Delisa Corporation has two divisions: Division L and Division Q. Data from the most recent month appear below: Total Company Division Division Sales
125,000
288,800
226,300 Contribution margin
62,500
111,650
76,860 Segment margin
27,710
36,910
540,240 The break-even in sales dollars for Division Q is closest to: (Round your intermediate calculations to 2 decimal places) Multiple Choice A)
202.26 C)
5,402,400
The Correct Answer and Explanation is:
To determine the break-even sales dollars for Division Q, the following formula is used:Break-even sales=Traceable fixed expensesContribution margin ratio\text{Break-even sales} = \frac{\text{Traceable fixed expenses}}{\text{Contribution margin ratio}}Break-even sales=Contribution margin ratioTraceable fixed expenses
From the data:
- Contribution margin for Division Q = 76,860
- Sales for Division Q = 226,300
- Segment margin for Division Q = 36,910
Now, calculate the traceable fixed expenses for Division Q:Traceable fixed expenses=Contribution margin−Segment margin=76,860−36,910=39,950\text{Traceable fixed expenses} = \text{Contribution margin} – \text{Segment margin} = 76,860 – 36,910 = 39,950Traceable fixed expenses=Contribution margin−Segment margin=76,860−36,910=39,950
Next, compute the contribution margin ratio for Division Q:Contribution margin ratio=Contribution marginSales=76,860226,300≈0.3397\text{Contribution margin ratio} = \frac{\text{Contribution margin}}{\text{Sales}} = \frac{76,860}{226,300} \approx 0.3397Contribution margin ratio=SalesContribution margin=226,30076,860≈0.3397
Now plug the values into the break-even formula:Break-even sales=39,9500.3397≈117,609.91\text{Break-even sales} = \frac{39,950}{0.3397} \approx 117,609.91Break-even sales=0.339739,950≈117,609.91
Final Answer:
Break-even sales for Division Q ≈ $117,609.91
Explanation ):
Break-even analysis identifies the sales level at which a business covers all its expenses, resulting in zero profit. For a specific division, such as Division Q in Delisa Corporation, this involves comparing its contribution margin to its traceable fixed expenses.
The contribution margin represents the portion of sales revenue remaining after deducting variable costs. This amount contributes to covering fixed expenses. The segment margin is the result after subtracting traceable fixed costs from the contribution margin.
To determine the break-even point in dollars, it’s necessary to first identify the division’s fixed costs, which are specific to that segment. For Division Q, this is obtained by subtracting the segment margin from the contribution margin, giving a total of $39,950 in traceable fixed expenses.
Then, the contribution margin ratio is calculated. This ratio shows the percentage of each sales dollar that contributes to covering fixed costs and generating profit. With a contribution margin of $76,860 and sales of $226,300, the ratio is approximately 0.3397 or 33.97%.
Finally, dividing the fixed expenses by the contribution margin ratio gives the break-even sales level. In this case, $39,950 divided by 0.3397 results in approximately $117,609.91. This is the sales amount Division Q needs to generate to avoid any losses, ensuring it breaks even without considering corporate-wide common fixed expenses.
This analytical approach enables financial managers to make informed operational and budgeting decisions.
