A company has fixed costs of $250,000 per year. They sell a single product for $25 per unit. Variable costs are $7 per unit. Given a combined state and local tax rate of 40%, how many units must be sold to earn an after-tax profit of $120,000?

A company has fixed costs of $250,000 per year. They sell a single product for $25 per unit. Variable costs are $7 per unit. Given a combined state and local tax rate of 40%, how many units must be sold to earn an after-tax profit of $120,000?

• A. 18,000
• B. 25,000
• C. 45,000
• D. 62,500

Answer: (B)

The key idea is translating the after-tax profit goal into a pre-tax target, then seeing how many units are needed to reach that pre-tax amount using the contribution margin. Each unit brings in P - V = 25 - 7 = 18 of contribution. To have after-tax profit of 120,000 with a 40% tax, you must first earn pre-tax profit of 120,000 / (1 - 0.40) = 200,000. The pre-tax profit is total contribution minus fixed costs, so total contribution must be 200,000 + 250,000 = 450,000. At 18 per unit, required units are 450,000 / 18 = 25,000. Therefore, 25,000 units must be sold.

The key idea is translating the after-tax profit goal into a pre-tax target, then seeing how many units are needed to reach that pre-tax amount using the contribution margin.

Each unit brings in P - V = 25 - 7 = 18 of contribution. To have after-tax profit of 120,000 with a 40% tax, you must first earn pre-tax profit of 120,000 / (1 - 0.40) = 200,000. The pre-tax profit is total contribution minus fixed costs, so total contribution must be 200,000 + 250,000 = 450,000. At 18 per unit, required units are 450,000 / 18 = 25,000. Therefore, 25,000 units must be sold.