7.3 - Break-even
The meaning of break-even and the break-even point
Break-even analysis is a technique used to work out the volume of sales a business must achieve to cover all its costs and start making a profit. It helps identify the point at which neither a profit nor a loss is made.
Key features of the break-even point
- Break-even point - The sales level where total revenue exactly matches total costs (fixed costs plus variable costs).
- Below break-even - When sales are lower than this point, total costs exceed revenue, resulting in a loss.
- Above break-even - When sales surpass this point, revenue is greater than total costs, generating a profit.
Applications of break-even analysis
- For new businesses - Conducting this analysis helps establish the required sales volume to cover costs, which is often included in business plans to convince lenders to offer finance.
- For established businesses - It is used when introducing new products to estimate potential profits and assess effects on cash flow.
Calculating the break-even point
The break-even point is found by considering the contribution per unit, which is the amount each sale contributes towards covering fixed costs after variable costs are deducted. Any contribution beyond fixed costs becomes profit.
Formula for contribution per unit
Where:
- Selling price per unit = The price at which each item is sold (£)
- Variable cost per unit = The cost that varies with each unit produced (£)
Formula for break-even point
Where:
- Fixed costs = Costs that remain constant regardless of output (£)
- Contribution per unit = As calculated above (£)
If the result is a decimal, round up to the nearest whole number to ensure all costs are covered.
Changes in variable costs or selling prices alter the break-even point. For example, raising the selling price increases the contribution per unit, reducing the number of units needed to break even.
Worked example - Calculating the break-even point
A business has fixed costs of £4,500, a selling price per unit of £15, and a variable cost per unit of £5. Calculate the break-even point in units.
Step 1: Identify the values
- Fixed costs = £4,500
- Selling price per unit = £15
- Variable cost per unit = £5
Step 2: Calculate contribution per unit
Step 3: Apply the break-even formula
Step 4: Interpretation
The business needs to sell 450 units to cover all costs and break even.
Break-even charts and their interpretation
Break-even charts visually represent the relationship between costs, revenue, and output, making it easier to see the break-even point and potential profits or losses.
Features of a break-even chart
- Axes - Output (number of units) is on the horizontal axis, while costs and revenue (£) are on the vertical axis.
- Fixed costs line - A horizontal line showing costs that do not change with output.
- Total costs line - Starts at the fixed costs level and rises as variable costs are added with increasing output.
- Revenue line - Starts at zero and increases with output, based on the selling price per unit.
- Break-even point - The point where the revenue line crosses the total costs line, indicating the output level where costs equal revenue.
- Profit and loss areas - Above the break-even point (revenue exceeds total costs) shows profit; below it (total costs exceed revenue) shows loss.
To find profit or loss at a specific output, subtract total costs from revenue at that point on the chart. If the selling price rises, the revenue line becomes steeper, intersecting the total costs line at a lower output, which reduces the break-even point.
The margin of safety
The margin of safety measures how much output can decrease before a business starts making a loss. It provides an indication of risk, with a larger margin suggesting greater stability.
Formula for margin of safety
Where:
- Actual output = The current or expected number of units sold
- Break-even output = As calculated previously
A small margin of safety highlights higher risk, prompting actions like cutting costs or boosting revenue to widen it.
Worked example - Calculating the margin of safety
A business has a break-even output of 450 units and actual sales of 680 units. Calculate the margin of safety.
Step 1: Identify the values
- Actual output = 680 units
- Break-even output = 450 units
Step 2: Apply the margin of safety formula
Step 3: Interpretation
Sales could drop by 230 units before the business begins to make a loss, indicating a moderate level of security.
Advantages and disadvantages of break-even analysis
Break-even analysis offers useful insights but has limitations that businesses should consider.
Advantages of break-even analysis
- Simple to carry out if accurate data is available.
- Gives rapid results, enabling quick managerial decisions.
- Helps predict how changes in sales influence costs, revenue, and profits.
- Shows the effects of altering prices or costs on the required sales volume.
- Supports efforts to secure funding by demonstrating viability to investors.
- Aids decisions on launching new products.
Disadvantages of break-even analysis
- Assumes variable costs increase linearly, without accounting for economies of scale that might reduce costs at higher outputs.
- Most effective for single products; it becomes more complex with multiple product lines.
- Relies on precise data, so inaccurate inputs lead to unreliable outcomes.
- Presumes all produced goods are sold, ignoring potential waste or unsold stock.
- Focuses only on the sales needed to break even, without estimating actual future sales.