# How do you define a relevant range?

The relevant range is the range of cost driver over which a specific linear relationship between cost and cost driver is valid. In other words, it is a range of activity over which the unit variable cost $$V_c^i$$ and the fixed costs $$FC_p$$ can be assumed constant.

Once you have identified a good cost driver for the costs you want to model over a period (by discussing with operation managers, using the scatter graph and analyzing correlations), you may still observe that your costs do not follow a straight line over the full range of activity. You will then cut the activity in smaller ranges over which the linearity assumption seems to hold, as in the following example: In this example, it appears reasonable to build a first linear cost equation for a low activity $$Q \in [0,500]$$. $$Q \in [0,500]$$ would thus be the relevant range of this first equation. $$Q \in [501,1000]$$ would be the relevant range of a second cost equation for a moderate level of activity and $$Q \in [1001,1500]$$ would be the relevant range of a third cost equation for a high level of activity.

In practice, plotting costs often do not provide such a clear cut pattern. It is therefore crucial to discuss first with operation managers to know at which volumes of activity the underlying cost function is likely to change (e.g. are there economies of scale, what is the capacity of individual workers or pieces of equipment, etc.).

Specifying a relevant range for every cost equation is necessary for the linearity assumption to hold and thus to be able to use a cost estimation technique. It is also necessary to know which equation you should use for cost prediction or cost control. Indeed, you will select a different cost equation if your manager wants to estimate the cost for Q = 478, for Q = 525 or Q = 1368.

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