Which formula gives the sales volume required to achieve a specified profit?

Which formula gives the sales volume required to achieve a specified profit?

• A. (Fixed costs + required profit) / contribution per unit
• B. (Fixed costs + required profit) / selling price per unit
• C. Fixed costs / contribution per unit
• D. Fixed costs × required profit / contribution per unit

Answer: (A)

To hit a specified profit, you need enough contribution to cover fixed costs plus the target profit. The contribution per unit is the amount each unit adds after variable costs, i.e., selling price minus variable cost per unit. So the required volume in units is (fixed costs + target profit) divided by contribution per unit. This directly links how much each unit contributes to covering fixed costs and then yielding the desired profit, so dividing the total required amount by the contribution per unit tells you how many units must be sold. With numbers: if fixed costs are 1,000, selling price is 10, variable cost per unit is 6 (contribution per unit = 4), and you want a profit of 2,000, then required volume = (1,000 + 2,000) / 4 = 750 units. Check: profit = 750 × 4 − 1,000 = 2,000. The other formulas don’t fit for aiming at a specific profit: using selling price per unit in the denominator ignores variable costs and overstates volume; fixed costs divided by contribution per unit gives the break-even volume (profit zero); and multiplying fixed costs by the required profit over contribution per unit doesn’t reflect how many units must be sold to cover both costs and target profit.

To hit a specified profit, you need enough contribution to cover fixed costs plus the target profit. The contribution per unit is the amount each unit adds after variable costs, i.e., selling price minus variable cost per unit. So the required volume in units is (fixed costs + target profit) divided by contribution per unit. This directly links how much each unit contributes to covering fixed costs and then yielding the desired profit, so dividing the total required amount by the contribution per unit tells you how many units must be sold.

With numbers: if fixed costs are 1,000, selling price is 10, variable cost per unit is 6 (contribution per unit = 4), and you want a profit of 2,000, then required volume = (1,000 + 2,000) / 4 = 750 units. Check: profit = 750 × 4 − 1,000 = 2,000.

The other formulas don’t fit for aiming at a specific profit: using selling price per unit in the denominator ignores variable costs and overstates volume; fixed costs divided by contribution per unit gives the break-even volume (profit zero); and multiplying fixed costs by the required profit over contribution per unit doesn’t reflect how many units must be sold to cover both costs and target profit.