to cover costs).
Smaller margin of safety.
2. Changes in Variable Costs
Increasing variable costs:
Lowers contribution per unit.
The total cost line becomes steeper.
Break-even output increases.
Profit margins are reduced.
Decreasing variable costs:
Increases contribution per unit.
Total cost line becomes flatter.
Break-even output decreases.
Higher potential profit.
3. Changes in Fixed Costs
Increasing fixed costs:
Fixed cost line moves upward.
Total cost line starts from a higher point.
Break-even output increases.
Profitability requires more output.
Decreasing fixed costs:
Fixed cost line shifts downward.
Break-even output decreases.
More of the revenue can go toward profit at lower output levels.
4. Changes in Output
While output does not affect the position of the break-even point, it does influence the level of profit or loss:
If output is above the break-even level, the business makes a profit.
If output is below, the business incurs a loss.
The difference between actual and break-even output is the margin of safety.
Worked Examples
Example 1: Basic Break-even Calculation
A company has the following financial details:
Selling price: £40
Variable cost: £25
Fixed costs: £6,000
Step 1:
Contribution per unit = 40 – 25 = £15
Step 2:
Break-even output = 6,000 ÷ 15 = 400 units
This means the company must sell 400 units to break even.
Example 2: Calculating Margin of Safety
Assume actual sales = 550 units
Break-even output = 400 units
Margin of safety = 550 – 400 = 150 units
So, the business can afford to lose 150 unit sales before facing a loss.
Example 3: Profit Calculation
With 550 units sold and a contribution per unit of £15:
Total contribution = 15 × 550 = £8,250
Fixed costs = £6,000
Profit = 8,250 – 6,000 = £2,250
Example 4: Revised Break-even after Cost Increase
If variable cost increases from £25 to £30:
New contribution per unit = 40 – 30 = £10
New break-even output = 6,000 ÷ 10 = 600 units
A 200-unit increase is needed to break even due to the higher costs.
Example 5: Price Decrease Effect
If the selling price drops to £35 (original variable cost £25):
New contribution per unit = 35 – 25 = £10
Break-even output = 6,000 ÷ 10 = 600 units
Revenue grows more slowly, and more units must be sold to cover the same fixed costs.
Example 6: Change in Fixed Costs
If fixed costs rise to £7,500 and contribution remains £15:
Break-even output = 7,500 ÷ 15 = 500 units
This increase requires an additional 100 units to be sold.
Formula Recap for Students
Use the following formulas frequently to master break-even analysis:
Break-even output = Fixed costs ÷ Contribution per unit
Contribution per unit = Selling price – Variable cost per unit
Total contribution = Contribution per unit × Output
Margin of safety = Actual output – Break-even output
Profit = Total contribution – Fixed costs
Understanding these formulas and how to apply them in different business contexts is key to success in both exams and real-world financial decision-making. Practice is essential to mastering the topic.
FAQ
Break-even analysis assumes that all units produced are sold, costs are clearly divided into fixed and variable, the selling price remains constant, and variable cost per unit does not change. It also assumes that productivity and efficiency remain stable. In reality, market conditions, discounts, economies of scale, and production inefficiencies often affect these variables. These assumptions limit the accuracy of break-even analysis in dynamic environments, making it most reliable in stable, short-term planning scenarios rather than long-term strategic forecasting.
Yes, but it becomes more complex. In multi-product businesses, break-even analysis must consider the weighted average contribution per unit across all products, based on their sales mix. The overall break-even output then reflects the expected blend of products sold. If the sales mix changes, the break-even point also shifts. Accurate break-even analysis in this context requires reliable sales forecasts and careful monitoring of product profitability to maintain a consistent and valid contribution margin across the product portfolio.
Break-even charts can be redrawn using the promotional selling price to see how it affects contribution per unit, total revenue, and the break-even point. If the price drops temporarily during a promotion, the total revenue line becomes flatter, and the break-even output increases. This visual tool allows businesses to estimate how many extra units must be sold to maintain profitability during the promotion. It helps assess whether the increased sales volume expected will compensate for the lower margin per unit.
While break-even analysis doesn't directly measure cash flow, it can help identify the minimum sales needed to stop losses and generate surplus cash. By calculating the lowest viable sales level, it assists in prioritising production and pricing strategies to maintain operations. A business in a cash flow crisis can also use break-even forecasts to decide which products to focus on—those with higher contribution margins—and to adjust costs or output levels to stabilise financial performance and avoid deeper cash shortfalls.
Break-even analysis can compare current and projected costs after investment. If new equipment reduces variable costs or increases output capacity, the contribution per unit may rise, leading to a lower break-even point. The business can then determine how long it would take to recover the investment by reaching and exceeding the new break-even level. Additionally, break-even charts can model scenarios based on different demand levels, helping managers judge whether the investment would improve overall profitability under realistic sales expectations.
Practice Questions
Explain how an increase in variable costs could affect a firm's break-even output and margin of safety. (6 marks)
An increase in variable costs reduces the contribution per unit because the difference between the selling price and variable cost decreases. As a result, the break-even output will rise since more units must be sold to cover fixed costs. This also narrows the margin of safety because the firm must now sell a higher quantity to break even, reducing the buffer between actual output and the break-even point. This could make the business more vulnerable to changes in demand, increasing financial risk and reducing profitability unless prices are raised or costs are controlled elsewhere.
Analyse how a business could use a break-even chart to support decision making when launching a new product. (9 marks)
A break-even chart visually shows the output level at which a new product covers its costs, helping managers estimate the viability of the launch. It assists in setting sales targets by identifying the minimum output required to avoid losses. The chart can also highlight how pricing or cost changes affect profitability, enabling informed choices about pricing strategy or cost control. It provides a clear way to assess risk by calculating the margin of safety. However, real-world uncertainty may limit accuracy, so it should be used alongside market research and other financial data for effective decision making.
