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fully accepted with Mr. Niszam answer
Gross margin comes after deducting the prime cost i.e. all manufacturing cost (both direct & indirect) from revenue whereas contribution margin is equal to revenue minus all direct costs.
The calculation of the Gross Profit is: Sales minus Cost of Goods Sold. The Cost of Goods Sold consists of the fixed and variable product costs, but it excludes all of the selling and administrative expenses. Contribution Margin is Net Sales minus the variable product costs and the variable period expenses.