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Chapter 3Chapter 3Variations of Cost Variations of Cost

BehaviorBehavior

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Understanding cost behavior is Understanding cost behavior is fundamental to management fundamental to management

accounting. There are numerous accounting. There are numerous real-world cases in which real-world cases in which

managers have made seriously managers have made seriously wrong decisions because they had wrong decisions because they had

erroneous cost behavior erroneous cost behavior information. This chapter deserves information. This chapter deserves

careful study.careful study.

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Objective 1Objective 1

Explain step-and mixed-Explain step-and mixed-cost behaviorcost behavior

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

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

Step costs (semi-Step costs (semi-fixed)fixed)

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

Fig. 3.1 Fig. 3.1 Step fixed costs regarded as a fixed costStep fixed costs regarded as a fixed cost

Total Total fixed fixed cost cost

(L.E.)(L.E.)AA

XX YY Level of Level of activityactivity

RelevaRelevant nt

rangerange

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

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

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

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

Activity level

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On the other hand, if the increases in On the other hand, if the increases in semi-fixed costs are large and the steps are semi-fixed costs are large and the steps are not too frequent (see fig. 3.3 ) , the not too frequent (see fig. 3.3 ) , the increase in the costs should be increase in the costs should be incorporated in the analysis as a step cost. incorporated in the analysis as a step cost. The analysis will therefore include L.E. SFThe analysis will therefore include L.E. SF11 for activity level between O and Qfor activity level between O and Q11, L.E. Sf2 , L.E. Sf2 for activity level between OQfor activity level between OQ11 and OQ and OQ22, and , and so onso on

Activity level

Fig. 3-3 semi- fixed costs Fig. 3-3 semi- fixed costs regarded as a step fixed cost regarded as a step fixed cost

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

Mixed costsMixed costs

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

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

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An example of a mixed costAn example of a mixed cost is rent that is computed is rent that is computed as a flat charge (the fixed component) plus a stated as a flat charge (the fixed component) plus a stated percentage of sales pounds (the variable component). percentage of sales pounds (the variable component). Fig. 3.4 shows a graph of a rent charge. The store pays 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 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 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 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. L.E. 4,000. If sales are L.E. 600,000, the rent is L.E. 7,000.7,000.

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

Expected production Expected production 2,000 2,000 unitsunits

3,000 3,000 unitsunits

Variable cost (units Variable cost (units ×× L.E. 1.2 ) L.E. 1.2 )

L.E. L.E. 2,4002,400

L.E.3,60L.E.3,6000

Fixed cost Fixed cost 4,8004,8004,8004,800Total predicted Total predicted maintenance costmaintenance cost

L.E L.E 7,200 7,200

8,4008,400

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

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

1)1)Plan costs: Suppose the company expected to Plan costs: Suppose the company expected to produce 4,000 units next month. The month’s produce 4,000 units next month. The month’s predicated maintenance costs are L.E. 4,800 predicated maintenance costs are L.E. 4,800 fixed plus the variable cost of L.E. 4,800 ( 4,000 fixed plus the variable cost of L.E. 4,800 ( 4,000 units times L.E. 1.2 ) , for a total of L.E. 9,600units times L.E. 1.2 ) , for a total of L.E. 9,600

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

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

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Objective 2Objective 2

Explain management Explain management influences on cost behaviorinfluences on cost behavior

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Management can influence cost Management can influence cost behavior through decisions about behavior through decisions about such factors as:such factors as: Product or service attributesProduct or service attributes CapacityCapacity TechnologyTechnology Policies to create incentives to Policies to create incentives to

control costs.control costs.

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

1.1. Product and Service DecisionsProduct and Service Decisions 1.1. Product and Service DecisionsProduct and Service Decisions

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

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

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

2.2. Capacity DecisionsCapacity Decisions2.2. Capacity DecisionsCapacity Decisions

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

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

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Discretionary fixed costsDiscretionary fixed costs are costs determined by are costs determined by

management as part of the periodic planningmanagement as part of the periodic planning

process in order to meet organization’s goals.process in order to meet organization’s goals.

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

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

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

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

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Example:Example:XYZ company is experiencing financial difficulties. XYZ company is experiencing financial difficulties.

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

Fixed costs Fixed costs Planned Planned AmountsAmounts

Advertising and promotion Advertising and promotion 30,00030,000DepreciationDepreciation 400,000400,000Employee trainingEmployee training 100,000100,000Management salariesManagement salaries 800,000800,000Mortgage paymentMortgage payment 250,000250,000Property taxesProperty taxes 600,000600,000Research and developmentResearch and development 1,500,0001,500,000TotalTotal 3,680,0003,680,000 Should XYZ reduce or eliminate any of these Should XYZ reduce or eliminate any of these

fixed costs? fixed costs?

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

The answerThe answer

Fixed costs Fixed costs Planned Planned Amounts Amounts

Committed :Committed :Depreciation Depreciation 400,000400,000Mortgage payment Mortgage payment 250,000250,000Property taxes Property taxes 600,000600,000 Total Total CommittedCommitted

1,250,0001,250,000

Discretionary (potential Discretionary (potential savings):savings):Advertising and promotion Advertising and promotion

30,00030,000

Employee training Employee training 100,000100,000Management salaries Management salaries 800,000800,000Research and development Research and development 1,500,0001,500,000

Total discretionaryTotal discretionary 2,430,0002,430,000 Total Total 3,680,0003,680,000

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

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

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

3.3. Technology DecisionsTechnology Decisions3.3. Technology DecisionsTechnology Decisions

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

4.4. Cost Control IncentivesCost Control Incentives4.4. Cost Control IncentivesCost Control Incentives

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Objective 3Objective 3

Measure cost functions and Measure cost functions and use them to predict costsuse them to predict costs

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

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

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Cost functions Cost functions To describe the relationship between a To describe the relationship between a

cost and its cost driver, managers often use cost and its cost driver, managers often use an algebraic equation called a cost function.an algebraic equation called a cost function.

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

Y = a + b Y = a + b xxWhereWhere::

Y = Total cost (dependent Y = Total cost (dependent variable)variable)..

a = Fixed portion of total costa = Fixed portion of total cost b = Variable cost per unit. (the rate at b = Variable cost per unit. (the rate at

which which cost changes in relation to cost changes in relation to changes in xchanges in x,, b represent the slope of the line)b represent the slope of the line)

x = Cost driver activity (independent x = Cost driver activity (independent variable)variable)..

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

GeometGeometryry

Cost Cost systemsystem

MeaningMeaning

YY TCTC==Total cost in a Total cost in a periodperiod..

AA TFCTFC==Total fixed cost in a Total fixed cost in a periodperiod

BB UVCUVC==Unit Variable costUnit Variable cost..

XX XX==Volume, that is Volume, that is number of units of number of units of activityactivity..

The equation then becomesThe equation then becomes: :

TC = TFC + (UVC TC = TFC + (UVC ×× X ) X )

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

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

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

TC = L.E.0 + (UVC TC = L.E.0 + (UVC ×× X ) X )

OOrr

Y = L.E.0 + b xY = L.E.0 + b x

TC = TFC + L.E.0 XTC = TFC + L.E.0 X

Y = a + L.E.0 xY = a + L.E.0 x

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

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

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

= L.E. 0 + L.E. 2 X= L.E. 0 + L.E. 2 XWhere :Where :

TC = Total indirect material cost.TC = Total indirect material cost.X = number of units produced.X = number of units produced.

TC = TFC + (UVC TC = TFC + (UVC ×× X ) X )

UVC (or b)= L.E. 2 L.EL.E..

Number of units Number of units producedproduced

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

TC = L.E. 10,000 + oxTC = L.E. 10,000 + ox

L.EL.E10,00010,000

Any measure of Any measure of activityactivity

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

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

Where: Where:

TC = Total annual repair and maintenance CostTC = Total annual repair and maintenance Cost

X = number of machine hours incurredX = number of machine hours incurred

UVC (or b)= L.E. 600

L.EL.E14,00014,000

Number of machine Number of machine hourshours

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Objective 4Objective 4

Analyze Mixed CostsAnalyze Mixed Costs

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

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

The high-low method

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

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

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Month Month Level of Level of activityactivity

in machine in machine hours hours

Utility cost Utility cost

Jan. Jan. 4,0004,000L.E. 320L.E. 320

Feb.Feb.9,0009,000640640

MarchMarch15,00015,000840840

AprilApril4,600 4,600 350350

MayMay3,0003,000280280

JuneJune8,6208,620640640

JulyJuly5,280 5,280 420420

AugustAugust5,000 5,000 415415

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

Step (1) Step (1)

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

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

Step (2) Step (2)

Machine Machine hours hours

Associated Associated total cost total cost

High activity High activity 9,000 9,000 L.E. 640L.E. 640

Low activity Low activity 3,0003,000 280280

ChangeChange 6,0006,000360360

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

UVC ( or b )= UVC ( or b )= Change in total costChange in total cost Change in activity levelChange in activity level

= = L.E. 360L.E. 360 6000 MH6000 MH

= L.E. 0.06 per machine hour= L.E. 0.06 per machine hour

Step (3) Step (3)

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

High level of activity : TVC = L.E. 0.06 High level of activity : TVC = L.E. 0.06 ××(9000)(9000) = L.E. 540= L.E. 540

Step (4) Step (4)

Low level of activity : TVC = L.E. 0.06 Low level of activity : TVC = L.E. 0.06 ×× (3000) (3000) = L.E. 180= L.E. 180

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Subtract total variable cost from total Subtract total variable cost from total cost at either level of activity to determine cost at either level of activity to determine fixed cost.fixed cost.(This can be shown as an adaptation of (This can be shown as an adaptation of

the straight – line formula :the straight – line formula :

High level of activity :High level of activity :TFC = L.E. 640 – ( 0.06 x 9000)TFC = L.E. 640 – ( 0.06 x 9000)

= L.E. 640 – L.E. 540 = L.E. 100= L.E. 640 – L.E. 540 = L.E. 100Low level of activity:Low level of activity:

TFC = L.E. 280 – ( L.E. 0.06 x 3000)TFC = L.E. 280 – ( L.E. 0.06 x 3000)= L.E. 280 – L.E. 180 = L.E. 100= L.E. 280 – L.E. 180 = L.E. 100

Step (5) Step (5)

a = Ya = Y + b x+ b x

OOrr

TFC = TC – (UVCTFC = TC – (UVC × × X)X)

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

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

OrOr

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

Where x represent machine hours.Where x represent machine hours.

Step (6) Step (6)

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

ignored the 15,000 machine hour activity level, ignored the 15,000 machine hour activity level, because it was considered to be outside the relevant because it was considered to be outside the relevant range.range.

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

Visual- Fit method ( the Scatter graph)

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The variable cost per unit can then The variable cost per unit can then be determined as follows :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 ) / xb = ( Y – a ) / x

OOrr

UVC = (TC – TFC ) / xUVC = (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.

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The utility cost data given previously The utility cost data given previously for XYZ company is graphed in Exhibit for XYZ company is graphed in Exhibit 3.6. The cost line in Exhibit 3.6 is sighted, 3.6. The cost line in Exhibit 3.6 is sighted, and y – intercept is estimated as L.E. 100. and y – intercept is estimated as L.E. 100. If 4,000 machine hours are chosen as the If 4,000 machine hours are chosen as the activity level, L.E. 330 is estimated as the activity level, L.E. 330 is estimated as the visual y – intercept of total utility cost. visual y – intercept of total utility cost. Using the equation above, solve for UVC Using the equation above, solve for UVC ( or b ) as follows:( or b ) as follows:UVC = ( L.E. 330 – L.E. 100 ) / 4000UVC = ( L.E. 330 – L.E. 100 ) / 4000

= L.E. 230 / 4000= L.E. 230 / 4000 = L.E. 0.0575= L.E. 0.0575

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

TC = L.E. 100 per month + ( L.E. TC = L.E. 100 per month + ( L.E. 0.575 0.575 ××machine hours or x ) machine hours or x )

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

Exhibit 3-6 the XYZ company utility costExhibit 3-6 the XYZ company utility cost

Thousands of machine hours

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

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

FirstFirstFirstFirst

SeconSecondd

SeconSecondd

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

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The estimate of the visual intercept of the The estimate of the visual intercept of the

y-axis (fixed cost) may be difficult to read on a y-axis (fixed cost) may be difficult to read on a

scatter graph. It is only coincidental that the scatter graph. It is only coincidental that the

estimate made for (TFC or a ) using the scatter graph estimate made for (TFC or a ) using the scatter graph

is the same amount as was calculated using the high-is the same amount as was calculated using the high-

low method. Although both fixed-cost amounts were low method. Although both fixed-cost amounts were

estimated as L.E. 100, the cost formula resulting estimated as L.E. 100, the cost formula resulting

from the scatter graph method was not the same as from the scatter graph method was not the same as

that of the high-low method. This difference was that of the high-low method. This difference was

caused by the fact that only two observations were caused by the fact that only two observations were

used by the high-low method whereas the line drawn used by the high-low method whereas the line drawn

using the scatter graph method was based on all using the scatter graph method was based on all

observations except outliers. observations except outliers.

ThirdThird ThirdThird

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Thank you

Thank you