Explain revenue, costs and contribution, calculate the break-even point and margin of safety, and use break-even analysis to support business decisions

What this dot point is asking

This outcome wants you to explain revenue, costs and contribution, to calculate the break-even point and the margin of safety, and to use break-even analysis to support decisions. The central idea is that the break-even point is the level of sales at which total revenue equals total cost, so the firm makes neither a profit nor a loss - and knowing it tells a business how much it must sell to survive.

The answer

Revenue, costs and contribution

• Revenue = selling price per unit times number of units sold.
• Fixed costs stay the same as output changes (rent, salaries).
• Variable costs change with output (materials per unit).
• Contribution per unit = selling price minus variable cost per unit. It is the amount each sale contributes toward fixed costs (and then profit):

The break-even point

The break-even point is the output at which total revenue = total cost. It is found by:

Below break-even the firm makes a loss; above it, a profit. Each unit sold beyond break-even adds its contribution to profit.

Margin of safety

The margin of safety is how far current (or planned) sales exceed the break-even point:

It shows how much sales could fall before the firm starts making a loss. A large margin of safety means lower risk.

Uses of break-even analysis

Break-even analysis helps a business:

• See how many units it must sell to cover costs.
• Judge the effect of changing the price, costs or output.
• Assess the risk of a new product or decision.
• Support a loan or investment case.

Limitations

Break-even assumes the selling price and costs stay constant and that everything made is sold, which is often unrealistic. It is a useful guide, not a guarantee, and the figures rest on forecasts that may be wrong.

Examples in context

Example 1. A new cafe's break-even target. A Singapore cafe with $12,000 monthly fixed costs sells coffees at$6 with a variable cost of $2, giving a$4 contribution. Its break-even is $\frac{12{,}000}{4} = 3{,}000$ coffees a month. The owner uses this to set a daily sales target (about 100 coffees a day) and to judge whether the location can realistically achieve it before signing the lease. Break-even turns a vague worry into a concrete sales goal.

Example 2. Testing a price decision. A manufacturer considers cutting its price to win sales. Break-even analysis shows that a lower price reduces the contribution per unit, which raises the break-even point, so it would need to sell many more units just to cover costs. By calculating the new break-even before deciding, the firm sees whether the expected extra sales are realistic. This shows break-even guiding a pricing decision rather than guessing.

Try this

Q1. Define the term contribution per unit. [2 marks]

• Cue. Contribution per unit is the selling price of a product minus its variable cost per unit; it is the amount each unit sold contributes toward covering fixed costs and then making a profit.

Q2. Fixed costs are $9,000, the price is$30 and the variable cost is $15. Calculate the break-even output. [2 marks]

• Cue. Contribution per unit = \30 - \15 = \15$; break-even =$\frac{\9{,}000}{\15} = 600$ units.

Q3. Explain why a business might want a large margin of safety. [4 marks]

• Cue. A large margin of safety means current sales are well above the break-even point, so sales could fall a long way before the firm starts making a loss. This reduces risk: if demand drops because of a downturn, a new competitor or seasonal dips, the business still covers its costs. A firm with only a small margin of safety is in danger from even a small fall in sales, so a larger margin gives greater financial security.