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 deluxe models sold at break-even?

Question

Quizplus · Accepted Answer

First, we need to calculate the Contribution Margin (CM) for each product:
- Standard model: $360 - $210 = $150 CM
- Deluxe model: $500 - $300 = $200 CM
- Superior model: $1,600 - $600 = $1,000 CM

Next, we need to determine the sales mix ratio, based on the information given:
- 8 standard models : 4 deluxe models : 1 superior model
- This can also be expressed as 8x : 4x : 1x (where x is the number of superior models sold)

To calculate the overall weighted-average CM per unit, we use the contribution margin per unit multiplied by the sales mix ratio:
Weighted-average CM = (8x * $150) + (4x * $200) + (1x * $1,000) / 13x
Weighted-average CM = ($1,800x + $800x + $1,000x) / 13x
Weighted-average CM = $3,600 / 13 = $276.92 per unit

Finally, we can calculate the break-even point (BEP) in units:
BEP (in units) = Total fixed expenses / Weighted-average CM per unit
BEP = $300,000 / $276.92 = 1,083.33 units

Since we cannot sell a fraction of a unit, we need to round up to the nearest whole unit. This means that the break-even point is 1,084 units. To find out how many deluxe models are sold at break-even, we use the sales mix ratio:
4x = 1,084
x = 271
Therefore, the number of deluxe models sold at break-even is 4x = 4 * 271 = 1,084 - 8x = 8 * 271 = 2,168. However, the question only asks for the number of deluxe models sold, which is 4x = 4 * 271 = 1,084. 
Therefore, the answer is (C) 400.