# Contribution margin-based pricing

Contribution margin-based pricing (German:Deckungsbeitrag) is a pricing strategy which works without any mention of gross margin percentages. It maximizes the profit derived from a company's assortment, based on the difference between a 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.

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. Due to the relative differences in order size and the efforts that a retailer or distributor have to make, different industries have different typical distribution margins. 

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.

## Relative contribution margin and Opportunity Cost

The relative contribution margin refers to the use of a production factor that is required for the generation of the contribution margin:

`Relative Contribution = Product's Contribution to Profit/Production factor`

If there is a bottleneck for a production factor within a company, and this factor may be used to produce multiple products, the relative contribution margin can be used to calculate which product exploits the factor most efficiently and should therefore be produced. An example is the time used on a certain production machine. The relative contribution margin (also referred to as a bottleneck specific contribution margin), shows you the Opportunity Cost in the event that you decide not to produce the product.

## Use in retail: Rekenen in Centen, in Plaats van Procenten

```Selling Price − Buying Price Per Unit = Contribution Margin Per Unit

Contribution Margin Per Unit x Units Sold = Stock Keeping Unit's Contribution to Profit

Contributions to Profit From All SKU's − Firm's Operating Expenses = Total Firm Profit```

Using this system, the gross margin percentage is considered totally irrelevant for merchandising decisions or as IKEA founder Ingvar Kamprad asked: "What the hell are percentages anyway?"

In 1906 C&A, the clothing retailer owned by the Brenninkmeijer family, stopped trying to increase gross margin percentages. They fixed the margin at 25% for decades and increased relative contribution per piece in stock per time period. Later when selling different commodities they shifted to relative contribution per square meter. They called this: Rekenen in Centen, in Plaats van Procenten. (Dutch for Calculating cash, not percentages).

ALDI used relative contribution margin based pricing per stock keeping unit from the very beginning in the 1950s.

## Limitations

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.