Delisa Corporation has two divisions: Division L and Division Q. Data from the most recent month appear below:
Total Company
Division L
Division Q
Sales
$
517,000
$
156,000
$
361,000
Variable expenses
255,960
82,680
173,280
Contribution margin
261,040
73,320
187,720
Traceable fixed expenses
171,000
49,000
122,000
Segment margin
90,040
$
24,320
$
65,720
Common fixed expenses
87,890
Net operating income
$
2,150
The break-even in sales dollars for Division Q is closest to
The Correct Answer and Explanation is :
To calculate the break-even sales for Division Q, we use the contribution margin ratio and the traceable fixed expenses specific to Division Q. The formula for break-even sales is:
[
\text{Break-even Sales} = \frac{\text{Traceable Fixed Expenses}}{\text{Contribution Margin Ratio}}
]
Step-by-Step Solution:
- Calculate the Contribution Margin Ratio for Division Q:
[
\text{Contribution Margin Ratio} = \frac{\text{Contribution Margin}}{\text{Sales}}
]
For Division Q:
[
\text{Contribution Margin Ratio} = \frac{187,720}{361,000} \approx 0.52 \text{ (or 52\%)}
] - Use the Formula for Break-even Sales:
[
\text{Break-even Sales} = \frac{\text{Traceable Fixed Expenses}}{\text{Contribution Margin Ratio}}
]
For Division Q:
[
\text{Break-even Sales} = \frac{122,000}{0.52} \approx 234,615.38
]
Thus, the break-even sales for Division Q is approximately $234,615.
Explanation (300 words):
The break-even sales for a division represent the sales amount required to cover all variable and fixed expenses, ensuring no profit or loss. For Division Q, this is determined using the contribution margin ratio, which is the percentage of sales revenue remaining after variable expenses are covered. This ratio indicates how much of each sales dollar contributes to fixed expenses and profit.
In the provided data, Division Q has a contribution margin of $187,720 and sales of $361,000, leading to a contribution margin ratio of 52%. This means 52% of each sales dollar is available to cover traceable fixed expenses ($122,000) and contribute to net operating income.
Using the formula (\text{Break-even Sales} = \frac{\text{Fixed Expenses}}{\text{Contribution Margin Ratio}}), we calculate that Division Q needs sales of approximately $234,615 to break even. At this level, the contribution margin will just cover the fixed expenses, resulting in zero net operating income for the division.
This calculation is crucial for managerial decision-making, as it helps assess the financial viability of Division Q. Knowing the break-even sales allows managers to set sales targets, evaluate pricing strategies, and control costs to ensure profitability.