Mixed costs or semi-variable costs, are types of cost that have a fixed element and a variable element. Enterprises find it useful to employ estimation techniques to determine mixed costs and analyze them into their fixed and variable elements, which can then be incorporated into the costing system.

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### Fixed and Variable Costs

Some of the costs borne by an enterprise vary according to the level of output, examples being the direct labor costs and the cost of materials used for making the products. However other costs are fixed, and therefore do not change whatever the number of units produced.

An example of a fixed cost would be the rent paid for the factory in which the products are manufactured. Certain costs are fixed within a certain range of output but may rise if output exceeds a certain threshold. For example, to achieve a certain level of output, the enterprise may need to rent a second factory, therefore paying more rent. Such costs are referred to as stepped costs, as they are fixed for a range of levels of output, but then increase steeply at certain threshold levels of output, then remaining fixed at that higher level until a further threshold (for example the need to rent a third factory) is reached.

All these types of cost are managed by incorporating them into the various costing systems used by enterprises. For example, marginal costing takes into account the contribution made by sales less variable costs, arriving at the amount of contribution available to cover the total fixed costs of the business.

Absorption costing works by attributing both fixed and variable costs to each unit of production, thereby absorbing fixed costs into the cost of the units produced, and arriving at the profit per unit (subject to over or under absorption at various different levels of output).

In reality, costs do not behave in the clear-cut manner in which they appear in theory. For example, direct labor costs do not vary exactly with output of the product. Where the output falls suddenly, it will often not be possible to reduce working hours or lay off workers, as this may be prohibited or restricted by labor laws and regulations. Overheads, that are normally regarded as fixed, will vary to some extent with output for example, as greater output gives rise to a need to incur more administrative costs.

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### Mixed Costs

Some costs have a fixed element and a variable element, and these are referred to as mixed costs or semi-variable costs. An example in everyday life is the cost of owning and using a mobile phone, which will have a fixed rental element and an element that varies with the number and duration of calls made, depending on the terms of the contract.

The characteristic of mixed costs is that they change with the level of output; however because the costs have a fixed element the change in the level of the mixed costs is not directly in proportion to the level of activity or output. For this reason, a business that has mixed costs, but does not have information about the size of the fixed and variable elements, may attempt to divide the mixed costs into their fixed and variable elements, so as to include these costs appropriately into their chosen costing system. Enterprises therefore, use some estimation techniques to determine mixed costs and allocate the fixed and variable elements of the costs as required by the costing system that they use.

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### High-Low Method

High-Low Method of Determining Mixed Costs The high-low method is an approximate method of analysing mixed costs, and is relatively straightforward to apply. This method involves looking at the costs at the time of highest and lowest activity, from which it is possible to calculate the variable cost per unit. The fixed costs can then be found by deducting variable costs from total costs at any particular level of activity. - slide 4 of 8
### High-Low Method

Some estimation techniques to identify mixed costs only seek to arrive at approximations of the fixed and variable element in the costs. Under the high-low method, the enterprise identifies the highest and lowest levels of activity for a particular period of time. The enterprise might then examine the particular cost heading, containing the mixed costs, and look at the total costs under that cost heading at the times of highest and lowest activity. The variable cost relating to the change in activity will be taken to be the difference in total costs between those highest and lowest levels of activity.

Therefore, by looking at the cost difference between the two levels of activity and dividing this by the difference in levels of activity at the two prices, it is possible to arrive at a figure for the variable cost per unit of activity. The fixed cost element would then simply be found by deducting the variable cost element from the total cost at that level of output.

If, for example, at the level of highest activity (an output of 10,000 units) a particular cost amounted to $100,000, and at the level of lowest activity (output of 8,000 units) the cost was $90,000, then the variable cost would be estimated by dividing $10,000 ($100,000 - $90,000) by the difference in units produced, which is 2,000 units (10,000 - 8,000).

The variable cost per unit would therefore be estimated at $5. Since at an output of 10,000 units the variable cost element is $50,000 ($5 x 10,000 units), the fixed cost is found by deducting the variable costs from total costs, in other words the fixed cost is also $50,000 ($100,000 - $50,000).

This can be confirmed by looking at the lowest level of output in the period, where the variable costs are $40,000 (8,000 units x $5) and the fixed cost is again calculated to be $50,000 ($90,000 - $40,000).

Using the high-low method is not necessarily accurate, because it depends on only two values for mixed costs and activity levels within a particular period of time. The use of this method involves the danger that the highest and lowest values within a particular period may be anomalous figures that give a misleading result. The high-low method is only accurate where the progression of costs in relation to output is linear. Where management needs a more accurate estimate of the variable and fixed cost elements, they must use other estimation techniques to determine fixed costs.

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Using the Method of Least Squares to Determine Mixed Costs The method of least squares depends on plotting values for mixed costs at various activity levels on a graph and drawing a line that minimises the squares of the distances of the points on the graph from the line. The X axis would represent the level of mixed costs and the Y axis would represent the activity level in terms of units of production. The level of fixed costs can be read from the point of intersection of this line with the X axis, while the slope of the line represents the variable costs per unit of production. This estimation technique to determine mixed costs is more accurate than the high-low method. - slide 6 of 8
### Method of Least Squares

A more precise method of determining the proportion of fixed and variable costs contained in mixed costs, is the method of least squares, or regression analysis. This begins by determining the level of the particular mixed cost at various levels of output, and plotting these as points on a graph with the X axis representing the level of output, and the Y axis representing the related mixed costs.

The method of least squares aims to distinguish a line that will pass through the set of points on the graph. The position and slope of the line will be determined by finding a line where the cumulative total of the squared distances between the points and the line, is the least possible. In other words, the line must pass as closely to all the points as possible so that the squared distances are minimized. To avoid the necessity for detailed calculations, enterprises will probably prefer to use a spreadsheet program that performs the necessary calculations.

The element representing fixed costs will be the level at which the line intersects the Y axis. The amount of variable costs per unit of output will be shown by the slope of the line on the graph, or calculated at a particular level of output by deducting the fixed costs from the total costs.

Alternatively, instead of devoting time and expense to performing detailed calculations, it would be possible to plot the points on a graph and estimate the line that would link them; this being known as the scattergraph method. As this method relies on estimation rather than precise calculations, it is less accurate than using the method of least squares. With the availability of software that will calculate the position with more accuracy, there is no need for enterprises to settle for a less reliable estimate, if they attach importance to identifying the fixed and variable cost elements with more accuracy.

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### Importance of Analyzing Mixed Costs

Once the semi-variable costs have been analyzed into fixed and variable elements, these elements can be incorporated into the costing system used by the enterprise, which may be a method such as marginal costing, full absorption costing or activity based costing. The use of some estimation techniques to determine mixed costs may involve extra work and expense, but this is worthwhile, because the estimation techniques allow management to keep control of the costs of the enterprise. They can thereby ensure that suitable cost information is available to enable them to take the optimal management decisions.

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### References

"Mixed or semivariable cost" on Accounting for Management, http://www.accountingformanagement.com/mixed_costs.htm

Chapter 18: "Cost-Volume-Profit and Business Scalability", http://www.principlesofaccounting.com/chapter%2018.htm

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