3.3.2 - Calculating break-even output

3.3.2 - Calculating break-even output

Learn what break-even means and find the output needed to cover all costs. Calculate it using contribution per unit, check whole-unit answers, and read the same result from a break-even chart.

Break-even and contribution

A business breaks even when its total revenue exactly equals its total costs for the period.

Break-even output

The level of output sold at which total revenue equals total costs, so the business makes neither a profit nor a loss.

Being able to pay one bill or cover only material costs is not the same as breaking even. Both fixed and variable costs must be covered. This simple model assumes all output is sold at the stated price.

Contribution per unit

Selling price per unit minus variable cost per unit: the amount from each sale available to cover fixed costs and, once these are covered, contribute to profit.

Illustrative data: a stationery maker sells a notebook for $8 and spends $3 on variable costs per notebook. Each sale contributes 8−3=58-3=5, or $5. The first $3 covers that unit's variable cost; the remaining $5 helps cover monthly fixed costs. Contribution is not automatically profit because fixed costs still need to be covered.

If monthly fixed costs are $1,200, 100 notebooks give total contribution of $500 and a $700 loss. At 240 notebooks, total contribution is $1,200 and all fixed costs are covered. After break-even, another notebook adds $5 to profit if price and costs remain unchanged.

Calculating required output

Dividing fixed costs by the contribution from each unit finds how many sales are needed to cover those fixed costs.

Contribution per unit=selling price per unit−variable cost per unit\text{Contribution per unit}=\text{selling price per unit}-\text{variable cost per unit} Break-even output=fixed costsselling price per unit−variable cost per unit\text{Break-even output}=\frac{\text{fixed costs}}{\text{selling price per unit}-\text{variable cost per unit}}

Use fixed costs for the stated period and prices/costs in the same currency. The answer is output units for that period, not currency.

For the illustrative notebook maker, break-even output is 1,200÷(8−3)=1,200÷5=2401{,}200\div(8-3)=1{,}200\div5=240 notebooks per month. Check it using revenue and costs: revenue is 240×8=1,920240\times8=1{,}920; total costs are 1,200+(240×3)=1,9201{,}200+(240\times3)=1{,}920. Profit is therefore zero.

A different illustrative maker has fixed costs of $1,000, price $7 and variable cost $4 per mug. The mathematical break-even point is 1,000÷3=333.33…1{,}000\div3=333.33\ldots mugs. If mugs are sold only as whole units, the minimum output avoiding a loss is 334. At 333, contribution is $999, leaving a $1 loss; at 334, contribution is $1,002, giving a $2 profit. Distinguish the mathematical intersection from a question asking for the minimum whole units; follow the stated rounding instruction.

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