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It seems that sometimes I may get desensitized by looking at operating margin if it is 35% vs 50%, I may think it is "no big deal", but it seems:

Sold item at     COGS and expenses     Operating Margin    Net Income before tax
------------     -----------------     ----------------    ---------------------
         $13                   $10                  23%                       $3
         $16                   $10                37.5%                       $6
         $19                   $10                  47%                       $9
         $22                   $10                54.5%                      $12

So it seems, from row 1 to row 3, the operating margin doubled, but the profit before tax actually tripled.

And what's more, the operating margin cannot be above 100%... so if it get to 55% or 58%, we may think it is "no big deal", but in fact, the profit before tax might have increased a lot?

For example, when we can sell the item at $22, the operating margin merely increased from 47% to 54.5%, so we may feel "it is only a few percent points", or 54.5 / 47 = 1.16, so it is a 16% increase, but the profit before tax actually went from $9 to $12, which is a good 33% increase?

And I think one good point about operating margin being so high in the 50% range, could mean, it is a business that is able to keep its pricing power, or else the operating margin has to be lower, such as 20% or 15%, so it might be a good business? On the flip side, it also means any changes to its competitive advantage, it may lose it pricing power and have a profit before tax drop from $12 to $6 easily, going down to half only.

Would this roughly be how to interpret operating margin? Is some concept incorrect in the above statement?

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Net_Income_before_tax / Sold_item_at = Operating_Margin, so yes, your interpretations are correct:

  • raise the selling price, and Operating Margin goes up;
  • reduce COGS and expenses (which increases Net Income before tax)and Operating Margin goes up;
  • do both, and Operating Margin goes way up.

Note that another way to compute it is: Operating Margin = 1 - COGS_and_expenses / Sold_item_at.

You're also right about "so it is a 16% increase, but the profit before tax actually went from $9 to $12, which is a good 33% increase".

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