Breakeven Output (AQA A-Level Business): Revision Notes

Breakeven output

Understanding breakeven output

You can calculate breakeven output mathematically, which allows you to verify the accuracy of breakeven charts. To perform this calculation, you need to understand the concept of contribution. Contribution helps businesses determine both their breakeven point and their level of profit.

What is contribution?

Contribution represents the amount of money remaining after variable costs have been subtracted from sales revenue. This leftover money contributes towards covering the business's fixed costs and, once those are covered, creating profit.

The basic formula for contribution is:

$\text{Contribution} = \text{Sales revenue} - \text{Variable costs}$

Understanding contribution is essential because it shows how much each sale actually contributes to the business after paying for the costs directly linked to producing that product or service. Variable costs change with output levels (such as raw materials or packaging), while fixed costs remain constant regardless of output (such as rent or salaries).

Calculating contribution per unit

You can also calculate contribution on a per-unit basis, which is particularly useful for working out breakeven output. The formula is:

$\text{Contribution per unit} = \text{Sales price per unit} - \text{Variable cost per unit}$

This tells you how much each individual product sold contributes towards fixed costs and profit.

Once you know the contribution per unit, you can calculate the total contribution by multiplying it by the number of units sold:

$\text{Total contribution} = \text{Unit contribution} \times \text{Output}$

Using contribution to calculate breakeven

Contribution serves two important purposes in financial analysis:

• Calculating the breakeven point
• Calculating the level of profit

The breakeven point is where a business makes neither a profit nor a loss. At this point, the business has sold just enough units to cover all its costs.

The formula for calculating breakeven output is:

$\text{Breakeven output} = \frac{\text{Fixed costs}}{\text{Contribution per unit}}$

This calculation tells you the number of units that need to be sold to break even.

Using contribution to calculate profit

Once you understand contribution, calculating profit becomes straightforward. The formula is:

$\text{Profit} = \text{Total contribution} - \text{Fixed costs}$

This works because contribution first covers fixed costs, and any contribution beyond that becomes profit. When a business reaches breakeven, its total contribution exactly equals its fixed costs, resulting in zero profit. Below breakeven, contribution hasn't yet covered all fixed costs, so the business makes a loss. Above breakeven, contribution exceeds fixed costs, creating profit.

The relationship between contribution, costs and profit

A breakeven diagram visually illustrates how contribution relates to profit and fixed costs. The diagram shows that at any level of output, revenue can be split into three components:

1. Variable costs (which increase with output)
2. Fixed costs (which remain constant)
3. Profit (which only appears once breakeven is exceeded)

The space between the revenue line and the variable costs represents contribution. This contribution is divided between covering fixed costs and generating profit.

Every unit sold below breakeven reduces losses, every unit at breakeven maintains the balance, and every unit above breakeven increases profit by the amount of the unit contribution.