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Problem 13

# How can the concept of a composite unit be used to explain why an unfavorable total sales-mix variance of contribution margin occurs?

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The concept of a composite unit can be used to explain the unfavorable total sales-mix variance of contribution margin by comparing the expected and actual sales mix performances in terms of contribution margins. A composite unit is a representative unit that contains a combination of products in a proportion equal to their respective sales mix. Calculating the expected and actual contribution margin per composite unit helps in identifying the impact of the sales mix on the contribution margin. If the actual sales mix is generating a lower contribution margin than expected, it suggests an unfavorable variance, possibly due to selling more low-margin products than high-margin products or selling lower-priced products at higher costs.
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## Step 1: Understand Sales-Mix Variance, Composite Unit, and Contribution Margin

: - Sales-mix variance: It is the difference between the actual sales mix and the expected sales mix, in terms of contribution margin. It measures the impact of the change in product mix on the total contribution margin. - Composite unit: A composite unit is a representative unit that contains a combination of products in a proportion equal to their respective sales mix. It helps in comparing actual and expected sales mix performances. - Contribution margin: The contribution margin is equal to the selling price per unit minus the variable cost per unit. It shows the portion of sales revenue that goes toward covering fixed costs and generating profit.

## Step 2: Calculate the Expected and Actual Contribution Margin per Composite Unit

: To understand the impact of the sales mix on the contribution margin, we need to calculate the expected and actual contribution margin per composite unit. Expected contribution margin per composite unit: 1. Calculate the expected contribution margin for each product. 2. Calculate the total expected composite unit volume. 3. Multiply the expected contribution margin per product by the respective proportion of the product in the sales mix. 4. Add these values together to get the expected contribution margin per composite unit. Actual contribution margin per composite unit: 1. Calculate the actual contribution margin for each product. 2. Calculate the total actual composite unit volume. 3. Multiply the actual contribution margin per product by the actual proportion of the product in the sales mix. 4. Add these values together to get the actual contribution margin per composite unit.

## Step 3: Assess the Sales-Mix Variance

: Now that we have the expected and actual contribution margin per composite unit, we can assess the sales-mix variance: 1. Subtract the expected contribution margin per composite unit from the actual contribution margin per composite unit. 2. Multiply this difference by the total actual composite unit volume. 3. The result is the total sales-mix variance of the contribution margin. If the total sales-mix variance is negative, it means there is an unfavorable total sales-mix variance of contribution margin. This means that the actual sales mix is generating a lower contribution margin than expected. This could be due to selling more low-margin products than high-margin products, or selling more lower-priced products at a higher cost than expected. In such cases, the concept of a composite unit helps explain this unfavorable variance by comparing the expected and actual sales mix performances in terms of contribution margins.

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