Contribution and Margin of Safety

Contribution per unit is the amount each unit contributes towards fixed costs and profit:

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

The contribution to sales (C/S) ratio (also called the profit-volume or P/V ratio) shows the contribution earned from each $1 of sales:

$\text{C/S ratio} = \frac{\text{Contribution per unit}}{\text{Selling price}} \;(\times 100\%)$

Example. Selling price $25, variable cost $15 → contribution = $10; C/S ratio = 10 ÷ 25 = 0.4 (40%). So every $1 of sales gives $0.40 of contribution.

The C/S ratio is useful when working in sales revenue rather than units (e.g. for a business selling many products), because break-even revenue and margin of safety in $ use it directly.

The break-even point is the level of output at which total contribution exactly equals fixed costs, so profit is zero (no profit, no loss).

In units:

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

In revenue:

$\text{Break-even (revenue)} = \frac{\text{Fixed costs}}{\text{C/S ratio}} \quad\text{(or break-even units} \times \text{selling price)}$

Example. Fixed costs $30,000; contribution $10/unit → break-even = 30,000 ÷ 10 = 3,000 units. At $25 each that is $75,000 of revenue (or 30,000 ÷ 0.4 = $75,000).

Above break-even, every extra unit's contribution is pure profit (fixed costs are already covered). Below it, the business makes a loss.

The margin of safety is the amount by which actual (or budgeted) sales exceed the break-even point — how far sales can fall before the business starts to make a loss:

$\text{Margin of safety (units)} = \text{Actual sales (units)} - \text{Break-even (units)}$

It can also be expressed as a percentage:

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

Example. Actual sales 5,000 units; break-even 3,000 units → margin of safety = 2,000 units, or 2,000 ÷ 5,000 = 40%.

A larger margin of safety means lower risk — sales can drop a long way before a loss. A small margin of safety is a warning that even a small fall in sales could cause a loss.

To find the output (or revenue) needed to earn a target profit, treat the target profit like an extra 'fixed cost' to be covered by contribution:

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

$\text{Revenue for target profit} = \frac{\text{Fixed costs} + \text{Target profit}}{\text{C/S ratio}}$

Example. Fixed costs $30,000; target profit $15,000; contribution $10/unit → (30,000 + 15,000) ÷ 10 = 4,500 units.

And to find the profit at a given output, work the other way:

$\text{Profit} = (\text{Units} \times \text{Contribution per unit}) - \text{Fixed costs}$

These four ideas — contribution, break-even, margin of safety and target profit — are the toolkit of cost-volume-profit (CVP) analysis covered in a later subtopic.