# Cost Behavior Analysis

Cost behavior refers to the way different types of production costs change when there is a change in level of production. There are three main types of costs according to their behavior: Fixed Costs:

Fixed costs are those which do not change with the level of activity within the relevant range. These costs will incur even if no units are produced. For example rent expense, straight-line depreciation expense, etc. Fixed cost per unit decreases with increase in production. Following example explains this fact:

Total Fixed Cost| $30,000| $30,000| $30,000|

÷ Units Produced| 5,000| 10,000| 15,000|

Fixed Cost per Unit| $6.00| $3.00| $2.00|

Variable Costs:

Variable costs change in direct proportion to the level of production. This means that total variable cost increase when more units are produced and decreases when less units are produced. Although variable in total, these costs are constant per unit. For example

Total Variable Cost| $10,000| $20,000| $30,000|

÷ Units Produced| 5,000| 10,000| 15,000|

Variable Cost per Unit| $2.00| $2.00| $2.00|

Mixed Costs:

Mixed costs or semi-variable costs have properties of both fixed and variable costs due to presence of both variable and fixed components in them. An example of mixed cost is telephone expense because it usually consists of a fixed component such as line rent and fixed subscription charges as well as variable cost charged per minute cost. Another example of mixed cost is delivery cost which has a fixed component of depreciation cost of trucks and a variable component of fuel expense. Since mixed cost figures are not useful in their raw form, therefore they are split into their fixed and variable components by using cost behavior analysis techniques such as High-Low Method, Scatter Diagram Method and Regression Analysis.

Cost Volume Formula

Cost volume formula is a cost accounting relation used to estimate production cost of a given number of units of a product. A linear cost volume formula is of the following form: y = a + bx|

In the above equation,

y stands for total production cost;

a for total fixed cost;

b for variable cost per unit; and

x for number of units

Total Fixed Cost is the sum of pure fixed cost, such as rent on factory building and property taxes; and the fixed component of mixed costs, such as total fixed cost on delivery trucks i.e. straight line depreciation expense. Variable Cost per Unit is the sum of pure variable cost per unit, such as material cost per unit; and the variable component of mixed cost, such as variable cost per unit on delivery trucks i.e. fuel expense. For this purpose, mixed costs are split into their fixed and variable components by using any of the following techniques: 1. High-Low Method

2. Scatter Graph Method

3. Regression Method

The cost volume formula we discussed here is in the form of linear equation. Cost volume formulas can also be quadratic or other complex forms which are more accurate and thus suitable for practical use. Example

Find total fixed cost, variable cost per unit, total cost of producing 30,000 units from the following cost volume formula: y = $43,000 + 6x

Solution

Total Fixed Cost = $43,000

Variable Cost per Unit = $6

Total Cost of Producing 30,000 Units = $43,000 + 6 × 30,000 = $223,000

High-Low Method

High-Low method is one of the several techniques used to split a mixed cost into its fixed and variable components (see cost classifications). Although easy to understand, high low method is relatively unreliable. This is because it takes two extreme data points from a set of actual data of various production levels and their corresponding total cost figures. These figures are used to calculate the approximate variable cost per unit (b) and total fixed cost (a) for the cost volume formula: y = a + bx|

High-Low Method Formulas

Variable Cost per Unit

Variable cost per unit (b) is calculated...

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