# Contribution margin-based pricing

Contribution margin-based pricing is a pricing strategy which maximizes the profit derived from an individual product, based on the difference between the product's price and variable costs (the product's contribution margin per unit), and on one’s assumptions regarding the relationship between the product’s price and the number of units that can be sold at that price. The product's contribution to total firm profit (i.e., to operating income) is maximized when a price is chosen that maximizes the 'Contribution Margin Per Unit X Number of Units Sold'.

## Theoretical basis

Contribution margin per unit is the difference between the price of a product and the sum of the variable costs of one unit of that product. Variable costs are all costs that will increase with greater unit sales of a product or decrease with fewer unit sales (i.e., leaving out fixed costs, which are costs that will not change with sales level over an assumed possible range of sales levels). Examples of variable costs are raw materials, direct labor (if such costs vary with sales levels), and sales commissions.[1]

The contribution margin per unit of each product multiplied by units sold equals the contribution to profit from sales of that product.

The total of Contributions to Profit from all a firm’s products minus the firm’s fixed costs equals the firm’s profit (more precisely, operating income).

To express the above in mathematical format:

Price - Variable Costs Per Unit = Contribution Margin Per Unit

Contribution Margin Per Unit x Units Sold = Product’s Contribution to Profit

Contributions to Profit From All Products – Firm’s Fixed Costs = Total Firm Profit


Therefore, using the simplified example of a single-product firm, a firm would maximize profit by determining the price that maximizes contribution to profit (i.e., contribution margin per unit multiplied by the number of units sold), since the fixed costs that will next be subtracted will, by definition, be a constant regardless of the number of units sold.

Assuming an inverse relationship between price and units sold (i.e., sales volume), as is the case for most products since a lower price will generally induce higher unit sales, the firm would assume likely unit sales levels at various price levels, calculate the contribution margin per unit for the product at each of those price levels, multiply the number of units by the corresponding Contribution Margin Per Unit at that price level and choose the highest result (i.e., the highest Contribution to Profit) to maximize profit.

Note that this approach determines the price that maximizes profit only for an individual product, and only over a given time horizon. There are other factors a firm must consider in setting the price for each product (i.e., factors other than profit-maximization for that product alone), particularly if they have multiple products. Some (but not all) of these other factors are:

• Impact on sales of other products of the firm (complementary sales; cannibalization; impact on brand image; impact on distribution or trade push of the firm’s other products; competitor reaction affecting the firm’s other products).
• The strategic role of the product and others in the product portfolio (price points and positioning of the other products; each product’s role in the firm’s cash flow).
• Plans to replace or modify the product (and hold distribution in the meantime).
• Economies of scale and scope, and experience curve effects on costs.
• Long-term strategy for the product.

## References

1. ^ Some costs often regarded as fixed costs, such as some elements of factory overhead, can (and should) be converted to Variable Costs and legitimately allocated to particular products if changes in such costs can be validly traced to changes in production and sales levels of each of those products. (One method of doing so is activity based costing.) Many companies, however, choose an arbitrary, invalid method of allocating such costs to each product, resulting in an inaccurate calculation of the true impact on profit of a sale of a unit of each product, a mistake that often leads to poor decision-making regarding pricing and other aspects of marketing. As an example, assume a product has a price of $13 and a variable cost of$10. If a firm inappropriately allocates $2 of fixed costs to that product, the firm will mistakenly believe that each unit sale of that product adds$1 to profit. Suppose market research projected that cutting the price to $12 would double sales volume. This firm would not sell the product for$12 because they would argue that price eliminated their profit margin. In reality, if the price were reduced to $12, contribution margin would be reduced from$3 per unit ($13 -$10) to $2 per unit ($12 - \$10). The price cut would actually increase profits because the one-third reduction in contribution margin would be more than made up for by the doubling in volume (units sold).