Chapter 3 - Texas A&M University–Corpus Christifaculty.tamucc.edu/shall/2302/Chapter Outlines/chap005.doc · Web viewCost Behavior: Analysis and Use Learning Objectives LO1. Understand

Chapter 5

Cost Behavior: Analysis and Use

Learning Objectives

LO1. Understand how fixed and variable costs behave and how to use them to predict costs.LO2. Use a scattergraph plot to diagnose cost behavior.LO3. Analyze a mixed cost using the high-low method.LO4. Prepare an income statement using the contribution format.LO5. (Appendix 5A) Analyze a mixed cost using the least-squares regression method.

New in this Edition• Many new In Business boxes have been added.• The end-of-chapter materials have been expanded by adding several new shorter exercises.

Chapter Overview

A. Types of Cost Behavior Patterns. (Exercises 5-1, 5-6, 5-7, 5-8, 5-11, and 5-12.) At least three cost behavior patterns—variable, fixed, and mixed—are found in most organizations. Of course, many other types of cost behavior patterns exist, but these three patterns are fairly common and the mixed cost model can be used to provide approximations to more complex cost behavior patterns within a relevant range. It is important for managers to understand the behavior of each type of cost.

1. Variable Costs. The total amount of a variable cost varies in direct proportion to changes in the activity level. When expressed on a per unit basis, variable costs are constant. Examples of costs that are normally variable with respect to output volume are listed in Exhibit 5-2. Be careful to point out to students that some of these costs may be fixed in some organizations. This is particularly true of direct labor and other employee wages and salaries that may be effectively fixed due to labor laws in a country, custom, labor contracts, or the organization’s personnel policies. Exhibit 5-8 in the text points out that in practice there is a wide variation in how some of these costs are classified by individual companies.

a. Activity base (cost driver). For a cost to be variable, it must be variable with respect to some activity base. An activity base is a measure of whatever causes the incurrence of a variable cost. Some of the most common activity bases are machine-hours, units produced, and units sold. A measure of activity should be used to allocate a cost for decision-making purposes only if it actually causes the cost.

b. True variable and step-variable costs. Some variable costs, such as direct materials, vary in direct proportion to the level of activity. These costs are called true variable

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costs. A cost that is obtainable only in large chunks and that increases or decreases in response to fairly wide changes in the activity level is known as a step-variable cost. For example, direct labor may be a step-variable cost when workers are only hired on a full-time basis. The difference between a true variable and a step-variable cost is illustrated in Exhibit 5-3 in the text.

c. In reality, many costs are curvilinear. Most frequently, costs increase less than proportionately with activity. Nevertheless, within any given narrow band of activity even a curvilinear cost function is approximately linear. This narrow band of activity within which a particular straight line is a reasonable approximation to the true underlying cost function is called its relevant range.

• Thus, within the relevant range, variable cost per unit can be assumed to be constant. Exhibit 5-4 in the text illustrates a curvilinear cost and the notion of the relevant range.

• The notion of the relevant range often causes confusion. Some individuals refer to the relevant range as the range of activity within which the company expects to operate or has operated in the recent past. That is not what we mean by the relevant range. The relevant range, as we use the term, is the range of activity within which a particular straight line provides a reasonable approximation to the real underlying cost function.

2. Fixed Costs. A fixed cost remains constant in total dollar amount within the relevant range. Since fixed costs remain constant in total, the amount of cost computed on a per unit basis becomes smaller as the number of units produced increases. Care must be exercised in interpreting fixed costs that have been expressed on a per unit basis; they should not be misinterpreted as variable costs.

a. For planning purposes, fixed costs can be viewed as either committed or discretionary.

• Committed fixed costs. Committed fixed costs relate to investment in buildings, equipment, and the basic organizational structure of a company. Committed fixed costs are long-term and can’t be significantly reduced even for a short period of time without seriously impairing long-run goals.

• Discretionary fixed costs. Discretionary fixed costs are those that management

adjusts periodically. Examples of discretionary fixed costs include advertising, research, and management development programs. The planning horizon for discretionary fixed costs is fairly short—usually a single year. Management may be able to adjust these fixed costs as circumstances change.

b. The relevant range for a fixed cost is that range of activity over which total fixed cost does not change. Exhibit 5-6 in the text illustrates this idea.

3. Mixed Costs. A mixed cost contains both variable and fixed cost elements. Many costs are mixed and can be expressed in terms of the cost formula Y = a + bX, where Y is the total estimated cost, a is the estimated total fixed cost, b is the estimated variable cost per unit of activity, and X is the amount of activity. Even when the underlying cost is not linear, this formula can provide a reasonable approximation to the underlying cost function within the relevant range.

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4. Classification of costs. A cost that is considered variable in one organization may be considered fixed in another due, for example, to differing employment policies. Exhibit 5-8 in the text shows that there is a lot of variation in how companies classify costs in terms of behavior.

B. Analysis of Mixed Costs. For planning and control purposes, mixed costs should be broken down into variable and fixed components. A number of methods can be used to analyze mixed costs. Account analysis and the engineering approach are mentioned briefly in this chapter and are covered in more detail in later chapters. This chapter discusses in more depth three techniques for analyzing past records of cost and activity—the scattergraph method, the high-low method, and least-squares regression.

1. The Scattergraph Method. (Exercises 5-2, 5-9, and 5-10.)

a. The data should be plotted no matter what method is ultimately used to estimate fixed and variable costs. A graph is constructed with cost on the vertical axis and activity on the horizontal axis. Costs at various levels of activity are then plotted on the graph. This plot will often provide important insights concerning the underlying relationship and can help in identifying nonlinearities and outliers (unusual points) that should be ignored.

b. While this is not ordinarily done in practice, a line can be fitted to the plotted points by eye with a straightedge. The line should be placed so that approximately equal numbers of points fall above and below it. While not strictly necessary, in the text and in problems we always draw the line through one of the points to simplify calculations. This line can then be used to derive what we call “quick-and-dirty” estimates of the fixed and variable costs. The fixed cost can be estimated by the vertical intercept. The variable cost per unit can be estimated by computing the slope of the line.

2. The High-Low Method. (Exercises 5-2, 5-4, 5-7, 5-8, 5-9, and 5-11.) The high-low method of analyzing mixed costs focuses exclusively on the high and low levels of activity. The difference in cost observed at these two extremes is divided by the change in activity to estimate the variable cost per unit of activity.

A major defect of the high-low method is that it utilizes only two points and ignores all of the other data. Generally, two points are not enough to produce accurate results. Moreover, the periods in which the high and low activity levels occur are often not typical of most periods.

3. The Least-Squares Regression Method. (Exercises 5-3 and 5-12.) Using mathematical formulas, the least-squares regression method fits a regression line that minimizes the sum of the squared errors. Exhibit 5-13 can be used as a basis for discussing the theory of least-squares regression.

a. We don’t go into the details of the computation of the least-squares regression estimates since computer software is widely used for performing this chore. The appendix to the chapter shows how to use Excel to do the necessary calculations.

b. In addition to estimates of the slope (variable cost per unit) and the intercept (total fixed cost), least-squares regression software can produce a variety of informative

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statistics. One of the most informative is the R2, which is a measure of the goodness of fit of the regression line. It tells us the percentage of the variation in the dependent variable (cost) that is explained by variation in the independent variable (activity). We do not show in the text how the R2 is computed, but you may want to discuss its interpretation with students.

c. Multiple regression analysis should be used when the cost is caused by more than one factor.

C. The Contribution Format. (Exercises 5-5 and 5-6.) Two major approaches can be used to prepare an income statement. The difference between these two approaches centers on the way in which costs are organized.

1. The Traditional Approach. The traditional approach to the income statement organizes data in a functional format, based on the functions of production, administration, and sales. The emphasis is on the purposes for which the costs were incurred. No attempt is made to identify the behavior of costs included under each functional heading. This approach is used to prepare income statements for external reporting purposes.

2. The Contribution Approach. The contribution approach to the income statement organizes costs by behavior, rather than by function.

a. The contribution approach separates costs into fixed and variable categories. Variable expenses are deducted to obtain the contribution margin. Fixed expenses are then deducted from the contribution margin to obtain net operating income.

b. The contribution approach to the income statement makes it much easier for managers to understand the relations between volume and expenses, and volume and profits. Variable and fixed costs are not lumped together. Since planning and decision-making often involve changes in the level of activity, contribution income statements can be very useful. Unfortunately, the contribution approach is seldom used in practice.

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Assignment Materials

Assignment TopicLevel of

DifficultySuggested

TimeExercise 5-1 Fixed and variable cost behavior Basic 15 min.Exercise 5-2 High-low method; scattergraph analysis.............................................Basic 45 min.Exercise 5-3 (Appendix 5A) Least-squares regression............................................Basic 30 min.Exercise 5-4 High-low method................................................................................Basic 20 min.Exercise 5-5 Contribution format income statement...............................................Basic 20 min.Exercise 5-6 Cost behavior; contribution format income statement........................Basic 20 min.Exercise 5-7 High-low method; predicting cost......................................................Basic 30 min.Exercise 5-8 High-low method; predicting cost .....................................................Basic 20 min.Exercise 5-9 Scattergraph analysis; high-low method.............................................Basic 30 min.Exercise 5-10 Scattergraph analysis..........................................................................Basic 30 min.Exercise 5-11 Cost behavior; high-low method.........................................................Basic 20 min.Exercise 5-12 (Appendix 5A) Least-squares regression............................................Basic 30 min.Problem 5-13 Cost behavior; high-low method; contribution income

statement........................................................................................Basic 45 min.Problem 5-14 Contribution format versus traditional income statement...................Basic 45 min.Problem 5-15 (Appendix 5A) Least-squares regression; scattergraph; cost

behavior .........................................................................................Basic 45 min.Problem 5-16 Identifying cost behavior patterns.......................................................Medium 30 min.Problem 5-17 High-low and scattergraph analysis....................................................Medium 45 min.Problem 5-18 (Appendix 5A) Least-squares regression method...............................Medium 30 min.Problem 5-19 Scattergraph analysis..........................................................................Medium 30 min.Problem 5-20 (Appendix 5A) Least-squares regression method...............................Medium 30 min.Problem 5-21 (Appendix 5A) Least-squares regression analysis;

contribution income statement ......................................................Medium 45 min.Problem 5-22 High-low method; cost of goods manufactured..................................Difficult 45 min.Problem 5-23 High-low method; predicting cost......................................................Difficult 45 min.Problem 5-24 High-low method; predicting cost......................................................Difficult 45 min.Case 5-25 (Appendix 5A) Analysis of mixed costs, job-cost system,

and activity-based costing..............................................................Difficult 90 min.Case 5-26 Scattergraph analysis; selection of an activity base............................Medium 45 min.Case 5-27 Analysis of mixed costs in a pricing decision.....................................Difficult 90 min.Case 5-28 (Appendix 5A) Mixed cost analysis by three methods.......................Difficult 90 min.

Essential Problems: Problem 5-13, Problem 5-17 or Problem 5-19, Problem 5-23 or Problem 5-24

Supplementary Problems: Problem 5-14, Problem 5-16, Problem 5-22, Case 5-25, Case 5-26, Case 5-27, Case 5-28

Appendix 5A Essential Problems: Problem 5-15Appendix 5A Supplementary Problems: Problem 5-18, Problem 5-20, Problem 5-21

Linked problems and exercises:Exercise 5-3 should be assigned in conjunction with Exercise 5-2Exercise 5-9 should be assigned in conjunction with Exercise 5-8Problem 5-18 should be assigned in conjunction with Problem 5-17

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Chapter 5Lecture Notes

Helpful Hint: The McGraw-Hill/Irwin Managerial/Cost Accounting video library does not contain a segment that relates to Chapter 5.

Chapter theme: Managers who understand how costs behave are better able to predict costs and make decisions under various circumstances. This chapter explores the meaning of fixed, variable and mixed costs (the relative proportions of which define an organization’s cost structure). It also introduces a new income statement called the contribution approach.

I. Types of cost behavior patterns

A. Variable costs

i. A variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level.

1. An activity base (also called a cost driver) is a measure of what causes the incurrence of variable costs. As the level of the activity base increases, the variable cost increases proportionally.

a. Units produced (or sold) is not the only activity base within companies. A cost can be considered variable if it varies with activity bases such as

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miles driven, machine hours, or labor hours.

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2. As an example of an activity base, consider your total long distance telephone bill. The activity base is the number of minutes that you talk.

ii. Variable costs remain constant if expressed on a per unit basis.

1. Referring to the telephone example, the cost per minute talked is constant (e.g., 10 cents per minute)

iii. Extent of variable costs

1. The proportion of variable costs differs across organizations. For example:

a. A public utility like Florida Power and Light, with large investments in equipment, will tend to have fewer variable costs.

b. A manufacturing company like Black and Decker will often have many variable costs associated with the manufacture and distribution of its products to customers.

c. A merchandising company like Wal-Mart will usually have a high proportion of variable costs such as the cost of merchandise purchased for resale.

d. Some service companies, such as restaurants, have a high proportion of variable costs due to their raw

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material costs. Other service companies, such as an architectural firm, have a high proportion of fixed

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costs in the form of highly trained salaried employees.

iv. Common examples of variable costs

1. Merchandising companies cost of goods sold

2. Manufacturing companies direct materials, direct labor, and variable overhead.

3. Merchandising and manufacturing companies commissions, shipping costs, and clerical costs such as invoicing.

4. Service companies supplies, travel, and clerical.

Helpful Hint: Students tend to assume that a certain type of cost is always variable or fixed. They should examine the facts of each situation before deciding whether a cost is fixed or variable. For example, a company’s employment policy may determine whether direct labor costs are fixed or variable with respect to volume of output.

B. True variable versus step-variable costs

i. True variable costs the amount used during the period varies in direct proportion to the activity level.

1. The long distance phone bill was one example of a true variable cost.

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2. Direct material is another example of a cost that behaves in a true variable pattern.

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a. Direct materials purchased but not used can be stored and carried forward to the next period as inventory.

ii. Step-variable costs A resource that is obtainable only in large chunks and whose costs change only in response to fairly wide changes in activity.

1. For example, maintenance workers are often considered to be a variable cost, but this labor cost does not behave as a true variable cost.

a. Small changes in the level of production are not likely to have any effect on the number of maintenance workers employed.

b. Only fairly wide changes in the activity level will cause a change in the number of maintenance workers employed.

i. Maintenance workers are obtainable only in large chunks of a whole person who is capable of working approximately 2,000 hours a year.

“In Business Insights”Step-variable costs can change for reasons that have nothing to do with changes in the activity level. For example:

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“Coping with the Fallout from September 11” (page 186)

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Filterfresh is a company that services coffee machines located in commercial offices.

Post September 11, heightened security clearance measures at customer locations have added about one hour per day to each deliveryman’s route.

This has required Filterfresh to hire 24 more delivery people to do the same work it did prior to September 11.

C. The linearity assumption and the relevant range

i. Economists correctly point out that many costs that accountants classify as variable costs actually behave in a curvilinear fashion.

ii. Nonetheless, within a narrow band of activity known as the relevant range, a curvilinear cost can be satisfactorily approximated by a straight line.

1. The relevant range is that range of activity within which the assumptions made about cost behavior are valid.

Helpful Hint: Slide 13 can be tied in with economics courses students have taken. Ask what happens to average costs when the cost curve bends downward and what economists call this part of the curve. Average costs are falling and this is roughly equivalent to what economists call “increasing returns to scale.” You can repeat the same question for the part of the curve that bends upward.

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D. Fixed costs

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i. A fixed cost is a cost whose total dollar amount remains constant as the activity level changes.

1. For example, your monthly basic telephone bill is probably fixed and does not change when you make more local calls.

ii. Average fixed costs per unit decrease as the activity level increases.

1. For example, the fixed cost per local call decreases as more local calls are made.

E. Types of fixed costs

i. Committed fixed costs

1. These costs are long-term in nature (i.e., greater than one year).

2. These costs cannot be significantly reduced even for short periods of time without seriously impairing the profitability or long-run goals of the organization.

a. Examples of committed-fixed costs include depreciation on buildings and equipment, and real estate taxes.

“In Business Insights”Committed fixed costs may be more flexible than they would appear at first glance. For example:

“Sharing Office Space to Reduce Committed Fixed Costs” (page 191)

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Doctors in private practice have been under enormous pressure in recent years to cut costs.

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Dr. Edward Betz of California reduced the committed fixed costs of maintaining his office by letting a urologist use the office on Wednesday afternoons and Friday mornings for $1,500 per month.

Dr. Betz uses these times to work on paperwork at home. He also makes up for lost time by treating patients on Saturdays.

ii. Discretionary fixed costs

1. These costs usually arise from annual decisions by management to spend in certain fixed cost areas.

2. These costs can be cut for short periods of time with minimal damage to the long-run goals of the organization.

a. Examples of discretionary fixed costs include advertising and research and development.

3. A cost may be discretionary or committed depending upon management’s strategy.

a. For example, some construction companies may layoff workers during months with minimal customer demand. However, other construction companies may opt to retain their workers all year.

“In Business Insights”The extent of a company’s discretionary fixed costs is a function of management choices. For example:

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“Cost Structure: A Management Choice” (page 184)

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Nucor Steel is the most successful U.S. steel company of recent years due in large part to its cost-efficiency.

Nucor treats all employees alike. There are no management dining rooms, company yachts or airplanes, no first-class travel for executives, and no support staff to pamper the upper echelons.

All of these management actions serve to lower discretionary fixed costs for Nucor.

In addition, Nucor relies upon fewer layers of management. In fact, although Nucor is the largest steel company in the U.S., its headquarters employs only 20 people.

iii. The trend toward fixed costs

1. The trend in many industries is toward greater fixed costs relative to variable costs. For example:

a. H&R Block employees used to fill out tax returns for customers by hand. Now, computer software is used to complete tax returns.

b. Safeway and Kroger employees used to key-in prices by hand on cash registers. Now, barcode readers enter price and other product information automatically.

c. As machines take over many mundane tasks previously performed by humans, “knowledge workers” are demanded for their minds rather than their muscles.

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i. Knowledge workers tend to be salaried, highly-trained and difficult to replace; consequently,

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the cost of compensating these valued employees in relatively fixed rather than variable.

“In Business Insights”By making investments in technology many internet companies have created radically different cost structures from their “bricks and mortar” counterparts. For example:

“Selling Online” (page 185) Onsale, an internet auctioneer of discontinued

computers and House of Fabrics, a traditional retailer, each has roughly the same revenue of about $250 million per year.

However, House of Fabrics, with 5,500 employees, has revenue per employee of about $90,000. At Onsale, with only 200 employees, the figure is $1.18 million per employee.

Onsale relies upon investments in technology to reduce its labor cost.

iv. Is labor a variable or a fixed cost?

1. The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom. For example:

a. In France, Germany, China, and Japan management has little flexibility in adjusting the size of the

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labor force; hence, labor costs are more fixed in nature.

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“In Business Insights”Survey research supports the assertion that labor costs are viewed as more fixed in nature in certain countries. For example:

“Cost Behavior in the U.S. and Japan” (page 195) A total of 257 American and 40 Japanese

manufacturing companies responded to a questionnaire concerning their management practices.

The findings indicate that approximately 40% of the Japanese companies surveyed viewed production labor as a fixed cost, while approximately 10% of U.S. companies surveyed viewed production labor as a fixed cost.

b. In the United States and the United Kingdom, management typically has much greater latitude; hence, labor costs are more variable in nature.

“In Business Insights”Regulatory requirements can influence the fixed versus variable nature of labor costs in American companies. For example:

“The Regulatory Burden” (page 193) Peter Drucker claims that “the driving force

behind the steady growth of temps…is the growing burden of rules and regulations for employers.”

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According to the Small Business Administration, the owner of a small business spends up to a

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quarter of his or her time on employment-related paperwork. Furthermore, the cost of complying with government regulations is over $5,000 per employee per year.

This motivates small businesses to rely upon temporary workers, thus converting labor from a fixed cost to a variable cost.

2. Within countries managers can view labor costs differently depending upon their strategy. Nonetheless, most companies in the United States continue to view direct labor as a variable cost.

“In Business Insights”Managers can view labor costs differently depending upon their strategy. For example:

“A Twist on Fixed and Variable Costs” (page 191) Mission Controls designs and installs automation

systems for food and beverage manufacturers. When sales drop, the founders of this company slash

their own salaries rather than laying off workers. This makes their own salaries somewhat variable,

while the wages and salaries of workers act more like fixed costs. The payoff is a loyal and committed work force.

“Labor at Southwest Airlines” (page 192) Southwest Airlines is the most profitable airline in

the United States.

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Prior to stepping down as President and CEO of the airline in 2001, Herb Kelleher wrote “The thing that

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would disturb me the most to see after I’m no longer CEO is layoffs at Southwest. Nothing kills your company’s culture like layoffs.”

Because of Southwest Airline’s commitment to its employees, all wages and salaries are basically committed fixed costs.

F. Fixed costs and the relevant range

i. The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat.

1. For example, assume office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet.

2. Fixed costs would increase in a step fashion at a rate of $30,000 for each additional 1,000 square feet.

ii. While this step-function pattern appears similar to the idea of step-variable costs, there are two important differences between step-variable costs and fixed costs.

1. Step-variable costs can often be adjusted quickly as conditions change, whereas fixed costs cannot be changed easily.

2. The width of the steps for fixed costs is wider than the width of the steps for step-variable costs.

a. For example, a step-variable cost such as maintenance workers may have steps with a width of 40 hours a week.

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b. However, fixed costs may have steps that have a width of thousands or tens of thousands of hours of activity.

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Helpful Hint: Discuss with students that over a given level of production, certain costs, such as custodial salaries, would remain fixed. However, if activity increases to the point where a second shift is needed, custodial salaries would need to increase since activity is outside the relevant range.

Quick Check cost behavior patterns

G. Mixed costs (also called semivariable costs)

i. A mixed cost contains both variable and fixed cost elements.

1. For example, utility bills often contain fixed and variable cost components.

a. The fixed portion of the utility bill is constant regardless of kilowatt hours consumed. This cost represents the minimum cost that is incurred to have the service ready and available for use.

b. The variable portion of the bill varies in direct proportion to the consumption of kilowatt hours.

ii. An equation can be used to express the relationship between mixed costs and the level of the activity. This equation can be used to calculate what the total mixed cost would be for any level of activity.

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1. The equation is Y = a + bXa. Y = The total mixed cost.

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

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

d. X = The level of activity.

iii. For example, if your fixed monthly utility charge is $40, your variable cost is .03 per kilowatt hour, and your monthly activity level was 2,000 kilowatt hours, this equation can be used to calculate your total utility cost of $100.

II. The analysis of mixed costs

A. Account analysis and the engineering approach

i. In account analysis, each account under consideration is classified as variable or fixed based on the analyst’s prior knowledge about how costs behave.

1. This approach is limited in value in the sense that it glosses over the fact that some accounts may have both fixed and variable components.

ii. The engineering approach classifies costs based upon an industrial engineer’s evaluation of production methods, material specifications, labor requirements, equipment usage, power consumption, as so on.

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1. This approach is particularly useful when no past experience is available concerning activity and costs.

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B. The scattergraph plot (also called the quick-and-dirty method)

i. The first step when using this method to analyze a mixed cost is to plot the data on a scattergraph.

1. The cost, which is known as the dependent variable, is plotted on the Y axis.

2. The activity, which is known as the independent variable, is plotted on the X axis.

ii. The second step is to examine the dots on the scattergraph to see if they are linear, such that a straight line can be drawn that approximates the relation between cost and activity.

1. If the dots are not linear, do not analyze the data any further. Instead, search for another independent variable that bears a stronger linear relationship with the dependent variable.

iii. The third step is to draw a straight line where, roughly speaking, an equal number of points reside above and below the line. Make sure that the straight line goes through at least one data point on the scattergraph.

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iv. The fourth step is to identify the Y intercept.

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1. This intercept represents the estimated fixed cost portion of the mixed cost ($10,000 in this example).

v. The fifth step is to estimate the variable cost per unit of the activity.

1. Select one point on the scattergraph that intersects the straight line.

2. Determine the total cost and the total activity level at the chosen point.

3. Subtract the fixed costs from the total costs to arrive at the total variable costs for the chosen activity level.

4. Divide the total variable costs by the activity level at the chosen point. This is the variable cost per unit of activity.

5. Construct an equation that can be used to estimate total costs at any activity level.

C. The high-low method

i. This method can be used to analyze mixed costs if a scattergraph plot reveals a linear relationship between the X and Y variables. For illustrative purposes, assume the following information.

ii. The first step is to choose the data points pertaining to the highest and lowest activity levels (high = 800 units; low = 500 units).

1. Notice, this method relies upon two data points to estimate the fixed and variable

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portions of a mixed cost, as opposed to one data point with the scattergraph method.

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iii. The second step is to determine the total costs associated with the two chosen points (high = $9,800; low = $7,400).

Helpful Hint: Emphasize that the high and low points are identified by the level of activity and not by the level of the cost.

iv. The third step is to calculate the change in cost between the two data points ($2,400) and divide it by the change in activity level between the two data points (300 units).

1. The quotient represents an estimate of variable cost per unit of activity ($8.00 per unit).

v. The fourth step is to take the total cost at either activity level (in this case, $9,800) and deduct the variable cost component ($6,400). The residual represents the estimate of total fixed costs ($3,400).

1. The variable cost component ($6,400) is determined by multiplying the level of activity (800 units) by the estimated variable cost per unit of the activity ($8.00 per unit).

vi. The fifth step is to construct an equation that can be used to estimate the total cost at any activity level (Y = $3,400 + $8.00X).

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Quick Check the high-low method

D. The least-squares regression method

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i. This method can be used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables.

ii. This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost. This method is superior to the scattergraph plot method that relies upon only one data point and the high-low method that uses only two data points to estimate the fixed and variable cost components of a mixed cost.

iii. The basic goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors. The regression errors are the vertical deviations from the data points to the regression line.

iv. The formulas that are used for least-squares regression are complex. Fortunately, computers can perform the calculations quickly. The observed values of the X and Y variables are entered into the computer and the software does the rest.

1. The output from the regression analysis can be used to create an equation that enables you to estimate total costs at any activity level.

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v. The key statistic to look at when evaluating regression results is called R2, which is a measure of “goodness of fit.”

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1. The R2 quantifies the percentage of the variation in the dependent variable that is explained by variation in the independent variable. The R2 varies from 0% to 100%, and the higher the percentage the better.

vi. This example assumes that a single factor drives the variable cost component of a mixed cost. If more than one factor drives the variable cost component, multiple regression can be used to perform the mixed cost analysis.

“In Business Insights”Least-squares regression can be used by companies to estimate the fixed and variable components of mixed costs. For example:

“Managing Power Consumption” (page 205) The Tata Iron Steel Company is one of the largest

companies in India. Management used simple least-squares regression to

estimate the fixed and variable components of its power consumption.

Total power consumption was the dependent variable and tons of steel processed was the independent variable.

The regression model estimated the fixed power consumption per month and the variable power cost per ton of steel processed.

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E. Comparing results from the three methods

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i. The three methods just discussed provide slightly different estimates of the fixed and variable cost components of the mixed cost. This is to be expected because each method uses differing amounts of the data points to provide estimates. Least-squares regression provides the most accurate estimates because it uses all of the data points.

III. The contribution approach income statement

A. The contribution approach provides an income statement format geared directly to cost behavior, which has been the focus of discussion in this chapter.

i. This approach separates costs into fixed and variable categories. Sales variable costs = contribution margin. The contribution margin fixed costs = net operating income.

ii. This approach is used as an internal planning and decision making tool. For example, this approach is useful for:

1. Cost-volume-profit analysis (chapter 6).2. Budgeting (chapter 9).3. Segmented reporting of profit data (chapter

12).4. Special decisions such as pricing and make

or buy analysis (chapter 13).

iii. The contribution approach differs from the traditional approach illustrated in chapter 2.

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1. The traditional approach organizes costs in a functional format. Costs relating to production, administration, and sales are

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grouped together without regard to their cost behavior.

2. The traditional approach is used primarily for external reporting purposes.

Helpful Hint: The income statement from the annual report of a well-known local manufacturing firm can be used to illustrate the functional income statement. Ask if the various expense categories on the income statement contain both fixed and variable costs. Also ask how to estimate the increase in profit that would result from a 4% increase in sales using the functional statement. There is no way to do this with reasonable accuracy, since there is no way to tell on a functional income statement what costs would increase.

IV. Appendix 5A: least-squares regression using Microsoft Excel (Slide #50 is a title slide)

A. The data set

i. Assume that you have the following data set and that you wish to use Microsoft Excel to estimate the variable and fixed cost components of your total meals cost.

ii. You will need to calculate three key pieces of information: the estimated variable cost per unit (called the slope of the line), the estimated fixed cost (called the intercept), and the R2.

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1. To get these three pieces of information you will need three Excel functions, namely LINEST, INTERCEPT, and RSQ.

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iii. The first step within Excel is to place your cursor in cell F4 and press the = key. Click on the pull down menu and scroll down to “More Functions.”

iv. When the function box opens, click on “Statistical” and then on “LINEST.”

v. Enter the cell range for the cost amounts in the “Known_y’s” box. Enter the cell range for the quantity amounts in the “Known_x’s” box.

1. The slope, or estimated variable cost per unit, is identified on the screen as shown. Click “OK” to put this value on your spreadsheet.

vi. Return to the function box and click on “Statistical” and then on “INTERCEPT.”

1. The estimated fixed cost is identified on the screen as shown.

vii. Return to the function box and click on “Statistical” and then on “RSQ.”

1. The estimated R2 for your estimated cost function is identified on the screen as shown.

Chapter 5

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TM 5-1

AGENDA: COST BEHAVIOR

1. Variable cost behavior.2. Types of fixed costs: committed and discretionary.3. Behavior of fixed costs in total and on a unit basis.4. Mixed costs (combination of fixed and variable).5. Scattergraph plot of a mixed cost.6. High-low method of mixed cost analysis.7. Least-squares regression method of mixed cost analysis.8. Contribution income statement.

© The McGraw-Hill Companies, Inc., 2006. All rights reserved.

TM 5-2

VARIABLE COST BEHAVIOR

Many costs can be described as variable, fixed, or mixed.A variable cost changes in total in proportion to changes

in activity; a variable cost is constant on a per-unit basis.

EXAMPLE: Each bicycle requires one bicycle chain costing $8.

.

Tota

l Cos

t of B

icyc

le C

hain

s

Number of Bicycles Produced100

$800 • $8 perbicyclechain

00


TM 5-3

EXAMPLES OF COSTS THAT ARE NORMALLY VARIABLE WITH RESPECT TO OUTPUT VOLUME

Merchandising companyCosts of goods (merchandise) sold

Manufacturing companyManufacturing costs:

Prime costs:Direct materialsDirect labor*

Variable portion of manufacturing overhead:Indirect materialsLubricantsSuppliesPower

Both merchandising and manufacturing companiesSelling, general, and administrative costs:

CommissionsClerical costs, such as invoicingShipping costs

Service organizationsSupplies, travel, clerical

*Whether direct labor is fixed or variable will depend on the labor laws of the country, custom, and the company’s employment contracts and policies.


TM 5-4

FIXED COST BEHAVIORA fixed cost remains constant in total amount throughout

wide ranges of activity.EXAMPLE: Fashion photographer Lori Yang rents studio

spaces in a prestige location for $50,000 a year. She measures her company’s activity in terms of the number of photo sessions.

Cost

Number of Photo Sessions

Cost ofStudioRental

$50,000

500 1,000


TM 5-5

FIXED COST BEHAVIOR (cont’d)A fixed cost varies inversely with activity if expressed on a

per unit basis.

.

$0

$40

$80

$120

$160

$200

0 500 1,000Number of Photo Sessions

Aver

age

Cos

t Per

Pho

to S

essi

on fo

r Stu

dio

Ren

tal


TM 5-6

TYPES OF FIXED COSTS• Committed fixed costs relate to investment in plant,

equipment, and basic administrative structure. It is difficult to reduce these fixed costs in the short-term. Examples include:

• Depreciation on plant facilities.• Taxes on real estate.• Salaries of key operating personnel.

• Discretionary fixed costs arise from annual decisions by management to spend in certain areas. These costs can often be reduced in the short-term. Examples include:

• Advertising.• Research.• Public relations.• Management development programs.

TREND TOWARD FIXED COSTSThe trend is toward greater fixed costs relative to variable costs. The reasons for this trend are:

• Increased automation of business processes.• Shift from laborers paid by the hour to salaried

knowledge workers.


TM 5-7

MIXED COSTS

A mixed (or semi-variable) cost contains elements of both variable and fixed costs.

Example: Lori Yang leases an automated photo developer for $2,500 per year plus 2¢ per photo developed.

.

Photos Developed10,0000

$0

$2,800Variable

CostElement

FixedCost

Element

$2,500

15,0005,000

Leas

e C

ost

Intercept = a

Slope = b

X

Y

Equation of a straight line: Y = a + bXY = $2,500 + $0.02X


TM 5-8

MIXED COSTS (cont’d)

A cost that is considered fixed in one company might be considered variable or mixed in another company.


TM 5-9

SCATTERGRAPH METHOD

As the first step in the analysis of a mixed cost, the cost and its activity base should be plotted on a scattergraph. This helps to quickly diagnose the nature of the relation between the cost and the activity base. Example: Piedmont Wholesale Florists has maintained records of the number of orders and billing costs in each quarter over the past several years.

Quarter

Number of

Orders

Billing Costs

Year 1—1st

1,500 $42,000

2nd 1,900 $46,000

3rd 1,000 $37,000

4th 1,300 $43,000

Year 2—1st

2,800 $54,000

2nd 1,700 $47,000

3rd 2,100 $51,000

4th 1,100 $42,000

Year 3—1st

2,000 $48,000

2nd 2,400 $53,000

3rd 2,300 $49,000

These data are plotted on the next page, with the activity (number of orders) on the horizontal X axis and the cost (billing costs) on the vertical Y axis.


TM 5-10

A COMPLETED SCATTERGRAPH

$0

$10,000

$20,000

$30,000

$40,000

$50,000

$60,000

0 500 1,000 1,500 2,000 2,500 3,000

$48,000

Number of Orders

Bill

ing

Cos

ts

X

Y

Regression Line

The relation between the number of orders and the billing cost is approximately linear. (A straight line that seems to reflect this basic relation was drawn with a ruler on the scattergraph.)

Since a straight line seems to be a reasonable fit to the data, we can proceed to estimate the variable and fixed elements of the cost using one of the following three methods.

1) Quick-and-dirty method based on the line in the scattergraph.

2) High-low method.


TM 5-11

3) Least-squares regression method.


TM 5-12

THE QUICK-AND-DIRTY METHOD

The straight line drawn on the scattergraph can be used to make a quick-and-dirty estimate of the fixed and variable elements of billing costs.

Recall that we are trying to estimate the fixed cost, a, and the variable cost per unit, b, in the linear equation Y= a + bX.

• The vertical intercept, approximately $30,000 in this case, is a rough estimate of the fixed cost.

• The slope of the straight line is an estimate of the variable cost per unit

Select a point falling on the line (in this case 2,000 orders):Total billing cost for 2,000 orders. $48,000Less fixed cost element

(intercept)................................... 30,000

Variable cost element for 2,000 orders

$18,000

Variable cost per unit = $18,000 ÷ 2,000 orders = $9 per order.

Therefore, the cost formula for billing costs is $30,000 per quarter plus $9 per order or:

Y = $30,000 + $9X,where X is the number of orders.

Because of the imprecision of this method of estimating the variable and fixed cost components of a mixed cost, it is seldom used in practice.

Nevertheless, it is always a good idea to plot the data on a scattergraph before using the more precise high-low or least-squares regression methods.


TM 5-13

ANALYSIS OF MIXED COSTS: HIGH-LOW METHOD

EXAMPLE: Kohlson Company has incurred the following shipping costs over the past eight months:

Units Sold

Shipping Cost

January. . . 6,000 $66,000February. 5,000 $65,000March...... 7,000 $70,000April........ 9,000 $80,000May......... 8,000 $76,000June........ 10,00

0$85,000

July.......................

12,000

$100,000

August.... 11,000

$87,000

With the high-low method, only the periods in which the lowest activity and the highest activity occurred are used to estimate the variable and fixed components of the mixed cost.

Units Sold

Shipping Cost

High activity level, July... 12,000 $100,000

Low activity level, February......................

5,000 65,000

Change........................... 7,000 $ 35,00 0


TM 5-14

The cost formula for shipping cost is:Y = $40,000 + $5X


TM 5-15

EVALUATION OF THE HIGH-LOW METHOD

.

$0

$20,000

$40,000

$60,000

$80,000

$100,000

0 2,000 4,000 6,000 8,000 10,000 12,000Units Sold

Ship

ping

Cos

ts

Y

X

VariableCost

$5/unit

FixedCost

$40,000

low levelof

activity

highlevel ofactivity

The high-low method suffers from two major defects:1. It throws away all but two data points.2. The high and low volume periods are often unusual.


TM 5-16

LEAST-SQUARES REGRESSION METHOD

The least-squares regression method for analyzing mixed costs uses mathematical formulas to determine the regression line that minimizes the sum of the squared “errors.”


TM 5-17

LEAST-SQUARES REGRESSION (cont’d)

Example: Montrose Hospital operates a cafeteria for employees. Management would like to know how cafeteria costs are affected by the number of meals served.

Meals Served

X

Total Cost

YApril.......... 4,000 $9,500May........... 1,000 $4,000June........... 3,000 $8,000July............ 5,000 $10,00

0August...... 10,000 $19,50

0September 7,000 $14,00

0

Statistical software or a spreadsheet program can do the computations required by the least-squares method. The results in this case are:

Intercept (fixed cost)....... $2,433Slope (variable cost)............. $1.68R2.......................................... 0.99

The fixed cost is therefore $2,433 per month and the variable cost is $1.68 per meal served, or:

Y = $2,433 + $1.68X,where X is meals served.

R2 is a measure of the goodness of fit of the regression line. In this case, it indicates that 99% of the variation in cafeteria costs is due to the number of meals served. This suggests a very good fit.


TM 5-16

TRADITIONAL VERSUS CONTRIBUTION INCOME STATEMENT

Traditional Approach(costs organized by function)

Contribution Approach(costs organized by behavior)

Sales............................ $60,000 Sales $60,000

Less cost of goods sold*.........................

34,000 Less variable expenses:

Gross margin............... 26,000 Variable production. $12,000

Less operating expenses:

Variable selling........ 3,000

Selling*..................... $15,000 Variable administrative.......

1,000 16,000

Administrative*......... 6,000 21,000 Contribution margin... 44,000Net operating income.. $ 5,000 Less fixed expenses:

Fixed production...... 22,000Fixed selling............. 12,000Fixed administrative 5,000 39,000

Net operating income $ 5,000 * Contains both variable and fixed elements since this is the income statement for a manufacturing company. If this were a merchandising company, then the cost of goods sold would be entirely variable.


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Chapter 3 - Texas A&M University–Corpus Christifaculty.tamucc.edu/shall/2302/Chapter Outlines/chap005.doc · Web viewCost Behavior: Analysis and Use Learning Objectives LO1. Understand