Cost Behavior Analysis and Justifications of Segmented Reporting

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Managerial Accounting and Cost Concepts 29

LEARNING OBJECTIVE 3 Understand cost behavior patterns including variable costs, fixed costs, and mixed costs.

Cost Classifications for Predicting Cost Behavior

It is often necessary to predict how a certain cost will behave in response to a change in ac -

tivity. For example, a manager at Qwest , a telephone company, may want to estimate the

impact a 5 percent increase in long-distance calls by customers would have on Qwest’s total

electric bill. Cost behavior refers to how a cost reacts to changes in the level of activity. As

the activity level rises and falls, a particular cost may rise and fall as well—or it may remain

constant. For planning purposes, a manager must be able to anticipate which of these will

happen; and if a cost can be expected to change, the manager must be able to estimate how

much it will change. To help make such distinctions, costs are often categorized as variable, fixed, or mixed. The relative proportion of each type of cost in an organization is known as its

cost structure . For example, an organization might have many fixed costs but few variable

or mixed costs. Alternatively, it might have many variable costs but few fixed or mixed costs.

Variable Cost

A variable cost varies, in total, in direct proportion to changes in the level of activity.

Common examples of variable costs include cost of goods sold for a merchandising com-

pany, direct materials, direct labor, variable elements of manufacturing overhead, such as

indirect materials, supplies, and power, and variable elements of selling and administra-

tive expenses, such as commissions and shipping costs. 1

For a cost to be variable, it must be variable with respect to something. That “some-

thing” is its activity base. An activity base is a measure of whatever causes the incurrence

of a variable cost. An activity base is sometimes referred to as a cost driver. Some of the

most common activity bases are direct labor-hours, machine-hours, units produced, and

units sold. Other examples of activity bases (cost drivers) include the number of miles

driven by salespersons, the number of pounds of laundry cleaned by a hotel, the number

of calls handled by technical support staff at a software company, and the number of beds

occupied in a hospital. While there are many activity bases within organizations, through-out this textbook, unless stated otherwise, you should assume that the activity base under consideration is the total volume of goods and services provided by the organization. We will specify the activity base only when it is something other than total output.

1 Direct labor costs often can be fixed instead of variable for a variety of reasons. For example, in some

countries, such as France, Germany, and Japan, labor regulations and cultural norms may limit manage-

ment’s ability to adjust the labor force in response to changes in activity. In this textbook, always assume

that direct labor is a variable cost unless you are explicitly told otherwise.

I N B U S I N E S S COST DRIVERS IN THE ELECTRONICS INDUSTRY Accenture Ltd. estimates that the U.S. electronics industry spends $13.8 billion annually to rebox, restock, and resell returned products. Conventional wisdom is that customers only return products when they are defective, but the data shows that this explanation only accounts for 5% of customer returns. The biggest cost drivers that cause product returns are that customers often inadvertently buy the wrong products and that they cannot understand how to use the products that they have pur-chased. Television manufacturer Vizio Inc. has started including more information on its packaging to help customers avoid buying the wrong product. Seagate Technologies is replacing thick instruc-tion manuals with simpler guides that make it easier for customers to begin using their products.

Source: Christopher Lawton, “The War on Returns,” The Wall Street Journal, May 8, 2008, pp. D1 and D6.

To provide an example of a variable cost, consider Nooksack Expeditions, a small

company that provides daylong whitewater rafting excursions on rivers in the North Cas-

cade Mountains. The company provides all of the necessary equipment and experienced

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30 Chapter 2

guides, and it serves gourmet meals to its guests. The meals are purchased from a caterer

for $30 a person for a daylong excursion. The behavior of this variable cost, on both a per

unit and a total basis, is shown below:

Number Cost of Meals Total Cost of Guests per Guest of Meals

250 . . . . . . . . . $30 $7,500 500 . . . . . . . . . $30 $15,000 750 . . . . . . . . . $30 $22,500 1,000 . . . . . . . . . $30 $30,000

While total variable costs change as the activity level changes, it is important to note

that a variable cost is constant if expressed on a per unit basis. For example, the per unit

cost of the meals remains constant at $30 even though the total cost of the meals increases

and decreases with activity. The graph on the left-hand side of Exhibit 2–2 illustrates that

the total variable cost rises and falls as the activity level rises and falls. At an activity level

of 250 guests, the total meal cost is $7,500. At an activity level of 1,000 guests, the total

meal cost rises to $30,000.

Fixed Cost

A fixed cost is a cost that remains constant, in total, regardless of changes in the level

of activity. Examples of fixed costs include straight-line depreciation, insurance, prop-

erty taxes, rent, supervisory salaries, administrative salaries, and advertising. Unlike

variable costs, fixed costs are not affected by changes in activity. Consequently, as

the activity level rises and falls, total fixed costs remain constant unless influenced

by some outside force, such as a landlord increasing your monthly rental expense. To

continue the Nooksack Expeditions example, assume the company rents a building

for $500 per month to store its equipment. The total amount of rent paid is the same

regardless of the number of guests the company takes on its expeditions during any

given month. The concept of a fixed cost is shown graphically on the right-hand side

of Exhibit 2–2 .

E X H I B I T 2 – 2 Variable and Fixed Cost Behavior

$30,000

$25,000

$20,000

$15,000

$10,000

$5,000

$0

Tot

al c

ost o

f mea

ls

0 250 500 750 1,000Number of guests

Total Cost of Meals

A variable cost increases,in total, in proportion to activity.

Cost ofbuildingrental

$500

$00 250 500 750 1,000 1,250

Number of guests

Total Cost of Renting the Building

Fixed costs remainconstant in total dollar

amount throughwide ranges of activity.


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As a general rule, we caution against expressing fixed costs on an average per unit basis in internal reports because it creates the false impression that fixed costs are like variable costs and that total fixed costs actually change as the level of activity changes.

For planning purposes, fixed costs can be viewed as either committed or discretion-ary. Committed fixed costs represent organizational investments with a multiyear planning

horizon that can’t be significantly reduced even for short periods of time without making

fundamental changes. Examples include investments in facilities and equipment, as well as

real estate taxes, insurance expenses, and salaries of top management. Even if operations are

interrupted or cut back, committed fixed costs remain largely unchanged in the short term

because the costs of restoring them later are likely to be far greater than any short-run savings

that might be realized. Discretionary fixed costs (often referred to as managed fixed costs ) usually arise from annual decisions by management to spend on certain fixed cost items.

Examples of discretionary fixed costs include advertising, research, public relations, manage-

ment development programs, and internships for students. Discretionary fixed costs can be

cut for short periods of time with minimal damage to the long-run goals of the organization.

The Linearity Assumption and the Relevant Range

Management accountants ordinarily assume that costs are strictly linear; that is, the rela-

tion between cost on the one hand and activity on the other can be represented by a

straight line. Economists point out that many costs are actually curvilinear; that is, the

Monthly Rental Cost Number of GuestsAverage Cost per

Guest

$500 250 $2.00$500 500 $1.00$500 750 $0.67$500 1,000 $0.50

Because total fixed costs remain constant for large variations in the level of activ-

ity, the average fixed cost per unit becomes progressively smaller as the level of activ-

ity increases. If Nooksack Expeditions has only 250 guests in a month, the $500 fixed

rental cost would amount to an average of $2 per guest. If there are 1,000 guests, the

fixed rental cost would average only 50 cents per guest. The table below illustrates this

aspect of the behavior of fixed costs. Note that as the number of guests increase, the

average fixed cost per guest drops.

I N B U S I N E S S FOOD COSTS AT A LUXURY HOTEL The Sporthotel Theresa ( http://www.theresa.at/ ), owned and operated by the Egger family, is a four star hotel located in Zell im Zillertal, Austria. The hotel features access to hiking, skiing, biking, and other activities in the Ziller alps as well as its own fitness facility and spa.

Three full meals a day are included in the hotel room charge. Breakfast and lunch are served buffet-style while dinner is a more formal affair with as many as six courses. The chef, Stefan Egger, believes that food costs are roughly proportional to the number of guests staying at the hotel; that is, they are a variable cost. He must order food from suppliers two or three days in advance, but he adjusts his purchases to the number of guests who are currently staying at the hotel and their consumption patterns. In addition, guests make their selections from the dinner menu early in the day, which helps Stefan plan which foodstuffs will be required for dinner. Consequently, he is able to prepare just enough food so that all guests are satisfied and yet waste is held to a minimum.

Source: Conversation with Stefan Egger, chef at the Sporthotel Theresa.


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32 Chapter 2

relation between cost and activity is a curve. Nevertheless, even if a cost is not strictly lin-

ear, it can be approximated within a narrow band of activity known as the relevant range

by a straight line as illustrated in Exhibit 2–3 . The relevant range is the range of activ-

ity within which the assumption that cost behavior is strictly linear is reasonably valid.

Outside of the relevant range, a fixed cost may no longer be strictly fixed or a variable

cost may not be strictly variable. Managers should always keep in mind that assumptions

made about cost behavior may be invalid if activity falls outside of the relevant range.

The concept of the relevant range is important in understanding fixed costs. For

example, suppose the Mayo Clinic rents a machine for $20,000 per month that tests blood

samples for the presence of leukemia cells. Furthermore, suppose that the capacity of the

leukemia diagnostic machine is 3,000 tests per month. The assumption that the rent for

the diagnostic machine is $20,000 per month is only valid within the relevant range of

0 to 3,000 tests per month. If the Mayo Clinic needed to test 5,000 blood samples per

month, then it would need to rent another machine for an additional $20,000 per month. It

would be difficult to rent half of a diagnostic machine; therefore, the step pattern depicted

in Exhibit 2–4 is typical for such costs. This exhibit shows that the fixed rental expense

E X H I B I T 2 – 3 Curvilinear Costs and the Relevant Range

E X H I B I T 2 – 4 Fixed Costs and the Relevant Range

Relevantrange

Cos

tVolume

Economist’scurvilinear

cost function

Accountant’sstraight-line

approximation

Number of Tests

Cos

t

$20,000

$40,000

$60,000

0 3,000 6,000 9,000


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Behavior of the Cost (within the relevant range)

Cost In Total Per Unit

Variable cost Total variable cost increases Variable cost per unit remains and decreases in proportion to constant. changes in the activity level.Fixed cost Total fi xed cost is not affected Fixed cost per unit decreases by changes in the activity level as the activity level rises and within the relevant range. increases as the activity level falls.

E X H I B I T 2 – 5 Summary of Variable and Fixed Cost Behavior

is $20,000 for a relevant range of 0 to 3,000 tests. The fixed rental expense increases to

$40,000 within the relevant range of 3,001 to 6,000 tests. The rental expense increases in

discrete steps or increments of 3,000 tests, rather than increasing in a linear fashion per test.

This step-oriented cost behavior pattern can also be used to describe other costs, such

as some labor costs. For example, salaried employee expenses can be characterized using

a step pattern. Salaried employees are paid a fixed amount, such as $40,000 per year, for

providing the capacity to work a prespecified amount of time, such as 40 hours per week

for 50 weeks a year ( = 2,000 hours per year). In this example, the total salaried employee

expense is $40,000 within a relevant range of 0 to 2,000 hours of work. The total salaried

employee expense increases to $80,000 (or two employees) if the organization’s work

requirements expand to a relevant range of 2,001 to 4,000 hours of work. Cost behavior

patterns such as salaried employees are often called step-variable costs. Step-variable

costs can often be adjusted quickly as conditions change. Furthermore, the width of the

steps for step-variable costs is generally so narrow that these costs can be treated essen-

tially as variable costs for most purposes. The width of the steps for fixed costs, on the

other hand, is so wide that these costs should be treated as entirely fixed within the rel-

evant range.

Exhibit 2–5 summarizes four key concepts related to variable and fixed costs. Study

it carefully before reading further.

I N B U S I N E S S HOW MANY GUIDES? Majestic Ocean Kayaking , of Ucluelet, British Columbia, is owned and operated by Tracy Morben-Eeftink. The company offers a number of guided kayaking excursions ranging from three-hour tours of the Ucluelet harbor to six-day kayaking and camping trips in Clayoquot Sound. One of the com-pany’s excursions is a four-day kayaking and camping trip to The Broken Group Islands in the Pacific Rim National Park. Special regulations apply to trips in the park—including a requirement that one certified guide must be assigned for every five guests or fraction thereof. For example, a trip with 12 guests must have at least three certified guides. Guides are not salaried and are paid on a per-day basis. Therefore, the cost to the company of the guides for a trip is a step-variable cost rather than a fixed cost or a strictly variable cost. One guide is needed for 1 to 5 guests, two guides for 6 to 10 guests, three guides for 11 to 15 guests, and so on.

Sources: Tracy Morben-Eeftink, owner, Majestic Ocean Kayaking. For more information about the company, see www.oceankayaking.com .

Mixed Costs

A mixed cost contains both variable and fixed cost elements. Mixed costs are also known

as semivariable costs. To continue the Nooksack Expeditions example, the company

incurs a mixed cost called fees paid to the state. It includes a license fee of $25,000 per

year plus $3 per rafting party paid to the state’s Department of Natural Resources. If the

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34 Chapter 2

company runs 1,000 rafting parties this year, then the total fees paid to the state would

be $28,000, made up of $25,000 in fixed cost plus $3,000 in variable cost. Exhibit 2–6

depicts the behavior of this mixed cost.

Even if Nooksack fails to attract any customers, the company will still have to pay

the license fee of $25,000. This is why the cost line in Exhibit 2–6 intersects the vertical

cost axis at the $25,000 point. For each rafting party the company organizes, the total cost

of the state fees will increase by $3. Therefore, the total cost line slopes upward as the

variable cost of $3 per party is added to the fixed cost of $25,000 per year.

Because the mixed cost in Exhibit 2–6 is represented by a straight line, the following

equation for a straight line can be used to express the relationship between a mixed cost

and the level of activity:

Y = a + bX

In this equation,

Y = The total mixed cost

a = The total fixed cost (the vertical intercept of the line)

b = The variable cost per unit of activity (the slope of the line)

X = The level of activity

Because the variable cost per unit equals the slope of the straight line, the steeper the

slope, the higher the variable cost per unit.

In the case of the state fees paid by Nooksack Expeditions, the equation is written as

follows:

E X H I B I T 2 – 6 Mixed Cost Behavior

$30,000

$29,000

$28,000

$27,000

$26,000

$25,000

$00 1,000500

Number of rafting parties

Cos

t of s

tate

lice

nse

fees

Variablecost

element

Fixedcost

element

Intercept = Total fixed cost

Slope = Variable cost per unit of activity

Y = $25,000 + $3.00X

Total Total Variable Activity

mixed fixed cost per level

cost cost unit of

activity

This equation makes it easy to calculate the total mixed cost for any level of activity

within the relevant range. For example, suppose that the company expects to organize

800 rafting parties in the next year. The total state fees would be calculated as follows:

Y = $25,000 + ($3.00 per rafting party × 800 rafting parties)

= $27,400


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The Analysis of Mixed Costs

Mixed costs are very common. For example, the overall cost of providing X-ray services

to patients at the Harvard Medical School Hospital is a mixed cost. The costs of equipment

depreciation and radiologists’ and technicians’ salaries are fixed, but the costs of X-ray film,

power, and supplies are variable. At Southwest Airlines , maintenance costs are a mixed cost.

The company incurs fixed costs for renting maintenance facilities and for keeping skilled

mechanics on the payroll, but the costs of replacement parts, lubricating oils, tires, and so

forth, are variable with respect to how often and how far the company’s aircraft are flown.

The fixed portion of a mixed cost represents the minimum cost of having a service

ready and available for use. The variable portion represents the cost incurred for actual consumption of the service, thus it varies in proportion to the amount of service actually

consumed.

Managers can use a variety of methods to estimate the fixed and variable compo-

nents of a mixed cost such as account analysis, the engineering approach, the high-low method, and least-squares regression analysis. In account analysis , an account is classi-

fied as either variable or fixed based on the analyst’s prior knowledge of how the cost in

the account behaves. For example, direct materials would be classified as variable and a

building lease cost would be classified as fixed because of the nature of those costs. The

engineering approach to cost analysis involves a detailed analysis of what cost behavior

should be, based on an industrial engineer’s evaluation of the production methods to be

used, the materials specifications, labor requirements, equipment usage, production effi-

ciency, power consumption, and so on.

The high-low and least-squares regression methods estimate the fixed and variable

elements of a mixed cost by analyzing past records of cost and activity data. We will use

an example from Brentline Hospital to illustrate the high-low method calculations and

to compare the resulting high-low method cost estimates to those obtained using least-

squares regression. Appendix 2A demonstrates how to use Microsoft Excel to perform

least-squares regression computations.

Diagnosing Cost Behavior with a Scattergraph Plot

Assume that Brentline Hospital is interested in predicting future monthly maintenance

costs for budgeting purposes. The senior management team believes that maintenance

cost is a mixed cost and that the variable portion of this cost is driven by the number of

patient-days. Each day a patient is in the hospital counts as one patient-day. The hospital’s

chief financial officer gathered the following data for the most recent seven-month period:

LEARNING OBJECTIVE 4 Analyze a mixed cost using a scattergraph plot and the high-low method.

Activity Level: MaintenanceMonth Patient-Days Cost Incurred

January . . . . . . . . 5,600 $7,900February . . . . . . 7,100 $8,500March . . . . . . . . . 5,000 $7,400April . . . . . . . . . . . 6,500 $8,200May . . . . . . . . . . 7,300 $9,100June . . . . . . . . . . 8,000 $9,800July . . . . . . . . . . 6,200 $7,800

The first step in applying the high-low method or the least-squares regression method

is to diagnose cost behavior with a scattergraph plot. The scattergraph plot of mainte-

nance costs versus patient-days at Brentline Hospital is shown in Exhibit 2–7 . Two things

should be noted about this scattergraph:

1. The total maintenance cost, Y, is plotted on the vertical axis. Cost is known as the

dependent variable because the amount of cost incurred during a period depends on


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36 Chapter 2

the level of activity for the period. (That is, as the level of activity increases, total cost

will also ordinarily increase.)

2. The activity, X (patient-days in this case), is plotted on the horizontal axis. Activity is

known as the independent variable because it causes variations in the cost.

From the scattergraph plot, it is evident that maintenance costs do increase with the num-

ber of patient-days in an approximately linear fashion. In other words, the points lie

more or less along a straight line that slopes upward and to the right. Cost behavior is

considered linear whenever a straight line is a reasonable approximation for the relation

between cost and activity.

Plotting the data on a scattergraph is an essential diagnostic step that should be per-

formed before performing the high-low method or least-squares regression calculations.

If the scattergraph plot reveals linear cost behavior, then it makes sense to perform the

high-low or least-squares regression calculations to separate the mixed cost into its vari-

able and fixed components. If the scattergraph plot does not depict linear cost behavior,

then it makes no sense to proceed any further in analyzing the data.

For example, suppose that Brentline Hospital’s management is interested in the rela-

tion between the hospital’s telephone costs and patient-days. Patients are billed directly for

their use of telephones, so those costs do not appear on the hospital’s cost records. Rather,

management is concerned about the charges for the staff’s use of telephones. The data for

this cost are plotted in Exhibit 2–8 . It is evident from the nonlinear data pattern that while

the telephone costs do vary from month to month, they are not related to patient-days.

Something other than patient-days is driving the telephone bills. Therefore, it would not

make sense to analyze this cost any further by attempting to estimate a variable cost per

patient-day for telephone costs. Plotting the data helps diagnose such situations.

Plotting the data on a scattergraph can also reveal nonlinear cost behavior patterns

that warrant further data analysis. For example, assume that Brentline Hospital’s managers

were interested in the relation between total nursing wages and the number of patient-days

at the hospital. The permanent, full-time nursing staff can handle up to 7,000 patient-days

in a month. Beyond that level of activity, part-time nurses must be called in to help out.

The cost and activity data for nurses are plotted on the scattergraph in Exhibit 2–9 (see

page 38). Looking at that scattergraph, it is evident that two straight lines would do a much

better job of fitting the data than a single straight line. Up to 7,000 patient-days, total nurs-

ing wages are essentially a fixed cost. Above 7,000 patient-days, total nursing wages are a

E X H I B I T 2 – 7 Scattergraph Method of Cost Analysis

$12,000Plotting the Data

$10,000

$8,000

$6,000

$4,000

$2,000

$0

Mai

nten

ance

cos

t

0 2,000 4,000 6,000 8,000 10,000

Patient-days

Y

X


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E X H I B I T 2 – 8 A Diagnostic Scattergraph Plot $16,000

$14,000

$12,000

$10,000

$8,000

$6,000

$4,000

$2,000

$0

Tel

epho

ne c

osts

0 2,000 4,000 6,000 8,000 10,000

Patient-days

Y

X

mixed cost. This happens because, as previously mentioned, the permanent, full-time nurs-

ing staff can handle up to 7,000 patient-days in a month. Above that level, part-time nurses

are called in to help, which adds to the cost. Consequently, two straight lines (and two

equations) would be used to represent total nursing wages—one for the relevant range of

5,600 to 7,000 patient-days and one for the relevant range of 7,000 to 8,000 patient-days.

I N B U S I N E S S OPERATIONS DRIVE COSTS White Grizzly Adventures is a snowcat skiing and snowboarding company in Meadow Creek, British Columbia, that is owned and operated by Brad and Carole Karafil. The company shuttles 12 guests to the top of the company’s steep and tree-covered terrain in a modified snowcat. Guests stay as a group at the company’s lodge for a fixed number of days and are provided healthy gourmet meals.

Brad and Carole must decide each year when snowcat operations will begin in December and when they will end in early spring, and how many nonoperating days to schedule between groups of guests for maintenance and rest. These decisions affect a variety of costs. Examples of costs that are fixed and variable with respect to the number of days of operation at White Grizzly include:

Source: Brad and Carole Karafil, owners and operators of White Grizzly Adventures, www.whitegrizzly.com.

Cost Behavior—Fixed or Variable with Respect to Cost Days of Operation

Property taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FixedSummer road maintenance and tree clearing . . . . . . . . FixedLodge depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FixedSnowcat operator and guides . . . . . . . . . . . . . . . . . . . . VariableCooks and lodge help . . . . . . . . . . . . . . . . . . . . . . . . . . . VariableSnowcat depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . VariableSnowcat fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VariableFood* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable

*The costs of food served to guests theoretically depend on the number of guests in residence. However, the lodge is almost always fi lled to its capacity of 12 persons when the snowcat operation is running, so food costs can be consid-ered to be driven by the days of operation.


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38 Chapter 2

The examples in Exhibits 2–8 and 2–9 illustrate why preparing a scattergraph plot is

an essential diagnostic step that should not be overlooked.

The High-Low Method

Assuming that the scattergraph plot indicates a linear relation between cost and activity,

the fixed and variable cost elements of a mixed cost can be estimated using the high-low method or the least-squares regression method. The high-low method is based on the

rise-over-run formula for the slope of a straight line. As previously discussed, if the rela-

tion between cost and activity can be represented by a straight line, then the slope of the

$180,000

$160,000

$140,000

$120,000

$100,000

$80,000

$60,000

$40,000

$20,000

$0

Tot

al n

ursi

ng w

ages

0 2,000 4,000 6,000 8,000 10,000

Patient-days

Relevant range Relevant range

Y

X

$180,000

$160,000

$140,000

$120,000

$100,000

$80,000

$60,000

$40,000

$20,000

$0

Tot

al n

ursi

ng w

ages

0 2,000 4,000 6,000 8,000 10,000

Patient-days

Y

X

E X H I B I T 2 – 9 More than One Relevant Range


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straight line is equal to the variable cost per unit of activity. Consequently, the following

formula can be used to estimate the variable cost:

Variable cost = Slope of the line = Rise ____ Run

= Y 2 − Y 1 _______ X 2 − X 1

To analyze mixed costs with the high-low method , begin by identifying the period with the

lowest level of activity and the period with the highest level of activity. The period with

the lowest activity is selected as the first point in the above formula and the period with the

highest activity is selected as the second point. Consequently, the formula becomes:

Variable cost = Y 2 − Y 1

_______

X 2 − X 1 =

Cost at the high activity level − Cost at the low activity level _________________________________________________

High activity level − Low activity level

or

Variable cost = Change in cost

_______________ Change in activity

Therefore, when the high-low method is used, the variable cost is estimated by dividing

the difference in cost between the high and low levels of activity by the change in activity

between those two points.

To return to the Brentline Hospital example, using the high-low method, we first

identify the periods with the highest and lowest activity —in this case, June and March.

We then use the activity and cost data from these two periods to estimate the variable cost

component as follows:

Variable cost = Change in cost

_______________ Change in activity

= $2,400 _______________

3,000 patient-days = $0.80 per patient-day

Having determined that the variable maintenance cost is 80 cents per patient-day, we

can now determine the amount of fixed cost. This is done by taking the total cost at either

the high or the low activity level and deducting the variable cost element. In the computa-

tion below, total cost at the high activity level is used in computing the fixed cost element:

Fixed cost element = Total cost − Variable cost element

= $9,800 − ($0.80 per patient-day × 8,000 patient-days)

= $3,400

Both the variable and fixed cost elements have now been isolated. The cost of main-

tenance can be expressed as $3,400 per month plus 80 cents per patient-day or as:

Y = $3,400 + $0.80X

Total Total

maintenance patient-days

cost

The data used in this illustration are shown graphically in Exhibit 2–10 . Notice that a

straight line has been drawn through the points corresponding to the low and high levels

Maintenance Patient-Days Cost Incurred

High activity level (June) . . . . . . . . 8,000 $9,800Low activity level (March) . . . . . . . 5,000 7,400Change . . . . . . . . . . . . . . . . . . . . . . 3,000 $2,400

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40 Chapter 2

of activity. In essence, that is what the high-low method does—it draws a straight line

through those two points.

Sometimes the high and low levels of activity don’t coincide with the high and low

amounts of cost. For example, the period that has the highest level of activity may not

have the highest amount of cost. Nevertheless, the costs at the highest and lowest levels of

activity are always used to analyze a mixed cost under the high-low method. The reason is

that the analyst would like to use data that reflect the greatest possible variation in activity.

The high-low method is very simple to apply, but it suffers from a major (and some-

times critical) defect—it utilizes only two data points. Generally, two data points are not

enough to produce accurate results. Additionally, the periods with the highest and lowest

activity tend to be unusual. A cost formula that is estimated solely using data from these

unusual periods may misrepresent the true cost behavior during normal periods. Such a

distortion is evident in Exhibit 2–10 . The straight line should probably be shifted down

somewhat so that it is closer to more of the data points. For these reasons, least-squares

regression will generally be more accurate than the high-low method.

The Least-Squares Regression Method

The least-squares regression method , unlike the high-low method, uses all of the data

to separate a mixed cost into its fixed and variable components. A regression line of

the form Y = a + bX is fitted to the data, where a represents the total fixed cost and

b represents the variable cost per unit of activity. The basic idea underlying the least-

squares regression method is illustrated in Exhibit 2–11 using hypothetical data points.

Notice from the exhibit that the deviations from the plotted points to the regression line

are measured vertically on the graph. These vertical deviations are called the regression

errors. There is nothing mysterious about the least-squares regression method. It simply

computes the regression line that minimizes the sum of these squared errors. The formu-

las that accomplish this are fairly complex and involve numerous calculations, but the

principle is simple.

E X H I B I T 2 – 1 0 High-Low Method of Cost Analysis

$12,000

$10,000

$8,000

$6,000

$4,000

$2,000

$0

Mai

nten

ance

cos

t

0 2,000 4,000 6,000 8,000 10,000Patient-days

Y

X

Slope =Variable cost:$0.80 perpatient-day

Intercept =Fixed cost:$3,400

Point relating to thehigh activity level

Point relating to thelow activity level

ActivityLevel

HighLow

Patient-Days

8,0005,000

MaintenanceCost

$9,800$7,400


Confi rming Pages


Fortunately, computers are adept at carrying out the computations required by the

least-squares regression formulas. The data—the observed values of X and Y —are

entered into the computer, and software does the rest. In the case of the Brentline Hos-

pital maintenance cost data, a statistical software package on a personal computer can

calculate the following least-squares regression estimates of the total fixed cost ( a ) and

the variable cost per unit of activity ( b ):

a = $3,431

b = $0.759

Therefore, using the least-squares regression method, the fixed element of the main-

tenance cost is $3,431 per month and the variable portion is 75.9 cents per patient-day.

In terms of the linear equation Y = a + bX, the cost formula can be written as

Y = $3,431 + $0.759X

where activity ( X ) is expressed in patient-days.

Appendix 2A discusses how to use Microsoft Excel to perform least-squares regres-

sion calculations. For now, you only need to understand that least-squares regression anal-

ysis generally provides more accurate cost estimates than the high-low method because,

rather than relying on just two data points, it uses all of the data points to fit a line that

minimizes the sum of the squared errors. The table below compares Brentline Hospital’s

cost estimates using the high-low method and the least-squares regression method:

E X H I B I T 2 – 1 1 The Concept of Least-Squares Regression

Error Regression lineY = a + bX

Y

XLevel of activity

Actual YEstimated Y

Cos

t

High-Low Method

Least-Squares Regression

Method

Variable cost estimate per patient-day . . . . . . . . . $0.800 $0.759Fixed cost estimate per month . . . . . . . . . . . . . . . $3,400 $3,431

When the least-squares regression method is used to create a straight line that mini-

mizes the sum of the squared errors, it results in a Y -intercept that is $31 higher than the

Y -intercept derived using the high-low method. It also decreases the slope of the straight

line resulting in a lower variable cost estimate of $0.759 per patient-day rather than $0.80

per patient-day as derived using the high-low method.


Cost Behavior Analysis and Justifications of Segmented Reporting

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