Description
The two basic cost behavior patterns - variable and fixed - were introduced in the previous chapter. Other cost behavior patterns, such as mixed costs, are variations of these two. Mixed costs exhibit characteristics of both variable and fixed costs. In this section, we will review both variable and fixed costs and examine the reality of how these costs often look in many organizations. We will also introduce stepped costs and mixed costs.
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Analyzing Cost-Volume-
Profit Relationships
1 Understand the key
factors involved in cost-
volume-profit (C-V-P)
analysis and why it is such
an important tool in man-
agement decision making.
2 Explain and analyze
the basic cost behavior
patterns—variable, fixed,
stepped, and mixed.
3 Analyze mixed costs
using the scattergraph and
high-low methods.
4 Perform C-V-P analy-
ses, and describe the ef-
fects potential changes in
C-V-P variables have on
company profitability.
5 Visualize C-V-P rela-
tionships using graphs.
6 Identify the limiting
assumptions of C-V-P
analysis, and explain the
issues of quality and time
relative to C-V-P analysis
decisions.
7 Analyze mixed costs
using the least squares
method.
8 Explain the effects of
sales mix on profitability.
9 Describe how fixed
and variable costs differ in
manufacturing, service,
merchandising, and e-
commerce organizations,
and illustrate these differ-
ences with the operating
leverage concept.
After studying this chapter, you
should be able to:
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If you’ve ever watched an international-caliber soccer
match, you know that goals are scarce. Each goal re-
quires extensive work, patient play, and many attempts.
This same approach seems to apply to the business of
professional soccer in the United States where MAJOR
LEAGUE SOCCER (MLS) completed its seventh season in
the United States in 2002. The year 2002 was a banner
year for U.S. soccer with the men’s national soccer team
reaching new heights by finally cracking the Top 10 of
the FIFA World Rankings and competing in the quarter-
finals of the World Cup in Korea/Japan (after taking last
place at the previous World Cup tournament). This fol-
lowed on the momentum generated by the U.S. women’s
team, which won the World Cup in 1999 and placed third
in the world in 2003. Nevertheless, MLS has so far been
unable to score financially in America where sports fans
continue to prefer attending basketball, football, and
even baseball games to watching the most popular sport
in the (rest of the) world.
Professional soccer has been launched several times
in the United States amid much fanfare, but so far each
attempt has failed. The last failure, that of the NORTH
AMERICAN SOCCER LEAGUE (NASL)—which brought Pelé,
Cruyff, Best, and Beckenbauer to the United States in
the early 1970s—was especially painful because, with
the big names, professional soccer looked so promising.
One of the major reasons previous efforts failed is that
fixed costs were too high for the small number of fans
and meager TV revenues. Each attempt ended up with
the team owners losing money. To better manage player
salaries, which are a significant part of the fixed costs
of running a soccer team, the MLS set up an unusual
single-entity structure in 1996, under which the league
owns all the teams as well as all player contracts, and
investors buy operating rights rather than setting up
franchises. The purpose of this structure is to eliminate
the financial disparities between large and small mar-
kets and to control player salaries and other fixed costs.
This approach has successfully kept players’ salaries low;
so low in fact that a number of players have filed class
action lawsuits arguing the MLS structure is holding down
salaries in violation of U.S. antitrust laws.
Despite these efforts to contain the fixed cost of
players’ salaries, MLS teams continue to lose millions of
dollars, largely due to their inability to generate enough
revenue from ticket sales alone to cover another signif-
icant fixed cost, the cost of the leases on the stadiums
in which they play their games. And while the cost of
these lease payments is high, the larger problem is that
soccer teams forced to rent their facilities are only able
to keep the revenue from ticket sales and are generally
cut off from the all-important ancillary revenue that ac-
companies each game—revenue from concessions, park-
ing, merchandise, stadium signage and naming rights,
and luxury boxes.
The situation faced currently by Nick Sakiewicz, gen-
eral manager of the METROSTARS in New Jersey, is pretty
typical of the rest of the league. New Jersey has long
been a hotbed of soccer in America, from producing three
of the greatest American players of all-time (Tab Ramos,
John Harkes, and Tony Meola) to being home to the win-
ningest high school soccer coach in U.S. history (Gene
Chyzowych of Columbia High School). Nonetheless, the
MetroStars can’t seem to break even financially. Part of
this shortfall stems from the $1.5 million annual rent
the MetroStars must pay to use Giants Stadium at the
Meadowlands. Worse, the Meadowlands stadium is also
used by two NFL teams (the GIANTS and the JETS), the
New Jersey State Fair, and multiple concerts, which
means that the MetroStars can only play one or two home
games each month in June and July. With most of the
home games being played in April and May, average at-
tendance is not as high as it could be (attendance in
2002 averaged just 19,000 per game). Hence, the team
loses millions of dollars every year.
General Manager Nick Sakiewicz is convinced that a
new stadium is crucial to the MetroStars’ financial suc-
cess. At an estimated cost of $152 million, Sakiewicz
wants to build a roofed, 25,000-seat stadium in Harrison
City (also in New Jersey) to be located in a vast com-
plex that would include residential housing, retail space,
and a shopping center. And although he believes that
more people would buy a ticket to come see the Met-
roStars play in their own stadium, what makes the con-
struction proposal most attractive is the ancillary revenue
that would finally belong to the team because it would
own the stadium. It is estimated that a crowd of 20,000
can generate an extra $100,000 in profit from conces-
sions, parking, and so forth. Sakiewicz believes strongly
that those kinds of numbers will move his soccer team
beyond the break-even point and into profitability.
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1 John McLaughlin, Sky, October 1997, pp. 27-32; Ridge Mahoney, “Homes of Their Own,” July 30, 2001,http://www.si.com; Chris Isidore, “New Homes Get Old Quickly,” July 27, 2001,http://www.cnnmoney.com;
and the homepage for the MetroStars,http://www.metrostars.com.
44 Part 1 Foundations
n the previous chapter, we discussed differ-
ent ways to categorize costs, and we briefly
illustrated how you can use these cost cate-
gories to make management decisions. We also em-
phasized the fact that management accounting is
defined as all accounting information that is useful
in planning, controlling, and evaluating an organi-
zation. Some costs, such as direct materials and di-
rect labor costs in a manufacturing firm, increase in
direct proportion to the number of products or ser-
vices produced. These are called variable costs. Other
costs, such as factory rent, remain the same no mat-
ter what the level of production is. These are called
fixed costs. We used these definitions of variable
costs and fixed costs in the previous chapter to in-
troduce you to cost-volume-profit (C-V-P) analysis,
a critical tool in the management process. C-V-P
analysis is used to make important planning deci-
sions concerning appropriate levels of production
and spending. C-V-P analysis allows a manager to
answer the very important question: How much do
I need to sell in order to earn a profit?
In this chapter, you will further explore the
C-V-P analysis tool to analyze relationships between
variable costs, fixed costs, and revenues. You will
learn that successful managers must think carefully
about cost behavior—how costs change in relation
to changes in activity levels, such as the number of
patients in a hospital or the pounds of ore processed
in a copper smelter. An understanding of how costs
behave in relation to levels of activity helps man-
agers predict the effects of their plans on future per-
formance. In addition, because the C-V-P analysis
technique is applicable to all types of firms, we will
discuss the behavior of costs in manufacturing, mer-
chandising, service, and e-commerce firms.
You will also use the knowledge of cost behav-
ior patterns to analyze the kinds of problems facing
organizations such as the MetroStars’ lack of prof-
itability as described in the opening scenario. As you
work through this chapter making calculations that
will determine how profits will change in relation
to changes in sales volume, fixed costs, and variable
costs, be sure to think about how these calculations
reflect the process of managing actual organizations.
For instance, because of decreased air travel in the
wake of the 9/11 attacks, the airline industry has
struggled to be profitable in light of the heavy fixed
costs of owning and operating commercial aircraft.
Many owners of retail outlets in a mall breathe a sigh
of relief each month on the day when enough profit
has been generated to allow them to pay the
monthly fixed cost of the lease payment to the mall.
The owner of a baseball team will look out over a
half-filled stadium on game day and worry that the
ticket sales may not have been enough to cover the
costs of paying the players and running the stadium.
Every business owner must carefully plan how he or
she is going to generate enough money to cover the
fixed costs of the business. Those who have a clear
idea of exactly how many airline seats, or pairs of
pants, or hot dogs must be sold to break even will
be in a better position to create and maintain prof-
itability in the organization.
We believe that the best way to appreciate the
importance of good management information is to
begin by using that data to make significant man-
agement planning decisions. Accordingly, this chap-
ter will give you lots of opportunities to practice.
Also note that although we will focus primarily on
examining the financial implications of cost-volume-
profit analysis decisions, we will also pay attention
to the effects these decisions have on quality and
time issues as well.
cost-volume-profit (C-V-P) analysis Techniques for determining
how changes in revenues, costs, and level of activity affect the prof-
itability of an organization.
cost behavior The way a cost is affected by changes in activity
levels.
i
Understanding Why C-V-P Analysis Is Important
Management must make many critical operating decisions that affect a firm’s profitability. With
respect to planning, management is often interested in the impact a particular action will have
on profitability. C-V-P analysis can help managers assess that impact. The following are exam-
ples of questions that can be answered with C-V-P analysis:
• When planning whether or not to open a scuba shop in the mall, how many customers
will need to be served each month in order to break even and be able to pay the monthly
store rental fee?
1 Understand the key
factors involved in cost-
volume-profit (C-V-P)
analysis and why it is
such an important tool in
management decision
making.
• How will the profits of a bookstore be affected if the store raises its prices by 10%, result-
ing in a reduction of 2% in the number of books sold?
• How many carpets must a fledgling entrepreneur clean in a month in order to generate a
net profit of $3,000 each month?
• By how much will the profits of a discount electronics store change if a $100,000 adver-
tising campaign increases the number of computers sold by 13%?
• How will the profits of a fast-food restaurant change if the restaurant stops selling milk
shakes and instead focuses on raising the volume of soft drink sales by 25%?
It should be clear to you from these examples that C-V-P analysis involves studying the in-
terrelationships among revenues, costs, levels of activity, and profits. However, quality of prod-
ucts and services and speed of production and delivery must also be considered as managers use
C-V-P analysis to determine product prices, the mix of products, market strategy, appropriate
sales commissions, advertising budgets, production schedules, and a host of other important
planning decisions. Although C-V-P analysis is most useful for planning, it can also be used to
assist with controlling decisions (e.g., are the costs too high for the level of sales?) and evaluat-
ing decisions (e.g., should we reward employees for holding costs down or be concerned that
sales growth has slowed?). In fact, a lot of what is done in management accounting involves
some aspect of C-V-P analysis because of the tremendous potential it has to help management
increase the profitability and effectiveness of an organization. For this reason, as you use this
chapter to learn the mechanics of C-V-P analysis, be sure to see how important it is to be able
to understand and manage costs. As you study C-V-P analysis, you will gain a better under-
standing of basic cost behavior patterns. And once you understand these cost behavior patterns
and how to work with them, you can use them to make effective planning, controlling, and
evaluating decisions.
45 Chapter 2 Analyzing Cost-Volume-Profit Relationships
of products, (5) the speed and quality of production, and
(6) the resulting profits. Understanding the interrelation-
ships of the key variables in C-V-P analysis can assist you
in planning and in making critical control and evaluation
decisions.
T O S UMMA R I Z E : C-V-P analysis is a very im-
portant concept in management accounting. Key factors in-
volved in C-V-P analysis include (1) the revenues derived
from the sales prices charged for goods and services, (2) the
fixed and variable costs, (3) the sales volume, (4) the mix
Basic Cost Behavior Patterns
The two basic cost behavior patterns—variable and fixed—were introduced in the previous
chapter. Other cost behavior patterns, such as mixed costs, are variations of these two. Mixed
costs exhibit characteristics of both variable and fixed costs. In this section, we will review both
variable and fixed costs and examine the reality of how these costs often look in many organi-
zations. We will also introduce stepped costs and mixed costs.
A quick example of what we’re talking about may be helpful before we dive into all the
details of working with cost behavior. A cost may be classified as either fixed or variable by the
way it reacts to changes in level of activity. Think of a doughnut shop such as KRISPY KREME
or WINCHELL’S. Activity in the shop may be measured in terms of the volume of doughnuts
sold, the number of customers served, the number of hours the shop is open, the number of em-
ployees, or the total square feet of the serving area, and so forth. Get the point? There are a lot
of ways to measure activity in this organization. There are also a lot of different kinds of costs.
The first task is to identify the costs and activities where we intend to focus our management
effort. Let’s say that we are initially interested in understanding how the number of doughnuts
sold impacts costs and profits. Which costs will change, and which costs will not change, as we
expect to sell more or less doughnuts? This is the starting point of C-V-P analysis. It seems log-
ical that as more doughnuts are sold, the cost of doughnut ingredients will increase. This is
a variable cost. On the other hand, we probably wouldn’t expect the cost of property taxes to
2 Explain and analyze
the basic cost behavior
patterns—variable, fixed,
stepped, and mixed.
increase as more doughnuts are sold. This is a fixed cost. However, there are costs that have
both variable and fixed components. For instance, the electricity costs to run the doughnut shop
will increase as we sell more doughnuts because of the cost of the power to make the additional
doughnuts. However, even if we don’t sell any doughnuts, we will have to pay the utility costs
of just keeping the shop open. Utility costs are a mixed cost. The cost of a supervisor’s salary
isn’t normally going to increase as we sell more doughnuts until we have so many customers
that we need to hire an additional supervisor to help with the higher volume. At this point, the
fixed cost of salaries will jump to a new level. This is an example of a stepped cost.
Overall, once we have defined the activity, measurements of changes in activity level can
be used to determine cost behavior patterns.
Measuring Level of Activity
Before we can manage an organization, we need to identify exactly what it is that we intend to
manage. In other words, what is the activity upon which we intend to focus our planning, con-
trolling, and evaluating efforts? In the doughnut shop example, it makes sense for management
to focus on increasing the number of doughnuts sold; management efforts can reasonably be
expected to influence the number of doughnuts sold. Activity is often measured in terms of
output, input, or a combination of the two. Some of the most common activity bases used are
number of units sold and number of units produced in manufacturing firms, number of units
sold in merchandising firms, and number of contract hours paid for or billed in service firms.
We will generally use production volume or sales volume as the activity basis in this chapter to
demonstrate the use of C-V-P analysis.
Note that just because a cost doesn’t vary with a particular activity base (e.g., total units
sold) does not mean it could never be considered as a variable cost. For example, the total cost
of wages for a doughnut shop may not vary with the amount of sales volume (the clerks get paid
the same whether they sell a lot of doughnuts or just a few), but total wages would vary based
on the number of hours per week that the store is open. So, if another type of activity other than
sales volume is more relevant in determining changes in the variable costs being planned, the
C-V-P analysis should be based on that activity. It all comes down to an issue of “focus.” Where
do you believe you can best focus your management attention in order to plan for and control
costs and profits—on store hours, doughnuts sold, or customers served? There is some subjec-
tivity in this focus decision. Nevertheless, managers must be careful to understand the various
activity bases within their company so that they can properly plan for and control costs. We will
discuss a number of alternative activity bases in a later chapter on managing inventory.
Manufacturing and merchandising companies with a single product generally measure
volume of activity in terms of output, for example, number of cars, television sets, or desks pro-
duced. However, many companies produce or sell several different products (refrigerators, toast-
ers, and irons, for example), and a simple total of all the products manufactured or sold during
a given period may not provide a good measure of activity. This is particularly true for manu-
facturing firms. For example, GENERAL ELECTRIC manufactures a wide variety of products,
ranging from light bulbs to locomotives. It obviously takes more effort (and consequently costs
more) to produce a locomotive than a light bulb; accordingly, it wouldn’t make any sense to
state that total production for a given day was 1,000,001—1,000,000 light bulbs and 1 loco-
motive. In multiproduct situations, these manufacturing firms usually use input measures, such
as direct labor hours worked, machine time used, or the time needed to set up a job, as the ac-
tivity base. Such specific input measures are often more useful than general output measures.
Variable Costs
Total variable costs change in direct proportion to changes in activity level. Examples are costs
of direct materials, which vary proportionately with the number of units produced, and sales
commissions, which vary proportionately with the sales volume. For instance, as an automo-
bile manufacturer, you might define the activity of focus as the number of cars produced. If
engines, tires, axles, and steering wheels are purchased from suppliers, the related costs would
be variable because the total cost of steering wheels, for example, would vary proportionately
46 Part 1 Foundations
variable costs Costs that
change in total in direct pro-
portion to changes in activity
level.
with the number of cars produced. If no cars are produced, there are no steering wheel costs;
if 1,000 cars are manufactured during a period, the total cost for steering wheels and other pur-
chased parts is 1,000 times the unit cost of each item. As more cars are produced, the total cost
of each item increases. The unit cost, however, remains constant. For example, if an auto com-
pany pays $150 per steering wheel, the total cost of steering wheels for 200 cars is $30,000; for
500 cars, it is $75,000. At both levels of activity, however, the unit cost is still $150. This re-
lationship between variable costs and level of activity is shown graphically in Exhibit 1, which
relates the number of cars produced to the total cost of the steering wheels used
in production.
In addition to sales commissions and materials, many other costs (such as
labor) have a variable cost behavior pattern. For example, if it takes four hours
of labor to assemble a frame and each hour costs $25, a unit labor cost of $100
per frame is a variable cost; the total labor cost would be $100 times the num-
ber of frames produced.
Curvilinear Variable Costs
Our definition of the variable cost behavior pattern specifies that variable costs have a linear
relationship to the level of activity; that is, when the level of activity increases, total variable
costs rise at a directly proportional rate. For example, if the level of activity doubles, the total
variable costs will also double; this is a called a linear relationship. The reality is that, in prac-
tice, a truly linear relationship usually does not exist. Overall, many variable costs are actually
curvilinear costs when considered over many activity levels. That is, these curvi-
linear costs actually vary at increasing or decreasing rates across large changes in
the activity level. To illustrate, think about a manufacturer that makes a very
specialized “premium natural” ice cream that is handmade. Now consider Ex-
hibit 2. The top diagram is a graph that shows the cost of raw materials (for
example, milk, sugar, and other ingredients) purchased from suppliers to make
ice cream. Because the ice cream maker gets a bigger price discount as it pur-
chases higher volumes of raw materials, the variable cost of these materials is not
linear but curvilinear. That is, the cost increases at a decreasing rate.
On the other hand, the manager of the ice cream production process faces
an understandable labor challenge—it is difficult to find people who can make
ice cream efficiently. Plans to increase the production volume of the operation
mean that the manager will have to hire more individuals for the ice cream
production crew. As the manager scrambles to satisfy her labor needs, she will
47 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 1: An Example of Variable Costs
Cars produced
0
15,000
30,000
45,000
60,000
75,000
90,000
$105,000
100 200 300 400 500 600 700
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Cost of steering
wheel: $150 each
STOP & THINK
In a manufacturing plant, are direct labor
costs variable or fixed? Does your answer
change if the direct labor employees be-
long to a powerful union?
FYI :
If you’ve had an introductory class in eco-
nomics, you have likely been introduced to
the term economies of scale. The cost of
milk that becomes cheaper as production
volume increases (top graph in Exhibit 2) is
a cost that displays economies of scale.
On the other hand, the direct labor costs to
produce ice cream that become more costly
as production increases (bottom graph in
Exhibit 2) represent costs with diseconomies
of scale.
curvilinear costs Variable
costs that do not vary in direct
proportion to changes in ac-
tivity level but vary at decreas-
ing or increasing rates due to
economies of scale, produc-
tivity changes, and so on.
48 Part 1 Foundations
Exhibit 2: Curvilinear Variable Costs
0
2,000
4,000
6,000
8,000
$10,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
T
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Gallons of ice cream produced weekly
0
5,000
10,000
15,000
20,000
$25,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
T
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Gallons of ice cream produced weekly
n
$6,200/4,000 gallons
? $1.55 average direct
material (milk) cost
per gallon within the
relevant range
n
$4,800/4,000
gallons ? $1.20
average direct
labor cost per
gallon within the
relevant range
probably have to increase the wages she offers in order to attract more employees. As a result,
the direct labor cost of each gallon of ice cream will increase as planned production volumes
go up because the wage rate of the workers goes up. Thus, this curvilinear variable cost increases
at an increasing rate, as depicted in the bottom graph in Exhibit 2. If you’ve ever had a class in
economics, then this concept of curvilinear costs is familiar to you. The fact that most variable
costs are curved instead of linear is an economic fact of most organizations. However, when
doing C-V-P analysis, we assume that costs are linear. This is a potentially limiting assumption
of C-V-P work; but, as you’ll see in the next section, it is an appropriate assumption for most
managers.
Relevant Range and the Linearity of Variable Costs
While this is never exactly true, it is usually safe to assume that variable costs are approximately
linear within a certain range of production, called the relevant range. To illustrate the relevant
range concept, let’s return to our ice cream manufacturing business. Realistically, the produc-
tion manager does not expect to vary weekly production volume outside the range of 3,000 to
5,000 gallons of ice cream. As displayed in Exhibit 2 for both milk material cost and direct
labor cost, a linear segment within the relevant range of weekly production can effectively ap-
proximate the curvilinear cost relationship of producing between 3,000 and 5,000
gallons of ice cream. By assuming a linear (rather than a curvilinear) relation-
ship, the variable costs of milk and direct labor are estimated at $1.55 and $1.20,
respectively, per gallon of ice cream using the costs in the midpoint of the rele-
vant range (weekly production of 4,000 gallons of ice cream).
Relevant range is an important concept. If activity increases or decreases sig-
nificantly, cost relationships will probably change. If production volume soars,
for example, such factors as overtime work and bulk-purchase discounts may
cause direct labor and materials costs per unit to change. That is why we say that
the definition of variable costs—costs that are constant per unit of activity—is
applicable only within relevant ranges. The important point to remember is that
whenever we define a particular variable cost, we are assuming that the cost is
within the relevant range of activity.
Fixed Costs
Fixed costs remain constant in total, regardless of activity level, at least within the relevant
range of activity. Examples include property taxes, insurance, executives’ salaries, plant depre-
ciation, and rent. Because total fixed costs remain constant as activity increases, the fixed cost
per unit (total fixed cost ? level of activity) decreases. Similarly, as the level of activity de-
creases, the fixed cost per unit increases. This is in contrast to variable costs, where the costs
per unit are assumed to remain constant through changes in the level of activity within the
relevant range.
Before we go any further, it is a good idea for us to remind ourselves why
identifying fixed and variable costs is important. Remember that this chapter is
about managing the relationships among costs, volume, and profit. In the pre-
vious chapter, we briefly introduced the concept of C-V-P and break-even analy-
sis. In the C-V-P formula below (which we introduced in the previous chapter),
you can see that calculating what a company needs to do to “break even” and
start making a profit requires a clear measure of total fixed costs and variable
costs per unit:
? Break-even sales (in units)
In an actual company, the fixed and variable costs are very challenging to
identify. That is why it is important that you understand the nature of cost be-
havior and how to classify costs as either fixed or variable. Once we’ve completed
our discussion of cost behavior, we’ll be ready to spend some time on this very
useful C-V-P formula later in this chapter.
Total fixed costs
??????
(Sales price per unit ? Variable cost per unit)
49 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Cauti on
The relevant range concept is particularly
difficult to apply when using C-V-P analysis
in companies in very high growth situations,
such as high-tech start-ups. If a company’s
sales are increasing by 60% each quarter,
for example, it is unlikely to remain in the
same “relevant range” from quarter to quar-
ter; so careful analysis of variable and fixed
costs must be repeated on a regular basis.
fixed costs Costs that remain
constant in total, regardless of
activity level, at least over a
certain range of activity.
Cauti on
While total variable costs increase as pro-
duction increases, the per-unit variable cost
is constant across activity levels within the
relevant range. In contrast, while total fixed
costs are constant over the relevant range,
the per-unit fixed cost changes with in-
creases or decreases in production. Many
introductory students of management ac-
counting become confused and forget that
per-unit variable costs are fixed and per-
unit fixed costs will vary over the relevant
range!
relevant range The range of
operating level, or volume of
activity, over which the rela-
tionship between total costs
(variable plus fixed) and ac-
tivity level is approximately
linear.
Stepped Fixed Costs
Let’s continue with our example of the ice cream manufacturer. The top graph
in Exhibit 3 shows the relationship between the production line supervisor cost
and the total number of gallons of ice cream produced. In this case, until weekly
ice cream production reaches 1,000 gallons a week, the manufacturing manager
is able to oversee all line workers. At 1,000 gallons a week production, however,
the manager expects to hire a production line supervisor at $500 per week to
provide more supervision of the workers. Further, the manager expects that she’ll
need to hire an additional supervisor each time weekly production is increased
another 2,000 gallons. Although the production line supervisor cost is changing
as the scale of ice cream production changes, we still consider this cost to be fixed
within the relevant range. Hence, as shown in the top graph in Exhibit 3, within
a relevant range of activity of between 3,000 and 5,000 gallons of ice cream, the
total fixed manufacturing supervisor cost of $1,000 does not change. On the
other hand, the per-unit supervisor cost will drop considerably as production in-
creases. For example, when the fixed supervisor cost is $1,000 and 3,000 gallons
of ice cream are being produced, the supervisor cost per gallon of ice cream is $0.33 ($1,000
? 3,000 gallons). With production of 4,000 gallons, however, this fixed cost is only $0.25
($1,000 ? 4,000 gallons) per gallon.
As you can see in Exhibit 3, the fixed cost of the production line supervision “steps up” as
the volume of ice cream production increases. Stepped costs are costs that change in total in
a stair-step fashion with changes in volume of activity. Another example of a stepped cost might
be the labor charges for the maintenance of the tools and machinery in a small manufacturing
plant. One maintenance worker can handle the upkeep of all the equipment during normal
FYI :
Have you ever wondered why you always
wait so long and why there are so many
patients at one time in a dentist’s office?
Think about the nature of the dentist’s costs.
Most costs are fixed—dentists’ salaries, rent
or depreciation, and so forth. When costs
are mostly fixed, seeing a high volume of
patients is important to cover the fixed costs.
Then, once fixed costs are covered, almost
all additional patient revenue becomes
profit. Thus, by squeezing in only a few
additional patients, dentists can increase
their profits substantially.
Fixed Costs Are Shifting Over
the past few decades, fixed
costs have increased as a per-
centage of total costs for many
manufacturing companies, pri-
marily due to the increase in
factory automation. As a ma-
chine replaces each manual job, costs change from
variable labor costs to fixed depreciation or rental
charges. It is important to note that many service
companies have much higher ratios of fixed-to-
variable costs than do manufacturing companies. The
costs of providing services in companies such as
banks, consulting agencies, and airlines typically do not vary
much depending on the volume of banking transactions, con-
sulting hours, or passengers carried. Perhaps more significantly,
e-commerce organizations often have even fewer variable costs
than service organizations do! Once the technology has been
put in place to run an e-commerce business, there is typically
very little additional cost of technology based on usage (within
the relevant range). Personnel costs in e-commerce organiza-
tions, such as engineering personnel, marketing teams, and ex-
ecutive personnel, also do not change much based on the
volume of customer use of the organization’s technology.
As fixed costs in manufacturing organizations increase, and
the economy continues to shift more and more to service and
e-commerce organizations, this fixed cost emphasis has a sig-
nificant effect on the decision-making process. When costs are
fixed, management’s ability to influence costs with activity-
level decisions is limited. With variable costs, management has
more flexibility to change activity levels and thereby increase
or decrease total operating cost structures. This trend
of replacing variable costs with fixed costs has an im-
portant impact on the cost structure of an organiza-
tion that is captured in the concept of operating
leverage, which is discussed in the expanded mater-
ial section of this chapter.
b u s i n e s s env i r onment
stepped costs Costs that
change in total in a stair-step
fashion (in large amounts)
with changes in volume of
activity.
levels of activity. However, when there is a significant increase in activity, a sec-
ond worker must be hired, and the maintenance cost approximately doubles.
Mixed Costs
Mixed costs, like curvilinear costs and stepped costs, are variations of the basic
fixed and variable cost behavior patterns. Specifically, mixed costs are costs that
contain both variable and fixed components. An example is rent that is based on
a fixed fee plus a percentage of total sales. Thus, the rental terms for an auto-
mobile dealer’s showroom might include a flat payment of $4,000 per month
plus 1% of each month’s sales. The 1% of sales is the variable portion, and the
$4,000 is the fixed cost. The total rent, therefore, would be considered a mixed
cost and could be diagrammed as shown in Exhibit 4. As this exhibit shows, the
cost of renting the showroom increases as sales increase. The total rent is $4,000 when there
are no sales; $6,000 when sales are $200,000 [$4,000 ?(0.01 ?$200,000)]; and $8,000 when
sales are $400,000 [$4,000 ? (0.01 ? $400,000)]. This increase is directly due to the variable
cost element, which increases in total as activity level (car sales) increases.
One of the important challenges in using C-V-P analysis in the planning process is the
need to effectively separate mixed costs into their fixed and variable cost components. Over
51 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 3: Stepped Fixed Costs
0
500
1,000
1,500
2,000
$2,500
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
T
o
t
a
l
p
r
o
d
u
c
t
i
o
n
l
i
n
e
s
u
p
e
r
v
i
s
o
r
c
o
s
t
s
(
$
)
Gallons of ice cream produced weekly
n
STOP & THINK
If the “steps” in a stepped cost are wide
compared to the relevant range (in other
words, the costs essentially are unchanged
within the relevant range), the costs are
usually treated as fixed. This would be the
case with the production line supervisor
costs in Exhibit 3. On the other hand,
how would you treat a stepped cost with
very narrow steps as is displayed in the
bottom graph in Exhibit 3?
mixed costs Costs that con-
tain both variable and fixed
cost components.
52 Part 1 Foundations
Exhibit 4: An Example of a Mixed Cost
Total sales
0
4,000
6,000
8,000
10,000
12,000
$14,000
$100,000 $200,000 $300,000 $400,000 $500,000
T
o
t
a
l
r
e
n
tc o c o Total mixed cost
$
e
s
Analysis of Mixed Costs
With an understanding of the different types of cost behavior, we can discuss how to iden-
tify and separate mixed costs into variable and fixed components. This separation is essential
because we have to clearly classify all costs as fixed or variable before doing C-V-P analysis.
When it comes to mixed costs, remember that the fixed portion represents the cost necessary
to maintain a service (such as a telephone) or a facility (such as a building), and the variable
portion covers actual use. Recall the example of the automobile showroom’s rental cost, part
of which was a flat monthly fee and part a percentage of sales. Other common mixed costs
are such overhead costs as electricity and repairs.
The most accurate way to separate the actual fixed and variable components of mixed
costs is to analyze each invoice. An electricity bill, for example, may include a flat monthly
service charge that would be classified as a fixed cost. Additional variable costs are those
3 Analyze mixed costs
using the scattergraph and
high-low methods.
change over the relevant range; therefore, fixed costs de-
crease per unit as the level of activity increases within the
relevant range. Stepped costs increase with the level of ac-
tivity but not smoothly. If the steps are wide in relation to
the relevant range, these costs can be treated as fixed; if
the steps are narrow, they can be treated as variable. Mixed
costs have both a fixed and a variable component. An in-
crease in a mixed cost with a rising level of activity is due
entirely to the variable cost element.
T O S UMMA R I Z E : Cost behavior is the way a
cost changes in response to changes in activity level. There
are two basic cost behavior patterns, variable and fixed. To-
tal variable costs change in direct proportion to changes in
the level of activity over the relevant range; therefore, vari-
able costs are constant per unit over this range. In analyz-
ing variable costs, we generally assume a linear relationship
between total costs and the level of activity within the rel-
evant range; outside of this range, variable costs are usu-
ally curvilinear. On the other hand, total fixed costs do not
the years several management accounting techniques have been developed by organizations for
this purpose. We will explore these mixed cost analysis methods in the next section of this
chapter.
53 Chapter 2 Analyzing Cost-Volume-Profit Relationships
based on the amount of electricity actually used during the month. This approach could be
very time consuming, however, and may not be cost effective (that is, it would cost more
to do the analysis than the detailed information is worth). An alternative approach is to an-
alyze the historical trend in past costs as the level of activity has changed as the basis for
classifying costs as fixed or variable. There are several methods of doing this. In this section,
we will introduce you to two methods: the scattergraph method and the high-low method.
In the expanded material, we introduce least squares analysis, a more sophisticated method
for analyzing mixed costs.
The Scattergraph, or Visual-Fit, Method
Probably the simplest method of separating mixed costs into their variable and fixed com-
ponents is the scattergraph (or visual-fit) method. Essentially, we’re talking here about sim-
ply looking at a trend of mixed cost points over time and learning how to “see” the fixed
and variable cost components. To do this, the total mixed cost for each level of activity is
plotted on a graph, and a straight line (called the regression line) is visually fitted through
the points. The idea is to position the line through the set of plotted data points in a way
that minimizes the average distance between all the data points and the fitted regression line.
With the regression line inserted into the graph, the fixed portion of the mixed cost is esti-
mated to be the amount on the cost (vertical) axis at the point where it is intercepted by the
regression line. The variable cost per unit (referred to as the variable cost rate) is equal to
the slope of the regression line, which is simply the change in cost divided by the change in
activity.
To illustrate the scattergraph method, let’s use the example of electricity
costs for an automobile manufacturer. In the analysis and calculations that fol-
low, all costs are assumed to fall within the relevant range of activity. In this ex-
ample, we use direct labor hours as a measure of the activity level.
Exhibit 5 shows a scattergraph on which electricity costs and direct labor
hours have been plotted. The regression line has been visually fitted to mini-
mize the distance between data points. It appears that the total fixed portion of
electricity cost is about $40,000 per month, which is where the regression line
intersects the cost axis. The variable cost rate is approximately $4.29 per direct labor hour,
which is the slope of the regression line. To calculate the slope, we use the following formula
and the data points of zero and 7,000 direct labor hours, respectively.
Variable cost rate ?
X ?
X ?
X ? $4.29 (rounded)
Obviously, the scattergraph method has some limitations as a cost estima-
tion tool. Perhaps the most critical limitation is that how the user fits the re-
gression line through the data points is entirely subjective. Consider Exhibit 5
once more. If you were the one fitting the regression line to these data points,
would you have set the line exactly where it is in this graph? Hopefully, your line
would have been quite close to the current line. Still, it probably wouldn’t have
been exactly the same, resulting in some small differences in your own estima-
tions of fixed and variable costs. Hence, the scattergraph method is a classic “quick
and dirty” management accounting technique. Yet, although the scattergraph
$30,000
?
7,000
$70,000 ? $40,000
???
7,000 ? 0
Change in (electricity) cost
?????
Change in activity (direct labor hours)
Cauti on
When making these cost graphs, remember
that the dollars go on the vertical axis and
the level of activity goes on the horizontal
axis.
Cauti on
Once the regression line has been fitted
through the data points, the scattergraph
method does not depend any longer on the
data points to estimate fixed and variable
costs. Cost estimations are entirely based
on points along the regression line. For in-
stance, notice that in this case we used the
points 0 and 7,000 along the visually fitted
regression line. However, we could have
used any two points on the regression line
(such as 2,000 direct labor hours and
10,000 direct labor hours) to calculate the
variable costs per direct labor hour.
scattergraph (visual-fit)
method A method of segre-
gating the fixed and variable
components of a mixed cost
by plotting on a graph total
costs at several activity levels
and drawing a regression line
through the points.
regression line On a scatter-
graph, the straight line that
most closely expresses the
relationship between the vari-
ables.
variable cost rate The
change in cost divided by the
change in activity; the slope
of the regression line.
54 Part 1 Foundations
Exhibit 5: Total Electricity Costs
2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000
T
o
t
a
l
e
l
e
c
t
r
i
c
i
t
y
c
o
s
t
$130,000
120,000
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
Direct labor hours
Regression line
Point at which the cost axis is
intercepted by the regression line
high-low method A method
of segregating the fixed and
variable components of a
mixed cost by analyzing the
costs at the highest and the
lowest activity levels within a
relevant range.
provides only subjective estimates of the fixed and variable portions of mixed costs, it can be
an extremely useful tool to describe and discuss cost behavior in the planning process. It is also
useful for thinking about how to control operating costs. For instance, it shows at a glance any
trends and abrupt changes in cost behavior patterns. As such, it can be used as a preliminary
step before using more sophisticated methods of cost evaluation.
The High-Low Method
A second approach to identifying fixed and variables costs is the high-low method, which an-
alyzes mixed costs on the basis of total costs incurred at both the highest and the lowest levels
of activity. To illustrate this method, we refer again to the electricity costs of the automobile
manufacturer. This time, however, we will focus on the following table of reported electricity
costs and direct labor hours worked. (The numbers in this table correspond exactly to the points
plotted in the scattergragh in Exhibit 5.)
Month Direct Labor Hours Worked Total Electricity Cost
January 7,000 $ 70,000
February 6,000 60,000
March 12,000 100,000
April 6,600 80,000
May 18,000 120,000
June 14,000 110,000
Although these two columns of figures do not visually show trends as clearly as the scattergraph
does, they do suggest that as the activity level (direct labor hours) increases, total electricity costs
increase. Given this relationship, the high-low method can be used to determine the fixed and
variable portions of the electricity cost as follows:
1. Identify the highest and lowest activity levels (18,000 hours in May and 6,000 hours in
February). As you can see, these two months also represent the highest and lowest levels
of electricity costs, or $120,000 and $60,000, respectively (although this may not always
be the case).
2. Determine the differences between the high and low points.
Total Electricity Cost Direct Labor Hours
High point (May) $120,000 18,000
Low point (February) 60,000 6,000
Difference $ 60,000 12,000
3. Calculate the variable cost rate (variable cost per unit). The formula is the same as the
one used to compute the slope of the regression line in the scattergraph method. The
results are different, of course, because the scattergraph method is based on a regression
line that is plotted, as much as possible, using all the data points, whereas the high-low
method uses only the highest and lowest data points.
Variable cost rate ?
?
? $5 per direct labor hour
4. Determine fixed costs based on the variable cost rate ($5 in this case). The formula for
this computation is:
Fixed costs ? Total costs ? Variable costs
At the high level of activity, the calculation is as follows:
X ? $120,000 ? (18,000 ? $5)
X ? $120,000 ? $90,000
X ? $30,000
You get the same result if you calculate fixed costs at the low level of activity as follows:
X ? $60,000 ? (6,000 ? $5)
X ? $60,000 ? $30,000
X ? $30,000
In summary, using the high-low method of analyzing mixed costs, the vari-
able portion of the total electricity cost is estimated to be $5 per direct labor
hour, and the fixed portion is $30,000 per month. This means that $30,000 ap-
pears to be the amount the company pays each month just to have electricity
available, and $5 is the average additional electricity cost for each hour of direct
labor worked.
$60,000
?
12,000
Change in costs
???
Change in activity
55 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Cauti on
Once you have selected the high and low
activity levels to use in the high-low
method, don’t use any other activity levels
or costs than these two data points to cal-
culate the fixed costs.
56 Part 1 Foundations
A Comparison of the Scattergraph and
High-Low Methods
As we have illustrated, the scattergraph and high-low methods may produce dif-
ferent results.
Method Variable Cost Rate Fixed Cost
Scattergraph $4.29 $40,000
High-low 5.00 30,000
Both methods are useful for a quick approximation. The scattergraph method
takes all the data into account. Therefore, this method tends to be more accu-
rate, although it is somewhat subjective and inconsistent because different peo-
ple might draw the line through the points differently. On the other hand, anyone
using the high-low method will consistently get the same results. However, be-
cause only two data points are used, the high-low method may not be represen-
cost axis (the fixed cost) and calculating the slope of the
line (the variable cost rate). With the high-low method, the
high and the low levels of activity are used to calculate first
the variable cost rate and then the fixed cost component.
T O S UMMA R I Z E : Two common techniques for
analyzing mixed costs are the scattergraph and high-low
methods. The scattergraph method involves visually fitting
a straight line (the regression line) through data points plot-
ted on a graph, then noting where the line intercepts the
FYI :
What if the highest and lowest levels of ac-
tivity do not correspond to the highest and
lowest levels of costs? This could easily (and
often does) happen in real-life companies.
Remember that the high-low method is a
method that determines approximately the
fixed and variable costs. Hence, companies
must then choose to base the estimate on
either the highest and lowest activities or the
highest and lowest costs. For simplicity, this
textbook will always present data such that
the highest and lowest levels of activity do
correspond to the highest and lowest levels
of costs.
tative of the costs incurred at all levels of activity. It is important that you realize that the math
used in the high-low method essentially plots the regression line through the two most extreme
points in a scattergraph. To understand what we mean, look at the scattergraph of the elec-
tricity cost data in Exhibit 5. Notice that the low point lies below the scattergraph regression
line and the high point lies above the scattergraph regression line. Now, if you were to draw a
straight line through the high and low points, that line would not be the same line created us-
ing the scattergraph (visual-fit) method, and may not necessarily represent all six data points
plotted. Nevertheless, you can use either method or both methods to predict future costs. If,
for example, management wants to know how much electricity will cost next month with 10,000
direct labor hours budgeted, the following calculations would be made:
Method Formula Estimated Cost
Scattergraph $40,000 ? 10,000($4.29) ? $82,900
High-low $30,000 ? 10,000($5.00) ? $80,000
As you can see, the total estimated costs resulting from these two methods, in this case, are rea-
sonably close to each other (although this may not necessarily be the case with sets of actual
cost and activity data in some real-life companies).
57 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Methods of C-V-P Analysis
Now that you have a better understanding of cost behaviors and can separate mixed costs into
their fixed and variable cost elements, you are ready to use your knowledge of cost behaviors
to make planning decisions. The previous chapter provided a quick introduction to C-V-P
analysis in the process of planning and analyzing decisions to prioritize Kevlar versus Teflon
products at DUPONT. However, in order to effectively use this valuable tool, we need a more
detailed discussion and lots of practice.
If you haven’t done so already, now is a good time to think of an actual business organi-
zation that is familiar to you, perhaps one by which you’ve been employed or are now em-
ployed. Think about the product or service this organization creates and the costs and processes
it uses. Now, as you study the C-V-P analysis method below, be sure to consider how this tool
4 Perform C-V-P analy-
ses, and describe the ef-
fects potential changes in
C-V-P variables have on
company profitability.
Managing an Airline in the
Post-9/11 Economy Is Not
Easy. Prior to the terrorist
tragedies in 2001, CONTINEN-
TAL AIRLINES was posting an
incredible string of consecutive
profitable quarters. Since filing
for bankruptcy protection in 1995, Continental re-
ported 24 straight quarters of profit, even when most
of the other major U.S. airlines reported losses. This
all changed, of course, on September 11, 2001. Since
then, Continental, the fifth largest airline in the
United States, has struggled very hard just to stay
alive. Both 2001 and 2002 resulted in significant operating
losses for Continental, as was the case with many of its com-
petitors. Continental, however, appears to be weathering the
storm better than most other airlines. In 2002, three of the
top seven U.S.-based international carriers filed bankruptcy. By
the end of the first quarter in 2003, TWA no longer existed,
and UNITED and US AIRWAYS were still struggling in bank-
ruptcy. In contrast, Continental Airlines again earned a cov-
eted spot on Fortune’s list of the 100 Best Companies to Work
For—the only airline to do so and the fifth consecutive year
for it to make the list. More importantly, in March 2002, Con-
tinental posted its first profitable month since 9/11, and Gor-
don Bethune, chairman and CEO, predicted that his company
would be able to break even in 2004. This progress is signifi-
cant in that the Air Transport Association (ATA) forecasts that
the overall airline industry will lose $7 billion in 2003.
How has Continental’s management team carried this com-
pany through a disastrous period of time for the airline indus-
try? For one thing, Continental Airlines’ management carefully
analyzed its costs, divided those costs into fixed and variable
components, and made several decisions to reduce fixed costs.
For example, Continental grounded planes and slashed excess
capacity. The airline eliminated 12,000 jobs in 2002 and planned
to cut another 1,200 jobs, including 25% of top management,
in 2003. All of this helped reduce Continental’s jet cost per
available seat mile by 3.8%, which is a significant percentage
in an industry defined by extremely thin profit margins.
With better control of its fixed costs, Continental Airlines
is again becoming profitable, and becoming profitable more
quickly than most of its competitors. Because of these cut costs,
Continental Airlines’ passengers pay lower fares than on other
airlines and receive better service. These lower fares and bet-
ter service enable Continental to fill more seats than its com-
petitors. Because its costs are low, it is profitable. Fixed costs
are now a smaller percentage of total costs at Continental Air-
lines than at almost all other airlines.
Sources: Adapted from PR Newswire, “Continental Airlines Re-
ports First Quarter Loss; Carrier Profitable for Month
of March, the First Profitable Month Since 9/11,” April
15, 2002; Continental Airlines 2002 Annual Report;
“Continental Air CEO Now Sees Break-Even Results
for 2004,” The Wall Street Journal, March 19, 2003.
b u s i n e s s env i r onment
would be used in your own organization to plan and manage costs and activities in order to
obtain desired results.
Contribution Margin
In order to effectively use C-V-P analysis, we first need to spend some time working with the
concept of contribution margin. Contribution margin is equal to sales revenue less variable
costs; it is the amount of revenue that remains to cover fixed costs and provide a profit for an
organization. For example, the contribution margin from the sale of one order of French fries
by a fast-food restaurant is the selling price less the variables costs
(potatoes, salt, container, cooking oil, wages of the cook) of pro-
ducing the fries. Any contribution margin generated by the sale of
an order of French fries can be used to pay the fixed costs of the
fast-food outlet, such as the monthly rent, the insurance, the super-
visor’s salary, and so forth. Contribution margin is one of the most
important management accounting concepts you will learn because
many operating decisions are made on the basis of how contribution
margin will be affected. A company may decide, for example, to ad-
vertise one product more than others because that product has a
higher contribution margin.
The Contribution Margin Income Statement
To illustrate the concept of contribution margin, let’s use the fol-
lowing format of a contribution margin income statement. The state-
ment data for Jewels Corporation, a producer of high-quality baseball
gloves, follow.
2
Jewels Corporation
Contribution Margin Income Statement
For the Month Ended November 30, 2006
Total Per Unit
Sales revenue (1,000 gloves) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $200,000 $200
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110,000 110
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 90,000 $ 90
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63,000
Profit* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 27,000
*In this chapter, “profit” means pretax income; the terms income and profit are interchangeable.
As this income statement shows, for internal decision-making purposes,
Jewels Corporation computes its contribution margin on a per-unit (glove) and
total-dollar basis. During November, Jewels’ per-unit contribution margin is
$90; the total contribution margin at a sales volume of 1,000 baseball gloves is
$90,000.
The per-unit contribution margin tells us that $90 is available from each
glove sold to cover fixed costs and provide a profit. By showing the $63,000 of
fixed costs separately, this income statement also tells us that Jewels must gen-
erate sufficient contribution margin to cover these costs before a profit can be
earned. With $200,000 of sales revenue, the contribution margin ($90,000) is
sufficient to cover the fixed costs and provide a profit of $27,000.
58 Part 1 Foundations
© 2003 Getty Images
The contribution margin gen-
erated by the sale of an order
of French fries can be used to
pay fixed costs such as rent,
insurance, and salaries. Now
you know why you often hear
that ever popular question
“Would you like fries with
that?” at fast-food restaurants.
contribution margin The
difference between total sales
and variable costs; the portion
of sales revenue available to
cover fixed costs and provide
a profit.
FYI :
French fries and soft drinks are good exam-
ples of products with a high contribution
margin. A $2 order of French fries might
have a contribution margin in excess of
$1.50. That’s why fast-food employees are
told to specifically ask customers if they
want fries and a drink with their order!
2 In this example, we assume that there is only one model of baseball glove, which sells for $200.
per-unit contribution
margin The excess of the
sales price of one unit over
its variable costs.
This type of contribution margin income statement is particularly useful as a planning tool.
The statement helps a company to project profits at any level of activity within the relevant
range. For example, if Jewels Corporation forecasts sales of 1,200 baseball gloves next month,
the company can prepare a forecasted (or pro-forma) income statement (in contribution mar-
gin format) as follows:
Jewels Corporation
Pro-Forma Contribution Margin Income Statement
For the Month Ended December 31, 2006
Sales revenue (1,200 gloves ? $200) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $240,000
Less variable costs (1,200 gloves ? $110) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132,000
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $108,000
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 45,000
Notice that with an increase in sales of 200 baseball gloves, the contribution margin in-
creases $18,000 ($108,000 ? $90,000). You can confirm this by multiplying the per-unit con-
tribution margin by the increase in volume ($90 per unit ? 200 gloves ? $18,000). Because
we assume that the increase in volume is still within the relevant range of activity (which is a
very important assumption!), the fixed costs remain at $63,000, and profit increases by the
$18,000 increase in contribution margin. The critical thing you should see here is that once
the fixed costs are covered, each subsequent dollar in contribution margin goes straight to profit!
In other words, when Jewels Corporation hits its break-even point (which is the point where
all fixed costs are covered), each additional glove sold will generate $90 in profit.
Notice the importance of accurately determining cost behavior when forecasting profit lev-
els. If one ignores cost behavior, then the $27,000 profit generated by November sales of 1,000
gloves may lead to the conclusion that each glove creates $27 ($27,000 profit/1,000 gloves) in
profit. With this incorrect information, the forecasted level of profit for December sales of 1,200
gloves is $32,400 ($27 per glove ? 1,200 gloves). This forecast differs significantly from the
$45,000 profit forecast above that stems from a correct consideration of the behavior (fixed or
variable) of Jewels Corporation’s costs.
The Contribution Margin Ratio
Knowing the contribution margin ratio, which is the percentage of sales revenue left after vari-
able costs are deducted, will help you compare the profitability of various products. For exam-
ple, if product A has a 60% contribution margin ratio and the contribution margin ratio of
product B is only 20%, the company should emphasize product A, assuming that other factors
are equal. As a concrete example, in a supermarket the prepared foods (baked goods, squeezed
juices, ready-to-eat barbecued chicken) have high contribution margin ratios whereas the sta-
ples such as milk and eggs have lower contribution margin ratios.
To illustrate the calculation of contribution margin ratios, let’s look again at the initial Jew-
els Corporation example. The ratio is computed as follows:
Ratio
Total Per Unit (Percentage)
Sales revenue (1,000 gloves) . . . . . . . . . . . . . . . $200,000 $200 100%
Less variable costs . . . . . . . . . . . . . . . . . . . . . . 110,000 110 55
Contribution margin . . . . . . . . . . . . . . . . . . . . . $ 90,000 $ 90 45%
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . 63,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 27,000
59 Chapter 2 Analyzing Cost-Volume-Profit Relationships
contribution margin ratio
The percentage of net sales
revenue left after variable
costs are deducted; the con-
tribution margin divided by
net sales revenue.
The contribution margin ratio is 45% of sales revenue ($90 ? $200), which means that
for every $1.00 increase in sales revenue, the contribution margin increases by $0.45 (45% of
$1.00). If fixed costs are already covered, profit will also increase by $0.45 for every $1.00 in-
crease in sales. As you can see, there is another ratio presented in these calculations—the vari-
able cost ratio. These two ratios are complements of each other. Hence, the variable cost ratio
($110 ? $200 ? 55%) plus the contribution margin ratio (45%) will always equal 100%.
This is important because whether we’re describing contribution margin ratios or variable cost
ratios, we are really talking about the same basic issue—the relationship of variable costs to sales
revenue.
With contribution margin or variable cost ratios, it is easy to analyze the impact of changes
in sales on the contribution margin. For example, if you estimate that Jewels’ sales will increase
by $20,000, you can apply the contribution margin ratio of 45% or the variable cost ratio of
55% and estimate that the contribution margin will increase by $9,000, which is equal to
$20,000 ?0.45 or $20,000 ?(1 ?0.55). The higher the contribution margin ratio, the larger
the share of each additional dollar of sales that goes toward covering fixed costs and increasing
profit.
The C-V-P Equation
As you can see, contribution margin calculations will be very useful to you when analyzing cost-
volume-profit relationships in the management planning process. Doing C-V-P analysis using
contribution margin calculations is a straightforward process. C-V-P analysis does require some
simple algebra; here is where you reap the benefits of paying attention during your eighth grade
math class.
We began this chapter with the assumption that all costs can be described as either fixed
or variable. To highlight the important idea that C-V-P analysis depends on dividing costs into
fixed and variable behavior patterns, we will develop the C-V-P equation as follows:
3
1. Because all costs can be classified as either variable or fixed, we can express the calcula-
tion of profit with the following basic formula:
Sales revenue ? Variable costs ? Fixed costs ? Profit
2. We can specify the formula more precisely by expressing the equation in units:
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? Profit
3. Or, we can express the equation using ratios:
Sales revenue ? (Variable cost ratio ? Sales revenue) ? Fixed costs ? Profit
These equations are quick and useful methods for examining the financial aspects of C-V-P
analysis problems. To illustrate, see if you can use the C-V-P equation based on units and the
data from the Jewels Corporation example to determine profit assuming that sales of 1,200
baseball gloves are expected.
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? Profit
($200 ? 1,200) ? ($110 ? 1,200) ? $63,000 ? Profit
$240,000 ? $132,000 ? $63,000 ? Profit
$45,000 ? Profit
Alternatively, you could calculate Jewels’ profits using the equation based on ratios.
60 Part 1 Foundations
3 Granted, fixed and variable costs often get “mixed together” and can be difficult (and sometimes impossible) to
separate. The fact that C-V-P analysis is based on an assumption that all costs can be divided clearly into fixed
and variable is one of the limitations of this technique.
Sales revenue ? (Variable cost ratio ? Sales revenue) ? Fixed costs ? Profit
$240,000 ? [($110 ? $200) ? $240,000] ? $63,000 ? Profit
$240,000 ? (0.55 ? $240,000) ? $63,000 ? Profit
$240,000 ? $132,000 ? $63,000 ? Profit
$45,000 ? Profit
Note that we calculated the same profit of $45,000 using both formula approaches. This
result is no surprise because these are simply alternative routes to the same destination. Both
methods are commonly used in business, depending on the data available for the analysis. So,
although there may appear to be many alternative ways to write the C-V-P formula, there is
really only one formula, and it is not hard to remember:
Sales revenue ? Variable costs ? Fixed costs ? Profit
Once you understand this fact, C-V-P analysis using the equation approach is basic math; you
merely insert the known elements into the formula and solve for the one unknown element.
Break-Even Point
In many cases, as a manager you will want to know how many units need to be sold to break
even. The break-even point is defined as the volume of activity at which total revenues equal
total costs, or where profit is zero. The break-even point may also be thought of as the volume
of activity at which the contribution margin equals the fixed costs.
Although the goal of business planning is to make a profit, not just to break even, know-
ing the break-even point can be useful in assessing the risk of selling a new product, setting
sales goals and commission rates, deciding on marketing and advertising strategies, and other
similar operating decisions. Because the break-even point is, by definition, that activity level at
which no profit or loss is earned, the basic C-V-P equation can be modified to calculate the
break-even point as follows:
Sales revenue ? Variable costs ? Fixed costs ? $0
As you can see, to compute the break-even point, all that you need to do is simply set income
equal to zero and then solve for the unknown—such as the number of units to be sold or the
total revenues to be achieved.
Let’s again use the Jewels Corporation example. How many units must Jewels sell to break
even? (Note that we will use “X ” to represent the unknown element, in this case, the number
of baseball gloves.)
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? $0
[Sales price ? (X)] ? [Variable cost ? (X)] ? Fixed costs ? $0
$200X ? $110X ? $63,000 ? $0
$90X ? $63,000
X ? $63,000 ? $90 ? 700 units (baseball gloves)
In this case, if Jewels sells 700 baseball gloves, the company will generate enough revenues
to cover its variable and fixed costs, earning zero profit [($200 ? 700) ? ($110 ? 700) ?
$63,000 ? $0]. Once you understand the basic C-V-P formula, you just set it up and solve
for whatever unknown you’re interested in planning. Think you’ve got it? Then try this one as
a check on yourself: Assuming that Jewels can sell only 600 baseball gloves, what price per glove
would the company have to use in order to break even?
4
61 Chapter 2 Analyzing Cost-Volume-Profit Relationships
break-even point The
amount of sales at which total
costs of the number of units
sold equal total revenues; the
point at which there is no
profit or loss.
4 (Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? $0
[(X) ? Units] ? (Variable cost ? Units) ? Fixed costs ? $0
[(X) ? 600] ? ($110 ? 600) ? $63,000 ? $0
600X ? $66,000 ? $63,000 ? $0
600X ? $129,000
X ? $215 (new baseball glove price)
Determining Sales Volume to Achieve Target Income
Another way we can use C-V-P analysis in the planning process is to determine what level of
activity is necessary to reach a target level of income. Instead of setting profit at $0 to do a
break-even analysis, we can just as easily set income in the formula at the targeted level and
then use the formula to plan or predict what fixed costs, variable costs, sales prices, and sales
volumes are needed to achieve the target level of income. Target income is usually defined as
the amount of income that will enable management to reach its objectives—paying dividends,
meeting analysts’ predictions, purchasing a new plant and equipment, or paying off existing
loans. Target income can be expressed as either a percentage of revenues or as a fixed amount.
To illustrate target income, suppose that we want to know how many baseball gloves must
be sold by Jewels Corporation to achieve a target income of $36,000, assuming no changes in
per-unit variable costs or total fixed costs. The calculation is as follows:
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? Target income
$200X ? $110X ? $63,000 ? $36,000
$90X ? $99,000
X ? 1,100 units (baseball gloves)
Thus, we can see that if Jewels sells 1,100 baseball gloves at a contribution margin of $90 each,
and assuming that fixed costs are $63,000, the company will earn a pretax profit of $36,000
[($90 ? 1,100 units) ? $63,000 ? $36,000].
A fixed dollar amount of income, such as the $36,000 that would be earned by selling
1,100 baseball gloves, is probably the most typical way of expressing a target income goal for
many companies. However, because investors often evaluate companies partially on the basis of
the return on sales revenue (or simply “return on sales”), management may want to state its
goal as a percentage return as opposed to a fixed amount of income. For example, if Jewels
Corporation set a target income of a 20% return on sales, the computation would be:
Sales revenue ? Variable costs ? Fixed costs ? 0.20 ? Sales revenue
$200X ? $110X ? $63,000 ? 0.2($200X)
$200X ? $110X ? $63,000 ? $40X
$200X ? $110X ? $40X ? $63,000
$50X ? $63,000
X ? $63,000 ? $50 ? 1,260 gloves
As we can see in this calculation, Jewels Corporation can earn a 20% return on sales by selling
1,260 baseball gloves.
Short-Cut Formulas for C-V-P Analysis
Notice that in the C-V-P analysis examples that we’ve worked through so far, the basic C-V-
P equation remains constant. That’s what makes this formula so powerful. Once you’re com-
fortable with it, you can use it to manage any number of factors in planning for profits. However,
you may remember from your brief introduction to C-V-P analysis in the previous chapter and
from our C-V-P formula example on page 49 that we calculated break-even sales in units di-
rectly using the following formula.
? Break-even sales (in units)
This formula is a “short-cut” version of the C-V-P formulas above. You can see that it is
simply the last step in the C-V-P calculation above for Jewels’ break-even point of 700 base-
ball gloves. So, if you understand the basic C-V-P equation, you can simply skip to the last step
of the calculation. There are short cuts for computing the level of sales for both break-even vol-
ume and target income volume. The short-cut formula for both the break-even volume and the
target income volume in units is:
Total fixed costs
??????
(Sales price per unit ? Variable cost per unit)
62 Part 1 Foundations
target income A profit level
desired by management.
return on sales revenue A
measure of operating perfor-
mance; computed by dividing
net income by total sales rev-
enue. Similar to profit margin.
Note that if you use this formula to determine the break-even volume, then you
will assume that target income is $0, giving you:
Plugging in the numbers for Jewels Corporation, the results are the same as shown
earlier. As you can see, the short-cut calculation for both the break-even volume
and the target income volume is really the same formula. For target sales:
? 1,100 units
For the break-even volume:
? 700 units
Always remember, though, that short cuts are useful, but they should not be ap-
plied until you fully understand the basic C-V-P relationships. In addition, man-
aging some aspects of the C-V-P relationships can be tricky when you use short
cuts. So if you ever get confused in solving a C-V-P analysis problem, just put
the problem back in the original C-V-P equation:
Sales revenue ? Variable costs ? Fixed costs ? Target income
Computation in Dollar Amounts versus Units
Before we finish with C-V-P equations, you should note that a variable cost ra-
tio is sometimes used instead of a per-unit variable cost. In such cases, the basic
C-V-P equation is modified as follows:
Sales revenue ? (Variable cost ratio ? Sales) ? Fixed costs ? Profit
Because the variable costs are stated as a percentage of sales dollars rather than on a per-unit
basis, this approach expresses activity in terms of sales dollars, not units. This is still the same
basic C-V-P equation, but setting up the equation using the variable cost ratio will result in a
break-even point in dollars instead of units. For example, the break-even point for Jewels Cor-
poration would then be expressed as $140,000 in sales revenue ($200 per unit ? 700 units)
instead of 700 units as previously illustrated. This may be verified using the preceding equa-
tion and a 55% variable cost ratio as follows:
Sales revenue ? (0.55)Sales revenue ? $63,000 ? $0
(0.45)Sales revenue ? $63,000
Sales revenue ? $140,000
The short-cut formula for break-even volume and target income volume in sales dollars is:
(Remember the following: Contribution margin ratio ? 1 ? Variable cost ratio.)
Fixed costs ? Target income
????
Contribution margin ratio
$63,000 ? $0
??
$90
$63,000 ? $36,000
???
$90
Fixed costs
????
Contribution margin per unit
Fixed costs ? Target income
????
Contribution margin per unit
5
63 Chapter 2 Analyzing Cost-Volume-Profit Relationships
5 Remember that per-unit contribution margin is the sales price per unit less the variable cost per unit.
Buy or Rent?
The Internet provides a terrific tool for ana-
lyzing the decision to rent an apartment
versus to buy a home. Go tohttp://www
.financenter.com and select the “Consumer
Tools” tab and click on the “Educators”
menu option. Then scroll down to “Home
Buying” and choose the “Deciding to Buy
or Rent” option. Use the following data:
monthly rent, $850; renter’s insurance, $15;
yearly rent increase, 4%; home purchase
price, $150,000; appreciation rate, 4%;
savings rate, 3%; state and federal tax rate,
32%; years before the home is sold, 4 years;
loan amount, $120,000; loan term, 30 years;
interest rate on loan, 7%; discount points,
1%; origination fee, $0; upfront costs,
$1,000; yearly property tax, $2,500; yearly
maintenance, $700; yearly insurance, $300;
selling costs, 10%.
Net Work:
1. If the above data represented your cur-
rent rent situation, how much is your initial
cost each month for a house versus an
apartment?
2. Should you consider buying a house?
3. Based on the graphs provided, what ap-
pear to be the three most important issues
about renting versus buying?
Measuring the Effect of Potential Changes
in C-V-P Variables
The basic techniques of C-V-P analysis that you have worked with in this chap-
ter are used almost daily by organizations in the management processes of plan-
ning, controlling, and evaluating. As a result of understanding C-V-P analysis,
you will be adept at evaluating the effects on profitability of the following com-
mon changes in C-V-P variables: (1) the amount of fixed costs, (2) the variable
cost rate, (3) the sales price, (4) the sales volume or the number of units sold,
and (5) combinations of these variables.
Changes in Fixed Costs
Many factors, such as an increase in property taxes or an increase in manage-
ment’s salaries, for example, will cause an increase in fixed costs. (Recall also from
the opening scenario for this chapter that building a new facility such as a stadium can also in-
crease fixed costs.) If all other factors remain constant, an increase in fixed costs always increases
the number of units needed to break even. Obviously, the number of units needed to reach a
target income will also increase. To illustrate, let’s return again to the Jewels Corporation and
IBM Gets on the Internet
Wave In 1998, if you wanted
an IBM desktop personal com-
puter (PC), you had to walk
into a store to make the pur-
chase. In hindsight, this was a
strange way to sell computers
for a company that believed itself to be at the fore-
front of the e-business revolution. And in hindsight,
this sales approach, being both slow and expensive,
clearly didn’t work. The PC division for IBM lost $986
million in 1998 and was bracing itself for similar
losses in 1999. Market analysts were pushing IBM to
sell its PC division based in Research Triangle Park in North
Carolina. Finally, in the last quarter of 1999, IBM officials an-
nounced that it would yank its entire line of home desktop PCs
from retail stores in the United States and sell the machines
almost exclusively over the Internet. IBM also launched a $20
million advertising campaign (TV and direct mail flyers) to back
up the move.
IBM’s decision to sell over the Internet was driven largely
by cut-throat pricing of components and systems by its major
competitors and suppliers, the overhead costs of selling through
dealers, and the inability to distinguish its product from dozens
of competitor PCs sitting next to it on the retail shelf. In 2000,
IBM followed the Internet decision by cutting $1.1 billion in
annual manufacturing and distribution expenses. These cost
savings were achieved largely by three means. First, IBM
changed the way the PCs are built and redesigned the PC prod-
uct to use as many industry standard parts as possible. Second,
by building PCs to order (i.e., only building PCs when an order
was placed), IBM was able to significantly reduce the amount
of inventory it had to keep on hand. Third, IBM told its sup-
pliers that it wanted 95% of its components ready on demand
in well-stocked mini-warehouses near IBM manufacturing facil-
ities. “The whole object is to not own the parts for very long,”
said Adalio Sanchez, general manager of manufacturing and
operations for the PC division.
The change to IBM’s PC business started to pay off as costs
were reduced and shipments increased using the new ShopIBM
Web site. Losses in the PC division were cut to $360 million in
1999 and $148 million in 2000. In 2001, after four straight
years of losing money, the PC division was back in the black
with a pretax profit of $99 million by the middle of the year.
In a business today where prices on desktop PCs are typically
in the $800 range, if IBM is $10 or $20 higher than the price
of a DELL or COMPAQ PC, it can lose the sale. Clearly, control-
ling costs and managing sales is becoming more and
more important in the very competitive PC market.
Sources: Ed Scannell, “IBM to Go Online with Home
PC Sales,” InfoWorld Daily News, October 19, 1999;
Lisa Smith, “IBM’s Personal Computer Unit Makes
Turnaround,” The Herald-Sun, March 22, 2001.
b u s i n e s s env i r onment
Cauti on
If you want to use C-V-P analysis to calcu-
late the necessary sales volume in terms of
dollars, the per-unit variable cost is not
used. Rather, use the variable cost ratio
times sales to determine total variable costs.
Many students make the mistake of multi-
plying the per-unit variable cost times sales
instead of the variable cost ratio times sales
to get total variable costs.
assume that we need to analyze the effect on profits if fixed costs increase from $63,000 to
$81,000. How many more baseball gloves must be sold to maintain Jewels’ income goal of
$36,000?
Sales revenue ? Variable costs ? Fixed costs ? Target income
$200X ? $110X ? $81,000 ? $36,000
$90X ? $117,000
X ? 1,300 gloves
Because of the added fixed costs, Jewels must now sell 1,300 baseball gloves, instead of 1,100, to
earn a target income of $36,000. The computations are quite simple. In fact, you may have found
them unnecessary, realizing that if fixed costs increase by $18,000 ($81,000 ? $63,000), and if
the unit contribution margin remains $90 per glove, 200 additional gloves ($18,000 ? $90) will
have to be sold in order to reach the $36,000 target income (1,100 ? 200 ? 1,300 gloves).
Changes in the Variable Cost Rate
Like an increase in fixed costs, an increase in the variable cost rate also increases the number of
units needed to break even or to reach target income levels, when all other factors remain con-
stant. Suppose that the variable cost rate increased from $110 per baseball glove to $130 per
glove because of higher wages for factory personnel, increased costs of direct materials, or other
factors. How does this cost increase affect the number of gloves needed to reach the target in-
come, assuming that fixed costs are again $63,000?
Sales revenue ? Variable costs ? Fixed costs ? Target income
$200X ? $130X ? $63,000 ? $36,000
$70X ? $99,000
X ? 1,415 gloves*
*Technically, if the C-V-P analysis results in a fractional answer, you should always round the answer up to the
next digit. In this case, if you round the calculated answer of 1,414.29 to 1,414 gloves, you won’t quite achieve
the target income of $36,000.
The increase in the variable cost rate reduces the unit contribution margin (from $90 to
$70), which means that more gloves must be sold to maintain the same target income. With a
unit contribution margin of $90, the company would make a $36,000 target income by sell-
ing 1,100 baseball gloves; with a unit contribution margin of only $70, an additional 315 (1,415
? 1,100) gloves must be sold to earn at least a $36,000 target income.
Changes in Sales Price
If all other variables remain constant, an increase in the sales price decreases the sales volume
needed to reach a target income. This is because an increase in sales price increases the contri-
bution margin per baseball glove, thereby decreasing the number of gloves that must be sold
to earn the same amount of target income.
To illustrate, assume that the demand for baseball gloves is overwhelming and that Jewels
cannot produce gloves fast enough. Hence, we make a decision to increase the price from $200
to $230 per glove. As a result of the price increase, the number of gloves that must be sold to
reach the target income of $36,000 decreases:
Sales revenue ? Variable costs ? Fixed costs ? Target income
$230X ? $110X ? $63,000 ? $36,000
$120X ? $99,000
X ? 825 gloves
With the sales price increase of $30 per glove, the contribution margin also increases $30
per glove to $120; and with a $120 contribution margin per glove, only 825 gloves need to be
sold to reach the $36,000 target income. Obviously, a decrease in the sales price would have
the opposite effect; it would increase the number of units needed to reach the target income.
65 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Changes in Sales Volume
As you have seen, the sales volume (the number of gloves to be sold) for the target income has
varied with each change in one of the other variables. When other variables remain constant,
an increase in the sales volume will result in an increase in income. Very simply, the more gloves
sold, the higher the income (as long as the contribution margin is positive!). The degree of
change in profits resulting from volume change depends on the size of the unit contribution
margin. To be specific, the change in income will be equal to the change in sales volume units
multiplied by the contribution margin per unit. So, when the unit contribution margin is high,
a slight change in volume results in a dramatic change in profit. With a lower unit contribu-
tion margin, the change in profit is less.
Simultaneous Changes in Several Variables
Thus far, we have examined changes in only one variable at a time. However, in your work in
actual business organizations, you will find that individual changes are quite rare. More often,
a decision will affect several variables, all at the same time. For example, should Jewels Cor-
poration increase fixed advertising costs by $20,000 and reduce the sales price by 10% if the
result would be to increase sales volume by 500 units? The impact on the target income from
these proposed changes is as follows:
Initial Data Proposed Changes
Sales price per glove . . . . . . . . . . . . . . . . . . . $200 $180 ($200 ? 90%)
Variable costs per glove . . . . . . . . . . . . . . . . $110 $110
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . $63,000 $83,000 ($63,000 ? $20,000)
Target income . . . . . . . . . . . . . . . . . . . . . . . . $36,000 X
Sales volume . . . . . . . . . . . . . . . . . . . . . . . . . 1,100 gloves 1,600 gloves (1,100 ? 500)
Computations and Result:
Sales revenue ? Variable costs ? Fixed costs ? Target income
($180 ? 1,600) ? ($110 ? 1,600) ? $83,000 ? X
$288,000 ? $176,000 ? $83,000 ? X
$29,000 ? X (target income)
The analysis shows that target income would drop by $7,000 ($36,000 ? $29,000) as a result
of these changes. So, our decision should be to not implement the proposed changes.
Consider another possible decision: Should Jewels automate part of its production, thereby
reducing (by $10) variable costs to $100 per unit and increasing (by $5,000) fixed costs to
$68,000? The computation is as follows:
Sales revenue ? Variable costs ? Fixed costs ? Target income
($200 ? 1,100) ? ($100 ? 1,100) ? $68,000 ? X
$220,000 ? $110,000 ? $68,000 ? X
$42,000 ? X (target income)
This analysis shows that implementing these proposed changes would be beneficial because
they would increase target income by $6,000 ($42,000 ?$36,000). Obviously, this is true only
if the assumptions can be relied on—that is, if fixed costs will rise by no more
than $5,000 and unit variable costs will decrease by a full $10.
Consider another example. Suppose Jewels Corporation could use part of
the excess capacity of its operating facilities to make baseball bats. These bats
would sell for $90 per unit, increase fixed costs by $40,000, and have a variable
cost per unit of $45. Jewels wants to add this new product line only if it can in-
crease income by $25,000. How many baseball bats must Jewels sell to reach this
target income? The computation follows:
66 Part 1 Foundations
Cauti on
Remember, any change that affects the
number of units sold changes both the total
sales revenue and total variable costs.
Sales revenue ? Variable costs ? Fixed costs ? Target income
$90X ? $45X ? $40,000 ? $25,000
$45X ? $65,000
X ? 1,445 baseball bats (rounded up)
Now that we have completed the C-V-P calculations, we must determine whether the company
can produce and sell 1,445 baseball bats. If that sales goal seems attainable, the facilities should
be used to make the bats. Don’t forget that making C-V-P calculations is the easy part of man-
aging an organization. It takes an excellent manager to successfully implement the results of a
C-V-P analysis into a real business process.
67 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Breaking Even in the Hotel
Industry An international ho-
tel chain undertook a project
to increase the effectiveness
of decision making of its prop-
erties in Europe, the Middle
East, and Africa. In 1996, com-
pany executives wanted to improve the financial
planning and control decisions of the hotel manage-
ment teams. The Europe, Middle East, Africa division
was responsible at that time for approximately 240
hotels. Essentially, the executives aimed to encour-
age a greater use of basic managerial accounting
techniques such as budgeting models and C-V-P analysis in
order to improve the profitability of individual hotels.
It was clear to the company that understanding how ho-
tel costs behaved is absolutely key to making good decisions
that affect market share analysis, annual budget preparation
and monitoring of results, sales volume and business mix de-
cisions, pricing policies, and cost management. In order to
identify the fixed and variable costs in the hotels, the com-
pany first worked with individual hotel management teams
within its organization who were intimately familiar with how
costs behaved based on changes in sales volumes (i.e., hotel
rooms rented). Initially, the company had these individuals de-
termine from their own experience which costs were fixed, vari-
able, or semi-variable (i.e., mixed) costs with respect to changes
in sales volume. Scattergraph and statistical analyses were then
used to estimate the fixed and variable proportions of the mixed
costs—again related to sales volume—and allocate these costs
to the main fixed and variable groups.
Computer spreadsheets were then used to assess key “what
if” questions. For instance, “What is the likely effect on profit
of a 3% shortfall in room revenue?”. . . or . . . “How will profit
change if a 5% growth in total sales volume occurs?” This alerts
managers to the critical areas of profitability and indicates
which revenue and cost areas require greater attention for a
given decision. It also enables management to gain an overall
indication of “profit stability” or “profit instability’” in relation
to changes in revenue and cost of particular hotel properties.
Knowledge of break-even levels and profit-and-loss implications
of different business scenarios are relevant if managers are to
make informed decisions which ensure survival, optimize prof-
its, and limit risk, giving rise to a feeling of “being more in
control” when making decisions.
In 1995, the year before the new management focus on
C-V-P analysis commenced, the average operating profit margin
in the Europe, Middle East, Africa division was 35%. In 1998,
the average operating profit margin was 39%. Although the ho-
tel executives do not believe that the new focus on C-V-P tools
is the only reason for this improvement, it has played a posi-
tive role in significantly adding to shareholder value.
Source: Ian C. Graham and Peter J. Harris, “Devel-
opment of a Profit Planning Framework in an Inter-
national Hotel Chain: A Case Study,” International
Journal of Contemporary Hospitality Management,
1999 (Issue 5), pp. 198–204.
b u s i n e s s env i r onment
68 Part 1 Foundations
Sales revenue ? Variable costs ? Fixed costs ?
Target income
Using this equation, you as a manager can work to plan,
control, and evaluate the costs, prices, and sales output of
the organization. The effects of changes in costs, prices,
and volume on profitability may be determined by C-V-P
analysis. Changes in individual variables or simultaneous
changes in several variables can be analyzed with this tech-
nique.
T O S UMMA R I Z E : The contribution margin is
sales revenue less variable costs and is the amount of rev-
enue left to cover fixed costs and provide a profit. The con-
tribution margin can be expressed in total dollars, on a
per-unit basis, or on a percentage basis. Because fixed costs
remain constant within a relevant range, once fixed costs
have been covered, income increases by the amount of the
per-unit contribution margin for every additional unit sold.
This relationship is used in C-V-P analysis. The basic C-V-P
equation is:
Using Graphs to “See” C-V-P Relationships
Earlier in this chapter, we talked about using scattergraph methods as a way to analyze cost be-
havior. Recall that once we have plotted the history of costs on a graph and visually fitted a re-
gression line through the data, we can then essentially “see” how the cost can be separated into
its fixed and variable cost components. Now, by simply adding a line to the cost chart to rep-
resent revenue, we can graphically work with cost-volume-profit relationships. In fact, using
graphs may be the most effective way to manage and communicate C-V-P information. This
graphical approach allows you to visually examine cost and revenue data over a range of activ-
ity rather than at a single volume. Sometimes, though, reading precise information from a graph
can be difficult. Hence, when analyzing specific proposals in the future, you will typically com-
bine the C-V-P equations discussed in the preceding section with the graphs discussed in this
section.
On a C-V-P graph, volume or activity level usually is shown on the horizontal axis, and
total dollars of sales and costs are shown on the vertical axis. Lines are then drawn to represent
total fixed costs, total costs, and total revenues. Exhibit 6 shows a C-V-P graph for Jewels Cor-
poration.
Remember that fixed and variable cost relationships are valid only for the relevant range
of activity (the screened area on the graph in Exhibit 6). In this case, fixed costs are $63,000,
and variable costs are $110 per glove over the range of activity between 400 and 1,200 gloves
sold. Total costs are $118,000 at 500 gloves [$63,000 ? ($110 ? 500 gloves)], $129,000
at 600 gloves [$63,000 ? ($110 ? 600 gloves)], and so on. Similarly, total revenues are
$100,000 at 500 gloves ($200 ? 500 gloves), $120,000 at 600 gloves, and so forth. The
break-even point, the point at which total revenues equal total costs, is 700 gloves, or $140,000
in sales.
As shown in Exhibit 7, we can use the graphic format to isolate such items of interest as
total variable costs, total fixed costs, the area in which losses occur, the area in which profits
will be realized, and the break-even point. Because C-V-P graphs illustrate a wide range of ac-
tivity, this tool can help in quickly determining approximately how much profit or loss will be
realized at various levels of sales.
The Profit Graph
With a few adjustments to a standard C-V-P graph, we can create what is called a profit graph,
which plots only profits and losses and omits costs and revenues. A profit graph is another
useful way to visualize how decisions regarding costs and revenues will impact profit. Exhibit
8 shows a profit graph for Jewels Corporation based on the same underlying data used in Ex-
hibit 6.
5 Visualize C-V-P rela-
tionships using graphs.
profit graph A graph that
shows how profits vary with
changes in volume.
Notice that, though the horizontal axis of the profit graph is the same as those of the pre-
vious graphs, the vertical axis represents only profits and losses. As long as the contribution
margin is positive, the maximum amount of losses that can occur is at a zero level of sales. With
no sales, total losses will be the amount of the fixed costs. With the axes properly labeled, we
can draw the profit line as follows:
1. Locate the loss for zero sales volume on the vertical axis. This is the total fixed cost, or
negative $63,000 in this case.
2. Locate the profit or loss at another sales volume. For example, at sales of 700 gloves,
profits are zero [$140,000 ? ($63,000 ? $77,000)], or at sales of 1,000 gloves, profits
are $27,000 [$200,000 ? ($63,000 ? $110,000)].
3. After the two profit or loss points have been identified, draw a line through them back
to the vertical axis.
Because of how simple it is to create, the profit graph is widely used for comparing competing
projects. It has the disadvantage, however, of not showing specifically how revenues and costs
vary with changes in sales volume.
A Comparison of C-V-P Graphs with C-V-P Equations
C-V-P graphs are very useful in understanding contribution margin income statements and
C-V-P equations. To illustrate this point, let’s again explore the question of what volume of
69 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 6: A Cost-Volume-Profit Graph
$200,000
180,000
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
Number of gloves sold
B e t
7 e
a e
2 g
c Total costs ?
0 1 g
i s
6
e
v
e
v
e
u
e
S
a
l
e
s
o
s
l
c
o
0
70 Part 1 Foundations
Exhibit 7: Cost-Volume-Profit Graphs
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Fixed Costs $
S
a
l
e
s
Number of gloves sold
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Area of Profit $
S
a
l
e
s
Number of gloves sold
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Area of Loss $
S
a
l
e
s
Number of gloves sold
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Variable Costs $
S
a
l
e
s
Number of gloves sold
Exhibit 8: Profit Graph for Jewels Corporation
$80,000
60,000
40,000
20,000
0
?20,000
?40,000
?60,000
?80,000
P
r
o
f
i
t
L
o
s
s
Number of gloves sold
A f l
activity Jewels Corporation needs to reach a target income of $36,000. This
was illustrated earlier with the equation approach, but it is repeated here to show
that the graph approach will produce the same quantitative results. As you can
see in Exhibit 9, Jewels Corporation must sell 1,100 baseball gloves to reach a
target income of $36,000.
71 Chapter 2 Analyzing Cost-Volume-Profit Relationships
STOP & THINK
When analyzing costs, volume, and profit,
do you think most managers would prefer
to use graphs or equations?
Exhibit 9: Comparison of C-V-P Equation with C-V-P Graph
Number of gloves sold
0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
P
r
o
f
i
t
L
o
s
s
$80,000
40,000
0
–40,000
–80,000
Profit Graph
Number of gloves sold
0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
S
a
l
e
s
$240,000
200,000
160,000
120,000
80,000
40,000
220,000
184,000
C-V-P Graph
es le e l
enue vee vv
,000 Profit 6,, 666 $36
al costs ta a tt
able costs ri i rr Var
ed costs eee x
a e Break even
p
36,000
g
o
ii point
a e
pppoint
o
o
C-V-P Equation
(Sales price ? Units) ? (Variable costs ? Units) ? Fixed costs ? Profit
$200X ? $110X ? $63,000 ? $36,000
$90X ? $99,000
X ? 1,100 gloves
72 Part 1 Foundations
over wide ranges of activity. The most common graphic ap-
proach involves plotting fixed costs as a horizontal line with
variable costs representing the distance between the fixed
costs and total costs line. A profit graph, which shows only
profit or loss and volume, is much simpler, but it does not
show how costs vary with changes in sales volume. Regard-
less of the approach, all variations of C-V-P analysis are
based on the same calculations and on the same underly-
ing concept of fixed and variable costs.
T O S UMMA R I Z E : The financial effects on cost-
volume-profit decisions can be examined by using either
equations or graphs. These methods of analysis can be used
to calculate the break-even point, which occurs at the point
where total revenues equal total fixed costs plus total vari-
able costs. These methods can also be used to project a tar-
get profit level, with profit being equal to the excess of
revenues over total costs. The graphic approaches are use-
ful because they highlight cost-volume-profit relationships
Limiting Assumptions of C-V-P Analysis
C-V-P analysis is an extremely useful tool to assist in making short-term operating decisions.
However, C-V-P analysis has some limiting assumptions that must not be overlooked.
The first key assumption underlying C-V-P analysis is that the behavior of revenues and
costs is linear throughout the relevant range. This means that C-V-P analysis is valid only for
a relevant range.
A second assumption is that all costs, including mixed costs, can be accurately divided into
fixed and variable categories. As we have seen in this chapter, some costs have characteristics of
both fixed and variable costs. These costs sometimes are not easily classified into their fixed and
variable components, which limits the accuracy of C-V-P analysis.
For companies with more than one product, a third major assumption in C-V-P analysis
is required—that the mix of a company’s products does not change over the relevant range.
The sales mix is the proportion of the total units sold (or the total dollar sales) represented by
each of a company’s products. Sales mix will be discussed in the expanded material section of
this chapter.
In addition to these three key assumptions, there are other limiting assumptions implicit in
C-V-P analysis. For example, C-V-P analysis assumes that efficiency and productivity are held
constant, that the prices of materials and other product components are constant, and that rev-
enues and costs can be analyzed using a single activity base, such as volume. A related and very
significant assumption, and one that clearly is not always valid, is that volume is the only, or even
the primary, driver of costs. As discussed below, delivery time and quality can also impact costs.
Because of the limiting assumptions just described, a manager must use reasonable caution
when making decisions using C-V-P analysis. Nevertheless, C-V-P analysis does provide a good
model for predicting future operating results when specific relationships are defined and rec-
ognized.
Issues of Quality and Time
The emphasis in this chapter has been primarily on costs and profits and how they change when
changes in variable costs, fixed costs, sales prices, and sales volume are made. Remember, how-
ever, that financial results are just one of several elements of performance that a manager must
consider. Good managers are equally interested in how these changes will affect the quality of
goods and services produced and sold and the speed at which products and services can be de-
livered to customers. If, for example, reducing fixed costs means that goods will be produced
more slowly or that the quality of manufactured products will be reduced, then a decision to
reduce fixed costs may be a poor one. On the other hand, if a company can automate a func-
tion using robotics instead of high-cost workers, for example, it may be possible to simultane-
ously reduce total costs, increase quality and consistency, and improve speed of production. To
determine whether quality and speed of production are good or bad, a management team may
6 Identify the limiting
assumptions of C-V-P
analysis, and explain the
issues of quality and time
relative to C-V-P analysis
decisions.
E M 73 Chapter 2 Analyzing Cost-Volume-Profit Relationships
need to compare its results with those of other firms, a process called benchmarking, which will
be introduced in a later chapter.
it is important to also consider how these changes will af-
fect the quality of goods and services and the speed at which
products and services can be delivered to customers. Deci-
sions that increase quality, reduce costs, and speed up pro-
duction are valuable changes and should be made; decisions
that have a negative effect on one or more of these vari-
ables must be carefully analyzed and trade-offs considered.
T O S UMMA R I Z E : C-V-P analysis is based on
three critical and limiting assumptions: (1) that the behav-
ior of revenues and costs is linear throughout the relevant
range, (2) that all costs can be categorized as either fixed
or variable, and (3) that the sales mix does not change.
When considering how changes in variable costs, fixed costs,
sales prices, sales volume, and sales mix will affect profits,
Thus far, we have covered various types of costs, simple methods of analyzing
mixed costs, and the basics of C-V-P analysis. In this expanded section, we cover
an additional, more advanced method of analyzing mixed costs—least squares
analysis. We also cover the effect of the sales mix on profitability and use the con-
cept of operating leverage to explore differences in cost structures among man-
ufacturing, merchandising, service, and e-commerce organizations.
Analysis of Mixed Costs—The Least Squares Method
Earlier, we described two common methods for analyzing mixed costs: the scattergraph and high-
low methods. These methods are relatively easy to use and provide useful estimates of the fixed
and variable components of mixed costs. A more sophisticated method for analyzing mixed costs
is the least squares method, which is the most accurate method of using a specific set of data to
determine the fixed and variable portions of a mixed cost. Like the scattergraph, the least squares
method fits a straight line through all points on a graph. However, instead of visually fitting the
regression line through the cost points, it uses statistical analysis to guarantee that the line is the
best possible fit for the applicable costs. As a result, the least squares method provides a better
analysis because it isn’t based on a subjective regression line like scattergraphs and because it uses
all the cost data points rather than just the high and low data points as with the high-low method.
The formula for the least squares method is based on the equation for a straight line:
Y ? a ? bX
You probably recognize this classic equation from previous math classes you may have had.
When this equation is used to do cost analysis, Y represents the total predicted cost; a repre-
sents the intercept and the fixed cost (if in the relevant range); b represents the variable cost
rate or the slope of the line; and X represents the activity level being considered. Using cost and
activity level data, this method involves the use of simultaneous equations to find the values of
a and b. Once computed, these values can be combined with the projected activity level X to
predict or estimate the total future cost Y. For example, if the values of a and b are computed
to be $200 and $5, respectively, then for an estimated activity level of 100 direct labor hours,
we can predict that:
Y (total predicted cost) ? $200 ? $5(100 hours)
Y ? $200 ? $500
Y ? $700
7 Analyze mixed costs
using the least squares
method.
least squares method A
method of segregating the
fixed and variable portions of
a mixed cost; the regression
line, a line of averages, is
statistically fitted through all
cost points.
You should understand that the regression line is basically a line of averages. Therefore, the
actual total cost for 100 direct labor hours might be somewhat different from the predicted cost
of $700. The method of least squares, however, attempts to minimize the differences between
predicted and actual costs. Once a regression line has been fitted to historical data, the fixed
and variable costs represented by the line can be used to predict the level of future costs.
Calculating the estimates of a (the intercept, or the total fixed cost) and b (the slope, or
variable cost rate) requires solving the following two simultaneous equations:
1. ?XY ? a?X ? b?X
2
2. ?Y ? na ? b?X
where
a ? fixed cost
b ? variable cost rate
n ? number of observations
? ? summation sign (which means the sum of all historical data indicated by the sign)
X ? activity level, or independent variable
Y ? total (predicted) mixed cost, or dependent variable
Actually, solving these equations is easy with a calculator or computer, but difficult and te-
dious by hand. Initially solving these equations by hand may be useful to you in learning ex-
actly how these equations work. However, as a manager working with cost estimations, you are
going to have computers available to analyze large amounts of data very quickly. Hence, we
will focus on describing and interpreting the typical output from a computerized application
of least squares analysis. We will leave it to math classes to illustrate the manual calculations of
the least squares method.
To illustrate the concept of least squares, let’s return once more to the electricity cost data
used earlier in this chapter to work with the scattergraph and high-low methods. Note that the
historical data that we are using for this example are given for only six months; thus, the re-
sulting regression equation will likely be less accurate than it would be with more data (say, 12
or 18 months of data).
Month Direct Labor Hours Worked Total Electricity Cost
January 7,000 $ 70,000
February 6,000 60,000
March 12,000 100,000
April 6,600 80,000
May 18,000 120,000
June 14,000 110,000
Using these data, the following output, shown in Exhibit 10, can be generated in just a
matter of minutes using the “data analysis” tool in Excel
®
, a Microsoft database software pro-
gram.
6
Now compare the least squares output with the results from our earlier work using the
scattergraph and high-low methods:
Fixed Costs Variable Cost per Direct Labor Hour
Scattergraph method $40,000 per month $4.29 per direct labor hour
High-low method 30,000 per month 5.00 per direct labor hour
Least squares analysis 40,402 per month 4.68 per direct labor hour
74 Part 1 E M Foundations
6 There are literally hundreds of software programs that can be used to run regressions or least squares analysis.
E M 75 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 10: Output of Least Squares Analysis Application
5,000 10,000 15,000 20,000
Hours
C
o
s
t
$140,000
120,000
100,000
80,000
60,000
40,000
20,000
Cost
Predicted Cost
Month Hours Cost
January 7,000 $ 70,000
February 6,000 60,000
March 12,000 100,000
April 6,600 80,000
May 18,000 120,000
June 14,000 110,000
Summary Output
Regression Statistics
Multiple R 0.962
R square 0.926
Adjusted R square 0.907
Standard error 7207.705
Observations 6
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept $40,402.03 $7,613.10 $5.31 0.0061 $19,264.63 $61,539.43
Hours $ 4.68 $ 0.66 $7.05 0.0021 $ 2.84 $ 6.52
76 Part 1 E M Foundations
Sales Mix
Earlier in this chapter, we described some important limiting assumptions of C-V-P analysis. As a
manager using C-V-P, you need to be aware of what this tool can and cannot do. One important
issue is that C-V-P analysis must be adjusted when a company starts changing the mix of products
that it sells. Sales mix is the proportion of the total units represented by each of a company’s prod-
ucts. To keep our discussions simple, in previous sections of the chapter we used examples of com-
panies with only one product. Many companies have more than one product, however, so you
need to understand how sales mix issues are resolved. To illustrate how a change in sales mix can
affect a company’s C-V-P relationships, let’s assume that Multi-Product, Inc., sells three different
products. Following are the monthly revenues and costs for each type of product:
8 Explain the effects of
sales mix on profitability.
sales mix The relative pro-
portion of total units sold (or
total sales dollars) that is rep-
resented by each of a com-
pany’s products.
the least squares method is more mathematically correct
than the scattergraph or high-low methods, it still should
be used with caution in analyzing mixed costs. Least squares
results can be quickly calculated using computer programs
such as Microsoft’s Excel
®.
T O S UMMA R I Z E : A more sophisticated tech-
nique for analyzing mixed costs is the least squares method.
The least squares method is essentially equivalent to sim-
ple regression analysis, using the equation for a straight line
(Y ? a ? bX) and simultaneous equations to calculate the
fixed and variable portions of a mixed cost. Even though
You can see that the least squares analysis results in fixed costs estimated at
$40,402 and the variable cost rate estimated to be $4.68 per direct labor hour.
As you can see, the results are more similar to the results of the scattergraph method
than to the results of the high-low method. Why do you think this is the case?
The reason is that both the scattergraph and least squares methods are essentially
using all of the historical data while the high-low method uses only two data points
(February and May).
We won’t take time in this chapter to understand all of the output shown
in Exhibit 10; what is most important is that you know three things: (1) the co-
efficient of the intercept, (2) the coefficient of the direct labor hours, and (3) the
R square summary statistic. The coefficient of the intercept, or $40,402.03 in
this case, is the estimate of total fixed costs. The coefficient of the direct labor
hours, or $4.68 in this case, is the estimate of the variable electricity cost per di-
rect labor hour. The R square (R
2
) is a descriptive statistic that provides infor-
mation about how well the regression line fits the data; in other words, R square
can be interpreted as the fraction of the variability in the data that is explained
by the computed regression statistics. For now, remember that a higher R
2
is bet-
ter, and an R
2
of 1.0 represents a perfect fit (meaning all data points were ex-
actly on the regression line). In this case, an R
2
of 0.926 is very high and suggests
that the computed regression statistics explain most of the variability in the data.
7
FYI :
An R
2
of more than 0.9 is actually not very
common in practice. It is often quite rare to
identify a single cost driver that explains
most of the variance of important costs in an
organization. Typically, organizations find
that there are many things that affect a par-
ticular cost (e.g., headcount, floor space, op-
erating hours, etc.), which requires that cost
analysis be based on multiple cost drivers.
The least squares analysis method we have
discussed here is also known as simple or
single linear regression. Multiple linear re-
gression, a technique you may have learned
about in a statistics class, uses a similar
approach to identify the impact of several
activities on changes in a specific cost.
7 The adjusted R
2
of 0.907 is a more conservative estimate of the variance explained in the data and is preferred
to the R
2
statistic in some circumstances.
Product A Product B Product C Total
Amount Percent Amount Percent Amount Percent Amount Percent
Sales revenue $25,000 100% $45,000 100.00% $30,000 100% $100,000 100%
Less variable costs 20,000 80 30,000 66.67 21,000 70 71,000 71
Contribution margin $ 5,000 20% $15,000 33.33% $ 9,000 30% $ 29,000 29%
Sales mix 25% 45% 30% 100%
Total sales are $100,000, which in this example includes $25,000 in sales of
Product A, $45,000 of Product B, and $30,000 of Product C. Therefore, the
sales mix is 25% Product A ($25,000 ? $100,000), 45% Product B ($45,000
? $100,000), and 30% Product C ($30,000 ? $100,000). With this sales mix,
the average variable cost ratio is 71%, which is determined by dividing total vari-
able costs of $71,000 by total sales of $100,000. If Multi-Product, Inc., had fixed
costs of $17,400 and desired a target income of $40,000, the necessary sales vol-
ume (in dollars) would be:
Sales revenue ? (0.71)Sales revenue ? $17,400 ? $40,000
(0.29)Sales revenue ? $57,400
Sales revenue ? $57,400 ? 0.29
Sales revenue ? $197,932 (rounded up)
Alternatively, you could calculate the average contribution margin ratio by subtracting the
total variable costs from total sales and dividing the result (total contribution margin of $29,000)
by total sales of $100,000. The company could then divide the average contribution margin
ratio (29%) into fixed costs plus target income ($17,400 ? $40,000). This revised, more com-
pact formula is simply a restatement of the preceding equation.
? ? $197,932 (rounded up)
Remember, though, that $197,932 in sales will achieve the target income only if the aver-
age variable cost and contribution margin ratios, and therefore the sales mix, do not change. In
order for you to better understand this fact, assume that the total sales revenue and the sales
price of each product remain the same but that the sales mix changes as follows:
$57,400
?
0.29
Fixed costs ? Target income
?????
Average contribution margin ratio
E M 77 Chapter 2 Analyzing Cost-Volume-Profit Relationships
FYI :
A computer can make sales mix and other
C-V-P analysis computations easier to do.
Using simulation or other programs, you can
quickly calculate the financial effects of
changes in the sales of one product or simul-
taneous changes in sales of several products.
Product A Product B Product C Total
Amount Percent Amount Percent Amount Percent Amount Percent
Sales revenue $50,000 100% $30,000 100.00% $20,000 100% $100,000 100%
Less variable costs 40,000 80 20,000 66.67 14,000 70 74,000 74
Contribution margin $10,000 20% $10,000 33.33% $ 6,000 30% $ 26,000 26%
Sales mix 50% 30% 20% 100%
As you can see in this example, the variable cost and contribution margin ratios for each
product remain the same, but the sales mix changes. Product A now comprises 50% of total
sales instead of 25%. Because Product A has a lower contribution margin ratio than Products
B and C, the average contribution margin ratio decreases from 29 to 26% (stated another way,
the average variable cost ratio increases from 71% to 74%). Now think about how this change
in the sales mix would affect profit and the volume of sales revenue needed to break even.
Would you expect the necessary sales volume to increase or decrease?
Let’s use the more compact formula based on the average contribution margin ratio to
calculate the new sales volume. When we run the new C-V-P calculation, the sales volume
needed to generate $40,000 of target income increases to $220,770, computed
as follows:
? ? $220,770 (rounded up)
The important thing that we’ve learned from these sales mix calculations
is that one sensible profit-maximizing strategy for management would be to
maintain as large a contribution margin as possible on all products and then
$57,400
?
0.26
Fixed costs ? Target income
?????
Average contribution margin ratio
STOP & THINK
Before moving on, can you calculate the
necessary sales volume of $220,770 in
the second sales mix example using the
familiar C-V-P equation: Sales revenue ?
Variable costs ? Fixed costs ? Target
income?
to emphasize those products with the largest individual contribution margins. In
the remaining chapters of this text, we discuss procedures that management can
use to control costs and, hence, maintain high contribution margins. The sec-
ond part of this strategy—emphasizing the products with the highest contribu-
tion margin ratios—is a marketing function. Multi-Product, Inc., for example,
should promote Product B more aggressively than Product A. With other fac-
tors being equal, a company should spend more advertising dollars and pay higher
sales commissions on its products with higher contribution margin ratios. In fact,
instead of paying commissions based on total sales, a good strategy would be to
base sales commissions on the total contribution margin generated. This way,
the mix of products that maximizes the sales staff’s commissions will be the mix
that provides the company with the greatest overall profit.
78 Part 1 E M Foundations
STOP & THINK
Would maximizing the sales of the high-
est contribution margin products still be
the best profit-maximizing strategy if the
company experienced production con-
straints such that producing more of the
highest contribution margin products se-
verely limited the quality or production
speed of other products?
things being equal, to maximize profits, management should
put greater emphasis on the sale of products with higher
contribution margin ratios.
T O S UMMA R I Z E : Sales mix is the proportion
of the total units sold represented by each of a company’s
products. Changes in sales mix can affect profits because
not all products have the same contribution margin. Other
Cost Structure in Different Types of Organizations
Now that we have nearly completed this chapter, we have developed a lot of insight into how
to think about and manage costs in the process of making profit-planning decisions. This chap-
ter is actually a lot about the strategy—the strategy of how a company works with its specific
types of costs and activities to create a profit. Overall, we now basically understand how cost-
volume-profit relationships and contribution margins highlight the different effects that vari-
able and fixed costs have on profitability. As we close this chapter, an important management
issue to be understood has to do with the amount of fixed costs a company has in its cost struc-
ture. The amount of fixed costs an organization commits itself to often has a lot to do with its
type of business, e.g., merchandising, manufacturing, or service. In addition, the arrival of e-
commerce into the economy is having an impact on cost structures of organizations. We’ll talk
more about differences between merchandising, manufacturing, service, and e-commerce com-
panies throughout the remaining chapters in this textbook. For now, we’ll simply illustrate the
differences among these organizations by applying the concept of operating leverage to illus-
trate how a company can manage risk (in terms of profits) by the way it organizes its cost struc-
ture—in other words, how much the company is committed to using fixed costs versus variable
costs to do business.
Imagine that you have worked with two of your college friends to design a new computer
software game that you expect to market to college campuses across the nation. You and your
partners have identified three ways to approach the market. First, you can take on the role of
the merchant by contracting with a software manufacturing company to handle all the pro-
duction of the packaged software. You can then concentrate on the sales and marketing of their
new game. This approach won’t require an expensive production facility, but the reality is that
you will have to pay a high price per unit to the company that handles the production of the
packaged software. In the second approach, you can take on the role of manufacturer by set-
ting up your own production facilities. In this case, because all of your effort will be dedicated
to producing the game, you will need to wholesale the software product to another merchant
company that will then resell the product to the actual customers. Finally, you can “virtually”
sell the game to other college students by contracting with an e-commerce company that will
host your software download site for a significant fixed fee per month. In any case, regardless
of whether you and your partners will wholesale the game to another merchant or retail the
9 Describe how fixed
and variable costs differ in
manufacturing, service,
merchandising, and e-
commerce organizations,
and illustrate these differ-
ences with the operating
leverage concept.
operating leverage The
extent to which fixed costs
are part of a company’s cost
structure; the higher the pro-
portion of fixed costs to vari-
able costs, the faster income
increases or decreases with
changes in sales volume.
game directly to the college student market, you have determined that you can sell the game
for $100. The costs of each of these methods of structuring your business are as follows:
E M 79 Chapter 2 Analyzing Cost-Volume-Profit Relationships
tremely committed to fixed costs with little or no variable
product costs. These cost structure differences are impor-
tant and are illustrated in the concept of operating lever-
age. Operating leverage relates to the amount of fixed costs
a company has in its cost structure. When sales are expected
to increase, high operating leverage results in higher in-
come, and vice versa.
T O S UMMA R I Z E : The relationship between
fixed and variable costs differs across different types of or-
ganizations. Generally, traditional merchandising companies
have relatively low levels of fixed costs and high levels of
variable costs. On the other hand, manufacturing companies
often have higher levels of fixed costs and lower levels of
variable costs. The emergence of e-commerce in this econ-
omy has resulted in some companies that are even more ex-
Variable Cost per Unit to Fixed Cost per Year for the
Manufacture or to Purchase from a Merchandising, Manufacturing, or
Business Structure Manufacturer E-Commerce Facility
Traditional retail merchant $80 $100,000
Manufacturer 25 375,000
E-commerce merchant 0 500,000
As you can see, one of the issues that you must decide when selecting your
company’s business structure is whether you and your partners want to commit
to high fixed costs in order to have low variable costs, or vice versa. This trade-
off of fixed versus variable costs is what we mean when we talk about operating
leverage. As total fixed costs increase and variable costs per unit decrease, the op-
erating leverage of the organization increases. In the example above, the operat-
ing leverage of your company will be very high if you choose to structure your
company as an e-commerce merchant. So, the question you should be asking
yourself is whether it is good or bad to have high operating leverage? The an-
swer is that it depends on whether the company is operating above or below the
break-even point.
The C-V-P graphs in Exhibit 11 show us the impact of operating leverage
for these three types of companies. The break-even point (which is the same for
all three companies) is at a sales volume of 5,000 games sold each year. At this
point, all three companies would generate the same level of profit—nothing. As
sales move above or below the break-even point, however, there are significant
differences in profit (i.e., the distance between the revenue line and the total
costs line) between the company structures. If sales are below the break-even
point, then structuring the company as an e-commerce merchant will generate
a lot of losses. If the company can sell more than 5,000 games per year, how-
ever, then the e-commerce merchant structure will generate the most profit per
year. Essentially, operating leverage is a measure of risk. With high levels of op-
erating leverage, the company is at risk of losing a lot of money if sales go down.
But business risk often has an upside. In the case of operating leverage, the risk
of loss is balanced by the potential for large gains in income as sales go up. So
your decision on how to structure your company partly depends on the impact
on operating leverage and on how much risk you are willing to accept.
Cauti on
Don’t confuse the concept of operating
leverage with the concept of financial lever-
age, though there is a lot of similarity in
these concepts. While both concepts focus
on risk and the sensitivity of profit to
changes in sales volume, financial leverage
has to do with the use of debt versus equity
to provide financing for a company. In gen-
eral, the financial leverage (and risk) of a
company increases as management chooses
to use debt, rather than equity, to raise
funds for the company. Similarly, the oper-
ating leverage (and risk) of a company in-
creases as management chooses to
emphasize fixed cost, rather than variable
cost, to create or obtain the product for sale
to the marketplace.
STOP & THINK
Think about the level of operating lever-
age you would expect to find in a service
organization such as a consulting com-
pany or a law firm. Would these kinds of
organizations typically have high or low
levels of operating leverage?
80 Part 1 E M Foundations
Exhibit 11: “Seeing” Operating Leverages
200,000
600,000
$1,000,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
0
400,000
800,000
Merchandising Structure
(Low Operating Leverage)
Revenue Total costs Fixed costs
200,000
600,000
$1,000,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
0
400,000
800,000
Manufacturing Structure
(Medium Operating Leverage)
Revenue Total costs Fixed costs
Sales in Total Variable Contribution Total Fixed Operating
Units Revenue Costs Margin Costs Income
Price per unit $ 100 3,000 $300,000 $(240,000) $ 60,000 $(100,000) $(40,000)
Variable cost per unit 80 5,000 500,000 (400,000) 100,000 (100,000) —
Total fixed costs 100,000 7,000 700,000 (560,000) 140,000 (100,000) 40,000
Sales in Total Variable Contribution Total Fixed Operating
Units Revenue Costs Margin Costs Income
Price per unit $ 100 3,000 $300,000 $ (75,000) $225,000 $(375,000) $(150,000)
Variable cost per unit 25 5,000 500,000 (125,000) 375,000 (375,000) —
Total fixed costs 375,000 7,000 700,000 (175,000) 525,000 (375,000) 150,000
E O C 81 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 11: (Concluded)
200,000
600,000
$1,000,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
0
400,000
800,000
E-Commerce Structure
(High Operating Leverage)
Revenue Total costs Fixed costs
Sales in Total Variable Contribution Total Fixed Operating
Units Revenue Costs Margin Costs Income
Price per unit $ 100 3,000 $300,000 $ — $300,000 $(500,000) $(200,000)
Variable cost per unit 0 5,000 500,000 — 500,000 (500,000) —
Total fixed costs 500,000 7,000 700,000 — 700,000 (500,000) 200,000
1
Understand the key factors involved in cost-volume-
profit (C-V-P) analysis and why it is such an impor-
tant tool in management decision making. C-V-P analysis
is a very important management concept. It is a technique
you will use as a manager to understand how profits may be
expected to vary in relation to changes in key variables: sales
price and volume, variable costs, fixed costs, and mix of prod-
ucts. C-V-P analysis is a particularly useful tool for planning
and making operating decisions. It can provide data to stim-
ulate increased sales efforts or cost reduction programs; assist
in production scheduling or marketing strategy; and help es-
tablish company policies, for example, the appropriate prod-
uct mix or the fixed cost structure of a company. In order to
be effective as a manager, you will need a comprehensive un-
derstanding and ability to use C-V-P analysis.
2
Explain and analyze the basic cost behavior patterns—
variable, fixed, mixed, and stepped. Understanding cost
behavior patterns can assist you in making key operating de-
cisions. The two basic cost behavior patterns are variable and
fixed. Costs that vary in total in direct proportion to changes
in the level of activity are variable costs. Therefore, per-unit
variable costs remain constant. Generally, we assume that
there is a linear relationship between variable costs and level
of activity within the relevant range; for other ranges, variable
costs are curvilinear. Costs that do not change in total with
changes in activity level (within the relevant range) are fixed
costs; thus, per-unit fixed costs decrease as level of activity in-
creases. Costs that contain both fixed and variable compo-
nents are mixed costs. Stepped costs increase in total in a
stair-step fashion with the level of activity. If the steps are
wide, the cost is treated as a fixed cost for analysis purposes;
if the steps are narrow, the cost is approximated as a variable
cost.
3
Analyze mixed costs using the scattergraph and high-
low methods. Before mixed costs can be analyzed and
used in decision making, they must be divided into their fixed
and variable components. The scattergraph and high-low
methods are commonly used to analyze mixed costs. The scat-
r e v i e w o f l e a r n i n g o b j e c t i v e s
82 Part 1 E O C Foundations
tergraph method involves visually plotting a straight line (the
regression line) through points on a graph of cost data at var-
ious activity levels. With the high-low method, the highest
and lowest levels of activity and their associated costs are used
to calculate the variable cost rate and the total fixed costs.
4
Perform C-V-P analyses, and describe the effects po-
tential changes in C-V-P variables have on company
profitability. C-V-P analysis is based on the computation of
contribution margin, which is sales revenue less variable costs.
Contribution margin is the amount available to cover fixed
costs and then provide a profit. C-V-P analysis is commonly
used to assess break-even points (where contribution margin
equals fixed costs) and to compute target income levels. The
basic C-V-P equation is:
Sales revenue ? Variable costs ? Fixed costs ? Profit
The C-V-P equation will be especially useful to you as a man-
ager in assessing how profits can be expected to change when
costs or sales revenue change. Increases in fixed or variable
costs result in a larger number of sales being required to break
even and reach target income levels. Increases in sales price
result in a decreased number of sales being required to break
even and reach target income levels.
5
Visualize C-V-P relationships using graphs. C-V-P
graphs and profit graphs are effective methods for visu-
alizing the effect of impacts on key variables in the C-V-P
equation. In addition, the graphic approach effectively allows
managers to simultaneously analyze several different activity
levels.
6
Identify the limiting assumptions of C-V-P analysis,
and explain the issues of quality and time relative to
C-V-P analysis decisions. C-V-P analysis has several limit-
ing assumptions, including the following: (1) cost and rev-
enue behavior patterns are linear and remain constant over
the relevant range, (2) all costs can be categorized as either
fixed or variable, and (3) the sales mix of products is constant
over the relevant range. When making changes in costs, rev-
enues, and volume, remember to consider the impact on the
quality of products or services and the speed at which those
products and services can be delivered to customers. Changes
that result in decreased costs that also decrease product or ser-
vice quality or that slow down the delivery of products or ser-
vices may not be good decisions.
7
Analyze mixed costs using the least squares method.
The least squares method uses a simple regression analy-
sis to identify the variable and fixed portions of mixed costs.
The formula for the least squares method is based on the fol-
lowing equation for a straight line:
Y ? a ? bX
where a is total fixed cost and b is per-unit variable cost. Least
square calculations can be easily performed using basic com-
puter software programs or programmed calculators. One out-
put of least square analysis calculations is the R
2
statistic,
which measures the amount of variance in the cost that is ex-
plained by changes in the activity level (depicted by X in the
equation above).
8
Explain the effects of sales mix on profitability. Sales
mix is the proportion of total units sold represented by
each of a company’s products. Because all products do not
have the same contribution margin ratios, changes in the sales
mix of products sold can significantly affect total profits.
When you are working as a manager to maximize profits, it
is best to maintain as large a contribution margin as possible
on all products and then emphasize those products with the
largest individual contribution margin ratios.
9
Describe how fixed and variable costs differ in manu-
facturing, service, merchandising, and e-commerce
organizations, and illustrate these differences with the
operating leverage concept. The trade-off between fixed
costs and variable costs is often related to whether a company
is structured as a manufacturing, merchandising, or service firm.
The advent of e-commerce has created the potential for com-
panies to have very high levels of fixed costs and very low lev-
els of variable costs. The impact of the fixed cost/variable cost
relationship on profits is captured in the concept of operating
leverage. Operating leverage is a measure of the extent to which
a company’s costs are fixed rather than variable. Companies
with higher fixed costs and lower per-unit variable costs will
experience higher operating leverage and, therefore, a tendency
for profits to increase at a faster rate when sales increase. Hence,
a company with high operating leverage will be more profitable
in good times but have higher losses in bad times.
break-even point, 61
contribution margin, 58
contribution margin ratio, 59
cost behavior, 44
cost-volume-profit (C-V-P) analysis,
44
k e y t e r m s & c o n c e p t s
E O C 83 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Variable and Fixed Costs Analyses
Blade Corporation manufactures two types of inline skates—a basic model and a racing model.
During the year 2006, Blade accumulated the following summary information about its two
products:
Racing Model Basic Model
Selling price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $130 $65
Number of units manufactured and sold . . . . . . . . . . . . . 14,000 9,000
Racing Model Basic Model
Units Costs Units Costs
January . . . . . . . . . . . . . . . . . . . . . . . . . . 1,200 $ 112,000 800 $ 39,600
February . . . . . . . . . . . . . . . . . . . . . . . . . 900 91,000 600 30,000
March . . . . . . . . . . . . . . . . . . . . . . . . . . . 800 76,400 450 25,800
April . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,400 124,800 900 36,900
May . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 950 92,650 1,000 47,000
June . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,600 146,800 1,200 57,300
July . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,400 134,600 1,300 60,600
August . . . . . . . . . . . . . . . . . . . . . . . . . . 1,700 154,500 650 32,195
September . . . . . . . . . . . . . . . . . . . . . . . . 1,550 140,200 850 44,250
October . . . . . . . . . . . . . . . . . . . . . . . . . . 1,500 134,500 500 27,000
November . . . . . . . . . . . . . . . . . . . . . . . . 600 62,500 350 20,700
December . . . . . . . . . . . . . . . . . . . . . . . . 400 44,000 400 22,000
Totals . . . . . . . . . . . . . . . . . . . . . . . . . . 14,000 $1,313,950 9,000 $443,345
Required:
1. Use the high-low method to estimate the variable and fixed production costs of both the
racing model and the basic model skates.
2. All selling costs are fixed, and they total $200,000 for the racing model and $80,000 for the
basic model. Prepare a contribution margin income statement for each model at sales of
10,000 racing and 10,000 basic skates.
Solution
1. Variable and Fixed Costs
The high-low method involves finding the variable and fixed costs at the high and low levels
of production. In this case:
r e v i e w p r o b l e m s
curvilinear costs, 47
fixed costs, 49
high-low method, 54
mixed costs, 51
per-unit contribution margin, 58
profit graph, 68
regression line, 53
relevant range, 49
return on sales revenue, 62
scattergraph (visual-fit) method, 53
stepped costs, 50
target income, 62
variable cost rate, 53
variable costs, 46
least squares method, 73
operating leverage, 78
sales mix, 76
Racing Model Basic Model
High-production month . . . . . . . . . . . . . . . . . . . . . . . . . 1,700 (Aug.) 1,300 (July)
Low-production month . . . . . . . . . . . . . . . . . . . . . . . . . . 400 (Dec.) 350 (Nov.)
Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,300 950
Total production costs of high month . . . . . . . . . . . . . . . $154,500 $60,600
Total production costs of low month . . . . . . . . . . . . . . . 44,000 20,700
Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $110,500 $39,900
Once the differences are known, the change in units (production) is divided into the change
in costs to determine the variable cost rate.
? Variable cost rate
Racing model: ? $85
Basic model: ? $42
Because total variable costs equal unit variable cost times number of units produced, and total
costs equal total variable costs plus total fixed costs, fixed costs can now be calculated.
Total costs ? (Variable cost per unit ? Number of units) ? Total fixed costs
Racing Model Basic Model
High production level (X) ? $154,500 ? $85(1,700) $60,600 ? $42(1,300)
X ? $154,500 ? $144,500 X ? $60,600 ? $54,600
X ? $10,000 X ? $6,000
Low production level (X) ? $44,000 ? $85(400) $20,700 ? $42(350)
X ? $44,000 ? $34,000 X ? $20,700 ? $14,700
X ? $10,000 X ? $6,000
Thus, we have the following:
Racing Model Basic Model
Variable cost rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 85 $ 42
Total fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10,000 6,000
2. Contribution Margin Income Statements
Blade Corporation
Contribution Margin Income Statements
For the Year Ended December 31, 2006
Racing Model Basic Model
Sales revenue (at 10,000 units) . . . . . . . . . . . . . . . . . . . . $1,300,000 $ 650,000
Less variable cost of goods sold* . . . . . . . . . . . . . . . . . . (850,000) (420,000)
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 450,000 $ 230,000
Less fixed cost of goods sold . . . . . . . . . . . . . . . . . . . . . (10,000) (6,000)
Less fixed selling costs . . . . . . . . . . . . . . . . . . . . . . . . . . (200,000) (80,000)
Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 240,000 $ 144,000
*$85 per unit for racing model; $42 per unit for basic model.
$39,900
?
950
$110,500
??
1,300
Change in costs
??
Change in units
84 Part 1 E O C Foundations
Assessing the Effects of Changes in Costs, Prices, and Volume
on Profitability
K&D Company plans the following for the coming year:
Sales volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000 units
Sales price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2.50 per unit
Variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1.30 per unit
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $60,000
Required:
1. Determine K&D’s target income.
2. Compute what the target income would be under each of the following independent as-
sumptions:
a. The sales volume increases 20%.
b. The sales price decreases 20%.
c. Variable costs increase 20%.
d. Fixed costs decrease 20%.
Solution
1. Target Income
Basic C-V-P equation: Sales revenue ? Variable costs ? Fixed costs ? Target income
(Units sold ? Sales price) ? (Units sold ? Variable unit cost) ? Fixed costs ? Target income
(100,000 ? $2.50) ? (100,000 ? $1.30) ? $60,000 ? X
$250,000 ? $130,000 ? $60,000 ? X
$60,000 ? X
This answer can be validated by dividing fixed costs by the per-unit contribution margin
to find the break-even point and then multiplying the excess units to be sold above the break-
even point by the per-unit contribution margin of $1.20 ($2.50 ? $1.30).
? Break-even point
? 50,000 units
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $1.20
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $60,000
2a. The sales volume increases 20%.
(100,000 ? 1.2 ? $2.50) ? (100,000 ? 1.2 ? $1.30) ? $60,000 ? X
$300,000 ? $156,000 ? $60,000 ? X
$84,000 ? X
In this case, the contribution margin does not change. Therefore, the answer can be vali-
dated by multiplying the units to be sold in excess of the break-even point by the per-unit con-
tribution margin of $1.20 to find the target income.
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70,000
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $1.20
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $84,000
$60,000
?
$1.20
Fixed costs
????
Per-unit contribution margin
E O C 85 Chapter 2 Analyzing Cost-Volume-Profit Relationships
2b. The sales price decreases 20%.
(100,000 ? $2.50 ? 0.8) ? (100,000 ? $1.30) ? $60,000 ? X
$200,000 ? $130,000 ? $60,000 ? X
$10,000 ? X
In this case, the contribution margin changes. Therefore, the answer can be validated by
dividing fixed costs by the new per-unit contribution margin of $0.70 ($2.00 ? $1.30) to find
the new break-even point and then multiplying the units to be sold in excess of the break-even
point by the new per-unit contribution margin.
? 85,715 units (new break-even point, rounded up)
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85,715
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14,285
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $0.70
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $10,000 (rounded)
2c. Variable costs increase 20%.
(100,000 ? $2.50) ? (100,000 ? $1.30 ? 1.2) ? $60,000 ? X
$250,000 ? $156,000 ? $60,000 ? X
$34,000 ? X
In this case, the contribution margin changes. Therefore, the answer can be validated by
dividing fixed costs by the new per-unit contribution margin of $0.94 ($2.50 ? $1.56) to find
the new break-even point and then multiplying the units to be sold in excess of the break-even
point by the new per-unit contribution margin.
? 63,830 units (new break-even point, rounded up)
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63,830
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36,170
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $0.94
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $34,000 (rounded)
2d. Fixed costs decrease 20%.
(100,000 ? $2.50) ? (100,000 ? $1.30) ? ($60,000 ? 0.8) ? X
$250,000 ? $130,000 ? $48,000 ? X
$72,000 ? X
In this case, the contribution margin does not change, but fixed costs, and hence the break-
even point, do. Therefore, the answer can be validated by dividing the per-unit contribution
margin of $1.20 into the new fixed costs to find the break-even point and then multiplying the
units to be sold in excess of the break-even point by the per-unit contribution margin.
? 40,000 units (new break-even point)
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40,000
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,000
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $1.20
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $72,000
$48,000 (new fixed costs)
?????
$1.20 (per-unit contribution margin)
$60,000 (fixed costs)
?????
$0.94 (new per-unit contribution margin)
$60,000 (fixed costs)
?????
$0.70 (new per-unit contribution margin)
86 Part 1 E O C Foundations
E O C 87 Chapter 2 Analyzing Cost-Volume-Profit Relationships
1. Explain how understanding cost behavior patterns can as-
sist management.
2. Discuss how level of activity is measured in manufactur-
ing, merchandising, and service firms.
3. What is meant by the linearity assumption, and why is
it made? Relate this assumption to the relevant-range
concept.
4. What factors in the current economy seem to have
caused the shift from variable to fixed cost patterns?
5. How should stepped costs be treated in the planning
process?
6. Why must all mixed costs be segregated into their fixed
and variable components?
7. What is the major weakness of the scattergraph, or visual-
fit, method of analyzing mixed costs?
8. What is the major limitation of the high-low method of
analyzing mixed costs?
9. What is the basic C-V-P equation? What is a more de-
tailed version of this equation?
10. What is the contribution margin, and why is it important
for managers to know the contribution margins of their
products?
11. How much will profits increase for every unit sold over
the break-even point?
12. What is the major advantage of using C-V-P graphs?
13. When other factors are constant, what is the effect on
profits of an increase in fixed costs? Of a decrease in vari-
able costs?
14. What are the limiting assumptions of C-V-P analysis?
15. How do the issues of quality and time relate to C-V-P
analysis decisions?
16. How does the method of least squares differ from the
scattergraph method?
17. What effect is a change in the sales mix likely to have on
a firm’s overall contribution margin ratio?
d i s c u s s i o n q u e s t i o n s
Measuring Level of Activity
Which one of the following is not an activity base used by a company?
a. Number of defects per hour in an assembly plant
b. Number of units sold for a merchandising firm
c. Number of units produced for a manufacturing firm
d. Number of client hours billed for an accounting firm
e. Number of hours a retail store is open
Variable Costs
Which one of the following would not be a variable cost for a construction company?
a. Cost of trusses used to construct a roof for a house
b. Cost of windows to be installed in a house
c. Salary paid to overall project supervisor
d. Cost of drywall to be installed in house
e. Cost of exterior house paint
Linearity of Variable Costs within the Relevant Range
The company has assembled the following data about its variable costs:
p r a c t i c e e x e r c i s e s
Practice 2-1
Practice 2-2
Practice 2-3
(continued)
Level of Activity Total Variable Cost
1,000 units $ 25,000
2,000 units 46,000
3,000 units 69,000
4,000 units 92,000
5,000 units 100,000
The company is currently producing 3,300 units. According to these data, what is the rel-
evant range over which the company can assume that the variable cost per unit is constant?
Fixed Costs
If the level of activity increases during the month, does the fixed cost per unit increase, de-
crease, or remain constant?
Break-Even Computation
The company reports the following items.
Direct materials per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 2.50
Direct labor per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.60
Variable overhead per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10
Monthly rent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,900.00
Monthly depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650.00
Other monthly fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2,680.00
Sales price per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.25
Using the above information, compute the company’s monthly break-even point (in units).
Stepped Fixed Costs
The company pays $3,000 per month to each of its four production supervisors. Each super-
visor can handle the workload associated with up to 2,400 units of production per month; the
current level of production is 9,000 units. If the company increases its level of production to
12,800 units per month, how much will the company pay, in total, for the salaries of the nec-
essary production supervisors?
Mixed Costs
The company’s president receives a $100,000 base salary and a bonus of 0.5% of sales for the
year. How much will the president earn at a sales level of $2,750,000 for the year?
Scattergraph Method
Which one of the following statements is incorrect?
a. The scattergraph method can be somewhat subjective depending on where one visually
places the regression line.
b. The scattergraph method is the most accurate method of analyzing mixed costs.
c. When graphing mixed costs, the dollars go on the vertical axis, and the level of activity goes
on the horizontal axis.
d. Regression lines attempt to minimize the average distance between all the data points and
the fitted regression line.
e. The slope of the regression line is equal to the variable cost per unit of activity.
Using the High-Low Method to Estimate the Variable Cost Rate
The company reports the following utility costs for different levels of activity during the first
half of the year:
88 Part 1 E O C Foundations
Practice 2-4
Practice 2-5
Practice 2-6
Practice 2-7
Practice 2-8
Practice 2-9
Month Machine Hours Total Utility Costs
January 470 $14,000
February 410 12,500
March 520 14,400
April 500 14,450
May 550 15,350
June 535 15,100
Using the high-low method, estimate the variable cost rate.
Using the High-Low Method to Estimate Fixed Costs
Refer to the data in Practice 2-9. Using the high-low method, estimate the fixed costs per month
based on the variable cost rate (computed in Practice 2-9).
Contribution Margin Income Statement
The company sells desks for $550 each. The variable cost per desk is $385. The company’s
monthly fixed costs are $72,000. Prepare a contribution margin income statement for a month
in which the company sells 500 desks.
Contribution Margin Ratio and Variable Cost Ratio
Refer to the data in Practice 2-11. Compute the contribution margin ratio and the variable cost
ratio.
The C-V-P Equation
The company sells lawnmowers for $895 each. The variable cost per lawnmower is $520. The
company’s monthly fixed costs are $84,500. Using the C-V-P equation, compute the amount
of profit the company will have for a month in which the company sells 375 lawnmowers.
Break-Even Units
The company sells shovels for $27.75 each. The variable cost per shovel is $14.25. The com-
pany’s monthly fixed costs are $2,538. Compute the number of shovels the company must sell
to break even.
Determining Sales Volume to Achieve Target Income
Refer to the data in Practice 2-14. How many shovels must the company sell to achieve a profit
of $10,000?
Determining Sales Volume to Achieve Target Return on Sales
The company sells pianos for $7,000 each. The variable cost per piano is $5,500. The com-
pany has fixed costs per month of $45,000. Compute the number of units the company must
sell in a month to achieve a 15% return on sales.
Break-Even Sales Revenue
The company has a variable cost ratio of 65% and monthly fixed costs of $91,000. What is
the company’s break-even point in terms of sales dollars?
C-V-P Analysis with Simultaneous Changes in Several Variables
The company currently sells 50,000 feet of cable each month for $3.50 per foot. The variable
cost of the cable is $1.10 per foot, and monthly fixed costs are $75,000. The company is con-
sidering whether to raise the sales price for the cable to $4.00 per foot. The marketing team has
determined that such an increase in sales price will discourage some customers from purchasing
E O C 89 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Practice 2-10
Practice 2-11
Practice 2-12
Practice 2-13
Practice 2-14
Practice 2-15
Practice 2-16
Practice 2-17
Practice 2-18
(continued)
the cable, so the company will be able to sell only 40,000 feet of cable per month. Calculate the
profit for the company under both of the following scenarios:
1. 50,000 feet of cable at $3.50 per foot.
2. 40,000 feet of cable at $4.00 per foot.
In terms of profit maximization, should the company raise the price per foot?
C-V-P Analysis with Simultaneous Changes in Several Variables
Refer to the data in Practice 2-18. The company is considering whether to change its produc-
tion process to reduce the variable cost per foot to $0.90 by raising fixed costs per month to
$83,000. This change will have no impact on selling price ($3.50) or sales volume (50,000
feet). In terms of profit maximization, should the company change its production process?
Interpreting a C-V-P Graph
90 Part 1 E O C Foundations
Practice 2-19
Practice 2-20
$200,000
180,000
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
Number sold
S
a
l
e
s
0
C
B
A
Look at the given C-V-P graph. Which one of the following sets of labels correctly labels items
A, B, and C in the C-V-P graph?
a. A: Total cost line; B: Fixed costs; C: Break-even point
b. A: Revenue line; B: Variable costs; C: Fixed costs
c. A: Fixed cost line; B: Break-even point; C: Fixed costs
d. A: Revenue line; B: Break-even point; C: Fixed costs
e. A: Total cost line; B: Break-even point; C: Fixed costs
Interpreting a Profit Graph
E O C 91 Chapter 2 Analyzing Cost-Volume-Profit Relationships
$80,000
60,000
40,000
20,000
0
?20,000
?40,000
?60,000
?80,000
P
r
o
f
i
t
L
o
s
s
Number sold
C
B
A
Practice 2-21
Practice 2-22
Practice 2-23
Look at the given profit graph. Which one of the following sets of labels correctly labels items
A, B, and C in the profit graph?
a. A: Area of loss; B: Break-even point; C: Area of profit
b. A: Area of loss; B: Area of profit; C: Break-even point
c. A: Break-even point; B: Area of loss; C: Area of profit
d. A: Area of profit; B: Break-even point; C: Area of loss
e. A: Area of profit; B: Area of loss; C: Break-even point
Limiting Assumptions of C-V-P Analysis
Which one of the following is not an assumption of C-V-P analysis?
a. Fixed costs are always greater than variable costs.
b. All costs can be divided into fixed and variable categories.
c. C-V-P analysis is valid only for a relevant range.
d. The mix of a company’s products does not change over the relevant range.
Least-Squares Method
The company reports the following costs at different levels of activity for the first half of the
year.
(continued)
Month Machine Hours Total Utility Costs
January 470 $14,000
February 410 12,500
March 520 14,400
April 500 14,450
May 550 15,350
June 535 15,700
Using Excel (or another program with statistical capabilities), estimate the company’s fixed
costs and variable costs per machine hour using the least-squares method.
Sales Mix
The company has fixed costs of $21,500 and the following sales mix.
Product A Product B Product C
Sales revenue . . . . . . . . . . . . . . . . . . . . . . . . . $35,000 $70,000 $45,000
Less variable costs . . . . . . . . . . . . . . . . . . . . . 20,000 50,000 36,000
Contribution margin . . . . . . . . . . . . . . . . . . . . $15,000 $20,000 $ 9,000
Using this same sales mix, calculate the required sales (in dollars) to earn a target income of
$25,000.
Cost Structure
If you experience much higher sales than expected this year, which kind of operating leverage
would you like to have in your company for profit maximization?
a. High operating leverage
b. Low operating leverage
c. Medium operating leverage
d. Operating leverage does not affect profitability.
92 Part 1 E O C Foundations
Practice 2-24
Practice 2-25
Variable and Fixed Costs Over the Relevant Range
Cook Corporation manufactures plastic garbage cans. In a typical year, the firm produces be-
tween 40,000 and 50,000 cans. At this level of production, fixed costs are $10,000 and vari-
able costs are $2 per can.
1. Graph the cost of producing cans, with cost as the vertical axis and production output as
the horizontal axis.
2. Indicate on the graph the relevant range of the $10,000 in fixed costs, and explain the sig-
nificance of the relevant range.
3. What would total production costs be if 46,000 cans were produced?
Fixed Costs—The Relevant Range
Sabrina Company manufactures large leisure boats. The following schedule shows total fixed
costs at various levels of boat production:
e x e r c i s e s
Exercise 2-1
Exercise 2-2
Units Produced Total Fixed Costs
0–100 $150,000
101–400 250,000
401–900 400,000
1. What is the fixed cost per unit when 75 boats are produced?
2. What is the fixed cost per unit when 300 boats are produced?
3. What is the fixed cost per unit when 750 boats are produced?
4. Plot total fixed costs on a graph similar to that shown in Exhibit 3.
Scattergraph Method of Analyzing Mixed Costs
Wyoming Company makes windmills. The company has the following total costs at the given
levels of windmill production:
Units Produced Total Costs
20 $16,000
30 22,000
40 20,000
50 28,000
1. Use the scattergraph method to estimate the fixed and variable elements of Wyoming’s total
costs.
2. Compute the total cost of making 44 windmills, assuming that total fixed costs are $10,000
and that the variable cost rate computed in part (1) does not change.
Scattergraph Method of Analyzing Mixed Costs
Given the following mixed costs at various levels of production, complete the requirements.
Month Units Produced Mixed Costs
January 2 $24.00
February 3 28.00
March 1 21.00
April 5 30.00
May 4 25.00
1. Plot the data on a scattergraph, and visually fit a straight line through the points.
2. Based on your graph, estimate the monthly fixed cost and the variable cost per unit pro-
duced.
3. Compute the total cost of producing eight units in a month, assuming that the same rele-
vant range applies.
4. Interpretive Question: Why is it so important to be able to determine the components of a
mixed cost?
Scattergraph Method and High-Low Method of Analyzing Mixed Costs
Sailmaster makes boats and has the following costs and production levels for the last eight
quarters:
E O C 93 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-3
Exercise 2-4
Exercise 2-5
(continued)
Quarter Boats Produced Total Costs
1 108 $101,250
2 128 168,750
3 185 189,000
4 245 200,145
5 311 276,200
6 352 255,250
7 389 305,700
8 428 376,500
1. Plot the data on a scattergraph, and visually fit a straight line through the points.
2. Based on your graph, estimate the quarterly fixed cost and the variable cost per unit produced.
3. Use the high-low method to compute the variable and fixed elements of Sailmaster’s total costs,
and then draw a straight line through the high and low data points on the scattergraph.
4. Compute the total cost of making 500 boats using first the scattergraph results and then us-
ing the high-low method results.
5. Comment on the differences between these two methods. Which method appears to most
accurately represent the actual variable and fixed costs for Sailmaster?
High-Low Method of Analyzing Mixed Costs
The Stamford Times has determined that the annual printing of 750,000 newspapers costs 11
cents per copy. If production were to be increased to 1,000,000 copies per year, the per-unit
cost would drop to 9 cents per copy.
1. Using the high-low method, determine the total fixed and variable costs of printing 750,000
newspapers.
2. Using the fixed and variable costs you determined in part (1), what would be the total cost
of producing 900,000 copies?
Contribution Margin Calculations
Jerry Stone owns and operates a small beach shop in a mall on Sanibel Island, Florida. For the
last six months, Jerry has had a display of sunglasses in the front window. Largely because of
the display, Jerry has sold 100 pairs of sunglasses per month at an average cost of $26 and sell-
ing price of $50. The sales volume has doubled since the display was put in the window. One-
fourth of Jerry’s storage space is occupied by 190 ice coolers. The coolers have not been selling
as well as Jerry hoped, but he is convinced that a front window display of coolers would in-
crease sales by 50%. The coolers cost Jerry a total of $2,280 and have been selling at a rate of
100 per month at $28 each.
1. Assuming that cost of goods sold is the only variable cost, compute the contribution margin
per unit for sunglasses and ice coolers.
2. Compute the total contribution margins for both sunglasses and ice coolers assuming win-
dow displays and no window displays for both items.
3. What are the economic costs associated with keeping the sunglass display in the store window?
4. What are the economic costs associated with replacing the sunglass display with an ice
cooler display?
Contribution Margin Income Statement
The following data apply to Gordon Company for 2006:
Sales revenue (10 units at $25 each) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $250
Variable selling expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Variable administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Fixed selling expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
94 Part 1 E O C Foundations
Exercise 2-6
Exercise 2-7
Exercise 2-8
Fixed administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 15
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Fixed manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Variable manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1. Prepare a contribution margin income statement. Assume there were no beginning or end-
ing inventories in 2006.
2. How much would Gordon Company have lost if only five units had been sold during 2006?
Analysis of a Contribution Margin Income Statement
Fill in the missing amounts for the following three cases:
Case I Case II Case III
Sales revenue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $50,000 $60,000 $ (7)
Variable cost of goods sold:
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $12,500 $ (4) $20,000
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) 15,000 20,000
Variable selling and administrative costs . . . . . . . . . . . . 3,500 (5) 10,000
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . $ (2) $20,000 $ (8)
Gross margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20,000 30,000 40,000
Fixed selling and administrative costs* . . . . . . . . . . . . . 5,500 10,000 (9)
Rent expense on office building . . . . . . . . . . . . . . . . . . (3) 5,000 2,000
Depreciation expense on delivery trucks . . . . . . . . . . . . 5,000 2,500 8,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 4,000 $ (6) $ 0
*Except rent and depreciation.
Analysis of the Contribution Margin
Dr. Hughes and Dr. Hawkins, owners of the Spanish Fork Care Clinic, have $150,000 of fixed
costs per year. They receive 20,000 patient visits in a year, charging each patient an average of
$20 per visit; variable costs average $2 per visit (needles, medicines, and so on).
1. What is the contribution margin per patient visit?
2. What is the total contribution margin per year?
3. What is the total pretax profit for a year?
4. Drs. Hughes and Hawkins can bring in another doctor at a salary of $100,000 per year. If
this new doctor can handle 5,000 patient visits per year, should the new doctor be hired?
(Assume no additional fixed costs will be incurred.)
Contribution Margin Analysis
Compute the missing amounts for the following independent cases. (Assume zero beginning
and ending inventories.)
Case I Case II Case III
Sales volume (units) . . . . . . . . . . . . . . . . . . . . . . . . . . 24,000 (5) 16,000
Sales price per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . $10 $8 (9)
Variable costs (total) . . . . . . . . . . . . . . . . . . . . . . . . . . (1) $200,000 $100,000
Contribution margin (total) . . . . . . . . . . . . . . . . . . . . . . (2) (6) $60,000
Contribution margin per unit (rounded) . . . . . . . . . . . . $4 $3 (10)
Fixed costs (total) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3) (7) (11)
Fixed costs per unit (rounded) . . . . . . . . . . . . . . . . . . . (4) $2 (12)
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $20,000 (8) $40,000
E O C 95 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-9
Exercise 2-10
Exercise 2-11
Break-Even Point and Target Income
Detienne Company manufactures and sells one product for $20 per unit. The unit contribu-
tion margin is 40% of the sales price, and fixed costs total $80,000.
1. Using the equation approach, compute:
a. The break-even point in sales dollars and units.
b. The sales volume (in units) needed to generate a profit of $40,000.
c. The break-even point (in units) if variable costs increase to 80% of the sales price and
fixed costs increase to $100,000.
2. See if you can recompute the solutions to 1(a), 1(b), and 1(c) in one equation step using
either the contribution margin ratio or the contribution margin dollars per unit.
Break-Even Point and Target Income
Steven Newman, Inc., estimates 2006 costs to be as follows:
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $5 per unit
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $8 per unit
Variable manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $3 per unit
Variable selling and administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2 per unit
Fixed expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $80,000
1. Assuming that Newman will sell 55,000 units, what sales price per unit will be needed to
achieve a $75,000 profit?
2. Assuming that Newman decides to sell its product for $23 per unit, determine the break-
even sales volume in dollars and units.
3. Assuming that Newman decides to sell its product for $23 per unit, determine the number
of units it must sell to generate a $100,000 profit.
Break-Even Point—Graphic Analysis
Using the graph below, answer the following questions:
96 Part 1 E O C Foundations
Exercise 2-12
Exercise 2-13
Exercise 2-14
$50
45
40
35
30
25
20
15
10
5
1 2 3 4 5 6 7 8 9 10 11
Volume (in thousands of units)
C
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0
1. Copy the graph and identify (label) fixed costs, variable costs, total revenues, the total cost
line, and the break-even point.
2. Determine the break-even point in both sales dollars and volume.
3. Suppose that as a manager you forecast sales volume at 7,000 units. At this level of sales,
what would be your total fixed costs, approximate variable costs, and profit (or loss)?
4. At a sales volume of 3,000 units, what would be the level of fixed costs, variable costs, and
approximate profit (or loss)?
The Profit Graph
Using the graph below, answer the following questions:
E O C 97 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-15
?300
?200
?100
0
?100
?200
?300
200 300 400 500
Volume of sales in units
I
n
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e
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100
1. What is the break-even point in sales volume (in units)?
2. Approximately what volume of sales (in units) must this company have to generate an in-
come of $300?
3. How much are the fixed costs?
Graphing Revenues and Costs
Montana Company manufactures chocolate candy. Its manufacturing costs are as follows:
Annual fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $15,000
Variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2 per box of candy
1. Plot variable costs, fixed costs, and total costs on a graph for activity levels of 0 to 30,000
boxes of candy.
2. Plot a revenue line on the graph, assuming that Montana sells the chocolates for $5 a box.
C-V-P Analysis
The Last Outpost is a tourist stop in a western resort community. Kerry Yost, the owner of the
shop, sells hand-woven blankets for an average price of $30 per blanket. Kerry buys the blan-
kets from weavers at an average cost of $21. In addition, he has selling expenses of $3 per blan-
ket. Kerry rents the building for $300 per month and pays one employee a fixed salary of $500
per month.
1. Determine the number of blankets Kerry must sell to break even.
2. Determine the number of blankets Kerry must sell to generate a profit of $1,000 per month.
3. Assume that Kerry can produce and sell his own blankets at a total variable cost of $16 per
blanket, but that he would need to hire one additional employee at a monthly salary of $600.
a. Determine the number of blankets Kerry must sell to break even.
b. Determine the number of blankets Kerry must sell to generate a profit of $1,000 per
month.
C-V-P Analysis—Changes in Variables
Tracy, Inc., estimates that next year’s results will be:
Sales revenue (75,000 units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 900,000
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (375,000)
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (300,000)
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 225,000
Recompute profit, assuming each of the following independent conditions:
1. A 9% increase in the contribution margin.
2. An 8% increase in the sales volume.
3. A 4% decrease in the sales volume.
Exercise 2-16
Exercise 2-17
Exercise 2-18
(continued)
4. A 6% increase in variable costs per unit.
5. A 5% decrease in fixed costs.
6. A 5% increase in fixed costs.
7. A 12% increase in the sales volume and a 6% increase in fixed costs.
C-V-P Analysis—Changes in Variables
Modern Fun Corporation sells electronic games. Its three salespersons are currently being paid
fixed salaries of $30,000 each; however, the sales manager has suggested that it might be more
profitable to pay the salespersons on a straight commission basis. He has suggested a commis-
sion of 15% of sales. Current data for Modern Fun Corporation are as follows:
Sales volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15,000 units
Sales price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $40 per unit
Variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $29 per unit
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $140,000
1. Assuming that Modern Fun Corporation has a target income of $50,000 for next year,
which alternative is more attractive?
2. The sales manager believes that by switching to a commission basis, sales will increase 20%.
If that is the case, which alternative is more attractive? (Assume that sales are expected to re-
main at 15,000 units under the fixed salary alternative.)
Mixed Costs—Least Squares Analysis
Given the following mixed costs at various levels of production, complete the requirements.
Month Units Produced Mixed Costs
January 8 $30
February 12 36
March 4 22
April 20 44
May 8 26
1. Using the least squares method (either the equation approach or a software package), calcu-
late the monthly fixed and variable components of the mixed costs.
2. Using the estimates from part (1), compute the total cost of producing 16 units in a month.
3. Describe a major advantage and a major disadvantage of the least squares method.
Sales Mix
Klein Brothers sells products X and Y. Because of the nature of the products, Klein sells two
units of product X for each unit of product Y. Relevant information about the products is as
follows:
X Y
Sales price per unit $10 $30
Variable cost per unit 8 18
1. Assuming that Klein’s fixed costs total $140,000, compute Klein’s break-even point in sales
dollars.
98 Part 1 E O C Foundations
Exercise 2-19
Exercise 2-20
Exercise 2-21
2. Assuming that Klein sells one unit of product X for each unit of product Y, and fixed costs
remain at $140,000, compute Klein’s break-even point in sales dollars.
3. Explain any differences in your answers to parts (1) and (2).
C-V-P Analysis
Mower Manufacturing’s income statement for January 2006 is given below.
Sales (25,000 units ? $25) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $625,000
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468,750
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $156,250
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 31,250
1. Calculate the company’s break-even point in sales dollars and units.
2. The company is contemplating the purchase of new production equipment that would re-
duce variable costs per unit to $16.25. However, fixed costs would increase to $175,000 per
month. Assuming sales of 26,000 units next month, prepare an income statement for both
the current and the proposed production methods. Calculate the break-even point (in dol-
lars and units) for the new production method.
3. Comment on the difference (if any) in the break-even point for the new production
method. What explains the difference in income at sales of 26,000 units between the two
production methods?
Operating Leverage
Ludlam Company and Kassandra Company both make school desks. They have the same pro-
duction capacity, but Ludlam is more automated than Kassandra. At an output of 2,500 desks
per year, the two companies have the following costs:
Ludlam Kassandra
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $137,500 $ 37,500
Variable costs at $20 per desk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Variable costs at $60 per desk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150,000
Total cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $187,500 $187,500
Unit cost (2,500 desks) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 75 $ 75
Assuming that both companies sell desks for $100 each and that there are no other costs or ex-
penses for the two firms, complete the following:
1. Which company will lose the least money if production and sales fall to 1,000 desks per
year?
2. What would be each company’s profit or loss at production and sales levels of 1,000 desks
per year?
3. What would be each company’s profit or loss at production and sales levels of 4,000 desks
per year?
E O C 99 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-22
Exercise 2-23
Graphing Revenues and Costs
Cloward and Hawkins, CPAs, took in $350,000 of gross revenues this year. Besides themselves,
they have two professional staff (one manager and one senior) and a full-time secretary. Fixed
operating expenses for the office were $50,000 last year. This year the volume of activity is up
p r o b l e m s
Problem 2-1
5%, and fixed operating expenses are still $50,000. Total variable operating costs, except for
bonuses, average $5 per billable hour. The billable time for all professionals is as follows:
Partners: 3,000 hours at $75/hour
Manager: 1,800 hours at $40/hour
Senior: 2,120 hours at $25/hour
Salaries for the professional staff are $40,000 and $28,000, respectively; the secretary is paid
$18,000. The partners each draw salaries of $60,000; plus they share a 5% bonus based on
gross revenues. The manager is given a 2% bonus, also based on gross revenues.
Required:
1. Plot the data on a graph clearly showing (a) fixed costs, (b) variable costs, (c) total costs, and
(d) total revenues.
2. How much profit did the CPA firm make this year (after partners’ salaries)?
High-Low and Scattergraph Methods of Analysis
Woodfield Company makes bed linens. During the first six months of 2006, Woodfield had
the following production costs:
Month Units Produced Total Costs
January 10,000 $ 68,000
February 20,000 100,000
March 15,000 90,000
April 8,000 52,000
May 17,000 94,000
June 12,000 74,000
Required:
1. Use the high-low method to compute the monthly fixed cost and the variable cost rate.
2. Plot the costs on a scattergraph.
3. Interpretive Question: Based on your scattergraph, do you think the fixed costs and the
variable cost rate determined in part (1) are accurate? Why?
Contribution Margin Income Statement
Early in 2007, Lili H Company (a retailing firm) sent the following income statement to its
stockholders:
Lili H Company
Income Statement
For the Year Ended December 31, 2006
Sales revenue (2,000 units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $240,000
Less cost of goods sold (variable) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160,000
Gross margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $80,000
Operating expenses:
Selling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 24,000
Administrative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16,000
Depreciation (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,000
Insurance (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Utilities ($80 fixed and $120 variable) . . . . . . . . . . . . . . . . . . . . . . . . 200 44,400
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $35,600
100 Part 1 E O C Foundations
Problem 2-2
Problem 2-3
Required:
1. Prepare a contribution margin income statement. (Assume that the fixed components of the
selling and administrative expenses are $12,000 and $8,000, respectively.)
2. Interpretive Question: Why is a contribution margin income statement helpful to man-
agement?
3. Interpretive Question: How would the analysis in part (1) be different if the depreciation
expense was considered a stepped cost with wide steps compared to the relevant range?
Contribution Margin Income Statement
Susan Young is an attorney for a small law firm in Arizona. She is also a part-time inventor
and an avid golfer. One day Susan’s golf foursome included a man named Henry Jones, a man-
ufacturer of Christmas ornaments. Henry explained to Susan that he manufactures an orna-
ment everyone loves, but stores will not carry the ornaments because they are very fragile and
often break during shipping. Susan told Henry about a plastic box she had developed recently
that would protect such fragile items during shipping. After crash testing the plastic box, Henry
offered Susan a contract to purchase 100,000 of the boxes for $2.20 each. Susan is convinced
that the box has many applications and that she can obtain future orders. Production of the
plastic boxes will take one year. Estimated costs for the first year are as follows:
Lease payments on building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $800 per month
Lease payments on machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2,200 per month
Cost to retool machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $10,000
Depreciation on machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $9,600
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.70 per box
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.30 per box
Indirect materials and other manufacturing overhead . . . . . . . . . . . . . . . . . $10,000
Interest on loan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2,500
Administrative salaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $15,000
Required:
1. Using the information provided, determine Susan’s contribution margin and projected profit
at a sales level of 100,000 boxes.
2. If Susan’s salary as an attorney is $44,500, determine how many boxes Susan must sell to
earn profits equal to her salary.
Functional and Contribution Margin Income Statements
Bassically Jammin’, Inc. (BJI) is a retail outlet for customized bass guitars. The average cost of
a bass guitar to the company is $1,000. BJI includes a markup of 50% of cost in the sales price.
In 2006, BJI sold 380 bass guitars and finished the year with the same amount of inventory it
had at the beginning of the year. Additional operating costs for the year were as follows:
Selling expenses:
Advertising (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 700 per month
Commissions (mixed) . . . . . . . . . . . . . . . . . . . . . . . . . . 3,000 per month plus 2% of sales
Depreciation (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 per month
Utilities (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 per month
Freight on delivery (variable) . . . . . . . . . . . . . . . . . . . . . 20 per bass guitar
Administrative expenses:
Salaries (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $4,200 per month
Depreciation (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 per month
Utilities (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 per month
Clerical (variable) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 per sale
Required:
1. Prepare a traditional income statement using the functional approach.
2. Prepare an income statement using the contribution margin format.
3. Interpretive Question: Which statement is more useful for decision making? Why?
E O C 101 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-4
Problem 2-5
Contribution Margin and Functional Income Statements
The following information is available for Dabney Company for 2006:
Sales revenue (at $20 per unit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $151,200
Fixed manufacturing costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24,000
Variable manufacturing costs (at $8 per unit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,480
Fixed selling expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70,000
Variable selling expenses (at $2 per unit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15,120
Required:
1. Prepare a contribution margin income statement.
2. Prepare a functional income statement.
3. Calculate the number of units sold.
4. Calculate the contribution margin per unit.
5. Interpretive Question: Why is a knowledge of the contribution margin more useful than
a knowledge of the markup per unit when management has to make a decision about prof-
itability?
Unifying Concepts: High-Low Method, Contribution Margins, and Analysis
Press Publishing Corporation has two major magazines: Star Life and Weekly News. During
2006, Star Life sold 3 million copies at $1.00 each, and Weekly News sold 2.1 million copies
at $1.10 each. Press Publishing accumulated the following cost information:
Star Life Weekly News
Copies Manufacturing Copies Manufacturing
Month Produced Cost Produced Cost
January 400,000 $170,000 300,000 $170,000
February 300,000 150,000 150,000 105,000
March 400,000 180,000 130,000 100,000
April 200,000 120,000 120,000 90,000
May 250,000 140,000 200,000 130,000
June 200,000 125,000 250,000 150,000
July 240,000 130,000 150,000 110,000
August 200,000 130,000 200,000 135,000
September 180,000 110,000 150,000 105,000
October 230,000 130,000 150,000 108,000
November 200,000 125,000 150,000 115,000
December 200,000 126,000 150,000 112,500
Required:
1. Use the high-low method to estimate the per-unit variable and total fixed manufacturing
costs of each magazine. (Round the variable cost rate to three decimal places.)
2. If all selling expenses are fixed and they total $500,000 for Star Life and $400,000 for
Weekly News, prepare contribution margin income statements for the two magazines at sales
of 3 million copies each.
3. Which magazine is more profitable at sales of 2 million copies?
4. Interpretive Question: If the same total dollar amount spent on either magazine will result
in the same number of new subscriptions, which magazine should be advertised?
Contribution Margin Analysis
Clearview Company is a manufacturer of glass vases. The following information pertains to
Clearview’s 2006 sales:
102 Part 1 E O C Foundations
Problem 2-6
Problem 2-7
Problem 2-8
Sales price per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 32
Variable costs per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Total fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500,000
Required:
1. Determine Clearview Company’s per-unit contribution margin and contribution margin
ratio.
2. Using the per-unit contribution margin and the contribution margin ratio, compute:
a. The break-even point in sales dollars and units.
b. The sales volume (in dollars and units) needed to generate a target income of $75,000.
3. Using the equation approach of C-V-P analysis, compute:
a. The break-even point in sales dollars and units.
b. The sales volume (in dollars and units) needed to generate a 15% return on sales.
Break-Even Analysis
Jane Tamlyn paid $225 to rent a carnival booth for four days. She has to decide whether to
sell doughnuts or popcorn. Doughnuts cost $1.80 per dozen and can be sold for $3.60 per
dozen. Popcorn will require a $113 rental fee for the popcorn maker and $0.08 per bag of pop-
corn for the popcorn, butter, salt, and bags; a bag of popcorn could sell for $0.45.
Required:
1. Compute the break-even point in dozens of doughnuts if Jane decides to sell doughnuts
exclusively and the break-even point in bags of popcorn if she decides to sell popcorn
exclusively.
2. Jane estimates that she can sell either 75 doughnuts or 45 bags of popcorn every hour the
carnival is open (10 hours a day for four days). Which product should she sell?
3. Jane can sell back to the baker at half cost any doughnuts she fails to sell at the carnival.
Unused popcorn must be thrown away. If Jane sells only 70% of her original estimate,
which product should she sell? (Assume that she bought or produced just enough to satisfy
the demands she originally estimated.)
C-V-P Graphic Analysis
Using the graph below, complete the requirements.
E O C 103 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-9
Problem 2-10
$35
30
25
20
15
10
5
1 2 3 4 5 6 7 8 9 10 11
Volume (in hundreds of units)
C
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0
Required:
1. Determine the following:
a. The break-even point in sales dollars and volume.
b. The sales price per unit.
c. Total fixed costs.
d. Total variable costs at the break-even point.
e. The variable cost per unit.
f. The unit contribution margin.
2. What volume of sales must the company generate to reach a target income of $7,500?
Contribution Margin Analysis—Changes in Variables
SMC, Inc., is a producer of hand-held electronic games. Its 2006 income statement was as
follows:
SMC, Inc.
Contribution Margin Income Statement
For the Year Ended December 31, 2006
Total Per Unit
Sales revenue (150,000 games) . . . . . . . . . . . . . . . . . . . . . . . . . . . $5,250,000 $35
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,750,000 25
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1,500,000 $10
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 600,000
In preparing its budget for 2007, SMC is evaluating the effects of changes in costs, prices, and
volume on profit.
Required:
1. Evaluate the following independent cases, and determine SMC’s 2007 budgeted profit or
loss in each case. (Assume that 2006 figures apply unless stated otherwise.)
a. Fixed costs increase $150,000.
b. Fixed costs decrease $100,000.
c. Variable costs increase $3 per unit.
d. Variable costs decrease $4 per unit.
e. Sales price increases $5 per unit.
f. Sales price decreases $5 per unit.
g. Sales volume increases 25,000 units.
h. Sales volume decreases 15,000 units.
i. Sales price decreases $4 per unit, sales volume increases 40,000 units, and variable costs
decrease by $2.50 per unit.
j. Fixed costs decrease by $100,000, and variable costs increase $4 per unit.
k. Sales volume increases 30,000 units, with a decrease in sales price of $2 per unit. Variable
costs drop $1.50 per unit, and fixed costs increase $50,000.
2. What sales volume in units would be needed to realize $1,000,000 in profit if SMC reduces
its price to $30?
Income Statement and Break-Even Analysis
Zimmerman Company records the following costs associated with the production and sale of
a steel slingshot:
Selling expenses:
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $6,500
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.50 per unit sold
Administrative expenses:
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $4,500
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.25 per unit sold
Manufacturing costs:
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $15,500
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $7.50 per unit produced
Required:
Assume that in 2006 the beginning and ending inventories were the same. Also assume that
2006 sales were 11,000 units at $11.50 per slingshot.
104 Part 1 E O C Foundations
Problem 2-11
Problem 2-12
1. Prepare a contribution margin income statement.
2. Determine the break-even point in sales dollars.
3. Interpretive Question: Zimmerman believes that sales volume could be improved 20% if
an additional commission of $0.50 per unit were paid to the salespeople. Zimmerman also
believes, however, that the same percentage increase could be achieved through an increase of
$3,000 in annual advertising expense. Which action, if either, should Zimmerman take? Why?
C-V-P Analysis—Changes in Variables
Wonder T Manufacturing Company produces lanterns. The firm has not been as profitable as
expected in the past three years. As a result, it has excess capacity that could be used to pro-
duce an additional 20,000 lanterns per year. However, any production above that amount would
require a capital investment of $100,000. Operating results for the previous year are shown
here. Assume that there is never any ending inventory.
Sales revenue (31,250 lanterns ? $40) . . . . . . . . . . . . . . . . . . . . . . $1,250,000
Variable costs (31,250 lanterns ? $25) . . . . . . . . . . . . . . . . . . . . . . $781,250
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400,000 1,181,250
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 68,750
Required:
Respond to the following independent proposals, and support your recommendations:
1. The production manager believes that profits could be increased through the purchase of
more automated production machinery, which would increase fixed costs by $100,000 and
reduce the variable costs by $2.00 per lantern. Is she correct if sales are to remain at 31,250
lanterns annually?
2. The sales manager believes that a 10% discount on the sales price would increase the sales vol-
ume to 40,000 units annually. If he is correct, would this action increase or decrease profits?
3. Would the implementation of both proposals be worthwhile?
4. The sales manager believes that an increase in sales commissions could improve the sales vol-
ume. In particular, he suggests that an increase of $2.50 per lantern would increase the sales
volume 30%. If he is correct, would this action increase profits?
5. The accountant suggests another alternative: Reduce administrative salaries by $15,000 so
that prices can be reduced by $0.50 per unit. She believes that this action would increase
the volume to 35,000 units annually. If she is correct, would this action increase profits?
6. The corporate executives finally decide to spend an additional $42,000 on advertising to
bring the sales volume up to 34,050 units. If the increased advertising can bring in these
extra sales, is this a good decision?
C-V-P Analysis—Return on Sales
The federal government recently placed a ceiling on the selling price of sheet metal produced
by MOB Company. In 2006, MOB was limited to charging a price that would earn a 20% re-
turn on gross sales. On the basis of this restriction, MOB had the following results for 2006:
Sales revenue (1,150,000 feet at $2.00 per foot) . . . . . . . . . . . . . . $2,300,000
Variable costs (1,150,000 feet ? $1.40) . . . . . . . . . . . . . . . . . . . . . $1,610,000
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230,000 1,840,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 460,000
In 2007, MOB predicted that the sales volume would decrease to 900,000 feet of sheet metal.
With this level of sales, however, the company anticipated no changes in the levels of fixed and
variable costs.
Required:
1. Determine MOB’s profit for 2007 if all forecasts are realized. Compute both the dollar
amount of profit and the percentage return on sales.
E O C 105 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-13
Problem 2-14
(continued)
2. MOB plans to petition the government for a price increase so that the 2006 rate of return
on sales (20%) can be maintained. What sales price should the company request, based on
2007 projections? (Round to the nearest cent.)
3. How much profit (in dollars) will MOB earn in 2007 if this sales price, as determined in
part (2), is approved?
4. Interpretive Question: What other factors must be considered by MOB and the government?
Unifying Concepts: C-V-P Analysis and Changes in Variables
The 2006 pro-forma income statement for Grover Company is as follows (ignore taxes):
Grover Company
Pro-Forma Income Statement
For the Year Ended December 31, 2006
Sales (50,000 units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $450,000
Cost of goods sold:
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 35,000
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,000
Variable manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . 14,000
Fixed manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5,000
Total cost of goods sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114,000
Gross margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $336,000
Selling expenses:
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 45,000
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102,000
Administrative expenses:
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15,000
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75,000
Total selling and administrative expenses . . . . . . . . . . . . . . . . . . . 237,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 99,000
Required:
1. Compute how many units must be sold to break even.
2. Compute the increase (decrease) in profit under the following independent situations:
a. Sales increase 25%.
b. Fixed selling and administrative expenses decrease 5%.
c. Contribution margin decreases 20%.
3. Compute sales in units and dollars at the break-even point if fixed costs increase from
$182,000 to $224,800.
4. Compute the number of units that must be sold if expected profit is $1 million.
Least Squares Methods
This problem uses the same data for Press Publishing Corporation as displayed in Problem 2-7.
Required:
Use the least squares method to estimate the per-unit variable and total fixed manufacturing
costs of the Star Life and Weekly News magazines. (Round the variable cost rate to three deci-
mal places.)
106 Part 1 E O C Foundations
Problem 2-15
Problem 2-16
Unifying Concepts: High-Low, Scattergraph, and Least Squares Methods
You have been hired as a consultant for Jones Inc. The company manufactures high-density
compact disks and sells them to a wide variety of business clients. Management is eager to learn
more about the company’s cost behavior. You have been provided the following data. Assume
all production falls within the relevant range.
Month Machine Hours Utility Costs
January 290 $10,700
February 280 10,400
March 320 11,600
April 340 12,100
May 350 12,400
June 290 10,750
July 300 10,800
August 300 10,900
September 310 11,200
October 340 12,200
November 290 10,600
December 310 11,000
Required:
1. Using the high-low method, compute the variable and fixed elements of Jones’ utility costs.
2. Plot the information on a scattergraph. Based on your graph, determine the unit variable
cost and monthly fixed costs.
3. Using the least squares method (either the equation approach or a software package), calcu-
late the variable and fixed cost components. Determine the cost formula.
4. Interpretive Question: Why are the variable cost per unit and fixed costs different for each
of these methods of analysis? Which method is the most accurate for determining variable
and fixed cost components?
Sales Mix
Mike’s Ice Cream Company produces and sells ice cream in three sizes: quart, half-gallon, and
gallon. Relevant information for each of the sizes is as follows:
Quart Half-Gallon Gallon
Average sales price . . . . . . . . . . . . . . . . . . . . . . . . . . $1.00 $1.85 $3.60
Less variable cost . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.80 1.40 2.40
Unit contribution margin . . . . . . . . . . . . . . . . . . . . . . $0.20 $0.45 $1.20
Sales mix (% of sales) . . . . . . . . . . . . . . . . . . . . . . . . 15% 60% 25%
Mike anticipates sales of $500,000 and fixed costs of $120,000 in 2006.
Required:
1. Determine the break-even sales volume in units and dollars for 2006.
2. Determine Mike’s 2006 projected profit.
3. Assume that Mike’s sales mix changes to 10% quarts, 40% half-gallons, and 50% gallons.
Determine Mike’s break-even sales volume in units and dollars.
Unifying Concepts: Break-Even Point and Operating Leverage
The summary data are provided on the following page for Spencer Mercantile Corporation and
James Service, Inc. During the year for which these data are reported, Spencer sold 50,000 units
and James sold 100,000 units.
E O C 107 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-17
Problem 2-18
Problem 2-19
(continued)
Spencer James
(000’s omitted) Mercantile Corporation Service, Inc.
Sales revenue . . . . . . . . . . . . . . . . . . . . . . . . . $1,040 $2,100
Less variable costs . . . . . . . . . . . . . . . . . . . . . 520 630
Contribution margin . . . . . . . . . . . . . . . . . . . . $ 520 $1,470
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . 200 600
Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 320 $ 870
Required:
1. Determine the break-even point for Spencer and James in both sales dollars and units.
2. Interpretive Question: Which company has a higher operating leverage? Why?
3. Interpretive Question: Based on your analysis of the cost structures of Spencer and James,
which company’s cost structure is better? What factors are important to consider in answer-
ing such a question?
108 Part 1 E O C Foundations
Case 2-1
Colorado Outdoors Federation
The Colorado Outdoors Federation sponsors an annual ban-
quet. This year the guest speaker is a noted wildlife photog-
rapher and lecturer. In planning for the event, the group’s
treasurer has determined the following costs:
Rental of meeting facility . . . . . . . . . . . . . . . . . . . . . . $250
Honorarium for speaker . . . . . . . . . . . . . . . . . . . . . . . 800
Tickets and advertising . . . . . . . . . . . . . . . . . . . . . . . 300
Cost of dinner (per person) . . . . . . . . . . . . . . . . . . . . 20
Door prizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
Last year, tickets were sold at $20 per person, and 350 peo-
ple attended the banquet. This year the planning committee
is hoping for an attendance of 450 at a price of $25 each.
1. a. At $25 per person, how many people must attend
the banquet for the Federation to break even?
b. How much profit (loss) will occur if 450 people attend?
2. Should the Federation increase its advertising costs by
$200 and its door prizes by $300 if it can expect 550
people to attend the banquet?
3. If the Federation maintains its original expected costs but
reduces the price per ticket from $25 to $22, it can ex-
pect 500 people to attend the banquet. Should the Feder-
ation reduce the price of its tickets to $22 per person?
Case 2-2
Entertainment Enterprises
Entertainment Enterprises, a firm that sells magazine sub-
scriptions, is experiencing increased competition from a num-
ber of companies. The president, Betty Kincher, has asked
you, the controller, to prepare an income statement that will
highlight the fixed and variable costs; this will provide more
useful information for planning and control purposes. Sales
revenues are $25 per subscription. An analysis of company
costs for the past six months reveals the following:
Administrative salaries . . . . . . . . . $10,000 per month
Advertising expense . . . . . . . . . . . $2,000 per month
Cost of goods sold . . . . . . . . . . . . $12.50 per subscription
Rent expense . . . . . . . . . . . . . . . . $5,000 per month
Sales commissions . . . . . . . . . . . . 15% of sales
In addition, the company makes most sales contacts
through an extensive telephone network. Consequently, the
telephone expense is significant and has both fixed and vari-
able components. Relevant data concerning the telephone ex-
pense for the past six months follow:
Month Unit Sales Telephone Expense
July . . . . . . . . . . . 4,000 $10,200
August . . . . . . . . 5,000 12,300
September . . . . . . 3,500 9,150
October . . . . . . . . 4,500 11,250
November . . . . . . 5,200 12,720
December . . . . . . 5,500 13,350
Prepare a management report for the president that:
1. Computes the fixed and variable portions of the tele-
phone expense using the high-low method. (Note: A scat-
tergraph may be used to visually check your answer.)
d i s c u s s i o n c a s e s
2. Presents a budgeted (pro-forma) contribution margin in-
come statement for Entertainment Enterprises for the
next six months (January through June), assuming that it
expects to sell 30,000 subscriptions at a price of $25
each.
3. Explains how the information provided in part (2) might
help the president make better management decisions.
C E O 109 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Judgment 2-1
You Decide: Should the management of a
company consider fixed costs in the decision-
making process, or should they ignore fixed
costs and base their decision on what makes
the most business sense?
Recently, the board of directors for a television manufactur-
ing company was considering a change in products from TVs
to computers. The board claims, after performing a C-V-P
analysis of a new computer manufacturing plant facility, that
the computer industry is more profitable and would increase
the bottom line immediately. However, just six months ear-
lier, the company built a state-of-the-art television manufac-
turing plant. The overhead costs on the television plant
represent a sizable portion of the company’s fixed costs. If the
board voted to begin computer manufacturing, a new plant
would need to be constructed. What should the board do?
Judgment 2-2
You Decide: Should companies have large
amounts of inventory on hand for customers,
or should companies keep inventory at a
minimum to free up cash for other parts of the
business?
Your uncle, Tim, started a very successful “home improve-
ment” business 10 years ago. He wanted to create a place where
people could go to get anything they needed to complete their
“do-it-yourself” home building projects. Coupled with excel-
lent service, Tim believes that he can gain and retain customers
by having a large assortment of inventory from which to
choose. In addition, he can obtain significant purchase dis-
counts by buying the inventory in large bulk. You argue that
maintaining amounts of inventory requires significant com-
mitments to fixed warehousing and other costs that could be
avoided by setting up an e-commerce Web site and taking cus-
tomer orders that are then acquired and delivered one cus-
tomer at a time. Although this approach will increase the
overall variable costs as a result of not receiving bulk discounts
on the smaller individual orders, you are able to demonstrate
with C-V-P analysis that there is less risk in your approach
to selling home improvement products. Your uncle strongly
argues that, “Having the inventory on hand for your cus-
tomers is the key to success. If I don’t have what they are look-
ing for, they will just go down the street to HOME DEPOT!
I have got to have inventory in the stores. There is no other
way!”
j u d g m e n t c a l l s
C o m p e t e n c y E n h a n c e m e n t O p p o r t u n i t i e s
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Analyzing Real Company Information
International Case
Ethics Case
Writing Assignment
The Debate
Internet Search
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The following additional assignments provide opportunities for students to develop critical thinking,
ethical perspectives, oral and written communication skills, experience with electronic research, and
teamwork through group and business activities.
110 Part 1 C E O Foundations
Analyzing Real Company Information
Analyzing 2-1 (Microsoft)
Annual revenues, as well as sales and marketing expenses, for the 1991–2002 years are pro-
vided below for MICROSOFT CORPORATION:
Microsoft Corporation (millions)
Year Sales and Marketing Expenses Annual Revenue
1991 $ 490 $ 1,847
1992 758 2,777
1993 1,086 3,786
1994 1,135 4,714
1995 1,564 6,075
1996 2,185 9,050
1997 2,411 11,936
1998 2,887 15,262
1999 3,238 19,747
2000 4,126 22,956
2001 4,885 25,296
2002 5,407 28,365
1. Operating output data, such as the number of software products sold each year, are not
provided in Microsoft’s Form 10-K. However, while it is a little odd to use revenues to pre-
dict marketing expense (instead of the other way around), it seems sensible that changes
in revenues can serve as an approximate measure of changes in the number of products
sold by Microsoft. Use the high-low method to analyze the data above to determine if
there is a relationship between revenues and sales and marketing expenses. (Hint: Don’t
round off the value you calculate for variable costs per revenue dollar.) What appears to be
the amount of fixed costs in these expenses? Does this fixed cost amount make sense?
(Note: Remember that the data are in millions of dollars!)
2. Using your calculator (or some computer software program such as Microsoft Excel
®),
compute a regression analysis on the data above. What do you learn from the analysis?
The Management’s Discussion in Microsoft’s 2002 Form 10-K generally uses the following
language to describe changes to sales and marketing expenses: “Sales and marketing ex-
penses increased due to higher relative headcount-related costs, higher marketing and
sales expenses associated with MSN (Microsoft’s popular portal destination on the Web),
the Microsoft Agility advertising campaign, and other new sales initiatives.” Does this
statement provide any help in understanding the analysis? (Hint: When setting up to per-
form the regression, remember that the revenue is the X variable and the sales and market-
ing expense is the Y variable.)
Analyzing 2-2 (Star Video)
It is likely that a number of grocery stores in your town have video rental departments. Gener-
ally, however, grocery stores do not focus much management attention on their small video
rental businesses. The main purpose of having a video department is to encourage more cus-
tomers to come into the store and purchase groceries! Nevertheless, a grocery store cannot
simply buy a large selection of videotapes, corner off a section of floor space, and start renting
tapes. Successfully managing a rental business requires being aware of an unimaginably large
number of video titles. Obviously, new movies are constantly being released, while old movies
gradually lose their appeal and are eventually scrapped. Further, large-scale video rental chains
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C E O 111 Chapter 2 Analyzing Cost-Volume-Profit Relationships
such as BLOCKBUSTER constantly track shifting consumer tastes for certain titles and movie
categories. These consumer preferences differ based on demographic data like geographic loca-
tion, average age, ethnicity, average income, etc. A grocery store really can’t manage all these
data without losing focus on its main business. Hence, most grocery stores contract out their
video rental business to a large-scale video management company. These management compa-
nies can purchase huge quantities of tapes, maintain large distribution warehouses, and track
demographic data that allow them to manage and move specific inventories to the appropriate
grocery store locations. In 1992, one such video management company, Star Video (not its real
name), was managing 86 stores representing three supermarket chains in five states—Arizona,
California, Montana, Washington, and Wyoming. Total revenue in 1992 for Star Video was $3.6
million. Star Video made all the inventory investments and handled all management activities
involved in providing video rentals at each of the 86 stores. Video rental revenue was then split
between Star Video and each grocery store, with Star Video keeping the lion’s share. Stores
liked this arrangement because they made most of their money on grocery sales to customers
who came to rent videotapes. Star Video needed to carefully manage revenue and costs at each
store in order to stay profitable. Following are the data for six stores located in Washington:
Monthly
Monthly Operating
Store Name Revenue Expenses
Moses Lake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 6,408 $ 3,295
W. Kennewick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,264 2,289
Pasco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,038 2,270
S. Kennewick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,692 2,142
E. Wenatchee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,395 1,316
Richland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2,104 1,516
Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $21,901 $12,828
Use the high-low method to analyze the operating expenses at these six stores. Determine if
operating expenses are related to store revenue. What appear to be the fixed costs of operating
each store? Create a graph and plot these costs using revenue on the horizontal axis and oper-
ating expenses on the vertical axis. Does the scattergraph agree or disagree with the results of
your high-low analysis?
International Case
The Paper Company
The GHANATA GROUP OF COMPANIES (GGC) is a locally owned and controlled company in Ghana,
West Africa. One of its principal operating divisions, THE PAPER COMPANY, is one of Africa’s
most modern and largest manufacturers/distributors of paper products. For both operating and
reporting purposes, The Paper Company is organized into product lines: scholastic, envelope, and
stationery. During the 1980s, the economy in Ghana was stagnant. The country faced severe eco-
nomic problems as a result of unfavorable trade terms with other countries. The official exchange
rate of U.S. $1.00 to the local currency, the cedi, was about 39.00 as of the end of 1984. (The
unofficial rate, e.g., the black market rate, was at least five times worse!) As a result of the
economy, it became very difficult for GGC to secure direct materials for its divisions. If a divi-
sion could secure direct materials, it could sell almost everything it produced. Hence, in terms
of being able to predict sales volumes, there was a great deal of risk for GGC divisions. The
1985 budgeted operating data for the three departments in The Paper Company were as follows:
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112 Part 1 C E O Foundations
The Paper Company
1985 Budgeted Operations Data
(Cedi 000’s)
Scholastic Envelope Stationery
Budgeted sales . . . . . . . . . . . . . . . . . . . . . . . $ 1,785,000 $ 984,000 $ 3,334,050
Budgeted variable costs . . . . . . . . . . . . . . . . . (410,550) (442,800) (2,200,473)
Contribution margin . . . . . . . . . . . . . . . . . . . $ 1,374,450 $ 541,200 $ 1,133,577
Budgeted fixed costs . . . . . . . . . . . . . . . . . . . (1,267,350) (482,160) (933,534)
Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 107,100 $ 59,040 $ 200,043
Using these operating data, create C-V-P graphs for each department. (Note: Since you don’t
have per-unit prices and costs, you may assume that the product sales price for each depart-
ment is $1 per unit, and then plot your graphs at 0, 2 million, and 4 million units.) Given the
high-risk business environment in Ghana at this time, which department presents the highest
risk to GGC? The lowest risk? Be sure to explain your answer in terms of operating leverage.
You may also want to consider each department’s break-even point compared to budgeted (ex-
pected) operations.
Source: A. Oppong, “The Paper Company,” The Journal of Accounting Case Research, Vol. 3, No. 2 (1996), pp.
80–88. Permission to use has been granted by Captus Press, Inc. and the Accounting Education Resource Centre
of The University of Lethbridge. [Journal Subscription: Captus Press, Inc., York University Campus, 4700 Keele
Street, North York, Ontario, M3J 1P3, by calling (416) 736-5537, or by fax at (416) 736-5793, E-mail:
[email protected], Internet:http://www.captus.com]
Ethics Case
Pickmore International
Joan Hildabrand is analyzing some cost data for her boss, Ross Cumings. The data relate to a
special sales order that Pickmore International is considering from a large customer in Singa-
pore. The following data are applicable to the product being ordered:
Normal unit sales price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $49.95
Variable unit manufacturing costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.50
Variable unit selling and administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.25
The customer is requesting that the sales order be accepted on the following terms:
a. The unit sales price would equal the unit contribution margin plus 10%.
b. Freight would be paid by the customer.
c. Pickmore International would pay a $5,000 “facilitating payment” to a “friend of the cus-
tomer” to get the product through customs more quickly.
In considering the order, Ross has indicated to Joan that this is a very important customer.
Furthermore, this work would help some employees earn a little extra Christmas money with
overtime.
1. What are the accounting and ethical issues involved in this case?
2. Should Joan recommend acceptance of the sales terms proposed for this special order?
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C E O 113 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Writing Assignment
Issues of Quality and Time on C-V-P Analysis Decisions
This chapter described how to analyze whether the difference between sales price and variable
costs, as well as the volume of sales, is sufficient to pay for all fixed costs in an organization
and provide a sufficient profit. A number of methods have been presented for analyzing these
costs, volume, and price relationships. These methods all focus on quantitative issues that af-
fect how a company manages its resources to maximize overall profits. However, there are a
number of qualitative issues involving quality and time that should also affect decisions about
what sales prices to set, how to manage fixed and variable costs, and which products should be
emphasized within the organization. One way to trade off fixed costs for variable costs is to
consider making large fixed cost investments in technology that result in automated produc-
tion, merchandising, and service processes. These kinds of investments allow some variable
costs, such as direct labor, to be reduced. Managing this cost trade-off often has strong impli-
cations on the quality of the product or service, as well as the timeliness with which it can be
delivered. Both of these qualitative issues eventually affect the quantitative issues of costs,
volume, and price. Go to your library and find an article describing one organization’s effort to
invest in automation or other technologies in order to reduce costs. Determine what quality
and time issues are affected by the investment. Write a one- to two-page memo describing
what you found.
The Debate
Which Cost Analysis Method Is Better?
Many costs within an organization are mixed costs, combining elements of both fixed and vari-
able costs. Separating these types of costs into their fixed and variable cost components is
necessary before C-V-P analysis work can be done. Two potential cost analysis methods are the
scattergraph (visual-fit) approach and the high-low approach. Each of these methods has both
disadvantages and advantages compared to the other.
Divide your group into two teams and prepare a two-minute oral argument supporting your
assigned position.
• One team represents “The scattergraph (visual-fit) method is superior!” Explain why this method
should be used for determining the variable and fixed cost components in a mixed cost.
• The other team represents “High-low; the way to go!” Explain why this method should be
used for determining the variable and fixed cost components in a mixed cost.
Internet Search
Applied Ethics Resources on WWW
We have discussed ethical issues for accountants in this text and have included an ethics case
at the end of each chapter. Obviously, ethical issues are of concern to accountants and all
other business professionals. There are a number of good resources on the Internet for those
interested in further exploring ethical issues in business (hopefully, we’re all interested in this
topic!). One of the better sites is Applied Ethics Resources on WWW Centre athttp://www
.ethicsweb.ca/resources/. Sometimes Web addresses change, so if this address doesn’t work,
access the Web site for this textbook (http://swain.swlearning.com) for an updated link.
Go to this site and explore the materials regarding applied ethics resources on the World
Wide Web. Find a publication that discusses either business or professional ethics. Write a short
paragraph that describes exactly where you found the article and give a brief summary.
?
?
?
doc_809922860.pdf
The two basic cost behavior patterns - variable and fixed - were introduced in the previous chapter. Other cost behavior patterns, such as mixed costs, are variations of these two. Mixed costs exhibit characteristics of both variable and fixed costs. In this section, we will review both variable and fixed costs and examine the reality of how these costs often look in many organizations. We will also introduce stepped costs and mixed costs.
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c h a p t e r
Analyzing Cost-Volume-
Profit Relationships
1 Understand the key
factors involved in cost-
volume-profit (C-V-P)
analysis and why it is such
an important tool in man-
agement decision making.
2 Explain and analyze
the basic cost behavior
patterns—variable, fixed,
stepped, and mixed.
3 Analyze mixed costs
using the scattergraph and
high-low methods.
4 Perform C-V-P analy-
ses, and describe the ef-
fects potential changes in
C-V-P variables have on
company profitability.
5 Visualize C-V-P rela-
tionships using graphs.
6 Identify the limiting
assumptions of C-V-P
analysis, and explain the
issues of quality and time
relative to C-V-P analysis
decisions.
7 Analyze mixed costs
using the least squares
method.
8 Explain the effects of
sales mix on profitability.
9 Describe how fixed
and variable costs differ in
manufacturing, service,
merchandising, and e-
commerce organizations,
and illustrate these differ-
ences with the operating
leverage concept.
After studying this chapter, you
should be able to:
©
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If you’ve ever watched an international-caliber soccer
match, you know that goals are scarce. Each goal re-
quires extensive work, patient play, and many attempts.
This same approach seems to apply to the business of
professional soccer in the United States where MAJOR
LEAGUE SOCCER (MLS) completed its seventh season in
the United States in 2002. The year 2002 was a banner
year for U.S. soccer with the men’s national soccer team
reaching new heights by finally cracking the Top 10 of
the FIFA World Rankings and competing in the quarter-
finals of the World Cup in Korea/Japan (after taking last
place at the previous World Cup tournament). This fol-
lowed on the momentum generated by the U.S. women’s
team, which won the World Cup in 1999 and placed third
in the world in 2003. Nevertheless, MLS has so far been
unable to score financially in America where sports fans
continue to prefer attending basketball, football, and
even baseball games to watching the most popular sport
in the (rest of the) world.
Professional soccer has been launched several times
in the United States amid much fanfare, but so far each
attempt has failed. The last failure, that of the NORTH
AMERICAN SOCCER LEAGUE (NASL)—which brought Pelé,
Cruyff, Best, and Beckenbauer to the United States in
the early 1970s—was especially painful because, with
the big names, professional soccer looked so promising.
One of the major reasons previous efforts failed is that
fixed costs were too high for the small number of fans
and meager TV revenues. Each attempt ended up with
the team owners losing money. To better manage player
salaries, which are a significant part of the fixed costs
of running a soccer team, the MLS set up an unusual
single-entity structure in 1996, under which the league
owns all the teams as well as all player contracts, and
investors buy operating rights rather than setting up
franchises. The purpose of this structure is to eliminate
the financial disparities between large and small mar-
kets and to control player salaries and other fixed costs.
This approach has successfully kept players’ salaries low;
so low in fact that a number of players have filed class
action lawsuits arguing the MLS structure is holding down
salaries in violation of U.S. antitrust laws.
Despite these efforts to contain the fixed cost of
players’ salaries, MLS teams continue to lose millions of
dollars, largely due to their inability to generate enough
revenue from ticket sales alone to cover another signif-
icant fixed cost, the cost of the leases on the stadiums
in which they play their games. And while the cost of
these lease payments is high, the larger problem is that
soccer teams forced to rent their facilities are only able
to keep the revenue from ticket sales and are generally
cut off from the all-important ancillary revenue that ac-
companies each game—revenue from concessions, park-
ing, merchandise, stadium signage and naming rights,
and luxury boxes.
The situation faced currently by Nick Sakiewicz, gen-
eral manager of the METROSTARS in New Jersey, is pretty
typical of the rest of the league. New Jersey has long
been a hotbed of soccer in America, from producing three
of the greatest American players of all-time (Tab Ramos,
John Harkes, and Tony Meola) to being home to the win-
ningest high school soccer coach in U.S. history (Gene
Chyzowych of Columbia High School). Nonetheless, the
MetroStars can’t seem to break even financially. Part of
this shortfall stems from the $1.5 million annual rent
the MetroStars must pay to use Giants Stadium at the
Meadowlands. Worse, the Meadowlands stadium is also
used by two NFL teams (the GIANTS and the JETS), the
New Jersey State Fair, and multiple concerts, which
means that the MetroStars can only play one or two home
games each month in June and July. With most of the
home games being played in April and May, average at-
tendance is not as high as it could be (attendance in
2002 averaged just 19,000 per game). Hence, the team
loses millions of dollars every year.
General Manager Nick Sakiewicz is convinced that a
new stadium is crucial to the MetroStars’ financial suc-
cess. At an estimated cost of $152 million, Sakiewicz
wants to build a roofed, 25,000-seat stadium in Harrison
City (also in New Jersey) to be located in a vast com-
plex that would include residential housing, retail space,
and a shopping center. And although he believes that
more people would buy a ticket to come see the Met-
roStars play in their own stadium, what makes the con-
struction proposal most attractive is the ancillary revenue
that would finally belong to the team because it would
own the stadium. It is estimated that a crowd of 20,000
can generate an extra $100,000 in profit from conces-
sions, parking, and so forth. Sakiewicz believes strongly
that those kinds of numbers will move his soccer team
beyond the break-even point and into profitability.
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1 John McLaughlin, Sky, October 1997, pp. 27-32; Ridge Mahoney, “Homes of Their Own,” July 30, 2001,http://www.si.com; Chris Isidore, “New Homes Get Old Quickly,” July 27, 2001,http://www.cnnmoney.com;
and the homepage for the MetroStars,http://www.metrostars.com.
44 Part 1 Foundations
n the previous chapter, we discussed differ-
ent ways to categorize costs, and we briefly
illustrated how you can use these cost cate-
gories to make management decisions. We also em-
phasized the fact that management accounting is
defined as all accounting information that is useful
in planning, controlling, and evaluating an organi-
zation. Some costs, such as direct materials and di-
rect labor costs in a manufacturing firm, increase in
direct proportion to the number of products or ser-
vices produced. These are called variable costs. Other
costs, such as factory rent, remain the same no mat-
ter what the level of production is. These are called
fixed costs. We used these definitions of variable
costs and fixed costs in the previous chapter to in-
troduce you to cost-volume-profit (C-V-P) analysis,
a critical tool in the management process. C-V-P
analysis is used to make important planning deci-
sions concerning appropriate levels of production
and spending. C-V-P analysis allows a manager to
answer the very important question: How much do
I need to sell in order to earn a profit?
In this chapter, you will further explore the
C-V-P analysis tool to analyze relationships between
variable costs, fixed costs, and revenues. You will
learn that successful managers must think carefully
about cost behavior—how costs change in relation
to changes in activity levels, such as the number of
patients in a hospital or the pounds of ore processed
in a copper smelter. An understanding of how costs
behave in relation to levels of activity helps man-
agers predict the effects of their plans on future per-
formance. In addition, because the C-V-P analysis
technique is applicable to all types of firms, we will
discuss the behavior of costs in manufacturing, mer-
chandising, service, and e-commerce firms.
You will also use the knowledge of cost behav-
ior patterns to analyze the kinds of problems facing
organizations such as the MetroStars’ lack of prof-
itability as described in the opening scenario. As you
work through this chapter making calculations that
will determine how profits will change in relation
to changes in sales volume, fixed costs, and variable
costs, be sure to think about how these calculations
reflect the process of managing actual organizations.
For instance, because of decreased air travel in the
wake of the 9/11 attacks, the airline industry has
struggled to be profitable in light of the heavy fixed
costs of owning and operating commercial aircraft.
Many owners of retail outlets in a mall breathe a sigh
of relief each month on the day when enough profit
has been generated to allow them to pay the
monthly fixed cost of the lease payment to the mall.
The owner of a baseball team will look out over a
half-filled stadium on game day and worry that the
ticket sales may not have been enough to cover the
costs of paying the players and running the stadium.
Every business owner must carefully plan how he or
she is going to generate enough money to cover the
fixed costs of the business. Those who have a clear
idea of exactly how many airline seats, or pairs of
pants, or hot dogs must be sold to break even will
be in a better position to create and maintain prof-
itability in the organization.
We believe that the best way to appreciate the
importance of good management information is to
begin by using that data to make significant man-
agement planning decisions. Accordingly, this chap-
ter will give you lots of opportunities to practice.
Also note that although we will focus primarily on
examining the financial implications of cost-volume-
profit analysis decisions, we will also pay attention
to the effects these decisions have on quality and
time issues as well.
cost-volume-profit (C-V-P) analysis Techniques for determining
how changes in revenues, costs, and level of activity affect the prof-
itability of an organization.
cost behavior The way a cost is affected by changes in activity
levels.
i
Understanding Why C-V-P Analysis Is Important
Management must make many critical operating decisions that affect a firm’s profitability. With
respect to planning, management is often interested in the impact a particular action will have
on profitability. C-V-P analysis can help managers assess that impact. The following are exam-
ples of questions that can be answered with C-V-P analysis:
• When planning whether or not to open a scuba shop in the mall, how many customers
will need to be served each month in order to break even and be able to pay the monthly
store rental fee?
1 Understand the key
factors involved in cost-
volume-profit (C-V-P)
analysis and why it is
such an important tool in
management decision
making.
• How will the profits of a bookstore be affected if the store raises its prices by 10%, result-
ing in a reduction of 2% in the number of books sold?
• How many carpets must a fledgling entrepreneur clean in a month in order to generate a
net profit of $3,000 each month?
• By how much will the profits of a discount electronics store change if a $100,000 adver-
tising campaign increases the number of computers sold by 13%?
• How will the profits of a fast-food restaurant change if the restaurant stops selling milk
shakes and instead focuses on raising the volume of soft drink sales by 25%?
It should be clear to you from these examples that C-V-P analysis involves studying the in-
terrelationships among revenues, costs, levels of activity, and profits. However, quality of prod-
ucts and services and speed of production and delivery must also be considered as managers use
C-V-P analysis to determine product prices, the mix of products, market strategy, appropriate
sales commissions, advertising budgets, production schedules, and a host of other important
planning decisions. Although C-V-P analysis is most useful for planning, it can also be used to
assist with controlling decisions (e.g., are the costs too high for the level of sales?) and evaluat-
ing decisions (e.g., should we reward employees for holding costs down or be concerned that
sales growth has slowed?). In fact, a lot of what is done in management accounting involves
some aspect of C-V-P analysis because of the tremendous potential it has to help management
increase the profitability and effectiveness of an organization. For this reason, as you use this
chapter to learn the mechanics of C-V-P analysis, be sure to see how important it is to be able
to understand and manage costs. As you study C-V-P analysis, you will gain a better under-
standing of basic cost behavior patterns. And once you understand these cost behavior patterns
and how to work with them, you can use them to make effective planning, controlling, and
evaluating decisions.
45 Chapter 2 Analyzing Cost-Volume-Profit Relationships
of products, (5) the speed and quality of production, and
(6) the resulting profits. Understanding the interrelation-
ships of the key variables in C-V-P analysis can assist you
in planning and in making critical control and evaluation
decisions.
T O S UMMA R I Z E : C-V-P analysis is a very im-
portant concept in management accounting. Key factors in-
volved in C-V-P analysis include (1) the revenues derived
from the sales prices charged for goods and services, (2) the
fixed and variable costs, (3) the sales volume, (4) the mix
Basic Cost Behavior Patterns
The two basic cost behavior patterns—variable and fixed—were introduced in the previous
chapter. Other cost behavior patterns, such as mixed costs, are variations of these two. Mixed
costs exhibit characteristics of both variable and fixed costs. In this section, we will review both
variable and fixed costs and examine the reality of how these costs often look in many organi-
zations. We will also introduce stepped costs and mixed costs.
A quick example of what we’re talking about may be helpful before we dive into all the
details of working with cost behavior. A cost may be classified as either fixed or variable by the
way it reacts to changes in level of activity. Think of a doughnut shop such as KRISPY KREME
or WINCHELL’S. Activity in the shop may be measured in terms of the volume of doughnuts
sold, the number of customers served, the number of hours the shop is open, the number of em-
ployees, or the total square feet of the serving area, and so forth. Get the point? There are a lot
of ways to measure activity in this organization. There are also a lot of different kinds of costs.
The first task is to identify the costs and activities where we intend to focus our management
effort. Let’s say that we are initially interested in understanding how the number of doughnuts
sold impacts costs and profits. Which costs will change, and which costs will not change, as we
expect to sell more or less doughnuts? This is the starting point of C-V-P analysis. It seems log-
ical that as more doughnuts are sold, the cost of doughnut ingredients will increase. This is
a variable cost. On the other hand, we probably wouldn’t expect the cost of property taxes to
2 Explain and analyze
the basic cost behavior
patterns—variable, fixed,
stepped, and mixed.
increase as more doughnuts are sold. This is a fixed cost. However, there are costs that have
both variable and fixed components. For instance, the electricity costs to run the doughnut shop
will increase as we sell more doughnuts because of the cost of the power to make the additional
doughnuts. However, even if we don’t sell any doughnuts, we will have to pay the utility costs
of just keeping the shop open. Utility costs are a mixed cost. The cost of a supervisor’s salary
isn’t normally going to increase as we sell more doughnuts until we have so many customers
that we need to hire an additional supervisor to help with the higher volume. At this point, the
fixed cost of salaries will jump to a new level. This is an example of a stepped cost.
Overall, once we have defined the activity, measurements of changes in activity level can
be used to determine cost behavior patterns.
Measuring Level of Activity
Before we can manage an organization, we need to identify exactly what it is that we intend to
manage. In other words, what is the activity upon which we intend to focus our planning, con-
trolling, and evaluating efforts? In the doughnut shop example, it makes sense for management
to focus on increasing the number of doughnuts sold; management efforts can reasonably be
expected to influence the number of doughnuts sold. Activity is often measured in terms of
output, input, or a combination of the two. Some of the most common activity bases used are
number of units sold and number of units produced in manufacturing firms, number of units
sold in merchandising firms, and number of contract hours paid for or billed in service firms.
We will generally use production volume or sales volume as the activity basis in this chapter to
demonstrate the use of C-V-P analysis.
Note that just because a cost doesn’t vary with a particular activity base (e.g., total units
sold) does not mean it could never be considered as a variable cost. For example, the total cost
of wages for a doughnut shop may not vary with the amount of sales volume (the clerks get paid
the same whether they sell a lot of doughnuts or just a few), but total wages would vary based
on the number of hours per week that the store is open. So, if another type of activity other than
sales volume is more relevant in determining changes in the variable costs being planned, the
C-V-P analysis should be based on that activity. It all comes down to an issue of “focus.” Where
do you believe you can best focus your management attention in order to plan for and control
costs and profits—on store hours, doughnuts sold, or customers served? There is some subjec-
tivity in this focus decision. Nevertheless, managers must be careful to understand the various
activity bases within their company so that they can properly plan for and control costs. We will
discuss a number of alternative activity bases in a later chapter on managing inventory.
Manufacturing and merchandising companies with a single product generally measure
volume of activity in terms of output, for example, number of cars, television sets, or desks pro-
duced. However, many companies produce or sell several different products (refrigerators, toast-
ers, and irons, for example), and a simple total of all the products manufactured or sold during
a given period may not provide a good measure of activity. This is particularly true for manu-
facturing firms. For example, GENERAL ELECTRIC manufactures a wide variety of products,
ranging from light bulbs to locomotives. It obviously takes more effort (and consequently costs
more) to produce a locomotive than a light bulb; accordingly, it wouldn’t make any sense to
state that total production for a given day was 1,000,001—1,000,000 light bulbs and 1 loco-
motive. In multiproduct situations, these manufacturing firms usually use input measures, such
as direct labor hours worked, machine time used, or the time needed to set up a job, as the ac-
tivity base. Such specific input measures are often more useful than general output measures.
Variable Costs
Total variable costs change in direct proportion to changes in activity level. Examples are costs
of direct materials, which vary proportionately with the number of units produced, and sales
commissions, which vary proportionately with the sales volume. For instance, as an automo-
bile manufacturer, you might define the activity of focus as the number of cars produced. If
engines, tires, axles, and steering wheels are purchased from suppliers, the related costs would
be variable because the total cost of steering wheels, for example, would vary proportionately
46 Part 1 Foundations
variable costs Costs that
change in total in direct pro-
portion to changes in activity
level.
with the number of cars produced. If no cars are produced, there are no steering wheel costs;
if 1,000 cars are manufactured during a period, the total cost for steering wheels and other pur-
chased parts is 1,000 times the unit cost of each item. As more cars are produced, the total cost
of each item increases. The unit cost, however, remains constant. For example, if an auto com-
pany pays $150 per steering wheel, the total cost of steering wheels for 200 cars is $30,000; for
500 cars, it is $75,000. At both levels of activity, however, the unit cost is still $150. This re-
lationship between variable costs and level of activity is shown graphically in Exhibit 1, which
relates the number of cars produced to the total cost of the steering wheels used
in production.
In addition to sales commissions and materials, many other costs (such as
labor) have a variable cost behavior pattern. For example, if it takes four hours
of labor to assemble a frame and each hour costs $25, a unit labor cost of $100
per frame is a variable cost; the total labor cost would be $100 times the num-
ber of frames produced.
Curvilinear Variable Costs
Our definition of the variable cost behavior pattern specifies that variable costs have a linear
relationship to the level of activity; that is, when the level of activity increases, total variable
costs rise at a directly proportional rate. For example, if the level of activity doubles, the total
variable costs will also double; this is a called a linear relationship. The reality is that, in prac-
tice, a truly linear relationship usually does not exist. Overall, many variable costs are actually
curvilinear costs when considered over many activity levels. That is, these curvi-
linear costs actually vary at increasing or decreasing rates across large changes in
the activity level. To illustrate, think about a manufacturer that makes a very
specialized “premium natural” ice cream that is handmade. Now consider Ex-
hibit 2. The top diagram is a graph that shows the cost of raw materials (for
example, milk, sugar, and other ingredients) purchased from suppliers to make
ice cream. Because the ice cream maker gets a bigger price discount as it pur-
chases higher volumes of raw materials, the variable cost of these materials is not
linear but curvilinear. That is, the cost increases at a decreasing rate.
On the other hand, the manager of the ice cream production process faces
an understandable labor challenge—it is difficult to find people who can make
ice cream efficiently. Plans to increase the production volume of the operation
mean that the manager will have to hire more individuals for the ice cream
production crew. As the manager scrambles to satisfy her labor needs, she will
47 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 1: An Example of Variable Costs
Cars produced
0
15,000
30,000
45,000
60,000
75,000
90,000
$105,000
100 200 300 400 500 600 700
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Cost of steering
wheel: $150 each
STOP & THINK
In a manufacturing plant, are direct labor
costs variable or fixed? Does your answer
change if the direct labor employees be-
long to a powerful union?
FYI :
If you’ve had an introductory class in eco-
nomics, you have likely been introduced to
the term economies of scale. The cost of
milk that becomes cheaper as production
volume increases (top graph in Exhibit 2) is
a cost that displays economies of scale.
On the other hand, the direct labor costs to
produce ice cream that become more costly
as production increases (bottom graph in
Exhibit 2) represent costs with diseconomies
of scale.
curvilinear costs Variable
costs that do not vary in direct
proportion to changes in ac-
tivity level but vary at decreas-
ing or increasing rates due to
economies of scale, produc-
tivity changes, and so on.
48 Part 1 Foundations
Exhibit 2: Curvilinear Variable Costs
0
2,000
4,000
6,000
8,000
$10,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
T
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Gallons of ice cream produced weekly
0
5,000
10,000
15,000
20,000
$25,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
T
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Gallons of ice cream produced weekly
n
$6,200/4,000 gallons
? $1.55 average direct
material (milk) cost
per gallon within the
relevant range
n
$4,800/4,000
gallons ? $1.20
average direct
labor cost per
gallon within the
relevant range
probably have to increase the wages she offers in order to attract more employees. As a result,
the direct labor cost of each gallon of ice cream will increase as planned production volumes
go up because the wage rate of the workers goes up. Thus, this curvilinear variable cost increases
at an increasing rate, as depicted in the bottom graph in Exhibit 2. If you’ve ever had a class in
economics, then this concept of curvilinear costs is familiar to you. The fact that most variable
costs are curved instead of linear is an economic fact of most organizations. However, when
doing C-V-P analysis, we assume that costs are linear. This is a potentially limiting assumption
of C-V-P work; but, as you’ll see in the next section, it is an appropriate assumption for most
managers.
Relevant Range and the Linearity of Variable Costs
While this is never exactly true, it is usually safe to assume that variable costs are approximately
linear within a certain range of production, called the relevant range. To illustrate the relevant
range concept, let’s return to our ice cream manufacturing business. Realistically, the produc-
tion manager does not expect to vary weekly production volume outside the range of 3,000 to
5,000 gallons of ice cream. As displayed in Exhibit 2 for both milk material cost and direct
labor cost, a linear segment within the relevant range of weekly production can effectively ap-
proximate the curvilinear cost relationship of producing between 3,000 and 5,000
gallons of ice cream. By assuming a linear (rather than a curvilinear) relation-
ship, the variable costs of milk and direct labor are estimated at $1.55 and $1.20,
respectively, per gallon of ice cream using the costs in the midpoint of the rele-
vant range (weekly production of 4,000 gallons of ice cream).
Relevant range is an important concept. If activity increases or decreases sig-
nificantly, cost relationships will probably change. If production volume soars,
for example, such factors as overtime work and bulk-purchase discounts may
cause direct labor and materials costs per unit to change. That is why we say that
the definition of variable costs—costs that are constant per unit of activity—is
applicable only within relevant ranges. The important point to remember is that
whenever we define a particular variable cost, we are assuming that the cost is
within the relevant range of activity.
Fixed Costs
Fixed costs remain constant in total, regardless of activity level, at least within the relevant
range of activity. Examples include property taxes, insurance, executives’ salaries, plant depre-
ciation, and rent. Because total fixed costs remain constant as activity increases, the fixed cost
per unit (total fixed cost ? level of activity) decreases. Similarly, as the level of activity de-
creases, the fixed cost per unit increases. This is in contrast to variable costs, where the costs
per unit are assumed to remain constant through changes in the level of activity within the
relevant range.
Before we go any further, it is a good idea for us to remind ourselves why
identifying fixed and variable costs is important. Remember that this chapter is
about managing the relationships among costs, volume, and profit. In the pre-
vious chapter, we briefly introduced the concept of C-V-P and break-even analy-
sis. In the C-V-P formula below (which we introduced in the previous chapter),
you can see that calculating what a company needs to do to “break even” and
start making a profit requires a clear measure of total fixed costs and variable
costs per unit:
? Break-even sales (in units)
In an actual company, the fixed and variable costs are very challenging to
identify. That is why it is important that you understand the nature of cost be-
havior and how to classify costs as either fixed or variable. Once we’ve completed
our discussion of cost behavior, we’ll be ready to spend some time on this very
useful C-V-P formula later in this chapter.
Total fixed costs
??????
(Sales price per unit ? Variable cost per unit)
49 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Cauti on
The relevant range concept is particularly
difficult to apply when using C-V-P analysis
in companies in very high growth situations,
such as high-tech start-ups. If a company’s
sales are increasing by 60% each quarter,
for example, it is unlikely to remain in the
same “relevant range” from quarter to quar-
ter; so careful analysis of variable and fixed
costs must be repeated on a regular basis.
fixed costs Costs that remain
constant in total, regardless of
activity level, at least over a
certain range of activity.
Cauti on
While total variable costs increase as pro-
duction increases, the per-unit variable cost
is constant across activity levels within the
relevant range. In contrast, while total fixed
costs are constant over the relevant range,
the per-unit fixed cost changes with in-
creases or decreases in production. Many
introductory students of management ac-
counting become confused and forget that
per-unit variable costs are fixed and per-
unit fixed costs will vary over the relevant
range!
relevant range The range of
operating level, or volume of
activity, over which the rela-
tionship between total costs
(variable plus fixed) and ac-
tivity level is approximately
linear.
Stepped Fixed Costs
Let’s continue with our example of the ice cream manufacturer. The top graph
in Exhibit 3 shows the relationship between the production line supervisor cost
and the total number of gallons of ice cream produced. In this case, until weekly
ice cream production reaches 1,000 gallons a week, the manufacturing manager
is able to oversee all line workers. At 1,000 gallons a week production, however,
the manager expects to hire a production line supervisor at $500 per week to
provide more supervision of the workers. Further, the manager expects that she’ll
need to hire an additional supervisor each time weekly production is increased
another 2,000 gallons. Although the production line supervisor cost is changing
as the scale of ice cream production changes, we still consider this cost to be fixed
within the relevant range. Hence, as shown in the top graph in Exhibit 3, within
a relevant range of activity of between 3,000 and 5,000 gallons of ice cream, the
total fixed manufacturing supervisor cost of $1,000 does not change. On the
other hand, the per-unit supervisor cost will drop considerably as production in-
creases. For example, when the fixed supervisor cost is $1,000 and 3,000 gallons
of ice cream are being produced, the supervisor cost per gallon of ice cream is $0.33 ($1,000
? 3,000 gallons). With production of 4,000 gallons, however, this fixed cost is only $0.25
($1,000 ? 4,000 gallons) per gallon.
As you can see in Exhibit 3, the fixed cost of the production line supervision “steps up” as
the volume of ice cream production increases. Stepped costs are costs that change in total in
a stair-step fashion with changes in volume of activity. Another example of a stepped cost might
be the labor charges for the maintenance of the tools and machinery in a small manufacturing
plant. One maintenance worker can handle the upkeep of all the equipment during normal
FYI :
Have you ever wondered why you always
wait so long and why there are so many
patients at one time in a dentist’s office?
Think about the nature of the dentist’s costs.
Most costs are fixed—dentists’ salaries, rent
or depreciation, and so forth. When costs
are mostly fixed, seeing a high volume of
patients is important to cover the fixed costs.
Then, once fixed costs are covered, almost
all additional patient revenue becomes
profit. Thus, by squeezing in only a few
additional patients, dentists can increase
their profits substantially.
Fixed Costs Are Shifting Over
the past few decades, fixed
costs have increased as a per-
centage of total costs for many
manufacturing companies, pri-
marily due to the increase in
factory automation. As a ma-
chine replaces each manual job, costs change from
variable labor costs to fixed depreciation or rental
charges. It is important to note that many service
companies have much higher ratios of fixed-to-
variable costs than do manufacturing companies. The
costs of providing services in companies such as
banks, consulting agencies, and airlines typically do not vary
much depending on the volume of banking transactions, con-
sulting hours, or passengers carried. Perhaps more significantly,
e-commerce organizations often have even fewer variable costs
than service organizations do! Once the technology has been
put in place to run an e-commerce business, there is typically
very little additional cost of technology based on usage (within
the relevant range). Personnel costs in e-commerce organiza-
tions, such as engineering personnel, marketing teams, and ex-
ecutive personnel, also do not change much based on the
volume of customer use of the organization’s technology.
As fixed costs in manufacturing organizations increase, and
the economy continues to shift more and more to service and
e-commerce organizations, this fixed cost emphasis has a sig-
nificant effect on the decision-making process. When costs are
fixed, management’s ability to influence costs with activity-
level decisions is limited. With variable costs, management has
more flexibility to change activity levels and thereby increase
or decrease total operating cost structures. This trend
of replacing variable costs with fixed costs has an im-
portant impact on the cost structure of an organiza-
tion that is captured in the concept of operating
leverage, which is discussed in the expanded mater-
ial section of this chapter.
b u s i n e s s env i r onment
stepped costs Costs that
change in total in a stair-step
fashion (in large amounts)
with changes in volume of
activity.
levels of activity. However, when there is a significant increase in activity, a sec-
ond worker must be hired, and the maintenance cost approximately doubles.
Mixed Costs
Mixed costs, like curvilinear costs and stepped costs, are variations of the basic
fixed and variable cost behavior patterns. Specifically, mixed costs are costs that
contain both variable and fixed components. An example is rent that is based on
a fixed fee plus a percentage of total sales. Thus, the rental terms for an auto-
mobile dealer’s showroom might include a flat payment of $4,000 per month
plus 1% of each month’s sales. The 1% of sales is the variable portion, and the
$4,000 is the fixed cost. The total rent, therefore, would be considered a mixed
cost and could be diagrammed as shown in Exhibit 4. As this exhibit shows, the
cost of renting the showroom increases as sales increase. The total rent is $4,000 when there
are no sales; $6,000 when sales are $200,000 [$4,000 ?(0.01 ?$200,000)]; and $8,000 when
sales are $400,000 [$4,000 ? (0.01 ? $400,000)]. This increase is directly due to the variable
cost element, which increases in total as activity level (car sales) increases.
One of the important challenges in using C-V-P analysis in the planning process is the
need to effectively separate mixed costs into their fixed and variable cost components. Over
51 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 3: Stepped Fixed Costs
0
500
1,000
1,500
2,000
$2,500
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
T
o
t
a
l
p
r
o
d
u
c
t
i
o
n
l
i
n
e
s
u
p
e
r
v
i
s
o
r
c
o
s
t
s
(
$
)
Gallons of ice cream produced weekly
n
STOP & THINK
If the “steps” in a stepped cost are wide
compared to the relevant range (in other
words, the costs essentially are unchanged
within the relevant range), the costs are
usually treated as fixed. This would be the
case with the production line supervisor
costs in Exhibit 3. On the other hand,
how would you treat a stepped cost with
very narrow steps as is displayed in the
bottom graph in Exhibit 3?
mixed costs Costs that con-
tain both variable and fixed
cost components.
52 Part 1 Foundations
Exhibit 4: An Example of a Mixed Cost
Total sales
0
4,000
6,000
8,000
10,000
12,000
$14,000
$100,000 $200,000 $300,000 $400,000 $500,000
T
o
t
a
l
r
e
n
tc o c o Total mixed cost
$
e
s
Analysis of Mixed Costs
With an understanding of the different types of cost behavior, we can discuss how to iden-
tify and separate mixed costs into variable and fixed components. This separation is essential
because we have to clearly classify all costs as fixed or variable before doing C-V-P analysis.
When it comes to mixed costs, remember that the fixed portion represents the cost necessary
to maintain a service (such as a telephone) or a facility (such as a building), and the variable
portion covers actual use. Recall the example of the automobile showroom’s rental cost, part
of which was a flat monthly fee and part a percentage of sales. Other common mixed costs
are such overhead costs as electricity and repairs.
The most accurate way to separate the actual fixed and variable components of mixed
costs is to analyze each invoice. An electricity bill, for example, may include a flat monthly
service charge that would be classified as a fixed cost. Additional variable costs are those
3 Analyze mixed costs
using the scattergraph and
high-low methods.
change over the relevant range; therefore, fixed costs de-
crease per unit as the level of activity increases within the
relevant range. Stepped costs increase with the level of ac-
tivity but not smoothly. If the steps are wide in relation to
the relevant range, these costs can be treated as fixed; if
the steps are narrow, they can be treated as variable. Mixed
costs have both a fixed and a variable component. An in-
crease in a mixed cost with a rising level of activity is due
entirely to the variable cost element.
T O S UMMA R I Z E : Cost behavior is the way a
cost changes in response to changes in activity level. There
are two basic cost behavior patterns, variable and fixed. To-
tal variable costs change in direct proportion to changes in
the level of activity over the relevant range; therefore, vari-
able costs are constant per unit over this range. In analyz-
ing variable costs, we generally assume a linear relationship
between total costs and the level of activity within the rel-
evant range; outside of this range, variable costs are usu-
ally curvilinear. On the other hand, total fixed costs do not
the years several management accounting techniques have been developed by organizations for
this purpose. We will explore these mixed cost analysis methods in the next section of this
chapter.
53 Chapter 2 Analyzing Cost-Volume-Profit Relationships
based on the amount of electricity actually used during the month. This approach could be
very time consuming, however, and may not be cost effective (that is, it would cost more
to do the analysis than the detailed information is worth). An alternative approach is to an-
alyze the historical trend in past costs as the level of activity has changed as the basis for
classifying costs as fixed or variable. There are several methods of doing this. In this section,
we will introduce you to two methods: the scattergraph method and the high-low method.
In the expanded material, we introduce least squares analysis, a more sophisticated method
for analyzing mixed costs.
The Scattergraph, or Visual-Fit, Method
Probably the simplest method of separating mixed costs into their variable and fixed com-
ponents is the scattergraph (or visual-fit) method. Essentially, we’re talking here about sim-
ply looking at a trend of mixed cost points over time and learning how to “see” the fixed
and variable cost components. To do this, the total mixed cost for each level of activity is
plotted on a graph, and a straight line (called the regression line) is visually fitted through
the points. The idea is to position the line through the set of plotted data points in a way
that minimizes the average distance between all the data points and the fitted regression line.
With the regression line inserted into the graph, the fixed portion of the mixed cost is esti-
mated to be the amount on the cost (vertical) axis at the point where it is intercepted by the
regression line. The variable cost per unit (referred to as the variable cost rate) is equal to
the slope of the regression line, which is simply the change in cost divided by the change in
activity.
To illustrate the scattergraph method, let’s use the example of electricity
costs for an automobile manufacturer. In the analysis and calculations that fol-
low, all costs are assumed to fall within the relevant range of activity. In this ex-
ample, we use direct labor hours as a measure of the activity level.
Exhibit 5 shows a scattergraph on which electricity costs and direct labor
hours have been plotted. The regression line has been visually fitted to mini-
mize the distance between data points. It appears that the total fixed portion of
electricity cost is about $40,000 per month, which is where the regression line
intersects the cost axis. The variable cost rate is approximately $4.29 per direct labor hour,
which is the slope of the regression line. To calculate the slope, we use the following formula
and the data points of zero and 7,000 direct labor hours, respectively.
Variable cost rate ?
X ?
X ?
X ? $4.29 (rounded)
Obviously, the scattergraph method has some limitations as a cost estima-
tion tool. Perhaps the most critical limitation is that how the user fits the re-
gression line through the data points is entirely subjective. Consider Exhibit 5
once more. If you were the one fitting the regression line to these data points,
would you have set the line exactly where it is in this graph? Hopefully, your line
would have been quite close to the current line. Still, it probably wouldn’t have
been exactly the same, resulting in some small differences in your own estima-
tions of fixed and variable costs. Hence, the scattergraph method is a classic “quick
and dirty” management accounting technique. Yet, although the scattergraph
$30,000
?
7,000
$70,000 ? $40,000
???
7,000 ? 0
Change in (electricity) cost
?????
Change in activity (direct labor hours)
Cauti on
When making these cost graphs, remember
that the dollars go on the vertical axis and
the level of activity goes on the horizontal
axis.
Cauti on
Once the regression line has been fitted
through the data points, the scattergraph
method does not depend any longer on the
data points to estimate fixed and variable
costs. Cost estimations are entirely based
on points along the regression line. For in-
stance, notice that in this case we used the
points 0 and 7,000 along the visually fitted
regression line. However, we could have
used any two points on the regression line
(such as 2,000 direct labor hours and
10,000 direct labor hours) to calculate the
variable costs per direct labor hour.
scattergraph (visual-fit)
method A method of segre-
gating the fixed and variable
components of a mixed cost
by plotting on a graph total
costs at several activity levels
and drawing a regression line
through the points.
regression line On a scatter-
graph, the straight line that
most closely expresses the
relationship between the vari-
ables.
variable cost rate The
change in cost divided by the
change in activity; the slope
of the regression line.
54 Part 1 Foundations
Exhibit 5: Total Electricity Costs
2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000
T
o
t
a
l
e
l
e
c
t
r
i
c
i
t
y
c
o
s
t
$130,000
120,000
110,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
Direct labor hours
Regression line
Point at which the cost axis is
intercepted by the regression line
high-low method A method
of segregating the fixed and
variable components of a
mixed cost by analyzing the
costs at the highest and the
lowest activity levels within a
relevant range.
provides only subjective estimates of the fixed and variable portions of mixed costs, it can be
an extremely useful tool to describe and discuss cost behavior in the planning process. It is also
useful for thinking about how to control operating costs. For instance, it shows at a glance any
trends and abrupt changes in cost behavior patterns. As such, it can be used as a preliminary
step before using more sophisticated methods of cost evaluation.
The High-Low Method
A second approach to identifying fixed and variables costs is the high-low method, which an-
alyzes mixed costs on the basis of total costs incurred at both the highest and the lowest levels
of activity. To illustrate this method, we refer again to the electricity costs of the automobile
manufacturer. This time, however, we will focus on the following table of reported electricity
costs and direct labor hours worked. (The numbers in this table correspond exactly to the points
plotted in the scattergragh in Exhibit 5.)
Month Direct Labor Hours Worked Total Electricity Cost
January 7,000 $ 70,000
February 6,000 60,000
March 12,000 100,000
April 6,600 80,000
May 18,000 120,000
June 14,000 110,000
Although these two columns of figures do not visually show trends as clearly as the scattergraph
does, they do suggest that as the activity level (direct labor hours) increases, total electricity costs
increase. Given this relationship, the high-low method can be used to determine the fixed and
variable portions of the electricity cost as follows:
1. Identify the highest and lowest activity levels (18,000 hours in May and 6,000 hours in
February). As you can see, these two months also represent the highest and lowest levels
of electricity costs, or $120,000 and $60,000, respectively (although this may not always
be the case).
2. Determine the differences between the high and low points.
Total Electricity Cost Direct Labor Hours
High point (May) $120,000 18,000
Low point (February) 60,000 6,000
Difference $ 60,000 12,000
3. Calculate the variable cost rate (variable cost per unit). The formula is the same as the
one used to compute the slope of the regression line in the scattergraph method. The
results are different, of course, because the scattergraph method is based on a regression
line that is plotted, as much as possible, using all the data points, whereas the high-low
method uses only the highest and lowest data points.
Variable cost rate ?
?
? $5 per direct labor hour
4. Determine fixed costs based on the variable cost rate ($5 in this case). The formula for
this computation is:
Fixed costs ? Total costs ? Variable costs
At the high level of activity, the calculation is as follows:
X ? $120,000 ? (18,000 ? $5)
X ? $120,000 ? $90,000
X ? $30,000
You get the same result if you calculate fixed costs at the low level of activity as follows:
X ? $60,000 ? (6,000 ? $5)
X ? $60,000 ? $30,000
X ? $30,000
In summary, using the high-low method of analyzing mixed costs, the vari-
able portion of the total electricity cost is estimated to be $5 per direct labor
hour, and the fixed portion is $30,000 per month. This means that $30,000 ap-
pears to be the amount the company pays each month just to have electricity
available, and $5 is the average additional electricity cost for each hour of direct
labor worked.
$60,000
?
12,000
Change in costs
???
Change in activity
55 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Cauti on
Once you have selected the high and low
activity levels to use in the high-low
method, don’t use any other activity levels
or costs than these two data points to cal-
culate the fixed costs.
56 Part 1 Foundations
A Comparison of the Scattergraph and
High-Low Methods
As we have illustrated, the scattergraph and high-low methods may produce dif-
ferent results.
Method Variable Cost Rate Fixed Cost
Scattergraph $4.29 $40,000
High-low 5.00 30,000
Both methods are useful for a quick approximation. The scattergraph method
takes all the data into account. Therefore, this method tends to be more accu-
rate, although it is somewhat subjective and inconsistent because different peo-
ple might draw the line through the points differently. On the other hand, anyone
using the high-low method will consistently get the same results. However, be-
cause only two data points are used, the high-low method may not be represen-
cost axis (the fixed cost) and calculating the slope of the
line (the variable cost rate). With the high-low method, the
high and the low levels of activity are used to calculate first
the variable cost rate and then the fixed cost component.
T O S UMMA R I Z E : Two common techniques for
analyzing mixed costs are the scattergraph and high-low
methods. The scattergraph method involves visually fitting
a straight line (the regression line) through data points plot-
ted on a graph, then noting where the line intercepts the
FYI :
What if the highest and lowest levels of ac-
tivity do not correspond to the highest and
lowest levels of costs? This could easily (and
often does) happen in real-life companies.
Remember that the high-low method is a
method that determines approximately the
fixed and variable costs. Hence, companies
must then choose to base the estimate on
either the highest and lowest activities or the
highest and lowest costs. For simplicity, this
textbook will always present data such that
the highest and lowest levels of activity do
correspond to the highest and lowest levels
of costs.
tative of the costs incurred at all levels of activity. It is important that you realize that the math
used in the high-low method essentially plots the regression line through the two most extreme
points in a scattergraph. To understand what we mean, look at the scattergraph of the elec-
tricity cost data in Exhibit 5. Notice that the low point lies below the scattergraph regression
line and the high point lies above the scattergraph regression line. Now, if you were to draw a
straight line through the high and low points, that line would not be the same line created us-
ing the scattergraph (visual-fit) method, and may not necessarily represent all six data points
plotted. Nevertheless, you can use either method or both methods to predict future costs. If,
for example, management wants to know how much electricity will cost next month with 10,000
direct labor hours budgeted, the following calculations would be made:
Method Formula Estimated Cost
Scattergraph $40,000 ? 10,000($4.29) ? $82,900
High-low $30,000 ? 10,000($5.00) ? $80,000
As you can see, the total estimated costs resulting from these two methods, in this case, are rea-
sonably close to each other (although this may not necessarily be the case with sets of actual
cost and activity data in some real-life companies).
57 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Methods of C-V-P Analysis
Now that you have a better understanding of cost behaviors and can separate mixed costs into
their fixed and variable cost elements, you are ready to use your knowledge of cost behaviors
to make planning decisions. The previous chapter provided a quick introduction to C-V-P
analysis in the process of planning and analyzing decisions to prioritize Kevlar versus Teflon
products at DUPONT. However, in order to effectively use this valuable tool, we need a more
detailed discussion and lots of practice.
If you haven’t done so already, now is a good time to think of an actual business organi-
zation that is familiar to you, perhaps one by which you’ve been employed or are now em-
ployed. Think about the product or service this organization creates and the costs and processes
it uses. Now, as you study the C-V-P analysis method below, be sure to consider how this tool
4 Perform C-V-P analy-
ses, and describe the ef-
fects potential changes in
C-V-P variables have on
company profitability.
Managing an Airline in the
Post-9/11 Economy Is Not
Easy. Prior to the terrorist
tragedies in 2001, CONTINEN-
TAL AIRLINES was posting an
incredible string of consecutive
profitable quarters. Since filing
for bankruptcy protection in 1995, Continental re-
ported 24 straight quarters of profit, even when most
of the other major U.S. airlines reported losses. This
all changed, of course, on September 11, 2001. Since
then, Continental, the fifth largest airline in the
United States, has struggled very hard just to stay
alive. Both 2001 and 2002 resulted in significant operating
losses for Continental, as was the case with many of its com-
petitors. Continental, however, appears to be weathering the
storm better than most other airlines. In 2002, three of the
top seven U.S.-based international carriers filed bankruptcy. By
the end of the first quarter in 2003, TWA no longer existed,
and UNITED and US AIRWAYS were still struggling in bank-
ruptcy. In contrast, Continental Airlines again earned a cov-
eted spot on Fortune’s list of the 100 Best Companies to Work
For—the only airline to do so and the fifth consecutive year
for it to make the list. More importantly, in March 2002, Con-
tinental posted its first profitable month since 9/11, and Gor-
don Bethune, chairman and CEO, predicted that his company
would be able to break even in 2004. This progress is signifi-
cant in that the Air Transport Association (ATA) forecasts that
the overall airline industry will lose $7 billion in 2003.
How has Continental’s management team carried this com-
pany through a disastrous period of time for the airline indus-
try? For one thing, Continental Airlines’ management carefully
analyzed its costs, divided those costs into fixed and variable
components, and made several decisions to reduce fixed costs.
For example, Continental grounded planes and slashed excess
capacity. The airline eliminated 12,000 jobs in 2002 and planned
to cut another 1,200 jobs, including 25% of top management,
in 2003. All of this helped reduce Continental’s jet cost per
available seat mile by 3.8%, which is a significant percentage
in an industry defined by extremely thin profit margins.
With better control of its fixed costs, Continental Airlines
is again becoming profitable, and becoming profitable more
quickly than most of its competitors. Because of these cut costs,
Continental Airlines’ passengers pay lower fares than on other
airlines and receive better service. These lower fares and bet-
ter service enable Continental to fill more seats than its com-
petitors. Because its costs are low, it is profitable. Fixed costs
are now a smaller percentage of total costs at Continental Air-
lines than at almost all other airlines.
Sources: Adapted from PR Newswire, “Continental Airlines Re-
ports First Quarter Loss; Carrier Profitable for Month
of March, the First Profitable Month Since 9/11,” April
15, 2002; Continental Airlines 2002 Annual Report;
“Continental Air CEO Now Sees Break-Even Results
for 2004,” The Wall Street Journal, March 19, 2003.
b u s i n e s s env i r onment
would be used in your own organization to plan and manage costs and activities in order to
obtain desired results.
Contribution Margin
In order to effectively use C-V-P analysis, we first need to spend some time working with the
concept of contribution margin. Contribution margin is equal to sales revenue less variable
costs; it is the amount of revenue that remains to cover fixed costs and provide a profit for an
organization. For example, the contribution margin from the sale of one order of French fries
by a fast-food restaurant is the selling price less the variables costs
(potatoes, salt, container, cooking oil, wages of the cook) of pro-
ducing the fries. Any contribution margin generated by the sale of
an order of French fries can be used to pay the fixed costs of the
fast-food outlet, such as the monthly rent, the insurance, the super-
visor’s salary, and so forth. Contribution margin is one of the most
important management accounting concepts you will learn because
many operating decisions are made on the basis of how contribution
margin will be affected. A company may decide, for example, to ad-
vertise one product more than others because that product has a
higher contribution margin.
The Contribution Margin Income Statement
To illustrate the concept of contribution margin, let’s use the fol-
lowing format of a contribution margin income statement. The state-
ment data for Jewels Corporation, a producer of high-quality baseball
gloves, follow.
2
Jewels Corporation
Contribution Margin Income Statement
For the Month Ended November 30, 2006
Total Per Unit
Sales revenue (1,000 gloves) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $200,000 $200
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110,000 110
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 90,000 $ 90
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63,000
Profit* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 27,000
*In this chapter, “profit” means pretax income; the terms income and profit are interchangeable.
As this income statement shows, for internal decision-making purposes,
Jewels Corporation computes its contribution margin on a per-unit (glove) and
total-dollar basis. During November, Jewels’ per-unit contribution margin is
$90; the total contribution margin at a sales volume of 1,000 baseball gloves is
$90,000.
The per-unit contribution margin tells us that $90 is available from each
glove sold to cover fixed costs and provide a profit. By showing the $63,000 of
fixed costs separately, this income statement also tells us that Jewels must gen-
erate sufficient contribution margin to cover these costs before a profit can be
earned. With $200,000 of sales revenue, the contribution margin ($90,000) is
sufficient to cover the fixed costs and provide a profit of $27,000.
58 Part 1 Foundations
© 2003 Getty Images
The contribution margin gen-
erated by the sale of an order
of French fries can be used to
pay fixed costs such as rent,
insurance, and salaries. Now
you know why you often hear
that ever popular question
“Would you like fries with
that?” at fast-food restaurants.
contribution margin The
difference between total sales
and variable costs; the portion
of sales revenue available to
cover fixed costs and provide
a profit.
FYI :
French fries and soft drinks are good exam-
ples of products with a high contribution
margin. A $2 order of French fries might
have a contribution margin in excess of
$1.50. That’s why fast-food employees are
told to specifically ask customers if they
want fries and a drink with their order!
2 In this example, we assume that there is only one model of baseball glove, which sells for $200.
per-unit contribution
margin The excess of the
sales price of one unit over
its variable costs.
This type of contribution margin income statement is particularly useful as a planning tool.
The statement helps a company to project profits at any level of activity within the relevant
range. For example, if Jewels Corporation forecasts sales of 1,200 baseball gloves next month,
the company can prepare a forecasted (or pro-forma) income statement (in contribution mar-
gin format) as follows:
Jewels Corporation
Pro-Forma Contribution Margin Income Statement
For the Month Ended December 31, 2006
Sales revenue (1,200 gloves ? $200) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $240,000
Less variable costs (1,200 gloves ? $110) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132,000
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $108,000
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 45,000
Notice that with an increase in sales of 200 baseball gloves, the contribution margin in-
creases $18,000 ($108,000 ? $90,000). You can confirm this by multiplying the per-unit con-
tribution margin by the increase in volume ($90 per unit ? 200 gloves ? $18,000). Because
we assume that the increase in volume is still within the relevant range of activity (which is a
very important assumption!), the fixed costs remain at $63,000, and profit increases by the
$18,000 increase in contribution margin. The critical thing you should see here is that once
the fixed costs are covered, each subsequent dollar in contribution margin goes straight to profit!
In other words, when Jewels Corporation hits its break-even point (which is the point where
all fixed costs are covered), each additional glove sold will generate $90 in profit.
Notice the importance of accurately determining cost behavior when forecasting profit lev-
els. If one ignores cost behavior, then the $27,000 profit generated by November sales of 1,000
gloves may lead to the conclusion that each glove creates $27 ($27,000 profit/1,000 gloves) in
profit. With this incorrect information, the forecasted level of profit for December sales of 1,200
gloves is $32,400 ($27 per glove ? 1,200 gloves). This forecast differs significantly from the
$45,000 profit forecast above that stems from a correct consideration of the behavior (fixed or
variable) of Jewels Corporation’s costs.
The Contribution Margin Ratio
Knowing the contribution margin ratio, which is the percentage of sales revenue left after vari-
able costs are deducted, will help you compare the profitability of various products. For exam-
ple, if product A has a 60% contribution margin ratio and the contribution margin ratio of
product B is only 20%, the company should emphasize product A, assuming that other factors
are equal. As a concrete example, in a supermarket the prepared foods (baked goods, squeezed
juices, ready-to-eat barbecued chicken) have high contribution margin ratios whereas the sta-
ples such as milk and eggs have lower contribution margin ratios.
To illustrate the calculation of contribution margin ratios, let’s look again at the initial Jew-
els Corporation example. The ratio is computed as follows:
Ratio
Total Per Unit (Percentage)
Sales revenue (1,000 gloves) . . . . . . . . . . . . . . . $200,000 $200 100%
Less variable costs . . . . . . . . . . . . . . . . . . . . . . 110,000 110 55
Contribution margin . . . . . . . . . . . . . . . . . . . . . $ 90,000 $ 90 45%
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . 63,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 27,000
59 Chapter 2 Analyzing Cost-Volume-Profit Relationships
contribution margin ratio
The percentage of net sales
revenue left after variable
costs are deducted; the con-
tribution margin divided by
net sales revenue.
The contribution margin ratio is 45% of sales revenue ($90 ? $200), which means that
for every $1.00 increase in sales revenue, the contribution margin increases by $0.45 (45% of
$1.00). If fixed costs are already covered, profit will also increase by $0.45 for every $1.00 in-
crease in sales. As you can see, there is another ratio presented in these calculations—the vari-
able cost ratio. These two ratios are complements of each other. Hence, the variable cost ratio
($110 ? $200 ? 55%) plus the contribution margin ratio (45%) will always equal 100%.
This is important because whether we’re describing contribution margin ratios or variable cost
ratios, we are really talking about the same basic issue—the relationship of variable costs to sales
revenue.
With contribution margin or variable cost ratios, it is easy to analyze the impact of changes
in sales on the contribution margin. For example, if you estimate that Jewels’ sales will increase
by $20,000, you can apply the contribution margin ratio of 45% or the variable cost ratio of
55% and estimate that the contribution margin will increase by $9,000, which is equal to
$20,000 ?0.45 or $20,000 ?(1 ?0.55). The higher the contribution margin ratio, the larger
the share of each additional dollar of sales that goes toward covering fixed costs and increasing
profit.
The C-V-P Equation
As you can see, contribution margin calculations will be very useful to you when analyzing cost-
volume-profit relationships in the management planning process. Doing C-V-P analysis using
contribution margin calculations is a straightforward process. C-V-P analysis does require some
simple algebra; here is where you reap the benefits of paying attention during your eighth grade
math class.
We began this chapter with the assumption that all costs can be described as either fixed
or variable. To highlight the important idea that C-V-P analysis depends on dividing costs into
fixed and variable behavior patterns, we will develop the C-V-P equation as follows:
3
1. Because all costs can be classified as either variable or fixed, we can express the calcula-
tion of profit with the following basic formula:
Sales revenue ? Variable costs ? Fixed costs ? Profit
2. We can specify the formula more precisely by expressing the equation in units:
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? Profit
3. Or, we can express the equation using ratios:
Sales revenue ? (Variable cost ratio ? Sales revenue) ? Fixed costs ? Profit
These equations are quick and useful methods for examining the financial aspects of C-V-P
analysis problems. To illustrate, see if you can use the C-V-P equation based on units and the
data from the Jewels Corporation example to determine profit assuming that sales of 1,200
baseball gloves are expected.
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? Profit
($200 ? 1,200) ? ($110 ? 1,200) ? $63,000 ? Profit
$240,000 ? $132,000 ? $63,000 ? Profit
$45,000 ? Profit
Alternatively, you could calculate Jewels’ profits using the equation based on ratios.
60 Part 1 Foundations
3 Granted, fixed and variable costs often get “mixed together” and can be difficult (and sometimes impossible) to
separate. The fact that C-V-P analysis is based on an assumption that all costs can be divided clearly into fixed
and variable is one of the limitations of this technique.
Sales revenue ? (Variable cost ratio ? Sales revenue) ? Fixed costs ? Profit
$240,000 ? [($110 ? $200) ? $240,000] ? $63,000 ? Profit
$240,000 ? (0.55 ? $240,000) ? $63,000 ? Profit
$240,000 ? $132,000 ? $63,000 ? Profit
$45,000 ? Profit
Note that we calculated the same profit of $45,000 using both formula approaches. This
result is no surprise because these are simply alternative routes to the same destination. Both
methods are commonly used in business, depending on the data available for the analysis. So,
although there may appear to be many alternative ways to write the C-V-P formula, there is
really only one formula, and it is not hard to remember:
Sales revenue ? Variable costs ? Fixed costs ? Profit
Once you understand this fact, C-V-P analysis using the equation approach is basic math; you
merely insert the known elements into the formula and solve for the one unknown element.
Break-Even Point
In many cases, as a manager you will want to know how many units need to be sold to break
even. The break-even point is defined as the volume of activity at which total revenues equal
total costs, or where profit is zero. The break-even point may also be thought of as the volume
of activity at which the contribution margin equals the fixed costs.
Although the goal of business planning is to make a profit, not just to break even, know-
ing the break-even point can be useful in assessing the risk of selling a new product, setting
sales goals and commission rates, deciding on marketing and advertising strategies, and other
similar operating decisions. Because the break-even point is, by definition, that activity level at
which no profit or loss is earned, the basic C-V-P equation can be modified to calculate the
break-even point as follows:
Sales revenue ? Variable costs ? Fixed costs ? $0
As you can see, to compute the break-even point, all that you need to do is simply set income
equal to zero and then solve for the unknown—such as the number of units to be sold or the
total revenues to be achieved.
Let’s again use the Jewels Corporation example. How many units must Jewels sell to break
even? (Note that we will use “X ” to represent the unknown element, in this case, the number
of baseball gloves.)
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? $0
[Sales price ? (X)] ? [Variable cost ? (X)] ? Fixed costs ? $0
$200X ? $110X ? $63,000 ? $0
$90X ? $63,000
X ? $63,000 ? $90 ? 700 units (baseball gloves)
In this case, if Jewels sells 700 baseball gloves, the company will generate enough revenues
to cover its variable and fixed costs, earning zero profit [($200 ? 700) ? ($110 ? 700) ?
$63,000 ? $0]. Once you understand the basic C-V-P formula, you just set it up and solve
for whatever unknown you’re interested in planning. Think you’ve got it? Then try this one as
a check on yourself: Assuming that Jewels can sell only 600 baseball gloves, what price per glove
would the company have to use in order to break even?
4
61 Chapter 2 Analyzing Cost-Volume-Profit Relationships
break-even point The
amount of sales at which total
costs of the number of units
sold equal total revenues; the
point at which there is no
profit or loss.
4 (Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? $0
[(X) ? Units] ? (Variable cost ? Units) ? Fixed costs ? $0
[(X) ? 600] ? ($110 ? 600) ? $63,000 ? $0
600X ? $66,000 ? $63,000 ? $0
600X ? $129,000
X ? $215 (new baseball glove price)
Determining Sales Volume to Achieve Target Income
Another way we can use C-V-P analysis in the planning process is to determine what level of
activity is necessary to reach a target level of income. Instead of setting profit at $0 to do a
break-even analysis, we can just as easily set income in the formula at the targeted level and
then use the formula to plan or predict what fixed costs, variable costs, sales prices, and sales
volumes are needed to achieve the target level of income. Target income is usually defined as
the amount of income that will enable management to reach its objectives—paying dividends,
meeting analysts’ predictions, purchasing a new plant and equipment, or paying off existing
loans. Target income can be expressed as either a percentage of revenues or as a fixed amount.
To illustrate target income, suppose that we want to know how many baseball gloves must
be sold by Jewels Corporation to achieve a target income of $36,000, assuming no changes in
per-unit variable costs or total fixed costs. The calculation is as follows:
(Sales price ? Units) ? (Variable cost ? Units) ? Fixed costs ? Target income
$200X ? $110X ? $63,000 ? $36,000
$90X ? $99,000
X ? 1,100 units (baseball gloves)
Thus, we can see that if Jewels sells 1,100 baseball gloves at a contribution margin of $90 each,
and assuming that fixed costs are $63,000, the company will earn a pretax profit of $36,000
[($90 ? 1,100 units) ? $63,000 ? $36,000].
A fixed dollar amount of income, such as the $36,000 that would be earned by selling
1,100 baseball gloves, is probably the most typical way of expressing a target income goal for
many companies. However, because investors often evaluate companies partially on the basis of
the return on sales revenue (or simply “return on sales”), management may want to state its
goal as a percentage return as opposed to a fixed amount of income. For example, if Jewels
Corporation set a target income of a 20% return on sales, the computation would be:
Sales revenue ? Variable costs ? Fixed costs ? 0.20 ? Sales revenue
$200X ? $110X ? $63,000 ? 0.2($200X)
$200X ? $110X ? $63,000 ? $40X
$200X ? $110X ? $40X ? $63,000
$50X ? $63,000
X ? $63,000 ? $50 ? 1,260 gloves
As we can see in this calculation, Jewels Corporation can earn a 20% return on sales by selling
1,260 baseball gloves.
Short-Cut Formulas for C-V-P Analysis
Notice that in the C-V-P analysis examples that we’ve worked through so far, the basic C-V-
P equation remains constant. That’s what makes this formula so powerful. Once you’re com-
fortable with it, you can use it to manage any number of factors in planning for profits. However,
you may remember from your brief introduction to C-V-P analysis in the previous chapter and
from our C-V-P formula example on page 49 that we calculated break-even sales in units di-
rectly using the following formula.
? Break-even sales (in units)
This formula is a “short-cut” version of the C-V-P formulas above. You can see that it is
simply the last step in the C-V-P calculation above for Jewels’ break-even point of 700 base-
ball gloves. So, if you understand the basic C-V-P equation, you can simply skip to the last step
of the calculation. There are short cuts for computing the level of sales for both break-even vol-
ume and target income volume. The short-cut formula for both the break-even volume and the
target income volume in units is:
Total fixed costs
??????
(Sales price per unit ? Variable cost per unit)
62 Part 1 Foundations
target income A profit level
desired by management.
return on sales revenue A
measure of operating perfor-
mance; computed by dividing
net income by total sales rev-
enue. Similar to profit margin.
Note that if you use this formula to determine the break-even volume, then you
will assume that target income is $0, giving you:
Plugging in the numbers for Jewels Corporation, the results are the same as shown
earlier. As you can see, the short-cut calculation for both the break-even volume
and the target income volume is really the same formula. For target sales:
? 1,100 units
For the break-even volume:
? 700 units
Always remember, though, that short cuts are useful, but they should not be ap-
plied until you fully understand the basic C-V-P relationships. In addition, man-
aging some aspects of the C-V-P relationships can be tricky when you use short
cuts. So if you ever get confused in solving a C-V-P analysis problem, just put
the problem back in the original C-V-P equation:
Sales revenue ? Variable costs ? Fixed costs ? Target income
Computation in Dollar Amounts versus Units
Before we finish with C-V-P equations, you should note that a variable cost ra-
tio is sometimes used instead of a per-unit variable cost. In such cases, the basic
C-V-P equation is modified as follows:
Sales revenue ? (Variable cost ratio ? Sales) ? Fixed costs ? Profit
Because the variable costs are stated as a percentage of sales dollars rather than on a per-unit
basis, this approach expresses activity in terms of sales dollars, not units. This is still the same
basic C-V-P equation, but setting up the equation using the variable cost ratio will result in a
break-even point in dollars instead of units. For example, the break-even point for Jewels Cor-
poration would then be expressed as $140,000 in sales revenue ($200 per unit ? 700 units)
instead of 700 units as previously illustrated. This may be verified using the preceding equa-
tion and a 55% variable cost ratio as follows:
Sales revenue ? (0.55)Sales revenue ? $63,000 ? $0
(0.45)Sales revenue ? $63,000
Sales revenue ? $140,000
The short-cut formula for break-even volume and target income volume in sales dollars is:
(Remember the following: Contribution margin ratio ? 1 ? Variable cost ratio.)
Fixed costs ? Target income
????
Contribution margin ratio
$63,000 ? $0
??
$90
$63,000 ? $36,000
???
$90
Fixed costs
????
Contribution margin per unit
Fixed costs ? Target income
????
Contribution margin per unit
5
63 Chapter 2 Analyzing Cost-Volume-Profit Relationships
5 Remember that per-unit contribution margin is the sales price per unit less the variable cost per unit.
Buy or Rent?
The Internet provides a terrific tool for ana-
lyzing the decision to rent an apartment
versus to buy a home. Go tohttp://www
.financenter.com and select the “Consumer
Tools” tab and click on the “Educators”
menu option. Then scroll down to “Home
Buying” and choose the “Deciding to Buy
or Rent” option. Use the following data:
monthly rent, $850; renter’s insurance, $15;
yearly rent increase, 4%; home purchase
price, $150,000; appreciation rate, 4%;
savings rate, 3%; state and federal tax rate,
32%; years before the home is sold, 4 years;
loan amount, $120,000; loan term, 30 years;
interest rate on loan, 7%; discount points,
1%; origination fee, $0; upfront costs,
$1,000; yearly property tax, $2,500; yearly
maintenance, $700; yearly insurance, $300;
selling costs, 10%.
Net Work:
1. If the above data represented your cur-
rent rent situation, how much is your initial
cost each month for a house versus an
apartment?
2. Should you consider buying a house?
3. Based on the graphs provided, what ap-
pear to be the three most important issues
about renting versus buying?
Measuring the Effect of Potential Changes
in C-V-P Variables
The basic techniques of C-V-P analysis that you have worked with in this chap-
ter are used almost daily by organizations in the management processes of plan-
ning, controlling, and evaluating. As a result of understanding C-V-P analysis,
you will be adept at evaluating the effects on profitability of the following com-
mon changes in C-V-P variables: (1) the amount of fixed costs, (2) the variable
cost rate, (3) the sales price, (4) the sales volume or the number of units sold,
and (5) combinations of these variables.
Changes in Fixed Costs
Many factors, such as an increase in property taxes or an increase in manage-
ment’s salaries, for example, will cause an increase in fixed costs. (Recall also from
the opening scenario for this chapter that building a new facility such as a stadium can also in-
crease fixed costs.) If all other factors remain constant, an increase in fixed costs always increases
the number of units needed to break even. Obviously, the number of units needed to reach a
target income will also increase. To illustrate, let’s return again to the Jewels Corporation and
IBM Gets on the Internet
Wave In 1998, if you wanted
an IBM desktop personal com-
puter (PC), you had to walk
into a store to make the pur-
chase. In hindsight, this was a
strange way to sell computers
for a company that believed itself to be at the fore-
front of the e-business revolution. And in hindsight,
this sales approach, being both slow and expensive,
clearly didn’t work. The PC division for IBM lost $986
million in 1998 and was bracing itself for similar
losses in 1999. Market analysts were pushing IBM to
sell its PC division based in Research Triangle Park in North
Carolina. Finally, in the last quarter of 1999, IBM officials an-
nounced that it would yank its entire line of home desktop PCs
from retail stores in the United States and sell the machines
almost exclusively over the Internet. IBM also launched a $20
million advertising campaign (TV and direct mail flyers) to back
up the move.
IBM’s decision to sell over the Internet was driven largely
by cut-throat pricing of components and systems by its major
competitors and suppliers, the overhead costs of selling through
dealers, and the inability to distinguish its product from dozens
of competitor PCs sitting next to it on the retail shelf. In 2000,
IBM followed the Internet decision by cutting $1.1 billion in
annual manufacturing and distribution expenses. These cost
savings were achieved largely by three means. First, IBM
changed the way the PCs are built and redesigned the PC prod-
uct to use as many industry standard parts as possible. Second,
by building PCs to order (i.e., only building PCs when an order
was placed), IBM was able to significantly reduce the amount
of inventory it had to keep on hand. Third, IBM told its sup-
pliers that it wanted 95% of its components ready on demand
in well-stocked mini-warehouses near IBM manufacturing facil-
ities. “The whole object is to not own the parts for very long,”
said Adalio Sanchez, general manager of manufacturing and
operations for the PC division.
The change to IBM’s PC business started to pay off as costs
were reduced and shipments increased using the new ShopIBM
Web site. Losses in the PC division were cut to $360 million in
1999 and $148 million in 2000. In 2001, after four straight
years of losing money, the PC division was back in the black
with a pretax profit of $99 million by the middle of the year.
In a business today where prices on desktop PCs are typically
in the $800 range, if IBM is $10 or $20 higher than the price
of a DELL or COMPAQ PC, it can lose the sale. Clearly, control-
ling costs and managing sales is becoming more and
more important in the very competitive PC market.
Sources: Ed Scannell, “IBM to Go Online with Home
PC Sales,” InfoWorld Daily News, October 19, 1999;
Lisa Smith, “IBM’s Personal Computer Unit Makes
Turnaround,” The Herald-Sun, March 22, 2001.
b u s i n e s s env i r onment
Cauti on
If you want to use C-V-P analysis to calcu-
late the necessary sales volume in terms of
dollars, the per-unit variable cost is not
used. Rather, use the variable cost ratio
times sales to determine total variable costs.
Many students make the mistake of multi-
plying the per-unit variable cost times sales
instead of the variable cost ratio times sales
to get total variable costs.
assume that we need to analyze the effect on profits if fixed costs increase from $63,000 to
$81,000. How many more baseball gloves must be sold to maintain Jewels’ income goal of
$36,000?
Sales revenue ? Variable costs ? Fixed costs ? Target income
$200X ? $110X ? $81,000 ? $36,000
$90X ? $117,000
X ? 1,300 gloves
Because of the added fixed costs, Jewels must now sell 1,300 baseball gloves, instead of 1,100, to
earn a target income of $36,000. The computations are quite simple. In fact, you may have found
them unnecessary, realizing that if fixed costs increase by $18,000 ($81,000 ? $63,000), and if
the unit contribution margin remains $90 per glove, 200 additional gloves ($18,000 ? $90) will
have to be sold in order to reach the $36,000 target income (1,100 ? 200 ? 1,300 gloves).
Changes in the Variable Cost Rate
Like an increase in fixed costs, an increase in the variable cost rate also increases the number of
units needed to break even or to reach target income levels, when all other factors remain con-
stant. Suppose that the variable cost rate increased from $110 per baseball glove to $130 per
glove because of higher wages for factory personnel, increased costs of direct materials, or other
factors. How does this cost increase affect the number of gloves needed to reach the target in-
come, assuming that fixed costs are again $63,000?
Sales revenue ? Variable costs ? Fixed costs ? Target income
$200X ? $130X ? $63,000 ? $36,000
$70X ? $99,000
X ? 1,415 gloves*
*Technically, if the C-V-P analysis results in a fractional answer, you should always round the answer up to the
next digit. In this case, if you round the calculated answer of 1,414.29 to 1,414 gloves, you won’t quite achieve
the target income of $36,000.
The increase in the variable cost rate reduces the unit contribution margin (from $90 to
$70), which means that more gloves must be sold to maintain the same target income. With a
unit contribution margin of $90, the company would make a $36,000 target income by sell-
ing 1,100 baseball gloves; with a unit contribution margin of only $70, an additional 315 (1,415
? 1,100) gloves must be sold to earn at least a $36,000 target income.
Changes in Sales Price
If all other variables remain constant, an increase in the sales price decreases the sales volume
needed to reach a target income. This is because an increase in sales price increases the contri-
bution margin per baseball glove, thereby decreasing the number of gloves that must be sold
to earn the same amount of target income.
To illustrate, assume that the demand for baseball gloves is overwhelming and that Jewels
cannot produce gloves fast enough. Hence, we make a decision to increase the price from $200
to $230 per glove. As a result of the price increase, the number of gloves that must be sold to
reach the target income of $36,000 decreases:
Sales revenue ? Variable costs ? Fixed costs ? Target income
$230X ? $110X ? $63,000 ? $36,000
$120X ? $99,000
X ? 825 gloves
With the sales price increase of $30 per glove, the contribution margin also increases $30
per glove to $120; and with a $120 contribution margin per glove, only 825 gloves need to be
sold to reach the $36,000 target income. Obviously, a decrease in the sales price would have
the opposite effect; it would increase the number of units needed to reach the target income.
65 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Changes in Sales Volume
As you have seen, the sales volume (the number of gloves to be sold) for the target income has
varied with each change in one of the other variables. When other variables remain constant,
an increase in the sales volume will result in an increase in income. Very simply, the more gloves
sold, the higher the income (as long as the contribution margin is positive!). The degree of
change in profits resulting from volume change depends on the size of the unit contribution
margin. To be specific, the change in income will be equal to the change in sales volume units
multiplied by the contribution margin per unit. So, when the unit contribution margin is high,
a slight change in volume results in a dramatic change in profit. With a lower unit contribu-
tion margin, the change in profit is less.
Simultaneous Changes in Several Variables
Thus far, we have examined changes in only one variable at a time. However, in your work in
actual business organizations, you will find that individual changes are quite rare. More often,
a decision will affect several variables, all at the same time. For example, should Jewels Cor-
poration increase fixed advertising costs by $20,000 and reduce the sales price by 10% if the
result would be to increase sales volume by 500 units? The impact on the target income from
these proposed changes is as follows:
Initial Data Proposed Changes
Sales price per glove . . . . . . . . . . . . . . . . . . . $200 $180 ($200 ? 90%)
Variable costs per glove . . . . . . . . . . . . . . . . $110 $110
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . $63,000 $83,000 ($63,000 ? $20,000)
Target income . . . . . . . . . . . . . . . . . . . . . . . . $36,000 X
Sales volume . . . . . . . . . . . . . . . . . . . . . . . . . 1,100 gloves 1,600 gloves (1,100 ? 500)
Computations and Result:
Sales revenue ? Variable costs ? Fixed costs ? Target income
($180 ? 1,600) ? ($110 ? 1,600) ? $83,000 ? X
$288,000 ? $176,000 ? $83,000 ? X
$29,000 ? X (target income)
The analysis shows that target income would drop by $7,000 ($36,000 ? $29,000) as a result
of these changes. So, our decision should be to not implement the proposed changes.
Consider another possible decision: Should Jewels automate part of its production, thereby
reducing (by $10) variable costs to $100 per unit and increasing (by $5,000) fixed costs to
$68,000? The computation is as follows:
Sales revenue ? Variable costs ? Fixed costs ? Target income
($200 ? 1,100) ? ($100 ? 1,100) ? $68,000 ? X
$220,000 ? $110,000 ? $68,000 ? X
$42,000 ? X (target income)
This analysis shows that implementing these proposed changes would be beneficial because
they would increase target income by $6,000 ($42,000 ?$36,000). Obviously, this is true only
if the assumptions can be relied on—that is, if fixed costs will rise by no more
than $5,000 and unit variable costs will decrease by a full $10.
Consider another example. Suppose Jewels Corporation could use part of
the excess capacity of its operating facilities to make baseball bats. These bats
would sell for $90 per unit, increase fixed costs by $40,000, and have a variable
cost per unit of $45. Jewels wants to add this new product line only if it can in-
crease income by $25,000. How many baseball bats must Jewels sell to reach this
target income? The computation follows:
66 Part 1 Foundations
Cauti on
Remember, any change that affects the
number of units sold changes both the total
sales revenue and total variable costs.
Sales revenue ? Variable costs ? Fixed costs ? Target income
$90X ? $45X ? $40,000 ? $25,000
$45X ? $65,000
X ? 1,445 baseball bats (rounded up)
Now that we have completed the C-V-P calculations, we must determine whether the company
can produce and sell 1,445 baseball bats. If that sales goal seems attainable, the facilities should
be used to make the bats. Don’t forget that making C-V-P calculations is the easy part of man-
aging an organization. It takes an excellent manager to successfully implement the results of a
C-V-P analysis into a real business process.
67 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Breaking Even in the Hotel
Industry An international ho-
tel chain undertook a project
to increase the effectiveness
of decision making of its prop-
erties in Europe, the Middle
East, and Africa. In 1996, com-
pany executives wanted to improve the financial
planning and control decisions of the hotel manage-
ment teams. The Europe, Middle East, Africa division
was responsible at that time for approximately 240
hotels. Essentially, the executives aimed to encour-
age a greater use of basic managerial accounting
techniques such as budgeting models and C-V-P analysis in
order to improve the profitability of individual hotels.
It was clear to the company that understanding how ho-
tel costs behaved is absolutely key to making good decisions
that affect market share analysis, annual budget preparation
and monitoring of results, sales volume and business mix de-
cisions, pricing policies, and cost management. In order to
identify the fixed and variable costs in the hotels, the com-
pany first worked with individual hotel management teams
within its organization who were intimately familiar with how
costs behaved based on changes in sales volumes (i.e., hotel
rooms rented). Initially, the company had these individuals de-
termine from their own experience which costs were fixed, vari-
able, or semi-variable (i.e., mixed) costs with respect to changes
in sales volume. Scattergraph and statistical analyses were then
used to estimate the fixed and variable proportions of the mixed
costs—again related to sales volume—and allocate these costs
to the main fixed and variable groups.
Computer spreadsheets were then used to assess key “what
if” questions. For instance, “What is the likely effect on profit
of a 3% shortfall in room revenue?”. . . or . . . “How will profit
change if a 5% growth in total sales volume occurs?” This alerts
managers to the critical areas of profitability and indicates
which revenue and cost areas require greater attention for a
given decision. It also enables management to gain an overall
indication of “profit stability” or “profit instability’” in relation
to changes in revenue and cost of particular hotel properties.
Knowledge of break-even levels and profit-and-loss implications
of different business scenarios are relevant if managers are to
make informed decisions which ensure survival, optimize prof-
its, and limit risk, giving rise to a feeling of “being more in
control” when making decisions.
In 1995, the year before the new management focus on
C-V-P analysis commenced, the average operating profit margin
in the Europe, Middle East, Africa division was 35%. In 1998,
the average operating profit margin was 39%. Although the ho-
tel executives do not believe that the new focus on C-V-P tools
is the only reason for this improvement, it has played a posi-
tive role in significantly adding to shareholder value.
Source: Ian C. Graham and Peter J. Harris, “Devel-
opment of a Profit Planning Framework in an Inter-
national Hotel Chain: A Case Study,” International
Journal of Contemporary Hospitality Management,
1999 (Issue 5), pp. 198–204.
b u s i n e s s env i r onment
68 Part 1 Foundations
Sales revenue ? Variable costs ? Fixed costs ?
Target income
Using this equation, you as a manager can work to plan,
control, and evaluate the costs, prices, and sales output of
the organization. The effects of changes in costs, prices,
and volume on profitability may be determined by C-V-P
analysis. Changes in individual variables or simultaneous
changes in several variables can be analyzed with this tech-
nique.
T O S UMMA R I Z E : The contribution margin is
sales revenue less variable costs and is the amount of rev-
enue left to cover fixed costs and provide a profit. The con-
tribution margin can be expressed in total dollars, on a
per-unit basis, or on a percentage basis. Because fixed costs
remain constant within a relevant range, once fixed costs
have been covered, income increases by the amount of the
per-unit contribution margin for every additional unit sold.
This relationship is used in C-V-P analysis. The basic C-V-P
equation is:
Using Graphs to “See” C-V-P Relationships
Earlier in this chapter, we talked about using scattergraph methods as a way to analyze cost be-
havior. Recall that once we have plotted the history of costs on a graph and visually fitted a re-
gression line through the data, we can then essentially “see” how the cost can be separated into
its fixed and variable cost components. Now, by simply adding a line to the cost chart to rep-
resent revenue, we can graphically work with cost-volume-profit relationships. In fact, using
graphs may be the most effective way to manage and communicate C-V-P information. This
graphical approach allows you to visually examine cost and revenue data over a range of activ-
ity rather than at a single volume. Sometimes, though, reading precise information from a graph
can be difficult. Hence, when analyzing specific proposals in the future, you will typically com-
bine the C-V-P equations discussed in the preceding section with the graphs discussed in this
section.
On a C-V-P graph, volume or activity level usually is shown on the horizontal axis, and
total dollars of sales and costs are shown on the vertical axis. Lines are then drawn to represent
total fixed costs, total costs, and total revenues. Exhibit 6 shows a C-V-P graph for Jewels Cor-
poration.
Remember that fixed and variable cost relationships are valid only for the relevant range
of activity (the screened area on the graph in Exhibit 6). In this case, fixed costs are $63,000,
and variable costs are $110 per glove over the range of activity between 400 and 1,200 gloves
sold. Total costs are $118,000 at 500 gloves [$63,000 ? ($110 ? 500 gloves)], $129,000
at 600 gloves [$63,000 ? ($110 ? 600 gloves)], and so on. Similarly, total revenues are
$100,000 at 500 gloves ($200 ? 500 gloves), $120,000 at 600 gloves, and so forth. The
break-even point, the point at which total revenues equal total costs, is 700 gloves, or $140,000
in sales.
As shown in Exhibit 7, we can use the graphic format to isolate such items of interest as
total variable costs, total fixed costs, the area in which losses occur, the area in which profits
will be realized, and the break-even point. Because C-V-P graphs illustrate a wide range of ac-
tivity, this tool can help in quickly determining approximately how much profit or loss will be
realized at various levels of sales.
The Profit Graph
With a few adjustments to a standard C-V-P graph, we can create what is called a profit graph,
which plots only profits and losses and omits costs and revenues. A profit graph is another
useful way to visualize how decisions regarding costs and revenues will impact profit. Exhibit
8 shows a profit graph for Jewels Corporation based on the same underlying data used in Ex-
hibit 6.
5 Visualize C-V-P rela-
tionships using graphs.
profit graph A graph that
shows how profits vary with
changes in volume.
Notice that, though the horizontal axis of the profit graph is the same as those of the pre-
vious graphs, the vertical axis represents only profits and losses. As long as the contribution
margin is positive, the maximum amount of losses that can occur is at a zero level of sales. With
no sales, total losses will be the amount of the fixed costs. With the axes properly labeled, we
can draw the profit line as follows:
1. Locate the loss for zero sales volume on the vertical axis. This is the total fixed cost, or
negative $63,000 in this case.
2. Locate the profit or loss at another sales volume. For example, at sales of 700 gloves,
profits are zero [$140,000 ? ($63,000 ? $77,000)], or at sales of 1,000 gloves, profits
are $27,000 [$200,000 ? ($63,000 ? $110,000)].
3. After the two profit or loss points have been identified, draw a line through them back
to the vertical axis.
Because of how simple it is to create, the profit graph is widely used for comparing competing
projects. It has the disadvantage, however, of not showing specifically how revenues and costs
vary with changes in sales volume.
A Comparison of C-V-P Graphs with C-V-P Equations
C-V-P graphs are very useful in understanding contribution margin income statements and
C-V-P equations. To illustrate this point, let’s again explore the question of what volume of
69 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 6: A Cost-Volume-Profit Graph
$200,000
180,000
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
Number of gloves sold
B e t
7 e
a e
2 g
c Total costs ?
0 1 g
i s
6
e
v
e
v
e
u
e
S
a
l
e
s
o
s
l
c
o
0
70 Part 1 Foundations
Exhibit 7: Cost-Volume-Profit Graphs
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Fixed Costs $
S
a
l
e
s
Number of gloves sold
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Area of Profit $
S
a
l
e
s
Number of gloves sold
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Area of Loss $
S
a
l
e
s
Number of gloves sold
Sales
revenue
Total costs
Variable costs
Fixed costs
Break-even
point
Variable Costs $
S
a
l
e
s
Number of gloves sold
Exhibit 8: Profit Graph for Jewels Corporation
$80,000
60,000
40,000
20,000
0
?20,000
?40,000
?60,000
?80,000
P
r
o
f
i
t
L
o
s
s
Number of gloves sold
A f l
activity Jewels Corporation needs to reach a target income of $36,000. This
was illustrated earlier with the equation approach, but it is repeated here to show
that the graph approach will produce the same quantitative results. As you can
see in Exhibit 9, Jewels Corporation must sell 1,100 baseball gloves to reach a
target income of $36,000.
71 Chapter 2 Analyzing Cost-Volume-Profit Relationships
STOP & THINK
When analyzing costs, volume, and profit,
do you think most managers would prefer
to use graphs or equations?
Exhibit 9: Comparison of C-V-P Equation with C-V-P Graph
Number of gloves sold
0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
P
r
o
f
i
t
L
o
s
s
$80,000
40,000
0
–40,000
–80,000
Profit Graph
Number of gloves sold
0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
S
a
l
e
s
$240,000
200,000
160,000
120,000
80,000
40,000
220,000
184,000
C-V-P Graph
es le e l
enue vee vv
,000 Profit 6,, 666 $36
al costs ta a tt
able costs ri i rr Var
ed costs eee x
a e Break even
p
36,000
g
o
ii point
a e
pppoint
o
o
C-V-P Equation
(Sales price ? Units) ? (Variable costs ? Units) ? Fixed costs ? Profit
$200X ? $110X ? $63,000 ? $36,000
$90X ? $99,000
X ? 1,100 gloves
72 Part 1 Foundations
over wide ranges of activity. The most common graphic ap-
proach involves plotting fixed costs as a horizontal line with
variable costs representing the distance between the fixed
costs and total costs line. A profit graph, which shows only
profit or loss and volume, is much simpler, but it does not
show how costs vary with changes in sales volume. Regard-
less of the approach, all variations of C-V-P analysis are
based on the same calculations and on the same underly-
ing concept of fixed and variable costs.
T O S UMMA R I Z E : The financial effects on cost-
volume-profit decisions can be examined by using either
equations or graphs. These methods of analysis can be used
to calculate the break-even point, which occurs at the point
where total revenues equal total fixed costs plus total vari-
able costs. These methods can also be used to project a tar-
get profit level, with profit being equal to the excess of
revenues over total costs. The graphic approaches are use-
ful because they highlight cost-volume-profit relationships
Limiting Assumptions of C-V-P Analysis
C-V-P analysis is an extremely useful tool to assist in making short-term operating decisions.
However, C-V-P analysis has some limiting assumptions that must not be overlooked.
The first key assumption underlying C-V-P analysis is that the behavior of revenues and
costs is linear throughout the relevant range. This means that C-V-P analysis is valid only for
a relevant range.
A second assumption is that all costs, including mixed costs, can be accurately divided into
fixed and variable categories. As we have seen in this chapter, some costs have characteristics of
both fixed and variable costs. These costs sometimes are not easily classified into their fixed and
variable components, which limits the accuracy of C-V-P analysis.
For companies with more than one product, a third major assumption in C-V-P analysis
is required—that the mix of a company’s products does not change over the relevant range.
The sales mix is the proportion of the total units sold (or the total dollar sales) represented by
each of a company’s products. Sales mix will be discussed in the expanded material section of
this chapter.
In addition to these three key assumptions, there are other limiting assumptions implicit in
C-V-P analysis. For example, C-V-P analysis assumes that efficiency and productivity are held
constant, that the prices of materials and other product components are constant, and that rev-
enues and costs can be analyzed using a single activity base, such as volume. A related and very
significant assumption, and one that clearly is not always valid, is that volume is the only, or even
the primary, driver of costs. As discussed below, delivery time and quality can also impact costs.
Because of the limiting assumptions just described, a manager must use reasonable caution
when making decisions using C-V-P analysis. Nevertheless, C-V-P analysis does provide a good
model for predicting future operating results when specific relationships are defined and rec-
ognized.
Issues of Quality and Time
The emphasis in this chapter has been primarily on costs and profits and how they change when
changes in variable costs, fixed costs, sales prices, and sales volume are made. Remember, how-
ever, that financial results are just one of several elements of performance that a manager must
consider. Good managers are equally interested in how these changes will affect the quality of
goods and services produced and sold and the speed at which products and services can be de-
livered to customers. If, for example, reducing fixed costs means that goods will be produced
more slowly or that the quality of manufactured products will be reduced, then a decision to
reduce fixed costs may be a poor one. On the other hand, if a company can automate a func-
tion using robotics instead of high-cost workers, for example, it may be possible to simultane-
ously reduce total costs, increase quality and consistency, and improve speed of production. To
determine whether quality and speed of production are good or bad, a management team may
6 Identify the limiting
assumptions of C-V-P
analysis, and explain the
issues of quality and time
relative to C-V-P analysis
decisions.
E M 73 Chapter 2 Analyzing Cost-Volume-Profit Relationships
need to compare its results with those of other firms, a process called benchmarking, which will
be introduced in a later chapter.
it is important to also consider how these changes will af-
fect the quality of goods and services and the speed at which
products and services can be delivered to customers. Deci-
sions that increase quality, reduce costs, and speed up pro-
duction are valuable changes and should be made; decisions
that have a negative effect on one or more of these vari-
ables must be carefully analyzed and trade-offs considered.
T O S UMMA R I Z E : C-V-P analysis is based on
three critical and limiting assumptions: (1) that the behav-
ior of revenues and costs is linear throughout the relevant
range, (2) that all costs can be categorized as either fixed
or variable, and (3) that the sales mix does not change.
When considering how changes in variable costs, fixed costs,
sales prices, sales volume, and sales mix will affect profits,
Thus far, we have covered various types of costs, simple methods of analyzing
mixed costs, and the basics of C-V-P analysis. In this expanded section, we cover
an additional, more advanced method of analyzing mixed costs—least squares
analysis. We also cover the effect of the sales mix on profitability and use the con-
cept of operating leverage to explore differences in cost structures among man-
ufacturing, merchandising, service, and e-commerce organizations.
Analysis of Mixed Costs—The Least Squares Method
Earlier, we described two common methods for analyzing mixed costs: the scattergraph and high-
low methods. These methods are relatively easy to use and provide useful estimates of the fixed
and variable components of mixed costs. A more sophisticated method for analyzing mixed costs
is the least squares method, which is the most accurate method of using a specific set of data to
determine the fixed and variable portions of a mixed cost. Like the scattergraph, the least squares
method fits a straight line through all points on a graph. However, instead of visually fitting the
regression line through the cost points, it uses statistical analysis to guarantee that the line is the
best possible fit for the applicable costs. As a result, the least squares method provides a better
analysis because it isn’t based on a subjective regression line like scattergraphs and because it uses
all the cost data points rather than just the high and low data points as with the high-low method.
The formula for the least squares method is based on the equation for a straight line:
Y ? a ? bX
You probably recognize this classic equation from previous math classes you may have had.
When this equation is used to do cost analysis, Y represents the total predicted cost; a repre-
sents the intercept and the fixed cost (if in the relevant range); b represents the variable cost
rate or the slope of the line; and X represents the activity level being considered. Using cost and
activity level data, this method involves the use of simultaneous equations to find the values of
a and b. Once computed, these values can be combined with the projected activity level X to
predict or estimate the total future cost Y. For example, if the values of a and b are computed
to be $200 and $5, respectively, then for an estimated activity level of 100 direct labor hours,
we can predict that:
Y (total predicted cost) ? $200 ? $5(100 hours)
Y ? $200 ? $500
Y ? $700
7 Analyze mixed costs
using the least squares
method.
least squares method A
method of segregating the
fixed and variable portions of
a mixed cost; the regression
line, a line of averages, is
statistically fitted through all
cost points.
You should understand that the regression line is basically a line of averages. Therefore, the
actual total cost for 100 direct labor hours might be somewhat different from the predicted cost
of $700. The method of least squares, however, attempts to minimize the differences between
predicted and actual costs. Once a regression line has been fitted to historical data, the fixed
and variable costs represented by the line can be used to predict the level of future costs.
Calculating the estimates of a (the intercept, or the total fixed cost) and b (the slope, or
variable cost rate) requires solving the following two simultaneous equations:
1. ?XY ? a?X ? b?X
2
2. ?Y ? na ? b?X
where
a ? fixed cost
b ? variable cost rate
n ? number of observations
? ? summation sign (which means the sum of all historical data indicated by the sign)
X ? activity level, or independent variable
Y ? total (predicted) mixed cost, or dependent variable
Actually, solving these equations is easy with a calculator or computer, but difficult and te-
dious by hand. Initially solving these equations by hand may be useful to you in learning ex-
actly how these equations work. However, as a manager working with cost estimations, you are
going to have computers available to analyze large amounts of data very quickly. Hence, we
will focus on describing and interpreting the typical output from a computerized application
of least squares analysis. We will leave it to math classes to illustrate the manual calculations of
the least squares method.
To illustrate the concept of least squares, let’s return once more to the electricity cost data
used earlier in this chapter to work with the scattergraph and high-low methods. Note that the
historical data that we are using for this example are given for only six months; thus, the re-
sulting regression equation will likely be less accurate than it would be with more data (say, 12
or 18 months of data).
Month Direct Labor Hours Worked Total Electricity Cost
January 7,000 $ 70,000
February 6,000 60,000
March 12,000 100,000
April 6,600 80,000
May 18,000 120,000
June 14,000 110,000
Using these data, the following output, shown in Exhibit 10, can be generated in just a
matter of minutes using the “data analysis” tool in Excel
®
, a Microsoft database software pro-
gram.
6
Now compare the least squares output with the results from our earlier work using the
scattergraph and high-low methods:
Fixed Costs Variable Cost per Direct Labor Hour
Scattergraph method $40,000 per month $4.29 per direct labor hour
High-low method 30,000 per month 5.00 per direct labor hour
Least squares analysis 40,402 per month 4.68 per direct labor hour
74 Part 1 E M Foundations
6 There are literally hundreds of software programs that can be used to run regressions or least squares analysis.
E M 75 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 10: Output of Least Squares Analysis Application
5,000 10,000 15,000 20,000
Hours
C
o
s
t
$140,000
120,000
100,000
80,000
60,000
40,000
20,000
Cost
Predicted Cost
Month Hours Cost
January 7,000 $ 70,000
February 6,000 60,000
March 12,000 100,000
April 6,600 80,000
May 18,000 120,000
June 14,000 110,000
Summary Output
Regression Statistics
Multiple R 0.962
R square 0.926
Adjusted R square 0.907
Standard error 7207.705
Observations 6
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept $40,402.03 $7,613.10 $5.31 0.0061 $19,264.63 $61,539.43
Hours $ 4.68 $ 0.66 $7.05 0.0021 $ 2.84 $ 6.52
76 Part 1 E M Foundations
Sales Mix
Earlier in this chapter, we described some important limiting assumptions of C-V-P analysis. As a
manager using C-V-P, you need to be aware of what this tool can and cannot do. One important
issue is that C-V-P analysis must be adjusted when a company starts changing the mix of products
that it sells. Sales mix is the proportion of the total units represented by each of a company’s prod-
ucts. To keep our discussions simple, in previous sections of the chapter we used examples of com-
panies with only one product. Many companies have more than one product, however, so you
need to understand how sales mix issues are resolved. To illustrate how a change in sales mix can
affect a company’s C-V-P relationships, let’s assume that Multi-Product, Inc., sells three different
products. Following are the monthly revenues and costs for each type of product:
8 Explain the effects of
sales mix on profitability.
sales mix The relative pro-
portion of total units sold (or
total sales dollars) that is rep-
resented by each of a com-
pany’s products.
the least squares method is more mathematically correct
than the scattergraph or high-low methods, it still should
be used with caution in analyzing mixed costs. Least squares
results can be quickly calculated using computer programs
such as Microsoft’s Excel
®.
T O S UMMA R I Z E : A more sophisticated tech-
nique for analyzing mixed costs is the least squares method.
The least squares method is essentially equivalent to sim-
ple regression analysis, using the equation for a straight line
(Y ? a ? bX) and simultaneous equations to calculate the
fixed and variable portions of a mixed cost. Even though
You can see that the least squares analysis results in fixed costs estimated at
$40,402 and the variable cost rate estimated to be $4.68 per direct labor hour.
As you can see, the results are more similar to the results of the scattergraph method
than to the results of the high-low method. Why do you think this is the case?
The reason is that both the scattergraph and least squares methods are essentially
using all of the historical data while the high-low method uses only two data points
(February and May).
We won’t take time in this chapter to understand all of the output shown
in Exhibit 10; what is most important is that you know three things: (1) the co-
efficient of the intercept, (2) the coefficient of the direct labor hours, and (3) the
R square summary statistic. The coefficient of the intercept, or $40,402.03 in
this case, is the estimate of total fixed costs. The coefficient of the direct labor
hours, or $4.68 in this case, is the estimate of the variable electricity cost per di-
rect labor hour. The R square (R
2
) is a descriptive statistic that provides infor-
mation about how well the regression line fits the data; in other words, R square
can be interpreted as the fraction of the variability in the data that is explained
by the computed regression statistics. For now, remember that a higher R
2
is bet-
ter, and an R
2
of 1.0 represents a perfect fit (meaning all data points were ex-
actly on the regression line). In this case, an R
2
of 0.926 is very high and suggests
that the computed regression statistics explain most of the variability in the data.
7
FYI :
An R
2
of more than 0.9 is actually not very
common in practice. It is often quite rare to
identify a single cost driver that explains
most of the variance of important costs in an
organization. Typically, organizations find
that there are many things that affect a par-
ticular cost (e.g., headcount, floor space, op-
erating hours, etc.), which requires that cost
analysis be based on multiple cost drivers.
The least squares analysis method we have
discussed here is also known as simple or
single linear regression. Multiple linear re-
gression, a technique you may have learned
about in a statistics class, uses a similar
approach to identify the impact of several
activities on changes in a specific cost.
7 The adjusted R
2
of 0.907 is a more conservative estimate of the variance explained in the data and is preferred
to the R
2
statistic in some circumstances.
Product A Product B Product C Total
Amount Percent Amount Percent Amount Percent Amount Percent
Sales revenue $25,000 100% $45,000 100.00% $30,000 100% $100,000 100%
Less variable costs 20,000 80 30,000 66.67 21,000 70 71,000 71
Contribution margin $ 5,000 20% $15,000 33.33% $ 9,000 30% $ 29,000 29%
Sales mix 25% 45% 30% 100%
Total sales are $100,000, which in this example includes $25,000 in sales of
Product A, $45,000 of Product B, and $30,000 of Product C. Therefore, the
sales mix is 25% Product A ($25,000 ? $100,000), 45% Product B ($45,000
? $100,000), and 30% Product C ($30,000 ? $100,000). With this sales mix,
the average variable cost ratio is 71%, which is determined by dividing total vari-
able costs of $71,000 by total sales of $100,000. If Multi-Product, Inc., had fixed
costs of $17,400 and desired a target income of $40,000, the necessary sales vol-
ume (in dollars) would be:
Sales revenue ? (0.71)Sales revenue ? $17,400 ? $40,000
(0.29)Sales revenue ? $57,400
Sales revenue ? $57,400 ? 0.29
Sales revenue ? $197,932 (rounded up)
Alternatively, you could calculate the average contribution margin ratio by subtracting the
total variable costs from total sales and dividing the result (total contribution margin of $29,000)
by total sales of $100,000. The company could then divide the average contribution margin
ratio (29%) into fixed costs plus target income ($17,400 ? $40,000). This revised, more com-
pact formula is simply a restatement of the preceding equation.
? ? $197,932 (rounded up)
Remember, though, that $197,932 in sales will achieve the target income only if the aver-
age variable cost and contribution margin ratios, and therefore the sales mix, do not change. In
order for you to better understand this fact, assume that the total sales revenue and the sales
price of each product remain the same but that the sales mix changes as follows:
$57,400
?
0.29
Fixed costs ? Target income
?????
Average contribution margin ratio
E M 77 Chapter 2 Analyzing Cost-Volume-Profit Relationships
FYI :
A computer can make sales mix and other
C-V-P analysis computations easier to do.
Using simulation or other programs, you can
quickly calculate the financial effects of
changes in the sales of one product or simul-
taneous changes in sales of several products.
Product A Product B Product C Total
Amount Percent Amount Percent Amount Percent Amount Percent
Sales revenue $50,000 100% $30,000 100.00% $20,000 100% $100,000 100%
Less variable costs 40,000 80 20,000 66.67 14,000 70 74,000 74
Contribution margin $10,000 20% $10,000 33.33% $ 6,000 30% $ 26,000 26%
Sales mix 50% 30% 20% 100%
As you can see in this example, the variable cost and contribution margin ratios for each
product remain the same, but the sales mix changes. Product A now comprises 50% of total
sales instead of 25%. Because Product A has a lower contribution margin ratio than Products
B and C, the average contribution margin ratio decreases from 29 to 26% (stated another way,
the average variable cost ratio increases from 71% to 74%). Now think about how this change
in the sales mix would affect profit and the volume of sales revenue needed to break even.
Would you expect the necessary sales volume to increase or decrease?
Let’s use the more compact formula based on the average contribution margin ratio to
calculate the new sales volume. When we run the new C-V-P calculation, the sales volume
needed to generate $40,000 of target income increases to $220,770, computed
as follows:
? ? $220,770 (rounded up)
The important thing that we’ve learned from these sales mix calculations
is that one sensible profit-maximizing strategy for management would be to
maintain as large a contribution margin as possible on all products and then
$57,400
?
0.26
Fixed costs ? Target income
?????
Average contribution margin ratio
STOP & THINK
Before moving on, can you calculate the
necessary sales volume of $220,770 in
the second sales mix example using the
familiar C-V-P equation: Sales revenue ?
Variable costs ? Fixed costs ? Target
income?
to emphasize those products with the largest individual contribution margins. In
the remaining chapters of this text, we discuss procedures that management can
use to control costs and, hence, maintain high contribution margins. The sec-
ond part of this strategy—emphasizing the products with the highest contribu-
tion margin ratios—is a marketing function. Multi-Product, Inc., for example,
should promote Product B more aggressively than Product A. With other fac-
tors being equal, a company should spend more advertising dollars and pay higher
sales commissions on its products with higher contribution margin ratios. In fact,
instead of paying commissions based on total sales, a good strategy would be to
base sales commissions on the total contribution margin generated. This way,
the mix of products that maximizes the sales staff’s commissions will be the mix
that provides the company with the greatest overall profit.
78 Part 1 E M Foundations
STOP & THINK
Would maximizing the sales of the high-
est contribution margin products still be
the best profit-maximizing strategy if the
company experienced production con-
straints such that producing more of the
highest contribution margin products se-
verely limited the quality or production
speed of other products?
things being equal, to maximize profits, management should
put greater emphasis on the sale of products with higher
contribution margin ratios.
T O S UMMA R I Z E : Sales mix is the proportion
of the total units sold represented by each of a company’s
products. Changes in sales mix can affect profits because
not all products have the same contribution margin. Other
Cost Structure in Different Types of Organizations
Now that we have nearly completed this chapter, we have developed a lot of insight into how
to think about and manage costs in the process of making profit-planning decisions. This chap-
ter is actually a lot about the strategy—the strategy of how a company works with its specific
types of costs and activities to create a profit. Overall, we now basically understand how cost-
volume-profit relationships and contribution margins highlight the different effects that vari-
able and fixed costs have on profitability. As we close this chapter, an important management
issue to be understood has to do with the amount of fixed costs a company has in its cost struc-
ture. The amount of fixed costs an organization commits itself to often has a lot to do with its
type of business, e.g., merchandising, manufacturing, or service. In addition, the arrival of e-
commerce into the economy is having an impact on cost structures of organizations. We’ll talk
more about differences between merchandising, manufacturing, service, and e-commerce com-
panies throughout the remaining chapters in this textbook. For now, we’ll simply illustrate the
differences among these organizations by applying the concept of operating leverage to illus-
trate how a company can manage risk (in terms of profits) by the way it organizes its cost struc-
ture—in other words, how much the company is committed to using fixed costs versus variable
costs to do business.
Imagine that you have worked with two of your college friends to design a new computer
software game that you expect to market to college campuses across the nation. You and your
partners have identified three ways to approach the market. First, you can take on the role of
the merchant by contracting with a software manufacturing company to handle all the pro-
duction of the packaged software. You can then concentrate on the sales and marketing of their
new game. This approach won’t require an expensive production facility, but the reality is that
you will have to pay a high price per unit to the company that handles the production of the
packaged software. In the second approach, you can take on the role of manufacturer by set-
ting up your own production facilities. In this case, because all of your effort will be dedicated
to producing the game, you will need to wholesale the software product to another merchant
company that will then resell the product to the actual customers. Finally, you can “virtually”
sell the game to other college students by contracting with an e-commerce company that will
host your software download site for a significant fixed fee per month. In any case, regardless
of whether you and your partners will wholesale the game to another merchant or retail the
9 Describe how fixed
and variable costs differ in
manufacturing, service,
merchandising, and e-
commerce organizations,
and illustrate these differ-
ences with the operating
leverage concept.
operating leverage The
extent to which fixed costs
are part of a company’s cost
structure; the higher the pro-
portion of fixed costs to vari-
able costs, the faster income
increases or decreases with
changes in sales volume.
game directly to the college student market, you have determined that you can sell the game
for $100. The costs of each of these methods of structuring your business are as follows:
E M 79 Chapter 2 Analyzing Cost-Volume-Profit Relationships
tremely committed to fixed costs with little or no variable
product costs. These cost structure differences are impor-
tant and are illustrated in the concept of operating lever-
age. Operating leverage relates to the amount of fixed costs
a company has in its cost structure. When sales are expected
to increase, high operating leverage results in higher in-
come, and vice versa.
T O S UMMA R I Z E : The relationship between
fixed and variable costs differs across different types of or-
ganizations. Generally, traditional merchandising companies
have relatively low levels of fixed costs and high levels of
variable costs. On the other hand, manufacturing companies
often have higher levels of fixed costs and lower levels of
variable costs. The emergence of e-commerce in this econ-
omy has resulted in some companies that are even more ex-
Variable Cost per Unit to Fixed Cost per Year for the
Manufacture or to Purchase from a Merchandising, Manufacturing, or
Business Structure Manufacturer E-Commerce Facility
Traditional retail merchant $80 $100,000
Manufacturer 25 375,000
E-commerce merchant 0 500,000
As you can see, one of the issues that you must decide when selecting your
company’s business structure is whether you and your partners want to commit
to high fixed costs in order to have low variable costs, or vice versa. This trade-
off of fixed versus variable costs is what we mean when we talk about operating
leverage. As total fixed costs increase and variable costs per unit decrease, the op-
erating leverage of the organization increases. In the example above, the operat-
ing leverage of your company will be very high if you choose to structure your
company as an e-commerce merchant. So, the question you should be asking
yourself is whether it is good or bad to have high operating leverage? The an-
swer is that it depends on whether the company is operating above or below the
break-even point.
The C-V-P graphs in Exhibit 11 show us the impact of operating leverage
for these three types of companies. The break-even point (which is the same for
all three companies) is at a sales volume of 5,000 games sold each year. At this
point, all three companies would generate the same level of profit—nothing. As
sales move above or below the break-even point, however, there are significant
differences in profit (i.e., the distance between the revenue line and the total
costs line) between the company structures. If sales are below the break-even
point, then structuring the company as an e-commerce merchant will generate
a lot of losses. If the company can sell more than 5,000 games per year, how-
ever, then the e-commerce merchant structure will generate the most profit per
year. Essentially, operating leverage is a measure of risk. With high levels of op-
erating leverage, the company is at risk of losing a lot of money if sales go down.
But business risk often has an upside. In the case of operating leverage, the risk
of loss is balanced by the potential for large gains in income as sales go up. So
your decision on how to structure your company partly depends on the impact
on operating leverage and on how much risk you are willing to accept.
Cauti on
Don’t confuse the concept of operating
leverage with the concept of financial lever-
age, though there is a lot of similarity in
these concepts. While both concepts focus
on risk and the sensitivity of profit to
changes in sales volume, financial leverage
has to do with the use of debt versus equity
to provide financing for a company. In gen-
eral, the financial leverage (and risk) of a
company increases as management chooses
to use debt, rather than equity, to raise
funds for the company. Similarly, the oper-
ating leverage (and risk) of a company in-
creases as management chooses to
emphasize fixed cost, rather than variable
cost, to create or obtain the product for sale
to the marketplace.
STOP & THINK
Think about the level of operating lever-
age you would expect to find in a service
organization such as a consulting com-
pany or a law firm. Would these kinds of
organizations typically have high or low
levels of operating leverage?
80 Part 1 E M Foundations
Exhibit 11: “Seeing” Operating Leverages
200,000
600,000
$1,000,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
0
400,000
800,000
Merchandising Structure
(Low Operating Leverage)
Revenue Total costs Fixed costs
200,000
600,000
$1,000,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
0
400,000
800,000
Manufacturing Structure
(Medium Operating Leverage)
Revenue Total costs Fixed costs
Sales in Total Variable Contribution Total Fixed Operating
Units Revenue Costs Margin Costs Income
Price per unit $ 100 3,000 $300,000 $(240,000) $ 60,000 $(100,000) $(40,000)
Variable cost per unit 80 5,000 500,000 (400,000) 100,000 (100,000) —
Total fixed costs 100,000 7,000 700,000 (560,000) 140,000 (100,000) 40,000
Sales in Total Variable Contribution Total Fixed Operating
Units Revenue Costs Margin Costs Income
Price per unit $ 100 3,000 $300,000 $ (75,000) $225,000 $(375,000) $(150,000)
Variable cost per unit 25 5,000 500,000 (125,000) 375,000 (375,000) —
Total fixed costs 375,000 7,000 700,000 (175,000) 525,000 (375,000) 150,000
E O C 81 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exhibit 11: (Concluded)
200,000
600,000
$1,000,000
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000
0
400,000
800,000
E-Commerce Structure
(High Operating Leverage)
Revenue Total costs Fixed costs
Sales in Total Variable Contribution Total Fixed Operating
Units Revenue Costs Margin Costs Income
Price per unit $ 100 3,000 $300,000 $ — $300,000 $(500,000) $(200,000)
Variable cost per unit 0 5,000 500,000 — 500,000 (500,000) —
Total fixed costs 500,000 7,000 700,000 — 700,000 (500,000) 200,000
1
Understand the key factors involved in cost-volume-
profit (C-V-P) analysis and why it is such an impor-
tant tool in management decision making. C-V-P analysis
is a very important management concept. It is a technique
you will use as a manager to understand how profits may be
expected to vary in relation to changes in key variables: sales
price and volume, variable costs, fixed costs, and mix of prod-
ucts. C-V-P analysis is a particularly useful tool for planning
and making operating decisions. It can provide data to stim-
ulate increased sales efforts or cost reduction programs; assist
in production scheduling or marketing strategy; and help es-
tablish company policies, for example, the appropriate prod-
uct mix or the fixed cost structure of a company. In order to
be effective as a manager, you will need a comprehensive un-
derstanding and ability to use C-V-P analysis.
2
Explain and analyze the basic cost behavior patterns—
variable, fixed, mixed, and stepped. Understanding cost
behavior patterns can assist you in making key operating de-
cisions. The two basic cost behavior patterns are variable and
fixed. Costs that vary in total in direct proportion to changes
in the level of activity are variable costs. Therefore, per-unit
variable costs remain constant. Generally, we assume that
there is a linear relationship between variable costs and level
of activity within the relevant range; for other ranges, variable
costs are curvilinear. Costs that do not change in total with
changes in activity level (within the relevant range) are fixed
costs; thus, per-unit fixed costs decrease as level of activity in-
creases. Costs that contain both fixed and variable compo-
nents are mixed costs. Stepped costs increase in total in a
stair-step fashion with the level of activity. If the steps are
wide, the cost is treated as a fixed cost for analysis purposes;
if the steps are narrow, the cost is approximated as a variable
cost.
3
Analyze mixed costs using the scattergraph and high-
low methods. Before mixed costs can be analyzed and
used in decision making, they must be divided into their fixed
and variable components. The scattergraph and high-low
methods are commonly used to analyze mixed costs. The scat-
r e v i e w o f l e a r n i n g o b j e c t i v e s
82 Part 1 E O C Foundations
tergraph method involves visually plotting a straight line (the
regression line) through points on a graph of cost data at var-
ious activity levels. With the high-low method, the highest
and lowest levels of activity and their associated costs are used
to calculate the variable cost rate and the total fixed costs.
4
Perform C-V-P analyses, and describe the effects po-
tential changes in C-V-P variables have on company
profitability. C-V-P analysis is based on the computation of
contribution margin, which is sales revenue less variable costs.
Contribution margin is the amount available to cover fixed
costs and then provide a profit. C-V-P analysis is commonly
used to assess break-even points (where contribution margin
equals fixed costs) and to compute target income levels. The
basic C-V-P equation is:
Sales revenue ? Variable costs ? Fixed costs ? Profit
The C-V-P equation will be especially useful to you as a man-
ager in assessing how profits can be expected to change when
costs or sales revenue change. Increases in fixed or variable
costs result in a larger number of sales being required to break
even and reach target income levels. Increases in sales price
result in a decreased number of sales being required to break
even and reach target income levels.
5
Visualize C-V-P relationships using graphs. C-V-P
graphs and profit graphs are effective methods for visu-
alizing the effect of impacts on key variables in the C-V-P
equation. In addition, the graphic approach effectively allows
managers to simultaneously analyze several different activity
levels.
6
Identify the limiting assumptions of C-V-P analysis,
and explain the issues of quality and time relative to
C-V-P analysis decisions. C-V-P analysis has several limit-
ing assumptions, including the following: (1) cost and rev-
enue behavior patterns are linear and remain constant over
the relevant range, (2) all costs can be categorized as either
fixed or variable, and (3) the sales mix of products is constant
over the relevant range. When making changes in costs, rev-
enues, and volume, remember to consider the impact on the
quality of products or services and the speed at which those
products and services can be delivered to customers. Changes
that result in decreased costs that also decrease product or ser-
vice quality or that slow down the delivery of products or ser-
vices may not be good decisions.
7
Analyze mixed costs using the least squares method.
The least squares method uses a simple regression analy-
sis to identify the variable and fixed portions of mixed costs.
The formula for the least squares method is based on the fol-
lowing equation for a straight line:
Y ? a ? bX
where a is total fixed cost and b is per-unit variable cost. Least
square calculations can be easily performed using basic com-
puter software programs or programmed calculators. One out-
put of least square analysis calculations is the R
2
statistic,
which measures the amount of variance in the cost that is ex-
plained by changes in the activity level (depicted by X in the
equation above).
8
Explain the effects of sales mix on profitability. Sales
mix is the proportion of total units sold represented by
each of a company’s products. Because all products do not
have the same contribution margin ratios, changes in the sales
mix of products sold can significantly affect total profits.
When you are working as a manager to maximize profits, it
is best to maintain as large a contribution margin as possible
on all products and then emphasize those products with the
largest individual contribution margin ratios.
9
Describe how fixed and variable costs differ in manu-
facturing, service, merchandising, and e-commerce
organizations, and illustrate these differences with the
operating leverage concept. The trade-off between fixed
costs and variable costs is often related to whether a company
is structured as a manufacturing, merchandising, or service firm.
The advent of e-commerce has created the potential for com-
panies to have very high levels of fixed costs and very low lev-
els of variable costs. The impact of the fixed cost/variable cost
relationship on profits is captured in the concept of operating
leverage. Operating leverage is a measure of the extent to which
a company’s costs are fixed rather than variable. Companies
with higher fixed costs and lower per-unit variable costs will
experience higher operating leverage and, therefore, a tendency
for profits to increase at a faster rate when sales increase. Hence,
a company with high operating leverage will be more profitable
in good times but have higher losses in bad times.
break-even point, 61
contribution margin, 58
contribution margin ratio, 59
cost behavior, 44
cost-volume-profit (C-V-P) analysis,
44
k e y t e r m s & c o n c e p t s
E O C 83 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Variable and Fixed Costs Analyses
Blade Corporation manufactures two types of inline skates—a basic model and a racing model.
During the year 2006, Blade accumulated the following summary information about its two
products:
Racing Model Basic Model
Selling price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $130 $65
Number of units manufactured and sold . . . . . . . . . . . . . 14,000 9,000
Racing Model Basic Model
Units Costs Units Costs
January . . . . . . . . . . . . . . . . . . . . . . . . . . 1,200 $ 112,000 800 $ 39,600
February . . . . . . . . . . . . . . . . . . . . . . . . . 900 91,000 600 30,000
March . . . . . . . . . . . . . . . . . . . . . . . . . . . 800 76,400 450 25,800
April . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,400 124,800 900 36,900
May . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 950 92,650 1,000 47,000
June . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,600 146,800 1,200 57,300
July . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,400 134,600 1,300 60,600
August . . . . . . . . . . . . . . . . . . . . . . . . . . 1,700 154,500 650 32,195
September . . . . . . . . . . . . . . . . . . . . . . . . 1,550 140,200 850 44,250
October . . . . . . . . . . . . . . . . . . . . . . . . . . 1,500 134,500 500 27,000
November . . . . . . . . . . . . . . . . . . . . . . . . 600 62,500 350 20,700
December . . . . . . . . . . . . . . . . . . . . . . . . 400 44,000 400 22,000
Totals . . . . . . . . . . . . . . . . . . . . . . . . . . 14,000 $1,313,950 9,000 $443,345
Required:
1. Use the high-low method to estimate the variable and fixed production costs of both the
racing model and the basic model skates.
2. All selling costs are fixed, and they total $200,000 for the racing model and $80,000 for the
basic model. Prepare a contribution margin income statement for each model at sales of
10,000 racing and 10,000 basic skates.
Solution
1. Variable and Fixed Costs
The high-low method involves finding the variable and fixed costs at the high and low levels
of production. In this case:
r e v i e w p r o b l e m s
curvilinear costs, 47
fixed costs, 49
high-low method, 54
mixed costs, 51
per-unit contribution margin, 58
profit graph, 68
regression line, 53
relevant range, 49
return on sales revenue, 62
scattergraph (visual-fit) method, 53
stepped costs, 50
target income, 62
variable cost rate, 53
variable costs, 46
least squares method, 73
operating leverage, 78
sales mix, 76
Racing Model Basic Model
High-production month . . . . . . . . . . . . . . . . . . . . . . . . . 1,700 (Aug.) 1,300 (July)
Low-production month . . . . . . . . . . . . . . . . . . . . . . . . . . 400 (Dec.) 350 (Nov.)
Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,300 950
Total production costs of high month . . . . . . . . . . . . . . . $154,500 $60,600
Total production costs of low month . . . . . . . . . . . . . . . 44,000 20,700
Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $110,500 $39,900
Once the differences are known, the change in units (production) is divided into the change
in costs to determine the variable cost rate.
? Variable cost rate
Racing model: ? $85
Basic model: ? $42
Because total variable costs equal unit variable cost times number of units produced, and total
costs equal total variable costs plus total fixed costs, fixed costs can now be calculated.
Total costs ? (Variable cost per unit ? Number of units) ? Total fixed costs
Racing Model Basic Model
High production level (X) ? $154,500 ? $85(1,700) $60,600 ? $42(1,300)
X ? $154,500 ? $144,500 X ? $60,600 ? $54,600
X ? $10,000 X ? $6,000
Low production level (X) ? $44,000 ? $85(400) $20,700 ? $42(350)
X ? $44,000 ? $34,000 X ? $20,700 ? $14,700
X ? $10,000 X ? $6,000
Thus, we have the following:
Racing Model Basic Model
Variable cost rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 85 $ 42
Total fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10,000 6,000
2. Contribution Margin Income Statements
Blade Corporation
Contribution Margin Income Statements
For the Year Ended December 31, 2006
Racing Model Basic Model
Sales revenue (at 10,000 units) . . . . . . . . . . . . . . . . . . . . $1,300,000 $ 650,000
Less variable cost of goods sold* . . . . . . . . . . . . . . . . . . (850,000) (420,000)
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 450,000 $ 230,000
Less fixed cost of goods sold . . . . . . . . . . . . . . . . . . . . . (10,000) (6,000)
Less fixed selling costs . . . . . . . . . . . . . . . . . . . . . . . . . . (200,000) (80,000)
Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 240,000 $ 144,000
*$85 per unit for racing model; $42 per unit for basic model.
$39,900
?
950
$110,500
??
1,300
Change in costs
??
Change in units
84 Part 1 E O C Foundations
Assessing the Effects of Changes in Costs, Prices, and Volume
on Profitability
K&D Company plans the following for the coming year:
Sales volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000 units
Sales price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2.50 per unit
Variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1.30 per unit
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $60,000
Required:
1. Determine K&D’s target income.
2. Compute what the target income would be under each of the following independent as-
sumptions:
a. The sales volume increases 20%.
b. The sales price decreases 20%.
c. Variable costs increase 20%.
d. Fixed costs decrease 20%.
Solution
1. Target Income
Basic C-V-P equation: Sales revenue ? Variable costs ? Fixed costs ? Target income
(Units sold ? Sales price) ? (Units sold ? Variable unit cost) ? Fixed costs ? Target income
(100,000 ? $2.50) ? (100,000 ? $1.30) ? $60,000 ? X
$250,000 ? $130,000 ? $60,000 ? X
$60,000 ? X
This answer can be validated by dividing fixed costs by the per-unit contribution margin
to find the break-even point and then multiplying the excess units to be sold above the break-
even point by the per-unit contribution margin of $1.20 ($2.50 ? $1.30).
? Break-even point
? 50,000 units
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $1.20
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $60,000
2a. The sales volume increases 20%.
(100,000 ? 1.2 ? $2.50) ? (100,000 ? 1.2 ? $1.30) ? $60,000 ? X
$300,000 ? $156,000 ? $60,000 ? X
$84,000 ? X
In this case, the contribution margin does not change. Therefore, the answer can be vali-
dated by multiplying the units to be sold in excess of the break-even point by the per-unit con-
tribution margin of $1.20 to find the target income.
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70,000
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $1.20
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $84,000
$60,000
?
$1.20
Fixed costs
????
Per-unit contribution margin
E O C 85 Chapter 2 Analyzing Cost-Volume-Profit Relationships
2b. The sales price decreases 20%.
(100,000 ? $2.50 ? 0.8) ? (100,000 ? $1.30) ? $60,000 ? X
$200,000 ? $130,000 ? $60,000 ? X
$10,000 ? X
In this case, the contribution margin changes. Therefore, the answer can be validated by
dividing fixed costs by the new per-unit contribution margin of $0.70 ($2.00 ? $1.30) to find
the new break-even point and then multiplying the units to be sold in excess of the break-even
point by the new per-unit contribution margin.
? 85,715 units (new break-even point, rounded up)
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85,715
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14,285
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $0.70
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $10,000 (rounded)
2c. Variable costs increase 20%.
(100,000 ? $2.50) ? (100,000 ? $1.30 ? 1.2) ? $60,000 ? X
$250,000 ? $156,000 ? $60,000 ? X
$34,000 ? X
In this case, the contribution margin changes. Therefore, the answer can be validated by
dividing fixed costs by the new per-unit contribution margin of $0.94 ($2.50 ? $1.56) to find
the new break-even point and then multiplying the units to be sold in excess of the break-even
point by the new per-unit contribution margin.
? 63,830 units (new break-even point, rounded up)
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63,830
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36,170
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $0.94
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $34,000 (rounded)
2d. Fixed costs decrease 20%.
(100,000 ? $2.50) ? (100,000 ? $1.30) ? ($60,000 ? 0.8) ? X
$250,000 ? $130,000 ? $48,000 ? X
$72,000 ? X
In this case, the contribution margin does not change, but fixed costs, and hence the break-
even point, do. Therefore, the answer can be validated by dividing the per-unit contribution
margin of $1.20 into the new fixed costs to find the break-even point and then multiplying the
units to be sold in excess of the break-even point by the per-unit contribution margin.
? 40,000 units (new break-even point)
Units sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Less break-even point (units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40,000
Excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,000
Per-unit contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ? $1.20
Target income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $72,000
$48,000 (new fixed costs)
?????
$1.20 (per-unit contribution margin)
$60,000 (fixed costs)
?????
$0.94 (new per-unit contribution margin)
$60,000 (fixed costs)
?????
$0.70 (new per-unit contribution margin)
86 Part 1 E O C Foundations
E O C 87 Chapter 2 Analyzing Cost-Volume-Profit Relationships
1. Explain how understanding cost behavior patterns can as-
sist management.
2. Discuss how level of activity is measured in manufactur-
ing, merchandising, and service firms.
3. What is meant by the linearity assumption, and why is
it made? Relate this assumption to the relevant-range
concept.
4. What factors in the current economy seem to have
caused the shift from variable to fixed cost patterns?
5. How should stepped costs be treated in the planning
process?
6. Why must all mixed costs be segregated into their fixed
and variable components?
7. What is the major weakness of the scattergraph, or visual-
fit, method of analyzing mixed costs?
8. What is the major limitation of the high-low method of
analyzing mixed costs?
9. What is the basic C-V-P equation? What is a more de-
tailed version of this equation?
10. What is the contribution margin, and why is it important
for managers to know the contribution margins of their
products?
11. How much will profits increase for every unit sold over
the break-even point?
12. What is the major advantage of using C-V-P graphs?
13. When other factors are constant, what is the effect on
profits of an increase in fixed costs? Of a decrease in vari-
able costs?
14. What are the limiting assumptions of C-V-P analysis?
15. How do the issues of quality and time relate to C-V-P
analysis decisions?
16. How does the method of least squares differ from the
scattergraph method?
17. What effect is a change in the sales mix likely to have on
a firm’s overall contribution margin ratio?
d i s c u s s i o n q u e s t i o n s
Measuring Level of Activity
Which one of the following is not an activity base used by a company?
a. Number of defects per hour in an assembly plant
b. Number of units sold for a merchandising firm
c. Number of units produced for a manufacturing firm
d. Number of client hours billed for an accounting firm
e. Number of hours a retail store is open
Variable Costs
Which one of the following would not be a variable cost for a construction company?
a. Cost of trusses used to construct a roof for a house
b. Cost of windows to be installed in a house
c. Salary paid to overall project supervisor
d. Cost of drywall to be installed in house
e. Cost of exterior house paint
Linearity of Variable Costs within the Relevant Range
The company has assembled the following data about its variable costs:
p r a c t i c e e x e r c i s e s
Practice 2-1
Practice 2-2
Practice 2-3
(continued)
Level of Activity Total Variable Cost
1,000 units $ 25,000
2,000 units 46,000
3,000 units 69,000
4,000 units 92,000
5,000 units 100,000
The company is currently producing 3,300 units. According to these data, what is the rel-
evant range over which the company can assume that the variable cost per unit is constant?
Fixed Costs
If the level of activity increases during the month, does the fixed cost per unit increase, de-
crease, or remain constant?
Break-Even Computation
The company reports the following items.
Direct materials per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 2.50
Direct labor per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.60
Variable overhead per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10
Monthly rent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,900.00
Monthly depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650.00
Other monthly fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2,680.00
Sales price per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.25
Using the above information, compute the company’s monthly break-even point (in units).
Stepped Fixed Costs
The company pays $3,000 per month to each of its four production supervisors. Each super-
visor can handle the workload associated with up to 2,400 units of production per month; the
current level of production is 9,000 units. If the company increases its level of production to
12,800 units per month, how much will the company pay, in total, for the salaries of the nec-
essary production supervisors?
Mixed Costs
The company’s president receives a $100,000 base salary and a bonus of 0.5% of sales for the
year. How much will the president earn at a sales level of $2,750,000 for the year?
Scattergraph Method
Which one of the following statements is incorrect?
a. The scattergraph method can be somewhat subjective depending on where one visually
places the regression line.
b. The scattergraph method is the most accurate method of analyzing mixed costs.
c. When graphing mixed costs, the dollars go on the vertical axis, and the level of activity goes
on the horizontal axis.
d. Regression lines attempt to minimize the average distance between all the data points and
the fitted regression line.
e. The slope of the regression line is equal to the variable cost per unit of activity.
Using the High-Low Method to Estimate the Variable Cost Rate
The company reports the following utility costs for different levels of activity during the first
half of the year:
88 Part 1 E O C Foundations
Practice 2-4
Practice 2-5
Practice 2-6
Practice 2-7
Practice 2-8
Practice 2-9
Month Machine Hours Total Utility Costs
January 470 $14,000
February 410 12,500
March 520 14,400
April 500 14,450
May 550 15,350
June 535 15,100
Using the high-low method, estimate the variable cost rate.
Using the High-Low Method to Estimate Fixed Costs
Refer to the data in Practice 2-9. Using the high-low method, estimate the fixed costs per month
based on the variable cost rate (computed in Practice 2-9).
Contribution Margin Income Statement
The company sells desks for $550 each. The variable cost per desk is $385. The company’s
monthly fixed costs are $72,000. Prepare a contribution margin income statement for a month
in which the company sells 500 desks.
Contribution Margin Ratio and Variable Cost Ratio
Refer to the data in Practice 2-11. Compute the contribution margin ratio and the variable cost
ratio.
The C-V-P Equation
The company sells lawnmowers for $895 each. The variable cost per lawnmower is $520. The
company’s monthly fixed costs are $84,500. Using the C-V-P equation, compute the amount
of profit the company will have for a month in which the company sells 375 lawnmowers.
Break-Even Units
The company sells shovels for $27.75 each. The variable cost per shovel is $14.25. The com-
pany’s monthly fixed costs are $2,538. Compute the number of shovels the company must sell
to break even.
Determining Sales Volume to Achieve Target Income
Refer to the data in Practice 2-14. How many shovels must the company sell to achieve a profit
of $10,000?
Determining Sales Volume to Achieve Target Return on Sales
The company sells pianos for $7,000 each. The variable cost per piano is $5,500. The com-
pany has fixed costs per month of $45,000. Compute the number of units the company must
sell in a month to achieve a 15% return on sales.
Break-Even Sales Revenue
The company has a variable cost ratio of 65% and monthly fixed costs of $91,000. What is
the company’s break-even point in terms of sales dollars?
C-V-P Analysis with Simultaneous Changes in Several Variables
The company currently sells 50,000 feet of cable each month for $3.50 per foot. The variable
cost of the cable is $1.10 per foot, and monthly fixed costs are $75,000. The company is con-
sidering whether to raise the sales price for the cable to $4.00 per foot. The marketing team has
determined that such an increase in sales price will discourage some customers from purchasing
E O C 89 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Practice 2-10
Practice 2-11
Practice 2-12
Practice 2-13
Practice 2-14
Practice 2-15
Practice 2-16
Practice 2-17
Practice 2-18
(continued)
the cable, so the company will be able to sell only 40,000 feet of cable per month. Calculate the
profit for the company under both of the following scenarios:
1. 50,000 feet of cable at $3.50 per foot.
2. 40,000 feet of cable at $4.00 per foot.
In terms of profit maximization, should the company raise the price per foot?
C-V-P Analysis with Simultaneous Changes in Several Variables
Refer to the data in Practice 2-18. The company is considering whether to change its produc-
tion process to reduce the variable cost per foot to $0.90 by raising fixed costs per month to
$83,000. This change will have no impact on selling price ($3.50) or sales volume (50,000
feet). In terms of profit maximization, should the company change its production process?
Interpreting a C-V-P Graph
90 Part 1 E O C Foundations
Practice 2-19
Practice 2-20
$200,000
180,000
160,000
140,000
120,000
100,000
80,000
60,000
40,000
20,000
100 200 300 400 500 600 700 800 900 1,000 1,100 1,200
Number sold
S
a
l
e
s
0
C
B
A
Look at the given C-V-P graph. Which one of the following sets of labels correctly labels items
A, B, and C in the C-V-P graph?
a. A: Total cost line; B: Fixed costs; C: Break-even point
b. A: Revenue line; B: Variable costs; C: Fixed costs
c. A: Fixed cost line; B: Break-even point; C: Fixed costs
d. A: Revenue line; B: Break-even point; C: Fixed costs
e. A: Total cost line; B: Break-even point; C: Fixed costs
Interpreting a Profit Graph
E O C 91 Chapter 2 Analyzing Cost-Volume-Profit Relationships
$80,000
60,000
40,000
20,000
0
?20,000
?40,000
?60,000
?80,000
P
r
o
f
i
t
L
o
s
s
Number sold
C
B
A
Practice 2-21
Practice 2-22
Practice 2-23
Look at the given profit graph. Which one of the following sets of labels correctly labels items
A, B, and C in the profit graph?
a. A: Area of loss; B: Break-even point; C: Area of profit
b. A: Area of loss; B: Area of profit; C: Break-even point
c. A: Break-even point; B: Area of loss; C: Area of profit
d. A: Area of profit; B: Break-even point; C: Area of loss
e. A: Area of profit; B: Area of loss; C: Break-even point
Limiting Assumptions of C-V-P Analysis
Which one of the following is not an assumption of C-V-P analysis?
a. Fixed costs are always greater than variable costs.
b. All costs can be divided into fixed and variable categories.
c. C-V-P analysis is valid only for a relevant range.
d. The mix of a company’s products does not change over the relevant range.
Least-Squares Method
The company reports the following costs at different levels of activity for the first half of the
year.
(continued)
Month Machine Hours Total Utility Costs
January 470 $14,000
February 410 12,500
March 520 14,400
April 500 14,450
May 550 15,350
June 535 15,700
Using Excel (or another program with statistical capabilities), estimate the company’s fixed
costs and variable costs per machine hour using the least-squares method.
Sales Mix
The company has fixed costs of $21,500 and the following sales mix.
Product A Product B Product C
Sales revenue . . . . . . . . . . . . . . . . . . . . . . . . . $35,000 $70,000 $45,000
Less variable costs . . . . . . . . . . . . . . . . . . . . . 20,000 50,000 36,000
Contribution margin . . . . . . . . . . . . . . . . . . . . $15,000 $20,000 $ 9,000
Using this same sales mix, calculate the required sales (in dollars) to earn a target income of
$25,000.
Cost Structure
If you experience much higher sales than expected this year, which kind of operating leverage
would you like to have in your company for profit maximization?
a. High operating leverage
b. Low operating leverage
c. Medium operating leverage
d. Operating leverage does not affect profitability.
92 Part 1 E O C Foundations
Practice 2-24
Practice 2-25
Variable and Fixed Costs Over the Relevant Range
Cook Corporation manufactures plastic garbage cans. In a typical year, the firm produces be-
tween 40,000 and 50,000 cans. At this level of production, fixed costs are $10,000 and vari-
able costs are $2 per can.
1. Graph the cost of producing cans, with cost as the vertical axis and production output as
the horizontal axis.
2. Indicate on the graph the relevant range of the $10,000 in fixed costs, and explain the sig-
nificance of the relevant range.
3. What would total production costs be if 46,000 cans were produced?
Fixed Costs—The Relevant Range
Sabrina Company manufactures large leisure boats. The following schedule shows total fixed
costs at various levels of boat production:
e x e r c i s e s
Exercise 2-1
Exercise 2-2
Units Produced Total Fixed Costs
0–100 $150,000
101–400 250,000
401–900 400,000
1. What is the fixed cost per unit when 75 boats are produced?
2. What is the fixed cost per unit when 300 boats are produced?
3. What is the fixed cost per unit when 750 boats are produced?
4. Plot total fixed costs on a graph similar to that shown in Exhibit 3.
Scattergraph Method of Analyzing Mixed Costs
Wyoming Company makes windmills. The company has the following total costs at the given
levels of windmill production:
Units Produced Total Costs
20 $16,000
30 22,000
40 20,000
50 28,000
1. Use the scattergraph method to estimate the fixed and variable elements of Wyoming’s total
costs.
2. Compute the total cost of making 44 windmills, assuming that total fixed costs are $10,000
and that the variable cost rate computed in part (1) does not change.
Scattergraph Method of Analyzing Mixed Costs
Given the following mixed costs at various levels of production, complete the requirements.
Month Units Produced Mixed Costs
January 2 $24.00
February 3 28.00
March 1 21.00
April 5 30.00
May 4 25.00
1. Plot the data on a scattergraph, and visually fit a straight line through the points.
2. Based on your graph, estimate the monthly fixed cost and the variable cost per unit pro-
duced.
3. Compute the total cost of producing eight units in a month, assuming that the same rele-
vant range applies.
4. Interpretive Question: Why is it so important to be able to determine the components of a
mixed cost?
Scattergraph Method and High-Low Method of Analyzing Mixed Costs
Sailmaster makes boats and has the following costs and production levels for the last eight
quarters:
E O C 93 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-3
Exercise 2-4
Exercise 2-5
(continued)
Quarter Boats Produced Total Costs
1 108 $101,250
2 128 168,750
3 185 189,000
4 245 200,145
5 311 276,200
6 352 255,250
7 389 305,700
8 428 376,500
1. Plot the data on a scattergraph, and visually fit a straight line through the points.
2. Based on your graph, estimate the quarterly fixed cost and the variable cost per unit produced.
3. Use the high-low method to compute the variable and fixed elements of Sailmaster’s total costs,
and then draw a straight line through the high and low data points on the scattergraph.
4. Compute the total cost of making 500 boats using first the scattergraph results and then us-
ing the high-low method results.
5. Comment on the differences between these two methods. Which method appears to most
accurately represent the actual variable and fixed costs for Sailmaster?
High-Low Method of Analyzing Mixed Costs
The Stamford Times has determined that the annual printing of 750,000 newspapers costs 11
cents per copy. If production were to be increased to 1,000,000 copies per year, the per-unit
cost would drop to 9 cents per copy.
1. Using the high-low method, determine the total fixed and variable costs of printing 750,000
newspapers.
2. Using the fixed and variable costs you determined in part (1), what would be the total cost
of producing 900,000 copies?
Contribution Margin Calculations
Jerry Stone owns and operates a small beach shop in a mall on Sanibel Island, Florida. For the
last six months, Jerry has had a display of sunglasses in the front window. Largely because of
the display, Jerry has sold 100 pairs of sunglasses per month at an average cost of $26 and sell-
ing price of $50. The sales volume has doubled since the display was put in the window. One-
fourth of Jerry’s storage space is occupied by 190 ice coolers. The coolers have not been selling
as well as Jerry hoped, but he is convinced that a front window display of coolers would in-
crease sales by 50%. The coolers cost Jerry a total of $2,280 and have been selling at a rate of
100 per month at $28 each.
1. Assuming that cost of goods sold is the only variable cost, compute the contribution margin
per unit for sunglasses and ice coolers.
2. Compute the total contribution margins for both sunglasses and ice coolers assuming win-
dow displays and no window displays for both items.
3. What are the economic costs associated with keeping the sunglass display in the store window?
4. What are the economic costs associated with replacing the sunglass display with an ice
cooler display?
Contribution Margin Income Statement
The following data apply to Gordon Company for 2006:
Sales revenue (10 units at $25 each) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $250
Variable selling expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Variable administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Fixed selling expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
94 Part 1 E O C Foundations
Exercise 2-6
Exercise 2-7
Exercise 2-8
Fixed administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 15
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Fixed manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Variable manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1. Prepare a contribution margin income statement. Assume there were no beginning or end-
ing inventories in 2006.
2. How much would Gordon Company have lost if only five units had been sold during 2006?
Analysis of a Contribution Margin Income Statement
Fill in the missing amounts for the following three cases:
Case I Case II Case III
Sales revenue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $50,000 $60,000 $ (7)
Variable cost of goods sold:
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $12,500 $ (4) $20,000
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) 15,000 20,000
Variable selling and administrative costs . . . . . . . . . . . . 3,500 (5) 10,000
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . $ (2) $20,000 $ (8)
Gross margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20,000 30,000 40,000
Fixed selling and administrative costs* . . . . . . . . . . . . . 5,500 10,000 (9)
Rent expense on office building . . . . . . . . . . . . . . . . . . (3) 5,000 2,000
Depreciation expense on delivery trucks . . . . . . . . . . . . 5,000 2,500 8,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 4,000 $ (6) $ 0
*Except rent and depreciation.
Analysis of the Contribution Margin
Dr. Hughes and Dr. Hawkins, owners of the Spanish Fork Care Clinic, have $150,000 of fixed
costs per year. They receive 20,000 patient visits in a year, charging each patient an average of
$20 per visit; variable costs average $2 per visit (needles, medicines, and so on).
1. What is the contribution margin per patient visit?
2. What is the total contribution margin per year?
3. What is the total pretax profit for a year?
4. Drs. Hughes and Hawkins can bring in another doctor at a salary of $100,000 per year. If
this new doctor can handle 5,000 patient visits per year, should the new doctor be hired?
(Assume no additional fixed costs will be incurred.)
Contribution Margin Analysis
Compute the missing amounts for the following independent cases. (Assume zero beginning
and ending inventories.)
Case I Case II Case III
Sales volume (units) . . . . . . . . . . . . . . . . . . . . . . . . . . 24,000 (5) 16,000
Sales price per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . $10 $8 (9)
Variable costs (total) . . . . . . . . . . . . . . . . . . . . . . . . . . (1) $200,000 $100,000
Contribution margin (total) . . . . . . . . . . . . . . . . . . . . . . (2) (6) $60,000
Contribution margin per unit (rounded) . . . . . . . . . . . . $4 $3 (10)
Fixed costs (total) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3) (7) (11)
Fixed costs per unit (rounded) . . . . . . . . . . . . . . . . . . . (4) $2 (12)
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $20,000 (8) $40,000
E O C 95 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-9
Exercise 2-10
Exercise 2-11
Break-Even Point and Target Income
Detienne Company manufactures and sells one product for $20 per unit. The unit contribu-
tion margin is 40% of the sales price, and fixed costs total $80,000.
1. Using the equation approach, compute:
a. The break-even point in sales dollars and units.
b. The sales volume (in units) needed to generate a profit of $40,000.
c. The break-even point (in units) if variable costs increase to 80% of the sales price and
fixed costs increase to $100,000.
2. See if you can recompute the solutions to 1(a), 1(b), and 1(c) in one equation step using
either the contribution margin ratio or the contribution margin dollars per unit.
Break-Even Point and Target Income
Steven Newman, Inc., estimates 2006 costs to be as follows:
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $5 per unit
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $8 per unit
Variable manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $3 per unit
Variable selling and administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2 per unit
Fixed expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $80,000
1. Assuming that Newman will sell 55,000 units, what sales price per unit will be needed to
achieve a $75,000 profit?
2. Assuming that Newman decides to sell its product for $23 per unit, determine the break-
even sales volume in dollars and units.
3. Assuming that Newman decides to sell its product for $23 per unit, determine the number
of units it must sell to generate a $100,000 profit.
Break-Even Point—Graphic Analysis
Using the graph below, answer the following questions:
96 Part 1 E O C Foundations
Exercise 2-12
Exercise 2-13
Exercise 2-14
$50
45
40
35
30
25
20
15
10
5
1 2 3 4 5 6 7 8 9 10 11
Volume (in thousands of units)
C
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(
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n
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0
1. Copy the graph and identify (label) fixed costs, variable costs, total revenues, the total cost
line, and the break-even point.
2. Determine the break-even point in both sales dollars and volume.
3. Suppose that as a manager you forecast sales volume at 7,000 units. At this level of sales,
what would be your total fixed costs, approximate variable costs, and profit (or loss)?
4. At a sales volume of 3,000 units, what would be the level of fixed costs, variable costs, and
approximate profit (or loss)?
The Profit Graph
Using the graph below, answer the following questions:
E O C 97 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-15
?300
?200
?100
0
?100
?200
?300
200 300 400 500
Volume of sales in units
I
n
c
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e
(
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)
100
1. What is the break-even point in sales volume (in units)?
2. Approximately what volume of sales (in units) must this company have to generate an in-
come of $300?
3. How much are the fixed costs?
Graphing Revenues and Costs
Montana Company manufactures chocolate candy. Its manufacturing costs are as follows:
Annual fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $15,000
Variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2 per box of candy
1. Plot variable costs, fixed costs, and total costs on a graph for activity levels of 0 to 30,000
boxes of candy.
2. Plot a revenue line on the graph, assuming that Montana sells the chocolates for $5 a box.
C-V-P Analysis
The Last Outpost is a tourist stop in a western resort community. Kerry Yost, the owner of the
shop, sells hand-woven blankets for an average price of $30 per blanket. Kerry buys the blan-
kets from weavers at an average cost of $21. In addition, he has selling expenses of $3 per blan-
ket. Kerry rents the building for $300 per month and pays one employee a fixed salary of $500
per month.
1. Determine the number of blankets Kerry must sell to break even.
2. Determine the number of blankets Kerry must sell to generate a profit of $1,000 per month.
3. Assume that Kerry can produce and sell his own blankets at a total variable cost of $16 per
blanket, but that he would need to hire one additional employee at a monthly salary of $600.
a. Determine the number of blankets Kerry must sell to break even.
b. Determine the number of blankets Kerry must sell to generate a profit of $1,000 per
month.
C-V-P Analysis—Changes in Variables
Tracy, Inc., estimates that next year’s results will be:
Sales revenue (75,000 units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 900,000
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (375,000)
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (300,000)
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 225,000
Recompute profit, assuming each of the following independent conditions:
1. A 9% increase in the contribution margin.
2. An 8% increase in the sales volume.
3. A 4% decrease in the sales volume.
Exercise 2-16
Exercise 2-17
Exercise 2-18
(continued)
4. A 6% increase in variable costs per unit.
5. A 5% decrease in fixed costs.
6. A 5% increase in fixed costs.
7. A 12% increase in the sales volume and a 6% increase in fixed costs.
C-V-P Analysis—Changes in Variables
Modern Fun Corporation sells electronic games. Its three salespersons are currently being paid
fixed salaries of $30,000 each; however, the sales manager has suggested that it might be more
profitable to pay the salespersons on a straight commission basis. He has suggested a commis-
sion of 15% of sales. Current data for Modern Fun Corporation are as follows:
Sales volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15,000 units
Sales price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $40 per unit
Variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $29 per unit
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $140,000
1. Assuming that Modern Fun Corporation has a target income of $50,000 for next year,
which alternative is more attractive?
2. The sales manager believes that by switching to a commission basis, sales will increase 20%.
If that is the case, which alternative is more attractive? (Assume that sales are expected to re-
main at 15,000 units under the fixed salary alternative.)
Mixed Costs—Least Squares Analysis
Given the following mixed costs at various levels of production, complete the requirements.
Month Units Produced Mixed Costs
January 8 $30
February 12 36
March 4 22
April 20 44
May 8 26
1. Using the least squares method (either the equation approach or a software package), calcu-
late the monthly fixed and variable components of the mixed costs.
2. Using the estimates from part (1), compute the total cost of producing 16 units in a month.
3. Describe a major advantage and a major disadvantage of the least squares method.
Sales Mix
Klein Brothers sells products X and Y. Because of the nature of the products, Klein sells two
units of product X for each unit of product Y. Relevant information about the products is as
follows:
X Y
Sales price per unit $10 $30
Variable cost per unit 8 18
1. Assuming that Klein’s fixed costs total $140,000, compute Klein’s break-even point in sales
dollars.
98 Part 1 E O C Foundations
Exercise 2-19
Exercise 2-20
Exercise 2-21
2. Assuming that Klein sells one unit of product X for each unit of product Y, and fixed costs
remain at $140,000, compute Klein’s break-even point in sales dollars.
3. Explain any differences in your answers to parts (1) and (2).
C-V-P Analysis
Mower Manufacturing’s income statement for January 2006 is given below.
Sales (25,000 units ? $25) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $625,000
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468,750
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $156,250
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 31,250
1. Calculate the company’s break-even point in sales dollars and units.
2. The company is contemplating the purchase of new production equipment that would re-
duce variable costs per unit to $16.25. However, fixed costs would increase to $175,000 per
month. Assuming sales of 26,000 units next month, prepare an income statement for both
the current and the proposed production methods. Calculate the break-even point (in dol-
lars and units) for the new production method.
3. Comment on the difference (if any) in the break-even point for the new production
method. What explains the difference in income at sales of 26,000 units between the two
production methods?
Operating Leverage
Ludlam Company and Kassandra Company both make school desks. They have the same pro-
duction capacity, but Ludlam is more automated than Kassandra. At an output of 2,500 desks
per year, the two companies have the following costs:
Ludlam Kassandra
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $137,500 $ 37,500
Variable costs at $20 per desk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000
Variable costs at $60 per desk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150,000
Total cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $187,500 $187,500
Unit cost (2,500 desks) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 75 $ 75
Assuming that both companies sell desks for $100 each and that there are no other costs or ex-
penses for the two firms, complete the following:
1. Which company will lose the least money if production and sales fall to 1,000 desks per
year?
2. What would be each company’s profit or loss at production and sales levels of 1,000 desks
per year?
3. What would be each company’s profit or loss at production and sales levels of 4,000 desks
per year?
E O C 99 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Exercise 2-22
Exercise 2-23
Graphing Revenues and Costs
Cloward and Hawkins, CPAs, took in $350,000 of gross revenues this year. Besides themselves,
they have two professional staff (one manager and one senior) and a full-time secretary. Fixed
operating expenses for the office were $50,000 last year. This year the volume of activity is up
p r o b l e m s
Problem 2-1
5%, and fixed operating expenses are still $50,000. Total variable operating costs, except for
bonuses, average $5 per billable hour. The billable time for all professionals is as follows:
Partners: 3,000 hours at $75/hour
Manager: 1,800 hours at $40/hour
Senior: 2,120 hours at $25/hour
Salaries for the professional staff are $40,000 and $28,000, respectively; the secretary is paid
$18,000. The partners each draw salaries of $60,000; plus they share a 5% bonus based on
gross revenues. The manager is given a 2% bonus, also based on gross revenues.
Required:
1. Plot the data on a graph clearly showing (a) fixed costs, (b) variable costs, (c) total costs, and
(d) total revenues.
2. How much profit did the CPA firm make this year (after partners’ salaries)?
High-Low and Scattergraph Methods of Analysis
Woodfield Company makes bed linens. During the first six months of 2006, Woodfield had
the following production costs:
Month Units Produced Total Costs
January 10,000 $ 68,000
February 20,000 100,000
March 15,000 90,000
April 8,000 52,000
May 17,000 94,000
June 12,000 74,000
Required:
1. Use the high-low method to compute the monthly fixed cost and the variable cost rate.
2. Plot the costs on a scattergraph.
3. Interpretive Question: Based on your scattergraph, do you think the fixed costs and the
variable cost rate determined in part (1) are accurate? Why?
Contribution Margin Income Statement
Early in 2007, Lili H Company (a retailing firm) sent the following income statement to its
stockholders:
Lili H Company
Income Statement
For the Year Ended December 31, 2006
Sales revenue (2,000 units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $240,000
Less cost of goods sold (variable) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160,000
Gross margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $80,000
Operating expenses:
Selling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 24,000
Administrative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16,000
Depreciation (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,000
Insurance (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Utilities ($80 fixed and $120 variable) . . . . . . . . . . . . . . . . . . . . . . . . 200 44,400
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $35,600
100 Part 1 E O C Foundations
Problem 2-2
Problem 2-3
Required:
1. Prepare a contribution margin income statement. (Assume that the fixed components of the
selling and administrative expenses are $12,000 and $8,000, respectively.)
2. Interpretive Question: Why is a contribution margin income statement helpful to man-
agement?
3. Interpretive Question: How would the analysis in part (1) be different if the depreciation
expense was considered a stepped cost with wide steps compared to the relevant range?
Contribution Margin Income Statement
Susan Young is an attorney for a small law firm in Arizona. She is also a part-time inventor
and an avid golfer. One day Susan’s golf foursome included a man named Henry Jones, a man-
ufacturer of Christmas ornaments. Henry explained to Susan that he manufactures an orna-
ment everyone loves, but stores will not carry the ornaments because they are very fragile and
often break during shipping. Susan told Henry about a plastic box she had developed recently
that would protect such fragile items during shipping. After crash testing the plastic box, Henry
offered Susan a contract to purchase 100,000 of the boxes for $2.20 each. Susan is convinced
that the box has many applications and that she can obtain future orders. Production of the
plastic boxes will take one year. Estimated costs for the first year are as follows:
Lease payments on building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $800 per month
Lease payments on machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2,200 per month
Cost to retool machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $10,000
Depreciation on machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $9,600
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.70 per box
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.30 per box
Indirect materials and other manufacturing overhead . . . . . . . . . . . . . . . . . $10,000
Interest on loan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2,500
Administrative salaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $15,000
Required:
1. Using the information provided, determine Susan’s contribution margin and projected profit
at a sales level of 100,000 boxes.
2. If Susan’s salary as an attorney is $44,500, determine how many boxes Susan must sell to
earn profits equal to her salary.
Functional and Contribution Margin Income Statements
Bassically Jammin’, Inc. (BJI) is a retail outlet for customized bass guitars. The average cost of
a bass guitar to the company is $1,000. BJI includes a markup of 50% of cost in the sales price.
In 2006, BJI sold 380 bass guitars and finished the year with the same amount of inventory it
had at the beginning of the year. Additional operating costs for the year were as follows:
Selling expenses:
Advertising (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 700 per month
Commissions (mixed) . . . . . . . . . . . . . . . . . . . . . . . . . . 3,000 per month plus 2% of sales
Depreciation (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 per month
Utilities (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 per month
Freight on delivery (variable) . . . . . . . . . . . . . . . . . . . . . 20 per bass guitar
Administrative expenses:
Salaries (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $4,200 per month
Depreciation (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 per month
Utilities (fixed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 per month
Clerical (variable) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 per sale
Required:
1. Prepare a traditional income statement using the functional approach.
2. Prepare an income statement using the contribution margin format.
3. Interpretive Question: Which statement is more useful for decision making? Why?
E O C 101 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-4
Problem 2-5
Contribution Margin and Functional Income Statements
The following information is available for Dabney Company for 2006:
Sales revenue (at $20 per unit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $151,200
Fixed manufacturing costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24,000
Variable manufacturing costs (at $8 per unit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,480
Fixed selling expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70,000
Variable selling expenses (at $2 per unit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15,120
Required:
1. Prepare a contribution margin income statement.
2. Prepare a functional income statement.
3. Calculate the number of units sold.
4. Calculate the contribution margin per unit.
5. Interpretive Question: Why is a knowledge of the contribution margin more useful than
a knowledge of the markup per unit when management has to make a decision about prof-
itability?
Unifying Concepts: High-Low Method, Contribution Margins, and Analysis
Press Publishing Corporation has two major magazines: Star Life and Weekly News. During
2006, Star Life sold 3 million copies at $1.00 each, and Weekly News sold 2.1 million copies
at $1.10 each. Press Publishing accumulated the following cost information:
Star Life Weekly News
Copies Manufacturing Copies Manufacturing
Month Produced Cost Produced Cost
January 400,000 $170,000 300,000 $170,000
February 300,000 150,000 150,000 105,000
March 400,000 180,000 130,000 100,000
April 200,000 120,000 120,000 90,000
May 250,000 140,000 200,000 130,000
June 200,000 125,000 250,000 150,000
July 240,000 130,000 150,000 110,000
August 200,000 130,000 200,000 135,000
September 180,000 110,000 150,000 105,000
October 230,000 130,000 150,000 108,000
November 200,000 125,000 150,000 115,000
December 200,000 126,000 150,000 112,500
Required:
1. Use the high-low method to estimate the per-unit variable and total fixed manufacturing
costs of each magazine. (Round the variable cost rate to three decimal places.)
2. If all selling expenses are fixed and they total $500,000 for Star Life and $400,000 for
Weekly News, prepare contribution margin income statements for the two magazines at sales
of 3 million copies each.
3. Which magazine is more profitable at sales of 2 million copies?
4. Interpretive Question: If the same total dollar amount spent on either magazine will result
in the same number of new subscriptions, which magazine should be advertised?
Contribution Margin Analysis
Clearview Company is a manufacturer of glass vases. The following information pertains to
Clearview’s 2006 sales:
102 Part 1 E O C Foundations
Problem 2-6
Problem 2-7
Problem 2-8
Sales price per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 32
Variable costs per unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Total fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500,000
Required:
1. Determine Clearview Company’s per-unit contribution margin and contribution margin
ratio.
2. Using the per-unit contribution margin and the contribution margin ratio, compute:
a. The break-even point in sales dollars and units.
b. The sales volume (in dollars and units) needed to generate a target income of $75,000.
3. Using the equation approach of C-V-P analysis, compute:
a. The break-even point in sales dollars and units.
b. The sales volume (in dollars and units) needed to generate a 15% return on sales.
Break-Even Analysis
Jane Tamlyn paid $225 to rent a carnival booth for four days. She has to decide whether to
sell doughnuts or popcorn. Doughnuts cost $1.80 per dozen and can be sold for $3.60 per
dozen. Popcorn will require a $113 rental fee for the popcorn maker and $0.08 per bag of pop-
corn for the popcorn, butter, salt, and bags; a bag of popcorn could sell for $0.45.
Required:
1. Compute the break-even point in dozens of doughnuts if Jane decides to sell doughnuts
exclusively and the break-even point in bags of popcorn if she decides to sell popcorn
exclusively.
2. Jane estimates that she can sell either 75 doughnuts or 45 bags of popcorn every hour the
carnival is open (10 hours a day for four days). Which product should she sell?
3. Jane can sell back to the baker at half cost any doughnuts she fails to sell at the carnival.
Unused popcorn must be thrown away. If Jane sells only 70% of her original estimate,
which product should she sell? (Assume that she bought or produced just enough to satisfy
the demands she originally estimated.)
C-V-P Graphic Analysis
Using the graph below, complete the requirements.
E O C 103 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-9
Problem 2-10
$35
30
25
20
15
10
5
1 2 3 4 5 6 7 8 9 10 11
Volume (in hundreds of units)
C
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t
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a
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0
Required:
1. Determine the following:
a. The break-even point in sales dollars and volume.
b. The sales price per unit.
c. Total fixed costs.
d. Total variable costs at the break-even point.
e. The variable cost per unit.
f. The unit contribution margin.
2. What volume of sales must the company generate to reach a target income of $7,500?
Contribution Margin Analysis—Changes in Variables
SMC, Inc., is a producer of hand-held electronic games. Its 2006 income statement was as
follows:
SMC, Inc.
Contribution Margin Income Statement
For the Year Ended December 31, 2006
Total Per Unit
Sales revenue (150,000 games) . . . . . . . . . . . . . . . . . . . . . . . . . . . $5,250,000 $35
Less variable costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,750,000 25
Contribution margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1,500,000 $10
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 600,000
In preparing its budget for 2007, SMC is evaluating the effects of changes in costs, prices, and
volume on profit.
Required:
1. Evaluate the following independent cases, and determine SMC’s 2007 budgeted profit or
loss in each case. (Assume that 2006 figures apply unless stated otherwise.)
a. Fixed costs increase $150,000.
b. Fixed costs decrease $100,000.
c. Variable costs increase $3 per unit.
d. Variable costs decrease $4 per unit.
e. Sales price increases $5 per unit.
f. Sales price decreases $5 per unit.
g. Sales volume increases 25,000 units.
h. Sales volume decreases 15,000 units.
i. Sales price decreases $4 per unit, sales volume increases 40,000 units, and variable costs
decrease by $2.50 per unit.
j. Fixed costs decrease by $100,000, and variable costs increase $4 per unit.
k. Sales volume increases 30,000 units, with a decrease in sales price of $2 per unit. Variable
costs drop $1.50 per unit, and fixed costs increase $50,000.
2. What sales volume in units would be needed to realize $1,000,000 in profit if SMC reduces
its price to $30?
Income Statement and Break-Even Analysis
Zimmerman Company records the following costs associated with the production and sale of
a steel slingshot:
Selling expenses:
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $6,500
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.50 per unit sold
Administrative expenses:
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $4,500
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $0.25 per unit sold
Manufacturing costs:
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $15,500
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $7.50 per unit produced
Required:
Assume that in 2006 the beginning and ending inventories were the same. Also assume that
2006 sales were 11,000 units at $11.50 per slingshot.
104 Part 1 E O C Foundations
Problem 2-11
Problem 2-12
1. Prepare a contribution margin income statement.
2. Determine the break-even point in sales dollars.
3. Interpretive Question: Zimmerman believes that sales volume could be improved 20% if
an additional commission of $0.50 per unit were paid to the salespeople. Zimmerman also
believes, however, that the same percentage increase could be achieved through an increase of
$3,000 in annual advertising expense. Which action, if either, should Zimmerman take? Why?
C-V-P Analysis—Changes in Variables
Wonder T Manufacturing Company produces lanterns. The firm has not been as profitable as
expected in the past three years. As a result, it has excess capacity that could be used to pro-
duce an additional 20,000 lanterns per year. However, any production above that amount would
require a capital investment of $100,000. Operating results for the previous year are shown
here. Assume that there is never any ending inventory.
Sales revenue (31,250 lanterns ? $40) . . . . . . . . . . . . . . . . . . . . . . $1,250,000
Variable costs (31,250 lanterns ? $25) . . . . . . . . . . . . . . . . . . . . . . $781,250
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400,000 1,181,250
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 68,750
Required:
Respond to the following independent proposals, and support your recommendations:
1. The production manager believes that profits could be increased through the purchase of
more automated production machinery, which would increase fixed costs by $100,000 and
reduce the variable costs by $2.00 per lantern. Is she correct if sales are to remain at 31,250
lanterns annually?
2. The sales manager believes that a 10% discount on the sales price would increase the sales vol-
ume to 40,000 units annually. If he is correct, would this action increase or decrease profits?
3. Would the implementation of both proposals be worthwhile?
4. The sales manager believes that an increase in sales commissions could improve the sales vol-
ume. In particular, he suggests that an increase of $2.50 per lantern would increase the sales
volume 30%. If he is correct, would this action increase profits?
5. The accountant suggests another alternative: Reduce administrative salaries by $15,000 so
that prices can be reduced by $0.50 per unit. She believes that this action would increase
the volume to 35,000 units annually. If she is correct, would this action increase profits?
6. The corporate executives finally decide to spend an additional $42,000 on advertising to
bring the sales volume up to 34,050 units. If the increased advertising can bring in these
extra sales, is this a good decision?
C-V-P Analysis—Return on Sales
The federal government recently placed a ceiling on the selling price of sheet metal produced
by MOB Company. In 2006, MOB was limited to charging a price that would earn a 20% re-
turn on gross sales. On the basis of this restriction, MOB had the following results for 2006:
Sales revenue (1,150,000 feet at $2.00 per foot) . . . . . . . . . . . . . . $2,300,000
Variable costs (1,150,000 feet ? $1.40) . . . . . . . . . . . . . . . . . . . . . $1,610,000
Fixed costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230,000 1,840,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 460,000
In 2007, MOB predicted that the sales volume would decrease to 900,000 feet of sheet metal.
With this level of sales, however, the company anticipated no changes in the levels of fixed and
variable costs.
Required:
1. Determine MOB’s profit for 2007 if all forecasts are realized. Compute both the dollar
amount of profit and the percentage return on sales.
E O C 105 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-13
Problem 2-14
(continued)
2. MOB plans to petition the government for a price increase so that the 2006 rate of return
on sales (20%) can be maintained. What sales price should the company request, based on
2007 projections? (Round to the nearest cent.)
3. How much profit (in dollars) will MOB earn in 2007 if this sales price, as determined in
part (2), is approved?
4. Interpretive Question: What other factors must be considered by MOB and the government?
Unifying Concepts: C-V-P Analysis and Changes in Variables
The 2006 pro-forma income statement for Grover Company is as follows (ignore taxes):
Grover Company
Pro-Forma Income Statement
For the Year Ended December 31, 2006
Sales (50,000 units) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $450,000
Cost of goods sold:
Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 35,000
Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60,000
Variable manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . 14,000
Fixed manufacturing overhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5,000
Total cost of goods sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114,000
Gross margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $336,000
Selling expenses:
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 45,000
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102,000
Administrative expenses:
Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15,000
Fixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75,000
Total selling and administrative expenses . . . . . . . . . . . . . . . . . . . 237,000
Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 99,000
Required:
1. Compute how many units must be sold to break even.
2. Compute the increase (decrease) in profit under the following independent situations:
a. Sales increase 25%.
b. Fixed selling and administrative expenses decrease 5%.
c. Contribution margin decreases 20%.
3. Compute sales in units and dollars at the break-even point if fixed costs increase from
$182,000 to $224,800.
4. Compute the number of units that must be sold if expected profit is $1 million.
Least Squares Methods
This problem uses the same data for Press Publishing Corporation as displayed in Problem 2-7.
Required:
Use the least squares method to estimate the per-unit variable and total fixed manufacturing
costs of the Star Life and Weekly News magazines. (Round the variable cost rate to three deci-
mal places.)
106 Part 1 E O C Foundations
Problem 2-15
Problem 2-16
Unifying Concepts: High-Low, Scattergraph, and Least Squares Methods
You have been hired as a consultant for Jones Inc. The company manufactures high-density
compact disks and sells them to a wide variety of business clients. Management is eager to learn
more about the company’s cost behavior. You have been provided the following data. Assume
all production falls within the relevant range.
Month Machine Hours Utility Costs
January 290 $10,700
February 280 10,400
March 320 11,600
April 340 12,100
May 350 12,400
June 290 10,750
July 300 10,800
August 300 10,900
September 310 11,200
October 340 12,200
November 290 10,600
December 310 11,000
Required:
1. Using the high-low method, compute the variable and fixed elements of Jones’ utility costs.
2. Plot the information on a scattergraph. Based on your graph, determine the unit variable
cost and monthly fixed costs.
3. Using the least squares method (either the equation approach or a software package), calcu-
late the variable and fixed cost components. Determine the cost formula.
4. Interpretive Question: Why are the variable cost per unit and fixed costs different for each
of these methods of analysis? Which method is the most accurate for determining variable
and fixed cost components?
Sales Mix
Mike’s Ice Cream Company produces and sells ice cream in three sizes: quart, half-gallon, and
gallon. Relevant information for each of the sizes is as follows:
Quart Half-Gallon Gallon
Average sales price . . . . . . . . . . . . . . . . . . . . . . . . . . $1.00 $1.85 $3.60
Less variable cost . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.80 1.40 2.40
Unit contribution margin . . . . . . . . . . . . . . . . . . . . . . $0.20 $0.45 $1.20
Sales mix (% of sales) . . . . . . . . . . . . . . . . . . . . . . . . 15% 60% 25%
Mike anticipates sales of $500,000 and fixed costs of $120,000 in 2006.
Required:
1. Determine the break-even sales volume in units and dollars for 2006.
2. Determine Mike’s 2006 projected profit.
3. Assume that Mike’s sales mix changes to 10% quarts, 40% half-gallons, and 50% gallons.
Determine Mike’s break-even sales volume in units and dollars.
Unifying Concepts: Break-Even Point and Operating Leverage
The summary data are provided on the following page for Spencer Mercantile Corporation and
James Service, Inc. During the year for which these data are reported, Spencer sold 50,000 units
and James sold 100,000 units.
E O C 107 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Problem 2-17
Problem 2-18
Problem 2-19
(continued)
Spencer James
(000’s omitted) Mercantile Corporation Service, Inc.
Sales revenue . . . . . . . . . . . . . . . . . . . . . . . . . $1,040 $2,100
Less variable costs . . . . . . . . . . . . . . . . . . . . . 520 630
Contribution margin . . . . . . . . . . . . . . . . . . . . $ 520 $1,470
Less fixed costs . . . . . . . . . . . . . . . . . . . . . . . 200 600
Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 320 $ 870
Required:
1. Determine the break-even point for Spencer and James in both sales dollars and units.
2. Interpretive Question: Which company has a higher operating leverage? Why?
3. Interpretive Question: Based on your analysis of the cost structures of Spencer and James,
which company’s cost structure is better? What factors are important to consider in answer-
ing such a question?
108 Part 1 E O C Foundations
Case 2-1
Colorado Outdoors Federation
The Colorado Outdoors Federation sponsors an annual ban-
quet. This year the guest speaker is a noted wildlife photog-
rapher and lecturer. In planning for the event, the group’s
treasurer has determined the following costs:
Rental of meeting facility . . . . . . . . . . . . . . . . . . . . . . $250
Honorarium for speaker . . . . . . . . . . . . . . . . . . . . . . . 800
Tickets and advertising . . . . . . . . . . . . . . . . . . . . . . . 300
Cost of dinner (per person) . . . . . . . . . . . . . . . . . . . . 20
Door prizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
Last year, tickets were sold at $20 per person, and 350 peo-
ple attended the banquet. This year the planning committee
is hoping for an attendance of 450 at a price of $25 each.
1. a. At $25 per person, how many people must attend
the banquet for the Federation to break even?
b. How much profit (loss) will occur if 450 people attend?
2. Should the Federation increase its advertising costs by
$200 and its door prizes by $300 if it can expect 550
people to attend the banquet?
3. If the Federation maintains its original expected costs but
reduces the price per ticket from $25 to $22, it can ex-
pect 500 people to attend the banquet. Should the Feder-
ation reduce the price of its tickets to $22 per person?
Case 2-2
Entertainment Enterprises
Entertainment Enterprises, a firm that sells magazine sub-
scriptions, is experiencing increased competition from a num-
ber of companies. The president, Betty Kincher, has asked
you, the controller, to prepare an income statement that will
highlight the fixed and variable costs; this will provide more
useful information for planning and control purposes. Sales
revenues are $25 per subscription. An analysis of company
costs for the past six months reveals the following:
Administrative salaries . . . . . . . . . $10,000 per month
Advertising expense . . . . . . . . . . . $2,000 per month
Cost of goods sold . . . . . . . . . . . . $12.50 per subscription
Rent expense . . . . . . . . . . . . . . . . $5,000 per month
Sales commissions . . . . . . . . . . . . 15% of sales
In addition, the company makes most sales contacts
through an extensive telephone network. Consequently, the
telephone expense is significant and has both fixed and vari-
able components. Relevant data concerning the telephone ex-
pense for the past six months follow:
Month Unit Sales Telephone Expense
July . . . . . . . . . . . 4,000 $10,200
August . . . . . . . . 5,000 12,300
September . . . . . . 3,500 9,150
October . . . . . . . . 4,500 11,250
November . . . . . . 5,200 12,720
December . . . . . . 5,500 13,350
Prepare a management report for the president that:
1. Computes the fixed and variable portions of the tele-
phone expense using the high-low method. (Note: A scat-
tergraph may be used to visually check your answer.)
d i s c u s s i o n c a s e s
2. Presents a budgeted (pro-forma) contribution margin in-
come statement for Entertainment Enterprises for the
next six months (January through June), assuming that it
expects to sell 30,000 subscriptions at a price of $25
each.
3. Explains how the information provided in part (2) might
help the president make better management decisions.
C E O 109 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Judgment 2-1
You Decide: Should the management of a
company consider fixed costs in the decision-
making process, or should they ignore fixed
costs and base their decision on what makes
the most business sense?
Recently, the board of directors for a television manufactur-
ing company was considering a change in products from TVs
to computers. The board claims, after performing a C-V-P
analysis of a new computer manufacturing plant facility, that
the computer industry is more profitable and would increase
the bottom line immediately. However, just six months ear-
lier, the company built a state-of-the-art television manufac-
turing plant. The overhead costs on the television plant
represent a sizable portion of the company’s fixed costs. If the
board voted to begin computer manufacturing, a new plant
would need to be constructed. What should the board do?
Judgment 2-2
You Decide: Should companies have large
amounts of inventory on hand for customers,
or should companies keep inventory at a
minimum to free up cash for other parts of the
business?
Your uncle, Tim, started a very successful “home improve-
ment” business 10 years ago. He wanted to create a place where
people could go to get anything they needed to complete their
“do-it-yourself” home building projects. Coupled with excel-
lent service, Tim believes that he can gain and retain customers
by having a large assortment of inventory from which to
choose. In addition, he can obtain significant purchase dis-
counts by buying the inventory in large bulk. You argue that
maintaining amounts of inventory requires significant com-
mitments to fixed warehousing and other costs that could be
avoided by setting up an e-commerce Web site and taking cus-
tomer orders that are then acquired and delivered one cus-
tomer at a time. Although this approach will increase the
overall variable costs as a result of not receiving bulk discounts
on the smaller individual orders, you are able to demonstrate
with C-V-P analysis that there is less risk in your approach
to selling home improvement products. Your uncle strongly
argues that, “Having the inventory on hand for your cus-
tomers is the key to success. If I don’t have what they are look-
ing for, they will just go down the street to HOME DEPOT!
I have got to have inventory in the stores. There is no other
way!”
j u d g m e n t c a l l s
C o m p e t e n c y E n h a n c e m e n t O p p o r t u n i t i e s
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Analyzing Real Company Information
International Case
Ethics Case
Writing Assignment
The Debate
Internet Search
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The following additional assignments provide opportunities for students to develop critical thinking,
ethical perspectives, oral and written communication skills, experience with electronic research, and
teamwork through group and business activities.
110 Part 1 C E O Foundations
Analyzing Real Company Information
Analyzing 2-1 (Microsoft)
Annual revenues, as well as sales and marketing expenses, for the 1991–2002 years are pro-
vided below for MICROSOFT CORPORATION:
Microsoft Corporation (millions)
Year Sales and Marketing Expenses Annual Revenue
1991 $ 490 $ 1,847
1992 758 2,777
1993 1,086 3,786
1994 1,135 4,714
1995 1,564 6,075
1996 2,185 9,050
1997 2,411 11,936
1998 2,887 15,262
1999 3,238 19,747
2000 4,126 22,956
2001 4,885 25,296
2002 5,407 28,365
1. Operating output data, such as the number of software products sold each year, are not
provided in Microsoft’s Form 10-K. However, while it is a little odd to use revenues to pre-
dict marketing expense (instead of the other way around), it seems sensible that changes
in revenues can serve as an approximate measure of changes in the number of products
sold by Microsoft. Use the high-low method to analyze the data above to determine if
there is a relationship between revenues and sales and marketing expenses. (Hint: Don’t
round off the value you calculate for variable costs per revenue dollar.) What appears to be
the amount of fixed costs in these expenses? Does this fixed cost amount make sense?
(Note: Remember that the data are in millions of dollars!)
2. Using your calculator (or some computer software program such as Microsoft Excel
®),
compute a regression analysis on the data above. What do you learn from the analysis?
The Management’s Discussion in Microsoft’s 2002 Form 10-K generally uses the following
language to describe changes to sales and marketing expenses: “Sales and marketing ex-
penses increased due to higher relative headcount-related costs, higher marketing and
sales expenses associated with MSN (Microsoft’s popular portal destination on the Web),
the Microsoft Agility advertising campaign, and other new sales initiatives.” Does this
statement provide any help in understanding the analysis? (Hint: When setting up to per-
form the regression, remember that the revenue is the X variable and the sales and market-
ing expense is the Y variable.)
Analyzing 2-2 (Star Video)
It is likely that a number of grocery stores in your town have video rental departments. Gener-
ally, however, grocery stores do not focus much management attention on their small video
rental businesses. The main purpose of having a video department is to encourage more cus-
tomers to come into the store and purchase groceries! Nevertheless, a grocery store cannot
simply buy a large selection of videotapes, corner off a section of floor space, and start renting
tapes. Successfully managing a rental business requires being aware of an unimaginably large
number of video titles. Obviously, new movies are constantly being released, while old movies
gradually lose their appeal and are eventually scrapped. Further, large-scale video rental chains
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C E O 111 Chapter 2 Analyzing Cost-Volume-Profit Relationships
such as BLOCKBUSTER constantly track shifting consumer tastes for certain titles and movie
categories. These consumer preferences differ based on demographic data like geographic loca-
tion, average age, ethnicity, average income, etc. A grocery store really can’t manage all these
data without losing focus on its main business. Hence, most grocery stores contract out their
video rental business to a large-scale video management company. These management compa-
nies can purchase huge quantities of tapes, maintain large distribution warehouses, and track
demographic data that allow them to manage and move specific inventories to the appropriate
grocery store locations. In 1992, one such video management company, Star Video (not its real
name), was managing 86 stores representing three supermarket chains in five states—Arizona,
California, Montana, Washington, and Wyoming. Total revenue in 1992 for Star Video was $3.6
million. Star Video made all the inventory investments and handled all management activities
involved in providing video rentals at each of the 86 stores. Video rental revenue was then split
between Star Video and each grocery store, with Star Video keeping the lion’s share. Stores
liked this arrangement because they made most of their money on grocery sales to customers
who came to rent videotapes. Star Video needed to carefully manage revenue and costs at each
store in order to stay profitable. Following are the data for six stores located in Washington:
Monthly
Monthly Operating
Store Name Revenue Expenses
Moses Lake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 6,408 $ 3,295
W. Kennewick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,264 2,289
Pasco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,038 2,270
S. Kennewick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,692 2,142
E. Wenatchee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,395 1,316
Richland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2,104 1,516
Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $21,901 $12,828
Use the high-low method to analyze the operating expenses at these six stores. Determine if
operating expenses are related to store revenue. What appear to be the fixed costs of operating
each store? Create a graph and plot these costs using revenue on the horizontal axis and oper-
ating expenses on the vertical axis. Does the scattergraph agree or disagree with the results of
your high-low analysis?
International Case
The Paper Company
The GHANATA GROUP OF COMPANIES (GGC) is a locally owned and controlled company in Ghana,
West Africa. One of its principal operating divisions, THE PAPER COMPANY, is one of Africa’s
most modern and largest manufacturers/distributors of paper products. For both operating and
reporting purposes, The Paper Company is organized into product lines: scholastic, envelope, and
stationery. During the 1980s, the economy in Ghana was stagnant. The country faced severe eco-
nomic problems as a result of unfavorable trade terms with other countries. The official exchange
rate of U.S. $1.00 to the local currency, the cedi, was about 39.00 as of the end of 1984. (The
unofficial rate, e.g., the black market rate, was at least five times worse!) As a result of the
economy, it became very difficult for GGC to secure direct materials for its divisions. If a divi-
sion could secure direct materials, it could sell almost everything it produced. Hence, in terms
of being able to predict sales volumes, there was a great deal of risk for GGC divisions. The
1985 budgeted operating data for the three departments in The Paper Company were as follows:
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112 Part 1 C E O Foundations
The Paper Company
1985 Budgeted Operations Data
(Cedi 000’s)
Scholastic Envelope Stationery
Budgeted sales . . . . . . . . . . . . . . . . . . . . . . . $ 1,785,000 $ 984,000 $ 3,334,050
Budgeted variable costs . . . . . . . . . . . . . . . . . (410,550) (442,800) (2,200,473)
Contribution margin . . . . . . . . . . . . . . . . . . . $ 1,374,450 $ 541,200 $ 1,133,577
Budgeted fixed costs . . . . . . . . . . . . . . . . . . . (1,267,350) (482,160) (933,534)
Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 107,100 $ 59,040 $ 200,043
Using these operating data, create C-V-P graphs for each department. (Note: Since you don’t
have per-unit prices and costs, you may assume that the product sales price for each depart-
ment is $1 per unit, and then plot your graphs at 0, 2 million, and 4 million units.) Given the
high-risk business environment in Ghana at this time, which department presents the highest
risk to GGC? The lowest risk? Be sure to explain your answer in terms of operating leverage.
You may also want to consider each department’s break-even point compared to budgeted (ex-
pected) operations.
Source: A. Oppong, “The Paper Company,” The Journal of Accounting Case Research, Vol. 3, No. 2 (1996), pp.
80–88. Permission to use has been granted by Captus Press, Inc. and the Accounting Education Resource Centre
of The University of Lethbridge. [Journal Subscription: Captus Press, Inc., York University Campus, 4700 Keele
Street, North York, Ontario, M3J 1P3, by calling (416) 736-5537, or by fax at (416) 736-5793, E-mail:
[email protected], Internet:http://www.captus.com]
Ethics Case
Pickmore International
Joan Hildabrand is analyzing some cost data for her boss, Ross Cumings. The data relate to a
special sales order that Pickmore International is considering from a large customer in Singa-
pore. The following data are applicable to the product being ordered:
Normal unit sales price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $49.95
Variable unit manufacturing costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.50
Variable unit selling and administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.25
The customer is requesting that the sales order be accepted on the following terms:
a. The unit sales price would equal the unit contribution margin plus 10%.
b. Freight would be paid by the customer.
c. Pickmore International would pay a $5,000 “facilitating payment” to a “friend of the cus-
tomer” to get the product through customs more quickly.
In considering the order, Ross has indicated to Joan that this is a very important customer.
Furthermore, this work would help some employees earn a little extra Christmas money with
overtime.
1. What are the accounting and ethical issues involved in this case?
2. Should Joan recommend acceptance of the sales terms proposed for this special order?
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C E O 113 Chapter 2 Analyzing Cost-Volume-Profit Relationships
Writing Assignment
Issues of Quality and Time on C-V-P Analysis Decisions
This chapter described how to analyze whether the difference between sales price and variable
costs, as well as the volume of sales, is sufficient to pay for all fixed costs in an organization
and provide a sufficient profit. A number of methods have been presented for analyzing these
costs, volume, and price relationships. These methods all focus on quantitative issues that af-
fect how a company manages its resources to maximize overall profits. However, there are a
number of qualitative issues involving quality and time that should also affect decisions about
what sales prices to set, how to manage fixed and variable costs, and which products should be
emphasized within the organization. One way to trade off fixed costs for variable costs is to
consider making large fixed cost investments in technology that result in automated produc-
tion, merchandising, and service processes. These kinds of investments allow some variable
costs, such as direct labor, to be reduced. Managing this cost trade-off often has strong impli-
cations on the quality of the product or service, as well as the timeliness with which it can be
delivered. Both of these qualitative issues eventually affect the quantitative issues of costs,
volume, and price. Go to your library and find an article describing one organization’s effort to
invest in automation or other technologies in order to reduce costs. Determine what quality
and time issues are affected by the investment. Write a one- to two-page memo describing
what you found.
The Debate
Which Cost Analysis Method Is Better?
Many costs within an organization are mixed costs, combining elements of both fixed and vari-
able costs. Separating these types of costs into their fixed and variable cost components is
necessary before C-V-P analysis work can be done. Two potential cost analysis methods are the
scattergraph (visual-fit) approach and the high-low approach. Each of these methods has both
disadvantages and advantages compared to the other.
Divide your group into two teams and prepare a two-minute oral argument supporting your
assigned position.
• One team represents “The scattergraph (visual-fit) method is superior!” Explain why this method
should be used for determining the variable and fixed cost components in a mixed cost.
• The other team represents “High-low; the way to go!” Explain why this method should be
used for determining the variable and fixed cost components in a mixed cost.
Internet Search
Applied Ethics Resources on WWW
We have discussed ethical issues for accountants in this text and have included an ethics case
at the end of each chapter. Obviously, ethical issues are of concern to accountants and all
other business professionals. There are a number of good resources on the Internet for those
interested in further exploring ethical issues in business (hopefully, we’re all interested in this
topic!). One of the better sites is Applied Ethics Resources on WWW Centre athttp://www
.ethicsweb.ca/resources/. Sometimes Web addresses change, so if this address doesn’t work,
access the Web site for this textbook (http://swain.swlearning.com) for an updated link.
Go to this site and explore the materials regarding applied ethics resources on the World
Wide Web. Find a publication that discusses either business or professional ethics. Write a short
paragraph that describes exactly where you found the article and give a brief summary.
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