# The contribution margin

What is the contribution margin? This important value is defined in the costs and performance calculation as the amount that is available to a company from a specific revenue to cover their fixed costs. The contribution margin may refer to an individual product, a group of products or the total sales, as required. It gives information about what proportion of the revenue contributes to covering fixed costs. Fixed costs are defined as costs that are separate from the revenue of the company. These can be rent, interest, depreciations, and sometimes even wage costs, for example. By contrast, variable costs are those that rise or fall based on production quantities (e.g. raw materials and transport costs).

Definition

Contribution margin describes the difference between the revenue and the variable costs of a company. You specify the contribution margin for a product, a group of products, or even the total sales. In order for a company to make a profit from its standard business operations, the contribution margin must be greater overall than the fixed costs.

## Why do we calculate the contribution margin?

The contribution margin gives meaningful results when it stands in relation to other values. If you compare the contribution margin to the fixed costs, you obtain information on whether the company is making profits or losses. The relationship between the contribution margin and a company’s customer base may also be relevant in identifying clients that are particularly valuable to the company.

• The contribution margin is greater than the fixed costs: the company is making a profit in the standard business operations, as the receipts exceed the expenses.
• The contribution margin is the same as fixed costs: the result in the standard business operations has reached the point where it is balanced (break-even point).
• The contribution margin is lower than the fixed costs: the company is making a loss in the standard business operations, as the expenses exceed the receipts.

You can improve the result by reducing the variable costs for the use of raw materials or in the production process, by increasing the revenue with sales efforts, for example, or also lower the fixed costs.

### What formula can you use to calculate the contribution margin?

You differentiate between the unit and total contribution margin. The calculation of the values is carried out using the relevant contribution margin formula.

Unit contribution margin: The difference between the unit price p and the variable unit costs cv yields the unit contribution margin. This value indicates how much a product or a service contributes to covering fixed costs per unit.

UCM = p – cv

Total contribution margin: By multiplying the unit contribution margin UCM by the amount of sales x you arrive at the total contribution margin TCM. With the help of the total contribution margin, you can identify how much the product or services have made in total (within a specific period).

TCM = UCM * x

## How is the contribution margin calculation made?

To identify the unit contribution margin and the total contribution margin, you can use single-stage or multi-stage contribution margin calculations. The relative contribution margin also enables you to identify an optimised production program.

The result of the single-stage contribution margin calculation provides information about the profitability of the company overall and is therefore of interest for general corporate decision-making in particular. With the multi-stage contribution margin calculation however, you can investigate the profitability of individual products, groups of products or areas of business, and make significant differentiated predictions for this.

### The single-stage contribution margin calculation

With the single-stage contribution margin calculation, you obtain the operating result by deducting the total fixed costs from the total contribution margin. There is no differentiation of the fixed costs, as in the single-stage contribution margin calculation these are not regarded as being influenceable in the period under consideration. The operating result is synonymous with the economic success of the company unit being considered, i.e. with its profit or loss.

Example 1 – single-stage contribution margin calculation:

1. You calculate the contribution margin for each individual partial revenue (here: models of bicycle) by subtracting the variable costsfrom the sales proceedsin question. Bicycle model A achieves sales of £\$20,000 and has variable costs of £\$5,000. The contribution margin is therefore £\$15,000.
2. Addthe individualcontribution marginstogether to obtain the total contribution margin.
3. Thendeduct the total fixed costs from the total contribution margin to determine the operating result. In the example, the total contribution margin comes to £\$23,000. Taking into account the fixed costs of £\$5,000, you come to the operating result of £\$18,000.

### Multi-stage contribution margin calculation

In contrast to the single-stage one, the multi-stage margin calculation considers the fixed costsat several stages separately from one another, a differentiation which may assume a variety of forms. In example 2, there should be a differentiation of fixed costs that can be assigned to the individual product, the associated company department and the overall company. The aim of the multi-stage contribution margin calculation is to allocate profitability to the specific reference objectsas far as possible, according to the costs-by-cause principle andwith transparency.

• Product-specific fixed costs: the costs can be allocated precisely to a product or service (depreciations for a machine that is used to produce bicycle model A for example).
• Fixed costs by department: the costs can be allocated to a company department (e.g. for the workshop for bicycle production).
• Company fixed costs: these are general fixed costs that cannot be allocated to a product or a department (e.g. management salaries).

Example 2 – multi-stage contribution margin calculation:

1. In the same way as for the single-stage contribution margin calculation, in the first stage you determine the contribution margin for each individual product and add the individual contributions (four in our example) to contribution margin I.
2. If you have identified the product-specific contribution margin, you thendeduct the associated fixed costs for each product and you obtain contribution margin II for the product. Thetotal of contribution margin II for each product from a department gives contribution margin II for this department, and the total of these amounts in turn gives contribution margin II for the overall operations.
3. You subtract the departmental fixed costs fromcontribution margin IIfor the department in each case, to obtain contribution margin III for each department.
4. Now put together the totals for contribution margin III in each case and you obtain contribution margin III for overall operations. To find the operating result, the final stage is to subtract the company fixed costs from this contribution margin III.

### What is the relative contribution margin?

The relative contribution margin relates the unit contribution margin to what is called the bottleneck factor. Examples of this are the capacity of a production machine or an employee. The relative contribution margin serves as a calculation aid to optimise aproduction program for limited capacities. The objective is to maximise the contribution margin of the relevant production unit. Its implementation aims for the priority production of products or services that promise a higher contribution margin. The relative contribution margin can be calculated based on this formula:

Example: The unit contribution margin for bicycle model A is £100. A certain machine is required for an hour for production. On the other hand, for bicycle model B, a production time of only 30 minutes with the same machine is necessary, so that the unit contribution margin is £60.

If the machine actually represents the bottleneck in the production and sales of bicycles, so if all other production and sales stations have a higher capacity, then bicycle B has a higher contribution margin than bicycle A and should therefore have production priority.

In practice, the comparisons are not that simple of course. In our example, twice as many bicycles of type B than type A would have to be produced for the calculation to be correct. However, the demand for B bicycles would not be sufficient to use the machine to capacity. The bottleneck would consequently no longer be the machine but the sales of bicycles of type B. Then the theoretically higher contribution margin would not be achieved in reality.