3.4 - Break-even Analysis
The meaning of break-even point and how to calculate it
The break-even point is the level of sales at which a business neither makes a profit nor suffers a loss. At this point, total revenue exactly matches total costs, covering both fixed costs and variable costs.
Calculating the break-even point in units
Where:
- Fixed costs = Expenses that do not vary with output (£)
- Selling price per unit = Amount charged for each item (£)
- Variable cost per unit = Cost associated with producing each item (£)
The difference between selling price per unit and variable cost per unit is called the contribution per unit.
Worked example - Calculating the break-even point
A small bakery has fixed costs of £6,000 per month, variable costs of £3.00 per cake, and sells each cake for £7.00. Calculate the break-even point in units.
Step 1: Identify the values
- Fixed costs = £6,000
- Variable cost per unit = £3.00
- Selling price per unit = £7.00
Step 2: Calculate the contribution per unit
Contribution per unit = £7.00 - £3.00 = £4.00
Step 3: Apply the break-even formula
Constructing and interpreting break-even charts
A break-even chart is a graph that plots total costs and total revenue against output levels, helping to visualise the break-even point and areas of profit or loss. The horizontal axis shows output, while the vertical axis shows costs, revenue, and profit.
Steps for constructing a break-even chart
- Calculate the break-even point using the formula.
- Select two output levels (including zero for simplicity) and work out total costs and total revenue for each.
- Plot these points on the graph: draw a line for total costs, and a line for total revenue.
- Identify the break-even point where the total cost and total revenue lines cross.
Interpreting features of a break-even chart
- Below break-even - Output levels where total costs exceed total revenue, resulting in a loss.
- Above break-even - Output levels where total revenue exceeds total costs, generating a profit.
- Applications - New businesses might aim to reach break-even in their first year, while larger firms use charts to assess new products or ventures.
The margin of safety
The margin of safety measures how much output can fall below current or planned sales before a business starts making a loss. It represents the buffer above the break-even point.
Calculating the margin of safety
Where:
- Actual or planned output = Number of units sold or expected to be sold
- Break-even output = Number of units needed to break even
On a break-even chart, the margin of safety is the horizontal distance between the break-even point and the actual or planned output level.
Worked example - Calculating the margin of safety
A clothing retailer has a break-even output of 1,800 units per month and plans to sell 2,800 units. Calculate the margin of safety.
Step 1: Identify the values
- Planned output = 2,800 units
- Break-even output = 1,800 units
Step 2: Apply the margin of safety formula
Step 3: Interpretation
The business can afford a drop of 1,000 units in sales before it begins to make a loss.
Effects of changes in costs and prices on break-even
Changes in selling prices, fixed costs, or variable costs alter the break-even point by shifting lines on the break-even chart.
Impacts of specific changes
| Change | Effect on break-even chart | Effect on break-even point |
|---|---|---|
| Increase in selling price | Total revenue line becomes steeper | Shifts left (lower output needed) |
| Decrease in selling price | Total revenue line becomes flatter | Shifts right (higher output needed) |
| Increase in fixed costs | Total cost line shifts upwards (parallel) | Shifts right (higher output needed) |
| Decrease in fixed costs | Total cost line shifts downwards (parallel) | Shifts left (lower output needed) |
| Increase in variable costs | Total cost line becomes steeper | Shifts right (higher output needed) |
| Decrease in variable costs | Total cost line becomes flatter | Shifts left (lower output needed) |
Limitations of break-even analysis
While break-even analysis is valuable for both small and large businesses, it has drawbacks that can affect its reliability.
Key limitations
- Straight-line assumption - Total costs and revenue are shown as straight lines, but in reality, costs may not rise steadily and revenue might vary.
- Sales assumption - It presumes all output produced is sold immediately, ignoring unsold stock.
- Data dependency - Results are only as accurate as the input data; poor estimates of costs or prices lead to misleading outcomes.