Calculating contribution per unit, the break-even point in units and in sales revenue, the margin of safety, and the output required for a target profit, and interpreting a break-even chart.

What this dot point is asking

The SQA wants you to use contribution to find the break-even point in units and in sales revenue, the margin of safety, and the output needed for a target profit, and to interpret a break-even chart.

Contribution: the key idea

Every unit sold brings in its selling price but costs its variable cost to make. What is left over - the contribution - first pays off the fixed costs, and once they are covered, becomes profit.

The break-even point

The break-even point is the level of output where the business makes neither a profit nor a loss: total revenue exactly equals total cost, so total contribution exactly equals fixed costs.

The margin of safety

The margin of safety shows how far current or planned sales are above the break-even point - how much sales could fall before the business starts to make a loss. A large margin of safety means lower risk.

Output for a target profit

To find how many units must be sold to reach a desired target profit, the contribution must cover both the fixed costs and the target profit.

The break-even chart

A break-even chart plots money (on the vertical axis) against output (on the horizontal axis). The total cost line starts at the fixed-cost level and rises by the variable cost per unit; the sales revenue line starts at the origin and rises by the selling price per unit. They cross at the break-even point. To the left of the crossing is a loss; to the right is a profit, and the widening gap between the lines shows profit growing.

Examples in context

A cafe selling coffees at $\pounds 3$ with a variable cost of $\pounds 1$ has a $\pounds 2$ contribution per cup. With $\pounds 2000$ of monthly fixed costs, it must sell $1000$ cups to break even; every cup beyond that adds $\pounds 2$ to profit. The owner can use the margin of safety to judge risk and the target-profit formula to set a sales goal. Break-even analysis turns the cost classifications into a decision tool, which is exactly what this dot point tests.

Try this

Q1. Selling price $\pounds 15$, variable cost $\pounds 9$. Find the contribution per unit. [1 mark]

• Cue. $15 - 9 = \pounds 6$.

Q2. Fixed costs $\pounds 12000$, contribution $\pounds 6$ per unit. Find the break-even point in units. [2 marks]

• Cue. $12000 \div 6 = 2000$ units.

Q3. For Q2, find the units needed for a $\pounds 3000$ profit. [2 marks]

• Cue. $(12000 + 3000) \div 6 = 2500$ units.