Revise Costs, scale of production and break-even analysis for Cambridge 7115 (4.2)

Before calculating break-even, find contribution per unit:

Contribution per unit = selling price − variable cost per unit

Total contribution from all units sold must cover fixed costs before any profit is made. At break-even, total contribution exactly equals fixed costs.

Break-even output (units) = $\frac{\text{Fixed costs}}{\text{Contribution per unit}}$

Break-even revenue = $\frac{\text{Fixed costs}}{\text{Contribution per unit} \div \text{Selling price}}$ (or FC ÷ C/S ratio)

A break-even chart plots cost and revenue against output (units on the x-axis, £ on the y-axis):

1. Fixed costs — a horizontal line (costs that do not change with output).
2. Total cost — starts at fixed costs and slopes upward (FC + total variable costs).
3. Total revenue — starts at the origin and slopes upward (price × quantity).

The break-even point is where TR and TC intersect. The profit region is to the right of break-even (TR > TC); the loss region is to the left.

The margin of safety measures how far actual (or budgeted) sales can fall before the business starts making a loss. A larger margin of safety means lower risk — the firm has a buffer against falling demand.

Margin of safety (units) = Actual output − Break-even output

Margin of safety (%) = $\frac{\text{Actual output} − \text{Break-even output}}{\text{Actual output}} \times 100$

Managers often need output for a target profit, not just break-even. Total contribution must cover fixed costs and the required profit.

Output for target profit = $\frac{\text{Fixed costs} + \text{Target profit}}{\text{Contribution per unit}}$

Break-even analysis is useful for short-run decisions (pricing, launch, capacity) but relies on simplifying assumptions. In evaluation questions, name the assumption and explain why it may not hold in reality.