Figure 4-5.Standlar Company makes wireless speakers. The standard model price is $360 and variable expenses are $210. The deluxe model price is $500 and variable expenses are $300. The superior model price is $1,600 and variable expense per unit is $600. Total fixed expenses are $300,000. Generally, Standlar sells 8 standard models and 4 deluxe models for every superior model sold.
-Refer to Figure 4-5. What is the number of superior models sold at break-even?

Question

Quizplus · Accepted Answer

To find the break-even point in units for the superior model, we first need to calculate the weighted average contribution margin per unit. Given the sales mix (8 standard, 4 deluxe, 1 superior), prices, and variable expenses for each model, we can calculate the contribution margin for each and then find the weighted average.Standard model contribution margin per unit = $360 - $210 = $150Deluxe model contribution margin per unit = $500 - $300 = $200Superior model contribution margin per unit = $1600 - $600 = $1000Given the sales mix, the weighted average contribution margin per unit can be calculated as follows:$$ \text{Weighted Average CM} = \frac{(8 \times 150) + (4 \times 200) + (1 \times 1000)}{8 + 4 + 1} $$$$ \text{Weighted Average CM} = \frac{1200 + 800 + 1000}{13} = \frac{3000}{13} \approx 230.77 $$To find the break-even point in units for the entire company, we use the formula:$$ \text{Break-even point in units} = \frac{\text{Total Fixed Expenses}}{\text{Weighted Average Contribution Margin per Unit}} $$$$ \text{Break-even point in units} = \frac{300,000}{230.77} \approx 1300 \text{ units (rounded)} $$Given the sales mix, for every 13 units sold (8 standard, 4 deluxe, 1 superior), there is 1 superior model sold. To find the number of superior models sold at break-even, we divide the total break-even units by the total units in the sales mix and multiply by the number of superior models:$$ \text{Number of superior models at break-even} = \frac{1300}{13} \times 1 = 100 $$Therefore, the number of superior models sold at break-even is 100.