Contribution Margin (CM)

Definition

Contribution -> total revenue of units which are contributing to Fixed Costs

Margin -> total revenue of units which are profit

Contribution Margin (CM) is the amount of money from the revenue that goes towards Fixed Costs & Profit.

Formula

\[\text{CM} = \text{Sales} - \text{Variable Costs}\]

Contribution Margin per Unit

\[\text{CMU} = \text{Selling Price per Unit} - \text{Variable Cost per Unit}\]

Contribution Margin Ratio

\[ \text{Contribution Margin Ratio (CMR)} = \frac{\text{Contribution Margin}}{\text{Sales}} = \frac{\text{Sales} - \text{Variable Costs}}{\text{Sales}} = \frac{\text{Amount Contributing to Fixed Costs and Profit}}{\text{Total Sales}} \]

\[ \text{CMR per Unit} = \text{Selling Price per Unit} - \text{Variable Costs per Unit} \]

Variable Expense Ratio

The proportion of sales revenue consumed by variable expenses.

\[ \text{Variable Expense Ratio} = \frac{\text{Variable Expenses}}{\text{Sales}} \]

Relationship between CM Ratio and Variable Expense Ratio

\[ \text{CMR} = 1 - \text{Variable Expense Ratio} \]

Key Points

• CMU (Contribution Margin per Unit) represents the amount each unit contributes to Profit & Fixed Costs.
• Contribution Margin is the total dollar amount going towards Fixed Costs & Profit.
• Contribution Margin per Unit represents the dollar contribution of each unit towards Fixed Costs & Profit.
• Contribution Margin Ratio represents the per dollar of revenue contribution towards Fixed Costs & Profit, distinguishing it from CM and CMU, which are based on a per unit basis.

Profit Equations

Here are some forms of the profit equation, designed to help you see the relationships between sales, variable costs, fixed costs, and contribution margin:

1. Using Contribution Margin Ratio

\[ \text{Profit} = (\text{CM Ratio} \times \text{Sales}) - \text{Fixed Expenses} \]

This formula highlights how the Contribution Margin Ratio (CMR) determines the portion of sales revenue available to cover fixed costs and contribute to profit.

2. Using Price and Quantity

\[ \text{Profit} = (\text{Selling Price per Unit (P)} \times \text{Quantity (Q)}) - (\text{Variable Cost per Unit (V)} \times \text{Quantity (Q)}) - \text{Fixed Expenses} \]

\[
\text{Profit} = (P \times Q - V \times Q) - \text{Fixed expenses}
\]

This equation breaks down profit by showing how each unit sold contributes to covering variable and fixed costs. When price per unit is greater than variable cost per unit, the remaining amount (contribution margin per unit) can help cover fixed costs.

3. Using Sales and Variable Expenses

\[ \text{Profit} = \text{Sales} - \text{Variable Expenses} - \text{Fixed Expenses} \]

This is the simplest form, showing that profit is what remains after covering both variable and fixed costs. It can help visualize profit as a function of total revenue minus all expenses.

Break Even via Units (Quantity of Units to Sell)

\[ \text{Break Even with Unit Sales} = \frac{\text{Fixed Costs}}{\text{CMU}} \]

In other words:

\[ \text{Unit Sales to Reach Profit of 0} = \frac{\text{All Fixed Costs}}{\text{Amount per unit contributing to fixed costs & profit}} \]

Target Profit via Units (Quantity of Units to Sell)

\[ \text{Unit Sales to Reach Target Profit} = \frac{\text{Fixed Costs} + \text{Target Profit (X)}}{\text{CMU}} \]

In other words:

\[ \text{Unit Sales to Reach Target Profit of } X = \frac{\text{All Fixed Costs} + X}{\text{Amount per unit contributing to fixed costs & profit}} \]

Unit Price to Reach Break Even & Target Profit

\[ \text{Price} = \frac{\text{Total Fixed Costs}}{\text{Quantity}} + \text{Total Variable Cost} \]