What is the equation for Quantity needed to sell to break even?

What is the equation for Quantity needed to sell to break even?

• A. Quantity = Total fixed costs / (Selling price - Unit variable cost)
• B. Quantity = Total revenue / Price
• C. Quantity = Total costs / Contribution margin
• D. Quantity = Selling price / (Fixed costs - Variable costs)

Answer: (A)

Break-even happens when revenue just covers all costs. To find how many units you must sell, focus on how much each unit adds to covering fixed costs after paying for the variable costs of producing that unit. That per-unit amount is the contribution margin: price minus variable cost per unit. The break-even quantity is fixed costs divided by this contribution per unit. So, if fixed costs are 1000, the selling price per unit is 50, and the variable cost per unit is 30, the contribution per unit is 20, and you’d need 1000 / 20 = 50 units to break even. Other formulas don’t reflect this idea: skipping costs and using revenue over price ignores costs; using total costs over the contribution margin mixes fixed and variable costs; and a denominator like (Fixed costs − Variable costs) isn’t meaningful in this context.

Break-even happens when revenue just covers all costs. To find how many units you must sell, focus on how much each unit adds to covering fixed costs after paying for the variable costs of producing that unit. That per-unit amount is the contribution margin: price minus variable cost per unit. The break-even quantity is fixed costs divided by this contribution per unit.

So, if fixed costs are 1000, the selling price per unit is 50, and the variable cost per unit is 30, the contribution per unit is 20, and you’d need 1000 / 20 = 50 units to break even.

Other formulas don’t reflect this idea: skipping costs and using revenue over price ignores costs; using total costs over the contribution margin mixes fixed and variable costs; and a denominator like (Fixed costs − Variable costs) isn’t meaningful in this context.