Algebra Question

A company wants to look at their YoY margin % changes on an absolute basis. (ex. if margin in '22 was 50% and margin in '23 was 80%, break out the drivers of the 30% change). I'm having difficulty getting to an answer because when you isolate revenue Yoy to find COGS driver, you get a different answer than if you isolate cogs driver to find revenue impact first.

I tried to simplify an example below to show the mechanics. In (x-y)/x = z, x=revenue, y=cogs, and z= profit margin %.

In scenario A (of (x-y)/x=z), x=4 and y=2, so z= 2/4 or 50%. In scenario B (of (x-y)/x=z), x=5 and y=1, so z= 4/5 or 80%. Z went from 50% to 80% between scenario A and B. Z increased 30% points. Can you break the 30% change into drivers? How much did the change in x contribute to the 30% change and how much did the change in Y contribute to the 30% change? The answer must add up to 30%. (example x=15% y=15%)


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Erdos Erdos
  • Erdos Erdos

    Let me know if you need any clarifications.

    • This is great, thank you. The only discrepancy I see is that to find the change in z due to the change in y, you multiplied 1/5 by (y1-y2). If you would have multipled by (y2-y1), or 1-2, the answer would have been negative. Which is correct? Multiplying by (y1-y2) or by (y2-y1)?

    • Erdos Erdos

      You are right. I revised my solution to include the minus sign. It should make much more sense now. Thank you for the coffees!

  • Thank you!

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