# How do you use cost functions for cost prediction?

The estimation techniques I have presented in the previous section result in linear cost functions in which a unit variable cost $$V_{c}^d$$ is associated with each cost driver $$d$$ and fixed costs $$FC_p$$ are associated with the period $$p$$. These cost functions can then be used to predict costs at different volumes of activity, i.e. for different $$Q_p^i$$. It is however important to keep in mind two limitations of these functions: the period and the relevant range.

Period consistency

First, ideally, you build build a cost function based on the period you are interested in. For instance, if you want to predict yearly costs, apply your estimation techniques on yearly observations. That way the fixed costs you estimate are already for the year (no need to do a conversion) and the resulting estimates for the year will be more reliable.

It is technically possible to transform a monthly cost function (i.e. a cost function which was built on monthly observations) into a yearly cost equation by multiplying the monthly fixed costs by the number of months in a year: 12. But for the reasons detailed in subsection 3.3.2, this will not produce the same estimates, so you should be cautious when doing that.

Relevant range

The cost function you will use for any type of cost and any cost driver is also determined by the volume of activity. You cannot predict the cost for a volume $$Q_p^d = 550$$ with a cost function the relevant range of which is $$Q_p^d \in [600,1400]$$ or with a cost function the relevant range of which is $$Q_p^d \in [0,500]$$. Make sure you select the appropriate cost function for the volume of cost driver you are interested in.

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