Break-even analysis, different cost structures, and income calculations LO C2, A1, P2 [The following information applies to the questions displayed below.] Henna Company produces and sells two products, Carvings and Mementos. It manufactures these products in separate factories and markets them through different channels. They have no shared costs. This year, the company sold 49,000 units of each product. Income statements for each product follow. Sales Variable costs Contribution margin Fixed costs Income Carvings $ 837,900 670,320 167,580 30,580 $ 137,000 Mementos $ 837,900 83,790 754, 110 617, 110 $ 137,000 Required: 1. Compute the break-even point in dollar sales for each product. (Enter CM ratio as percentage rounded to 2 decimal places.) PRODUCT CARVINGS Contribution Margin Ratio Numerator: Sales 1 Denominator:
The Correct Answer and Explanation is :
To compute the break-even point in dollar sales for each product, we first need to calculate the contribution margin ratio (CM ratio) for each product, and then use the break-even formula.
1. Contribution Margin (CM) Ratio:
The contribution margin ratio is calculated using the formula:
[
\text{CM Ratio} = \frac{\text{Contribution Margin}}{\text{Sales}}
]
For Carvings:
- Contribution Margin = \$167,580
- Sales = \$837,900
[
\text{CM Ratio for Carvings} = \frac{167,580}{837,900} \times 100 = 20\% \quad (\text{rounded to two decimal places})
]
For Mementos:
- Contribution Margin = \$754,110
- Sales = \$837,900
[
\text{CM Ratio for Mementos} = \frac{754,110}{837,900} \times 100 = 89.9\% \quad (\text{rounded to one decimal place})
]
2. Break-Even Point Calculation:
The break-even point in dollar sales is calculated using the formula:
[
\text{Break-even Sales} = \frac{\text{Fixed Costs}}{\text{CM Ratio}}
]
For Carvings:
- Fixed Costs = \$30,580
- CM Ratio = 20%
[
\text{Break-even Sales for Carvings} = \frac{30,580}{0.20} = 152,900
]
For Mementos:
- Fixed Costs = \$617,110
- CM Ratio = 89.9%
[
\text{Break-even Sales for Mementos} = \frac{617,110}{0.899} = 686,791.99 \quad (\text{rounded to two decimal places})
]
Final Answer:
- Carvings Break-even Sales = \$152,900
- Mementos Break-even Sales = \$686,792 (rounded to nearest dollar)
Explanation:
- The contribution margin ratio reflects the proportion of sales revenue that contributes to covering fixed costs and generating profit. A higher CM ratio means that a larger portion of each sale contributes to fixed costs and profit.
- Break-even point is the level of sales at which total revenue equals total costs (both fixed and variable), resulting in zero profit. We calculate it by dividing the fixed costs by the CM ratio.
- For Carvings, with a lower CM ratio of 20%, the company needs to generate \$152,900 in sales to cover its fixed costs. For Mementos, with a higher CM ratio of 89.9%, it only needs to generate \$686,792 to break even, highlighting the efficiency of the Mementos product in terms of profitability.