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My question is about Price-Volume-Mix analysis in the area of managerial accounting or business controlling. Other people also call it profit-margin variance analysis, and other names might exist. But the goal of the analysis is to understand the contributing factors that drive up or down the profit-margin. The main contributing factors are sales volume, sales price, unit cost, mix and etc.

My question is mainly about the mix calculation. So far I’ve seen two different ways of calculating mix effect. And the two ways appear to have different intentions and thus different mathematics formula behind.

Method 1:

Step 1 Mix% (Quantity) Variance = (Sales quantity of Product A in 2016)/(Sales quantity of Total in 2016) – (Sales quantity of Product A in 2015)/(Sales quantity of Total in 2015)

Step 2 Mix Effect on Profit = Mix% (Quantity) Variance × Sales quantity of Total in 2016 × (Sales Price in 2015 – Unit Cost in 2015)

Method 2:

Step 1 Mix% (Revenue) Variance = (Sales Revenue of Product A in 2016)/(Sales Revenue of Total in 2016) – (Sales Revenue of Product A in 2015)/(Sales Revenue of Total in 2015)

Step 2 BPR Difference = Product A’s Profit Margin% in 2015 – Total Profit Margin% in 2015

Step 3 Mix Effect on Profit = Mix% (Revenue) Variance × BPR Difference × Total Sales Revenue 2016

I used to use method 1, but just got to know method 2 recently. Though I am not a mathematic specialist, I feel the BPR difference in method 2 not fit into the context of the analysis. The price-volume-mix is to compare across two periods (or compare realized with budget), while the BPR difference is comparing the margin of one individual product to the total margin. As I perceived, multiplying with BPR will change the course of the initial comparison of two periods, thus become irrelevant to the cross-period price-volume-mix analysis. What do everyone think, or correct me if I am wrong?

There're also other differences between the two methods such as the mix% variance calculation based on quantity versus revenue.

You can find the literature about method 2 here: http://www.volume-and-mix-analysis.com/uploads/1/7/0/2/17027570/mix_matters.pdf

http://www.volume-and-mix-analysis.com/uploads/1/7/0/2/17027570/mix_variances_in_profit_rate_analysis.pdf

Sean
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My Answer (Method 2):

Method 2 subsumes that all price and cost variances have been previously eliminated in the analysis; it is Mix Analysis only. It does not address price and cost variances; it does not intend to do so. It directly addresses only the pure mathematics of mix variance. Price and cost variances should have already been eliminated/recognized via other methodologies. In other words, the following mathematical identity is imperative and must be implicitly recognized:

Product A’s Profit Margin% in 2016 == Product A’s Profit Margin% in 2015

The Total Profit Margin% in 2015 is a simple "weighted average" (weighted by the mix of products which comprise the total). The BPR Difference is static for 2015 in that it remains a constant no matter what the 2016 vs 2015 mix deltas become. Thus it has no "cross-period" affect. The only numerical functionality which affects mix variance is the variability of the Mix% Variance (the mix delta) of Step 1.

The mix algorithm's methodology works equally well on quantity (Units and Profit/Unit) or revenue (Sales and Profit/Sales$). The usage simply depends upon what is most meaningful in the particular managerial accounting scenario.

Frank
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