Contribution-, Gross-, and Operating Margin

Can someone clarify what the difference between the above margins is (preferably with an easy example)? I am particularly confused as to where to draw the line between the costs considered for Gross Margins and Operating Margins.

I assume Contribution Margin (1) is the marginal profitability of a business and takes just the variable part of COGS into account that you incur by deciding to produce one more unit. Gross Margin (2) is closely related, but includes also the part of COGS that is more fixed in nature and Operating Margin (3) tells you the overall profitability of the operations, i.e. all costs included that are necessary to run the business (prior to taxes and lending).

However, what is actually the fixed part of COGS that is considered in (2)? Intuitively, I'd assume the salary of the production manager, electricity for the hall, D&A of the machine, marketing of the product, etc. But that's all SG&A and considering it would already yield (3), right?

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