Product X sells for $20 per unit and has a contribution margin rate of 40 percent. Fixed expenses total $120 000 annually. How many units of Product X must be sold to yield a profit of $30 000?

Question

Quizplus · Accepted Answer

To calculate the break-even point, we need to use the formula:

Break-even point (in units) = Fixed expenses / Contribution margin per unit

Contribution margin per unit = Selling price per unit × Contribution margin rate = $20 × 0.40 = $8

Break-even point (in units) = $120,000 / $8 = 15,000 units

To yield a profit of $30,000, we need to calculate the total contribution margin required as follows:

Total contribution margin = Fixed expenses + Target profit
Total contribution margin = $120,000 + $30,000 = $150,000

Using the formula:

Total contribution margin = Selling price per unit × Number of units sold × Contribution margin rate

Number of units sold = Total contribution margin / (Selling price per unit × Contribution margin rate)
Number of units sold = $150,000 / ($20 × 0.40) = 18,750 units

Therefore, the answer is B), 18,750 units.

Product X Sells for $20 Per Unit and Has a Contribution