Contribution Margin - Explanation

Explanation

Contribution margin can be thought of as the fraction of sales that contributes to the offset of fixed costs. Alternatively, unit contribution margin is the amount each unit sale adds to profit: it's the slope of the Profit line.

Cost-Volume-Profit Analysis (CVP): assuming the linear CVP model, the computation of Profit and Loss (Net Income) reduces as follows:

\begin{align} \text{PL} &= \text{TR} - \text{TC}\\ &= \left(\text{C}+\text{V}\right)\times \text{X} - \left(\text{TFC} + \text{V} \times \text{X}\right)\\ &= \text{C} \times \text{X} - \text{TFC} \end{align}

where TC = TFC + TVC is Total Cost = Total Fixed Cost + Total Variable Cost and X is Number of Units. Thus Profit is Unit Contribution times Number of Units, minus the Total Fixed Costs.

The above formula is derived as follows:

From the perspective of the matching principle, one breaks down the revenue from a given sale into a part to cover the Unit Variable Cost, and a part to offset against the Total Fixed Costs. Breaking down Total Costs as:

one breaks down Total Revenue as:

\begin{align} \text{TR} &= \text{P} \times \text{X}\\ &= \bigl(\left(\text{P} - \text{V} \right)+\text{V}\bigr)\times \text{X}\\ &= \left(\text{C}+\text{V}\right)\times \text{X}\\ &= \text{C}\times\text{X} + \text{V}\times \text{X} \end{align}

Thus the Total Variable Costs offset, and the Net Income (Profit and Loss) is Total Contribution Margin minus Total Fixed Costs:

\begin{align} \text{PL} &= \text{TR} - \text{TC}\\ &= \left(\text{C}+\text{V}\right)\times \text{X} - \left(\text{TFC} + \text{V} \times \text{X}\right)\\ &= \text{C} \times \text{X} - \text{TFC}\\ &= \text{TCM} - \text{TFC} \end{align}

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