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Chapter 3 Variations of Cost Behavior. Understanding cost behavior is fundamental to management accounting. There are numerous real-world cases in which managers have made seriously wrong decisions because they had erroneous cost behavior information. This chapter deserves careful study.

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Chapter 3 Variations of Cost Behavior

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Chapter 3Variations of Cost Behavior

Understanding cost behavior is fundamental to management accounting. There are numerous real-world cases in which managers have made seriously wrong decisions because they had erroneous cost behavior information. This chapter deserves careful study.

Objective 1

Explain step-and mixed-cost behavior

Chapter 2 described two patterns of cost behavior: variable and fixed costs. In addition to these pure versions of cost two additional types of costs combine characteristics of both fixed and variable cost behavior. These are step costs and mixed costs.

Step costs (semi-fixed)

: are fixed for a given level of activity but they eventually increase by a constant amount at some critical points. We can distinguish fixed costs from semi-fixed costs by the range between the activity levels before the steps in total fixed costs occur. If the ranges between the steps are relatively wide and apply to a specific, broad range of activity, the cost is considered a fixed cost over that range of activity.

Relevant range

In fig. 3.1 we assume that the firm is committed to the fixed cost between activity level X and Y and cannot increase its activity beyond Y within the current accounting period. Hence this cost is regarded as a fixed cost.

Fig. 3.1

Step fixed costs regarded as a fixed cost

Total fixed cost (L.E.)




Level of activity

It is assumed that the firm plans to operate at a level of activity between point X and Y resulting in fixed costs of o A.

An example of a semi-fixed cost is the salaries of supervisors; assume that the supervisory staff can supervise direct labor up to 500 hours of activity per week. For each increase in 500 hours of activity per week the supervision cost of an additional supervisor.

The treatment of semi-fixed costs depend on the frequency of the steps and the amount of the increase at each point. If the steps are close together as in Fig. 3.2 the semi fixed costs may be approximated by a variable cost as represented by the straight line in fig. 3.2

Fig. 3-2 Semi-fixed costs approximated as a variable cost .

Activity level

On the other hand, if the increases in semi-fixed costs are large and the steps are not too frequent (see fig. 3.3 ) , the increase in the costs should be incorporated in the analysis as a step cost. The analysis will therefore include L.E. SF1 for activity level between O and Q1, L.E. Sf2 for activity level between OQ1 and OQ2, and so on

Fig. 3-3 semi- fixed costs

regarded as a step fixed cost

Activity level

Mixed costs

Mixed costs contain elements of both fixed and variable-cost behavior. Like step costs, the fixed element is determined by the planned range of activity level. Unlike step costs, however, usually in a mixed cost there is only one relevant range of activity and one level of fixed costs. The variable-cost element of the mixed cost is a purely variable cost that varies proportionately with activity within the single relevant range. In a mixed cost the variable cost is incurred in addition to the fixed cost : the total mixed cost is the sum of the fixed cost plus the variable cost.

Mixed cost is a purely variable cost that varies proportionately with activity within the single relevant range. In a mixed cost, the variable cost is incurred in addition to the fixed cost : The total mixed cost is the sum of the fixed cost plus the variable cost.

Note: A mixed cost does not fluctuate in direct proportion with activity, nor does it remain constant with changes in activity.

An example of a mixed cost is rent that is computed as a flat charge (the fixed component) plus a stated percentage of sales pounds (the variable component). Fig. 3.4 shows a graph of a rent charge. The store pays rent to the owners of the shopping center at a flat rate of L.E. 1000 per month plus 10% of sales. If the shop has sales of L.E. 300,000 in a month, its total rent is L.E. 4,000. If sales are L.E. 600,000, the rent is L.E. 7,000.

Another example of a mixed costis maintenance. The XYZ company maintenance cost has a monthly fixed component of L.E. 4,800 for maintenance worker salaries. In addition, maintenance charges for items such as lubricants and replacement parts average L.E. 1,200 for every unit produced. Total monthly maintenance cost can be predicted by multiplying the L.E. 1,200 per-unit variable cost times the number of units produced and adding the L.E. 4,800 fixed cost as follows:

Cost accountants often separate mixed costs into their variable and fixed components so that changes in these costs are more readily apparent. This separation allows managers to focus on two basic types of costs: variable and fixed.

An administrator at XYZ company could use knowledge of the maintenance department cost behavior to :

Plan costs: Suppose the company expected to produce 4,000 units next month. The month’s predicated maintenance costs are L.E. 4,800 fixed plus the variable cost of L.E. 4,800 ( 4,000 units times L.E. 1.2 ) , for a total of L.E. 9,600

2) Provide feedback to managers: suppose actual maintenance costs were L.E. 11,000 in a month when production were 4,000 units as planned. Managers would want to know why the maintenance department overspent by L.E. 1,400 ( L.E. 11,000 less the planned L.E. 9,600 ) so that they could take corrective action.

3) Make decisions: for example, manager could evaluate an alternative to acquire a new highly automated equipment against doing maintenance work manually.

Objective 2

Explain management influences on cost behavior

Management can influence cost behavior through decisions about such factors as:

  • Product or service attributes

  • Capacity

  • Technology

  • Policies to create incentives to control costs.

  • Product and Service Decisions

Manager’s choice of product mix, design, quality, features, distribution, and so on, influence product and service costs. These decisions should be made in a cost/benefit framework.

  • Capacity Decisions

Strategic decisions about the scale and scope of an organization’s activities generally result in fixed level of capacity costs.

Capacity costs are the fixed costs of being able to achieve a desired level of production or to provide a desired level of service while maintaining product or service attribute, such as quality.

All fixed costs fall into two basic categories: committed and discretionary. The difference between the two categories is primarily the time horizon for which management binds itself to the cost.

Committed fixed costs are costs related to the possession of basic plant assets or personnel structure that an organization must have to operate. The level of committed costs is normally dictated by long-term management decisions involving the desired level of operations. Committed costs include depreciation, lease rental interest payments on long-term debts, and executive (key personnel) salaries. Such costs can not easily be reduced, even during temporary slowdowns in activity.

Note: A committed cost is an item of cost that can not be changed in the short run. It results from a commitment made in the past.

Discretionary fixed costs are costs determined by

management as part of the periodic planning

process in order to meet organization’s goals.

Discretionary costs relate to activities that are important to the organization but viewed as optional. Discretionary cost activities are usually service oriented and include advertising, research and development , and employee

training and development. There is no “ correct” amount at which to set funding for discretionary costs, and in case of cash flow shortages or forecasted operating losses, managers may reduce these expenditures.

Note: The discretionary fixed costs have no obvious relationship to levels of output activity. The amount spent can be changed at the discretion of management. The planned amounts of discretionary costs are negotiated between the manager and his superior during the budget process.

Distinguishing committed and discretionary fixed costs would be the first step to identify where costs could be reduced .


XYZ company is experiencing financial difficulties. Sales for its major product are depressed, and XYZ management is considering cutting back on costs temporarily. XYZ management must determine which of the following fixed costs to reduce or eliminate and how much money each would save:

Should XYZ reduce or eliminate any of these fixed costs?

The answer

The answer depends on the company long-run outlook. XYZ could reduce costs but also greatly reduce its ability to compete in the future if it cuts carelessly. Rearranging these costs by categories of committed and discretionary costs yields the following analysis:

XYZ would be unwise to eliminate all of discretionary costs arbitrarily.

Nevertheless, discretionary fixed costs would be the company’s first step to identify where costs could be reduced.

  • Technology Decisions

One of the most critical decision that managers make is the type of technology that the organization will use to produce its products or deliver its services. Choice of technology ( for example, labor intensives capital intensive ) may have a great impact on the costs of products and services.

  • Cost Control Incentives

Finally future costs may be affected by the incentives that management creates for employees to control costs. A strong form of feedback, and a sound system of compensations could cause the supervisors to watch costs carefully and to find ways to reduce costs without reducing quality of products or services.

Objective 3

Measure cost functions and use them to predict costs

The decision making, planning and control activities of management accounting require accurate and useful estimates of future fixed and variable costs.

The first step in estimating or predicting costs is cost measurement or measuring cost behavior as a function of appropriate cost drivers. The second step is to use these cost measures to estimate future costs at expected, future levels of cost driver activity.

Cost functions

To describe the relationship between a cost and its cost driver, managers often use an algebraic equation called a cost function.

Because of the linearity assumption, the general formula for a straight line can be used to describe any type of cost within a relevant range of activity. The straight-line formula is :

Y = a + b x


Y = Total cost (dependent variable).

a = Fixed portion of total cost

b = Variable cost per unit. (the rate at which cost changes in relation to changes in x,

b represent the slope of the line)

x = Cost driver activity (independent variable).

We shall use this basic equation, but will use symbols that stands for the particular relationship we are studying as follows:

The equation then becomes :

TC = TFC + (UVC × X )

An entirely variable cost is represented by the straight – line formula in the following manner :

TC = L.E.0 + (UVC × X )

A zero is shown as the value of TFC ( or a ) because there is no fixed cost.

A purely fixed cost is shown in the straight line formula as :


Y = L.E.0 + b x

TC = TFC + L.E.0 X

Y = a + L.E.0 x

Fixed cost is the value of a ; zero is substituted in the formula for b (or UVC ), since there is no cost component that varies with an activity base.

A mixed cost has values for both a (TFC) and b (UVC) values in the formula. Exhibit 3.5 illustrates the use of the straight-line formula for each type of cost behavior.

Exhibit 3.5 uses of the straight-line cost formula to explain or predict a variable cost such as indirect materials when the cost per unit is L.E. 2 :

TC = TFC + (UVC × X )

= L.E. 0 + L.E. 2 X

Where :

TC = Total indirect material cost.

X = number of units produced.


UVC (or b)= L.E. 2

Number of units produced

to explain or predict a fixed cost such as building rent of L.E. 10,000 per year : TC = L.E. 10,000 + ox



Any measure of activity

To explain or predict a mixed cost such as repairs and maintenance when the fixed element is L.E. 14,000 per year plus L.E. 600 per machine hour :

TC = L.E. 14,000+L.E. 600x


TC = Total annual repair and maintenance Cost

X = number of machine hours incurred

UVC (or b)= L.E. 600



Number of machine hours

Objective 4

Analyze Mixed Costs

Since a mixed cost contains amounts for both the fixed and variable values, some methods must be used to separate the mixed cost into its two component elements. The simplest method to use is the high-low method.

is a separation technique that chooses actual observations of a total cost at two levels of activity and calculates the change in both activity and cost. The observations selected are the highest and lowest activity levels if these levels are representative of normal costs within the relevant range.

The high-low method

Notethat the selections of “high” and “low” are made on the basis of activity levels rather than costs. The reason for this selection is that the purpose of the analysis is to understand how costs change in relation to activity changes. Activities cause costs to change rather than the opposite relationship.

The high-low method is illustrated using machine hours and utility cost information for XYZ company. The company’s normal operating range of activity is between 3,000 and 10,000 machine hours. The following machine hours and utility cost information is available :

Step (1)

Select the highest and lowest level of activity within the relevant range and obtain the costs associated with those levels. These levels and costs are 3,000 and 9,000 hours and L.E. 280 and L.E. 640, respectively.

Note that since march reflects data outside the relevant range, this observation should be disregarded in analyzing the utility cost.

Calculate the change in cost compared to the change in activity.

Step (2)

Determine the relationship of cost change to activity change to find the variable cost element.

Step (3)

UVC ( or b )= Change in total cost

Change in activity level

= L.E. 360

6000 MH

= L.E. 0.06 per machine hour

Compute total variable cost (TVC) at earlier level of activity.

Step (4)

High level of activity : TVC = L.E. 0.06 ×(9000)

= L.E. 540

Low level of activity : TVC = L.E. 0.06 × (3000)

= L.E. 180

Subtract total variable cost from total cost at either level of activity to determine fixed cost.(This can be shown as an adaptation of the straight – line formula :

Step (5)

High level of activity :

TFC = L.E. 640 – ( 0.06 x 9000)

= L.E. 640 – L.E. 540 = L.E. 100

Low level of activity:

TFC = L.E. 280 – ( L.E. 0.06 x 3000)

= L.E. 280 – L.E. 180 = L.E. 100

a = Y+ b x


TFC = TC – (UVC × X)

Substitute the fixed and variable cost values in the straight-line formula to get an equation that can be used to estimate total cost at any level of activity within the relevant range.

Step (6)

Y = L.E. 100 + L.E. 0.06 x


TC = L.E. 100 + L.E. 0.06 x

Where x represent machine hours.

Notethat total mixed cost increases or decreases with changes in activity. The change in cost is equal the change in activity times the unit variable cost; the fixed cost element does not fluctuate because of changes in activity. Therefore, any increase or decrease in total cost is due to the increase or decrease in the independent variable. The variable cost per unit of activity reflects the average change in cost for each additional unit of activity. For XYZ company this average is L.E. 0.06 per machine hour use.

The values selected for use in the high low method ignored the 15,000 machine hour activity level, because it was considered to be outside the relevant range.

Visual- Fit method ( the Scatter graph)

A method in which the cost analyst visually fits a straight line through a plot of all the available data, not just between the high point and the low point, making it more reliable than the high-low method. A straight line is drawn through the plotted point. The line drawn should be the one that appears to best fit the data. The point at which the line intercepts the Y-axis (vertical axis) represent an estimate of the fixed cost component of the mixed cost.

The variable cost per unit can then be determined as follows :

  • 1) Subtract the estimated fixed cost from total cost at a level of activity that falls on the line, and

  • 2) Divide the result of (1) by the activity level chosen. In equation form, variable cost is calculated as :

  • b = ( Y – a ) / x


    UVC = (TC – TFC ) / x

    Where TC (or Y ) = any value on the Y-axis using a selected associated value for x

    TFC (or a ) = estimated fixed cost from sighted line.

    The utility cost data given previously for XYZ company is graphed in Exhibit 3.6. The cost line in Exhibit 3.6 is sighted, and y – intercept is estimated as L.E. 100. If 4,000 machine hours are chosen as the activity level, L.E. 330 is estimated as the visual y – intercept of total utility cost. Using the equation above, solve for UVC ( or b ) as follows:

    UVC = ( L.E. 330 – L.E. 100 ) / 4000

    = L.E. 230 / 4000

    = L.E. 0.0575

    The linear-cost function measured by the visual fit method is :

    TC = L.E. 100 per month + ( L.E.

    0.575 ×machine hours or x )

    Although the visual- fit method can use all the data, The placement of the line and the measurement of the fixed and variable costs are subjective.

    Exhibit 3-6 the XYZ company utility cost

    Thousands of machine hours

    Three things are important to note about the scatter graph method:


    It provides a means for easily identifying abnormal or non-representative points. These points (called outliers ) fall outside the relevant range of activity. Exhibit 3.6 reveals an outlier at 15,000 machine hours.


    The original information on actual activity – to- cost relationship is not used in determining the variable cost amount. Estimates are made of the activity-to-cost relationships that lie on the line. The scatter graph line may not pass through any or all of the actual observation points; this is acceptable as long as the line is representative of the actual data.


    The estimate of the visual intercept of the y-axis (fixed cost) may be difficult to read on a scatter graph. It is only coincidental that the estimate made for (TFC or a ) using the scatter graph is the same amount as was calculated using the high-low method. Although both fixed-cost amounts were estimated as L.E. 100, the cost formula resulting from the scatter graph method was not the same as that of the high-low method. This difference was caused by the fact that only two observations were used by the high-low method whereas the line drawn using the scatter graph method was based on all observations except outliers.

    Thank you

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