If you simply resolve this equation for the critical quantity, this critical quantity, the break-even quantity, is the fixed costs divided by your contribution margin. You have here, 0 equals the contribution margin, CM, times the quantity, Q, minus the fixed cost, CF. This volume can be determined by setting this profit equation equal to 0. If you take that as the starting point, then it's quite easy to determine the volume that allows you to basically break-even in terms of profit. The contribution margin minus the fixed costs would be the profit. If you look at the first two items here, revenues minus variable costs, then we know already that this is nothing else than the contribution margin of a company. Now the starting point is the profit equation, which is revenue minus costs, or in more detail, revenues minus variable costs minus fixed costs. This is a basic requirement for break-even analysis, being able to distinguish between variable costs and fixed costs. Only if you distinguish between variable and fixed costs, you can do the cost volume profit analysis. An important ingredient is that your cost function distinguishes between variable and fixed costs. You compare the costs for the product with the revenues. If you want to do cost-volume profit analysis for a single product, you basically have to consider the costs of the same product and the revenues of the single product, and if you bring that together, then you have the profit function, and this profit function basically is the starting point. We now consider cost-volume profit analysis for the simple case, the case for a single product.
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