# contribution margin

The contribution margin ( English contribution margin is) in the cost accounting , the difference between the achieved revenue (turnover) and the variable costs . It is therefore the amount that is available to cover the fixed costs . The contribution margin can be based on the total quantity (DB) of a product as well as on a unit of measure (db) ( piece size ).

Strictly speaking, one cannot speak of a contribution margin calculation. There are several different models that strive for the same goal but pursue different paths. The primary purpose of the contribution margin calculations is to determine the success and, secondly, to calculate the quotation to establish a price.

## Project of the contribution margin calculation

In the mostly used in German-speaking full cost accounting is directly between a payers attributable costs ( unit costs ) and not direct costs ( overheads ) distinguished. The overhead costs are distributed to the products using an allocation key . A typical representative of this method is the overhead calculation . The levy will never be perfect, so that as the levy increases, it becomes less and less transparent whether a product can still be produced or sold at a cost-covering level.

At this point, considerations of alternative concepts come into play, from which on the one hand the planned cost calculation and on the other hand the contribution margin calculation result.

## Mathematical definition

The contribution margin is defined by the formula ${\ displaystyle DB}$ ${\ displaystyle DB: = E (x) -K_ {v} = db \ cdot {\ rm {quantity}}}$ ,

where denotes the revenue of the period and the variable costs of the period. ${\ displaystyle E (x)}$ ${\ displaystyle K_ {v}}$ The contribution margin per unit of measure (also piece contribution margin or, rarely, margin ) is calculated by ${\ displaystyle db}$ ${\ displaystyle db = p-k_ {v}}$ ,

here is the unit price (or revenue per unit of measure ) and is the variable unit cost. ${\ displaystyle p}$ ${\ displaystyle e}$ ${\ displaystyle k_ {v}}$ ## Relative contribution margin

The relative contribution margin (including gross profit rate ) includes the factor consumption that is required to generate the contribution margin:

${\ displaystyle rDB = {{\ rm {Contribution margin}} \ over {\ rm {Production factor consumption}}}}$ .

If there is a bottleneck for a production factor within a company and several products can be manufactured from this factor, the relative contribution margin can be used to determine which product uses the factor most efficiently and should therefore be produced. The relative contribution margin (also referred to here as bottleneck-specific contribution margin ) indicates the opportunity costs in the event that a decision is made against manufacturing the product.

One example is the shortage of production capacity, which means that the time required for production is included as a decisive determinant in the calculation. In this case the relative contribution margin results from:

${\ displaystyle rDB = {{\ rm {Contribution margin}} \ over {\ rm {Time unit}}}}$ .

## Contribution margin calculation

The breakeven analysis is a method for determining the operating results of a company using the margins of manufactured products. A distinction is made between the single-level contribution margin accounting ( direct costing ) and the multi-level contribution margin accounting ( fixed cost accounting ). With the single-level contribution margin calculation, the summed up contribution margins are first determined and the complete fixed costs are then deducted from them.

The multi-level contribution margin calculation tries to split up the block of fixed costs further and assign the costs to the corporate divisions causing them. As with all cost accounting methods, the retrospective analysis of the contribution margin accounting is unsuitable because it is not linked to the process that has already run, in order to enable a controlling intervention in ongoing business operations. There are definitely companies that have established 5-step, sometimes even 13-step or even multi-step contribution margin accounting.

### Example of a single-level contribution margin calculation

Example for a detailed single-level contribution margin calculation:

Product A % Product B % total %
Sales € 300,000 100 € 500,000 100 € 800,000 100
Variable costs € 140,000 47 € 250,000 50 € 390,000 49
contribution margin € 160,000 53 € 250,000 50 € 410,000 51
Fixed costs € 260,000 32
Result € 150,000 19th

For product A and product B, the contribution margin results from:${\ displaystyle DB}$ ${\ displaystyle DB = {\ text {Sales}} - {\ text {variable costs}}}$ .

If we deduct the fixed costs from the contribution margin, we get the result .

### Example of a multi-level contribution margin calculation

A multi-level contribution margin calculation for a production company with 2 product groups, several areas and products is presented by T. Balaguer in a basic accounting course:

 Companies Total Area I (e.g. product line 1) Area II (e.g. product line 2) Group A Group B Group A Group B Product IAa Product IAb Product IBa Product IIAa Product IIBa proceeds 5000 4000 3000 2000 1000 15000 minus var. manufacturing costs 1200 1100 1000 700 600 4600 = Contribution margin I. 3800 2900 2000 1300 400 10400 minus product fixed costs 700 600 500 300 200 2300 = Contribution margin II 3100 2300 1500 1000 200 8100 minus group fixed costs 900 600 200 100 1800 = Contribution margin III 4500 900 800 100 6300 minus area fixed costs 3000 1200 4200 = Contribution margin IV 2400 -300 2100 minus company fixed costs 1500 1500 = Operating success (product success) 600 600

Even if the table appears understandable, the following notes must be observed in practice. The division into variable and fixed costs is not as clear in practice as the examples suggest. There are certain costs, for example set-up costs , that cannot be clearly assigned. The respective data, for example the revenues, must be identifiable as separate revenues (or costs) achieved with the product. This is not always guaranteed and the limit of differentiation is limited by the accuracy of the data acquisition. After all, the allocation of fixed costs to groups or areas is to a certain extent arbitrary, for example it cannot be precisely determined whether an advertisement for a certain product also influences sales of another product.