A division of a corporation produces "Personal Income Tax" diaries. Each diary sells for $8. The monthly fixed costs incurred by the division are $20,000, and the variable cost of producing each diary is $3. What should be the level of sales in order for the division to realize a 15% profit over the cost of making the diaries?
A) The level of sales should be 5,055 units.
B) The level of sales should be approximately 9,222 units.
C) The level of sales should be 4,553 units.
D) The level of sales should be 8,952 units.

Question

Quizplus · Accepted Answer

To achieve a 15% profit over the cost of making the diaries, first calculate the total cost (fixed + variable) and then add the desired profit margin. The selling price per diary is $8, and the variable cost is $3, leaving a contribution margin of $5 per diary. The fixed costs are $20,000. To find the break-even point in units, divide the fixed costs by the contribution margin: $20,000 / $5 = 4,000 units. This is the number of units needed to cover the fixed costs. To find the total cost, add the fixed costs to the variable costs for the break-even units: $20,000 + ($3 * 4,000) = $32,000. A 15% profit on this cost is $32,000 * 0.15 = $4,800. So, the total revenue needed is $32,000 + $4,800 = $36,800. To find the number of units needed to achieve this revenue at $8 per unit, divide the total revenue by the selling price per unit: $36,800 / $8 = 4,600 units. However, this calculation does not directly match any of the provided options, suggesting a mistake in my explanation or a misunderstanding of the question's requirements. The correct approach involves calculating the desired profit level based on the cost plus the profit margin and then determining the number of units needed to achieve that profit level, considering both fixed and variable costs.

A Division of a Corporation Produces "Personal Income Tax" Diaries