# What are the purposes of cost estimation?

From a technical perspective, cost estimation is a set of techniques used to build linear cost functions. A cost function is a mathematical expression describing cost behavior patterns, i.e. how costs change with changes in the cost driver for a period and within a given range of activity:

$TC_p = \sum_{d = 1}^{l} Q_p^d \times V_c^d + FC_p \\ \text{for } Q_p^d \in [Q_{min}^d,Q_{max}^d]$

where $$TC_p$$ is the total cost we want to model over the period $$p$$ (e.g. day, week, month), $$Q_p^d$$ is the volume of a cost driver $$d$$ in period $$p$$, $$V_c^d$$ is the change in total cost for any change in the cost driver $$d$$, $$FC_p$$ a fixed amount of costs incurred during a period $$p$$, and $$[Q_{min}^d,Q_{max}^d]$$ is a periodic range of activity over which this cost function is a valid mathematical representation of the costs we want to model.

Cost estimation refers to a set of techniques used to build linear cost equations allowing you to predict total costs for specific volumes of activity.

Assuming $$l = 1$$, i.e. there is only one cost driver, the previous function can be represented on a scatter graph. A scatter graph is a visual representation of the relationship between a cost and its cost driver. It takes the level of activity as the X axis (independent variable) and the total cost as a Y axis (dependent variable): Cost estimation techniques separate total costs into these different components. Cost functions can of course be more complex than that; but for most managerial purposes and for reasons I will explain later, this simple form is both sufficient and preferable.

Why would we want to build such cost functions? We have already indicated that cost estimation is heavily used in activity-based costing or to compute predetermined overhead rates in normal or standard costing (Chapter 2). These functions are also extensively used to know the cost structure of a company and infer from this cost structure operating risks (Chapter 4), forecast costs and set targets for expected levels of activity (Chapter 5), understand the sources of discrepancies between targets and performance (Chapter 6), and finally assess the economic consequences of alternative courses of action (Chapter 7). So these cost functions are really at the core of management accounting.

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