Which expression gives the quantity of units required to reach a specific profit?

Which expression gives the quantity of units required to reach a specific profit?

• A. Contribution per unit / Fixed costs
• B. (Fixed costs + Required profit) / Contribution per unit
• C. (Fixed costs - Required profit) / Contribution per unit
• D. Fixed costs / Selling price per unit

Answer: (B)

To reach a specific profit, you focus on how much each unit actually contributes after covering variable costs. That contribution per unit times the number of units sold gives the total available to cover fixed costs and then provide profit. If you want a target profit P, the profit equation is: (contribution per unit) × Q − fixed costs = P. Rearranging gives (contribution per unit) × Q = fixed costs + P, so Q = (fixed costs + P) / (contribution per unit). This is exactly the form that uses fixed costs plus the required profit, all divided by the contribution per unit. If P were zero, this reduces to break-even: fixed costs divided by contribution per unit. The other options don’t fit because they either divide by the wrong factor (selling price rather than contribution) or combine the terms inappropriately (subtracting the profit or mixing the order).

To reach a specific profit, you focus on how much each unit actually contributes after covering variable costs. That contribution per unit times the number of units sold gives the total available to cover fixed costs and then provide profit. If you want a target profit P, the profit equation is: (contribution per unit) × Q − fixed costs = P. Rearranging gives (contribution per unit) × Q = fixed costs + P, so Q = (fixed costs + P) / (contribution per unit). This is exactly the form that uses fixed costs plus the required profit, all divided by the contribution per unit.

If P were zero, this reduces to break-even: fixed costs divided by contribution per unit. The other options don’t fit because they either divide by the wrong factor (selling price rather than contribution) or combine the terms inappropriately (subtracting the profit or mixing the order).