# Different Calculation Models

## Cost models

Several methods of solving the calculation problem exist. The most common procedures are split into the following three models, each with its own "cost school."

o Full cost model - absorption cost model: This model is used by many companies as a method of measuring the lowest price the product could be sold for. This model distributes both fixed and variable costs to the cost bearer; i.e. both direct as indirect variable and fixed costs are distributed. Often the distribution key for the fixed costs becomes quite arbitrary, i.e. random. The issue here is that the indirect fixed costs cannot be logically distributed, and should not be included in the optimization considerations, at least not in the short-term.

o Contribution margin model - Cost-volume-profit-model: This model is the most classic and applied model in Denmark. Among those who use or have used this model are Danish professors: Palle Hansen and Zakken Worre, both from CBS. This method distributes the variable costs to the cost bearers; i.e. both the direct and indirect variable costs are distributed. To some extent the model distributes variable costs to the cost bearers by using distribution keys. The distribution keys are usually sufficiently objective, but the adjustment of the time horizon to the calculation task is the great concern of this model. Here, the problem is that the sales and administration costs are partially variable within a certain time horizon; how far should this time horizon go?

o Activity Based Costing (ABC): Is represented by R. Cooper and Rober Kaplan15. This method distributes the direct costs on cost objects; i.e. the method distributed both direct variable and the direct fixed costs of a given activity, but does not attempt to distribute the indirect cost. The ABC model is increasingly applied by many companies. The model distributes all the costs caused by a given action, which is quite logical but has a downside in that the cost definition obtained is not coherent with an optimization model, neither the "total model" nor the MC model.

The differences between the three models are shown in figure 4.1. A brief verbal sketch of the model's illustrated points:

o The contribution margin model only distributes the direct and indirect variable costs

o The ABC model distributes the direct variable costs and the direct fixed costs.

The indirect variable costs are to a certain extent distributed using of cost drivers.

o The full cost model distributes all costs

Figure 4.1

* The ABC model does not distribute all indirect variable costs

Advantages and drawbacks of the different models are discussed later, although such a discussion is similar to standing in the eye of the storm. Experts and researchers, also at CBS, disagree on the different models, and especially about which one of them is the best. It may be sensible to argue that it depends on which type of calculation task is to be performed.

## Variable costs and capacity costs

All the models have in common that they represent a trade-off between living up to sound economic reasoning and being practically applicable. It is for instance a theoretical weakness that the models, only to a very limited extent, include a time perspective (short-term, long-term).16 This time factor, though not present in all models, is fixed, and cannot adapted to the specific decision-making task. Resultantly, the models generally use differing definitions of variable and fixed costs (also called capacity costs).

Here are the definitions professor Zakken Worre, applied in the marginal contribution model17:

o Variable costs are costs that in a any situation are given by the amount of activity and type of activity.

o The firm's capacities are the number of factors (in the widest sense), that are not in any situation controlled by the amount of the activity and the type of activity. We define capacity costs as the costs caused by a (red. production) capacity.

Worre's definition of variable costs may be criticized as too narrow, it only embraces costs that are directly tied to the specific product unit, and furthermore, there is no implied time variability.

But the definition illustrates the difference between the polished cost theory and the more pragmatic calculation discipline. The contribution margin model has thus been constructed based upon the firm's accounting system, which does not traditionally include any aspects of time.

All the models contain more than just the principles of how to handle the joint costs, but in this chapter the models are presented focusing on that topic. Later, the full cost model and the contribution margin model are shortly introduced, while the ABC model is presented more thoroughly.

## The full cost model

The philosophy of the full cost model (also called the cost absorption model) is that all the firm's costs at one time or another have to be attributed to or distributed between the cost bearers (typically products). That is to say, a part of the overhead fixed (capacity) costs is assigned to each specific cost bearer, and added to the variable costs of the good. In this manner, the good's own price is found.

All capacity costs are distributed to the cost bearers, according to distribution keys. The distribution keys in the full cost model are often considered arbitrary (random) in the sense that the distribution of the costs has nothing to do with how much the specific cost bearer use of the company resources.

In the figure below illustrates the emergence of the sales price of a good as the sum of the variable costs of the good, the good's share of the over head fixed (capacity) costs, and the net profit.

 Sales price Net profit Own price + net profit Own price Part of the over­head fixed (ca­pacity) costs Distributed through distribution keys = distributed fixed costs + the variable costs below Cost price Variable costs Distributed over a fixed time horizon to each unit, possibly through a distribu­tion key.

## The contribution margin model

The contribution margin model is based on the idea that the capacity costs are not to be distributed on to the cost bearers at all. The only costs that are attributed to a product are the ones that are directly connected to the product (i.e. variable costs). It is based on this information that financial control and decisions are to be carried out.

In this sense, the contribution margin model is as true to the economic marginal theory's marginal reasoning as possible. As mentioned earlier, the weakness is that the established time horizon must be extremely secure. The precision of the measurements are dependent on the complexity of the production, i.e. the number of processes, products, etc. Moreover MC is easily confused with the AVC, i.e. linear cost functions.

 Sales price Net profit Own price + net profit Own price Part of the over­head fixed (ca­pacity) costs Distributed through distribution keys = distributed fixed costs + the variable costs below Cost price Variable costs Distributed over a fixed time horizon to each unit, possibly through a distribu­tion key.