CHAPTER 3

COST-VOLUME-PROFIT ANALYSIS
LEARNING OBJECTIVES
1. Understand the assumptions underlying cost-volume-profit (CVP) analysis
2. Explain the features of CVP analysis
3. Determine the breakeven point and output level needed to achieve a target operating income using the
equation, contribution margin, and graph methods
4. Understand how income taxes affect CVP analysis
5. Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with
uncertainty
6. Use CVP analysis to plan fixed and variable costs
7. Apply CVP analysis to a company producing different products
8. Adapt CVP analysis to situations in which a product has more than one cost driver
9. Distinguish between contribution margin and gross margin

CHAPTER OVERVIEW
Chapter 3 presents the cost-volume-profit (CVP) analysis model. Much what-if knowledge may be
derived from the use of a model, certainly the case with CVP analysis. Models are developed from
known relationships and used for forecasting. CVP uses one cost driver, volume of units produced and
sold, and uses the behavior of costs, variable or fixed, in relation to that cost driver. As with all models, a
complex situation is simplified. The assumptions of CVP analysis identify the simplifications made.
Throughout the chapter, reference is made to changes in the CVP model to allow for more complexity.
The complexities do not render the model useless, they generally require additional factors be considered
for producing better predictions.
Relevant information for strategic and planning decisions can be made readily available. The text focuses
on accountants providing value for decision makers. CVP analysis is a useful tool for providing
cost/beneficial information on a timely basis. The basic CVP model deserves careful study. The last
section of the appendix is noteworthy. With the emphasis on decision making in the text, the point made
about distinguishing between a good decision and a good outcome and/or a good decision and a bad
outcome seems especially relevant.

Cost-Volume-Profit Analysis

27

TEACHING TIP: An excellent article on the value of models is Going Forward in Reverse by Einhorn
& Hogarth, Harvard Business Review, Jan./Feb. 1987, pp. 66-70.

CHAPTER OUTLINE
I.
I

Basic Cost-Volume-Profit (CVP) model

A. Definition of CVP analysis: examines the behavior of total revenues, total costs, and operating
income as changes occur in output level, selling price, variable cost per unit, and/or fixed costs

Learning Objective 1:
Understand the assumptions underlying cost-volume-profit (CVP) analysis
B. Assumptions
1. Simplifications of complex relationships
a. Number of output units only revenue driver and only cost driver
b. Total costs can be separated into the primary categories of variable costs and fixed costs
c. Total revenues and total costs are linear within the relevant range (and time period)
d. Unit selling price, unit variable costs, and fixed costs known and constant
e. Single product or constant sales mix
f.

Time value of money effects ignored

2. Complexities noted in chapter that affect basic model

a. Multiple revenue and multiple cost drivers
b. Lack of linearity
Do multiple choice 1.

Assign Exercise 3-16.

Learning Objective 2:
Explain the features of CVP analysis
C. Features and terminology
1. Income model: Revenues Expenses = Income
2. Contribution margin: Total revenues Total variable costs
a. Calculated per unit: Selling price/unit Variable cost/unit [Exhibit 3-1]
b. Calculated as a percent of sales or ratio: Contribution Margin/Sales
c. Calculated as a total: Sales (Revenues) Variable costs

28 Chapter 3

3. Multiple-step-type income statement: Rev VC = CM FC = OI

4. Operating income versus Net income
a. OI + Nonoperating Rev. Nonoperating Costs Income Tax = NI
b. Chapter 3 assumes zero for nonoperating revenues and expenses
Do multiple choice 2.

Assign Exercises 3-17 and 3-20.

II. Breakeven concept

A. Definition of breakeven point: quantity of output sold at which total revenues equal total costs
Learning Objective 3:
Determine the breakeven point and output level needed to achieve a target operating income using the
equation, contribution margin, and graph methods
B. Contribution margin approach to calculation
1. Equation method: (USP x Q) (UVC x Q) FC = OI
2. Contribution margin method
a. Per unit approach that calculates breakeven in units of output [Use algebraic equation
UCM x Q = FC + OI >UCM x Q = Total CM to calculate Q , units, as FC + OI = CM]
b. Ratio or percentage approach that calculates breakeven in dollars of revenue [Use
equation CM% x Revenues = FC + OI>CM% x Revenues = Total CM to calculate
Revenues by dividing both sides by CM%: CM% = CM/Revenues]
3. Graph method: x-axis output units, y-axis dollars; total revenue and total cost lines intersect at
breakeven output quantity [Exhibits 3-2 and 3-3]
Do multiple choice 3.

Assign Exercises 3-21 and 3-23 and Problem 3-34.

TEACHING TIP: Exercise 3-23 is a good example to use before studying sales mix. This exercise uses
an average revenue amount for the calculations. When studying sales mix, referencing an average sales
check per customer provides an illustration of differing products, from a cup of coffee to a full dinner.
More sales checks for cups of coffee than for full dinners would change the average downward.
C. Useful for target income
1. Operating income: FC + Target OI can be divided by UCM for units of output or divided by
CM% for dollars of revenue (sales)
Learning Objective 4:
Understand how income taxes affect CVP analysis
2. Net income: Target OI must be adjusted by incorporating income tax
Cost-Volume-Profit Analysis

29

Target net income/(1 Tax rate) = Target operating income

TEACHING TIP: The use of the income statement format may be helpful to some students,
Target Operating Income
100%TOI
{
$40,000}
Tax (Tax Rate x TOI) 35%
-35%TOI
{.35x40,000
14,000}
Target Net Income
65%TOI = $26,000 > TOI = $26,000 / 0.65 = $40,000
3. Any of the three approaches for calculating breakeven may be used for target income
TEACHING TIP: A caution for students when calculating target income, especially if using total rather
than unit costs: variable costs in total are variable with respect to volume and will change if output units
change or are expected to change. Use of an equation with contribution margin is helpful. To calculate
revenues use the equation, CM% x Revenues = CM in total dollars, or to calculate output units, UCM x Q
= CM in total dollars. [CM in total dollars in equal to FC + target OI.]
Do multiple choice 4.

Assign Problem 3-36.

D. Effect of income taxes: BEP unaffected by income taxes because no tax is no operating income
Do multiple choice 5.

Assign Problem 3-39.

Learning Objective 5:
Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with
uncertainty
E. Useful for decision making
1. Can incorporate changes in total fixed costs, selling price per unit (changes CM per unit), unit
variable cost, and units sold
2. Helps managers by estimating long-term profitability of choices
3. Evaluates risk to operating income if original predicted data not achieved
III. Sensitivity analysis [Exhibit 3-4]
A. Definitions
1. Sensitivity analysis: what-if technique managers use to examine how a result will change
if original predicted data not achieved or if an underlying assumption changes
2. Uncertainty: possibility that an actual amount will deviate from an expected amount
B. Used before committing costs
1. Analysis of changes in operating income for changes underlying assumptions
2. Systematic and efficient approach

30 Chapter 3

3. Allows for calculation of margin of safety: amount of budgeted revenues over and above
breakeven revenues
4. [Appendix] Probability and expected value incorporated
Do multiple choice 6.

Assign Problems 3-38, 3-40 and 3-41.

Learning Objective 6:
Use CVP analysis to plan fixed and variable costs
II C. Highlights risks and returns
1. Highlights risks and returns as fixed costs are substituted for variable costs in cost structure
TEACHING TIP: A section in the chapter appendix references a managers attitude toward risk (each
decision has its own attitude as well as each manager has such an attitude). Following are descriptive
phrases for discussing risk attitudes: (1) risk neutral: decision maker weighs each dollar as a full dollar,
no more, no less; (2) risk averse: decision maker weighs loss of dollar as greater than gain of dollar; (3)
risk seeking: decision maker weighs gain of dollar as greater than loss of dollar.
2. Demand for product or service is variable [Exhibit 3-5]
3. Use of operating leverage: effect fixed costs have on changes in operating income as
changes occur in units sold (contribution margin)degree of operating leverage equals
contribution margin divided by operating income [Concepts in Action]
Do multiple choice 7.

Assign Exercise 3-26.

TEACHING TIP: Operating leverage is obviously named for the lever effect that comes from the use
of fixed costs to generate more profit. Costs are incurred to generate revenues. If the choice exists to
incur fixed or variable cost, and fixed is chosen, then variable cost would be less, yielding a larger
contribution margin and the possibility of larger profit. Once the fixed costs are recovered, the
contribution margin is profit. This effect can be seen on a breakeven graph. The intersecting revenue and
total cost lines create equal and opposite angles at the intersection point. One can note that the risk
(downside) is equal to the reward (upside). The larger the fixed cost, the wider the intersection angles
usually: the greater the opportunity for reward, the greater the possibility of loss.
4. Cost labels as fixed or variable
a. Time frame affects costs: shorter the time frame, more costs fixed
b. Relevant range assumes limits for constancy of total fixed costs or unit variable costs
c. Specific question/decision affects relevancy of cost classification
IV. Products and CVP: A complexity
Learning Objective 7:
Apply CVP analysis to company producing different products

Cost-Volume-Profit Analysis

31

A. Sales mix: CVP assumption for one product or a constant mix of different products
1. No unique breakeven point when selling a mix of multiple products: each new mix, a new
BEP
2. Profit varies even though same total quantity of units sold: Mix with more units of larger
dollar amount of contribution margin per unit yields greater profit{affects BEP}
3. Profit varies even though same total dollars of revenue: Mix with more units of larger
contribution margin ratio sold yields greater profit
Do multiple choice 8.

Assign Exercise 3-28 and Problems 3-44 and 3-46.

B. Service as a product
1. Define product or output unit for measurement
2. Use CVP model for relationship between revenues, variable costs and fixed costs
3. Use CVP analysis for prediction and consideration for adjusting operations
Learning Objective 8:
Adapt CVP analysis to situations in which a product has more than one cost driver
C. Multiple cost drivers
1. No unique breakeven point
2. CVP model can be adapted by changes to the variable cost for situation but simple formula
cannot be used
Do multiple choice 9.

Assign Exercise 3-30 and Problem 3-43.

Learning Objective 9:
Distinguish between contribution margin and gross margin
D. CVP uses contribution margin as opposed to gross margin* on financial accounting income
statements
1. Service-sector companies
a. Costs primarily classified as either variable or fixed for calculating contribution margin
b. Do not have cost of goods sold so cannot use gross margin emphasis
2. Merchandising-sector companies
a. Costs are primarily classified as either variable or fixed for calculating contribution
margin

32 Chapter 3

b. Costs are primarily classified as either cost of goods sold or operating costs for gross
margin emphasis
c. If any fixed costs were included in cost of goods sold, they would be reclassified as
operating costs for contribution margin emphasis
3. Manufacturing-sector companies
a. Costs primarily classified as variable or fixed for calculating contribution margin
b. Costs primarily classified as manufacturing or nonmanufacturing in calculating gross
margin
c. Variable nonmanufacturing costs above the margin line for contribution margin
calculation but below for gross margin
d. Fixed manufacturing costs above the margin line for gross margin calculation but
below for contribution margin
e. Fixed manufacturing costs used as per unit cost for cost of goods sold (gross margin) but
as total cost for contribution margin
4. For statement comparison purposes costs should be classified with both classifications
a. Variable manufacturing and variable nonmanufacturing
b. Fixed manufacturing and fixed nonmanufacturing
* Gross margin can be expressed as a total, as an amount per unit, or as a percentage. If gross margin is expressed
as a percentage the basis could be revenue or cost of goods sold. Conversion is simple from one base to the other,
but the base must be noted for one to know to convert. See TEACHING TIP for conversion.

TEACHING TIP: Quick conversion calculation for GM as a percentage of CGS or revenue:

Revenue
125%
100%
Revenue
100%
150%
CGS
100%
80%
CGS
66.7%
100%
Gross margin
25%
20%
Gross margin
33.3%
50%
Conversion: Divide GM (as a percentage of CGS) by revenue (when CGS is 100%) to convert GM to a
percentage of revenue: 25%/125% = 20%; a markup of 25% with a margin of 20% or for GM as a
percentage of CGS when originally given as percentage of revenue: 33.3%/66.7% = 50%; a margin of
33.3% with a markup of 50%.
Do multiple choice 10.

Assign Exercise 3-31.

V. Appendix: Decision models and uncertainty [Exhibit 3-6]

A. Use of a decision model
B. Identify events (differentiated from actions)
C. Consider past experience to project probabilities
D. Incorporate risk attitude
E. Distinguish between good decision and good outcome

Cost-Volume-Profit Analysis

33

CHAPTER QUIZ SOLUTIONS: 1.a

34 Chapter 3

2.c 3.b 4.a 5.c 6.d 7.b 8.c 9.b 10.d

CHAPTER QUIZ
1.

Which of the following is not an assumption of cost-volume-profit analysis?

a.
b.
c.
d.

2.

The time value of money is incorporated in the analysis.

Costs can be classified into variable and fixed components.
The behavior of revenues and expenses is accurately portrayed as linear over the relevant range.
The number of output units is the only driver.

Contribution margin is calculated as

a.
b.
c.
d.

total revenue total fixed costs.

total revenue total manufacturing costs (CGS).
total revenue total variable costs.
operating income + total variable costs.

Questions 35 are based on the following data:

Tee Times, Inc., produces and sells the finest quality golf clubs in all of Clay County. The company
expects the following revenues and costs in 2003 for its Elite Quality golf club sets:
Revenues (400 sets sold @ $600 per set)
Variable costs
Fixed costs
3.

How many sets of clubs must be sold for Tee Times, Inc., to reach their breakeven point?
a. 400

4.

c. 200

d. 150

b. 500

c. 400

d. 300

What amount of sales must Tee Times, Inc., have to earn a target net income of $63,000 if they have
a tax rate of 30%?
a. $489,000

6.

b. 250

How many sets of clubs must be sold to earn a target operating income of $90,000?
a. 700

5.

$240,000
160,000
50,000

b. $429,000

c. $420,000

d. $300,000

One way for managers to cope with uncertainty in profit planning is to

a.
b.
c.
d.

use CVP analysis because it assumes certainty.

recommend management hire a futurist whose work it is to predict business trends.
wait to see what does happen and prepare a report based on actual amounts.
use sensitivity analysis to explore various what-if scenarios in order to analyze changes in
revenues or costs or quantities.

Cost-Volume-Profit Analysis

35

7.

The Beta Mu Omega Chi (BMOC) fraternity is looking to contract with a local band to perform at its
annual mixer. If BMOC expects to sell 250 tickets to the mixer at $10 each, which of the following
arrangements with the band will be in the best interest of the fraternity?
a.
b.
c.
d.

8.

Twin Products Company produces and sells two products. Product M sells for $12 and has variable
costs of $6. Product W sells for $15 and has variable costs of $10. Twin predicted sales of 25,000
units of M and 20,000 of W. Fixed costs are $60,000 per month. Assume that Twin achieved its
sales goal of $600,000 for September, but fell short of its expected operating income of $190,000.
Which of the following descriptions best describes the actual results reported of revenue of $600,000
and operating income of less than $190,000?
a.
b.
c.
d.

9.

$2500 fixed fee

$1000 fixed fee plus $5 per person attending
$10 per person attending
$25 per couple attending

Twin sold 50,000 of M and no product W.

Twin sold more of both products M and W than expected.
Twin sold more of product W and less of product M than expected.
Twin sold more of product M and less of product W than expected.

In the situation of multiple cost drivers, CVP analysis can be

a. modified so that the various simple formulas can be used by applying them separately to each
cost driver.
b. used with the same formulas as used with a single cost driver.
c. changed by incorporating all of the cost drivers into the breakeven formula to calculate the
unique point of output at which the company would break even.
d. adapted by incorporating the cost drivers into the calculation of the variable costs.

10. Which of the following statements is true?

a. Gross margin can be used only in financial accounting income statements.
b. Gross margin implies a different cost classification usage than the term contribution margin
when used in income statements.
c. Contribution margin can be used in place of gross margin if management prefers that
terminology in their financial statements.
d. Only manufacturing-sector companies use the term gross margin in their income statements.

36 Chapter 3

WRITING/DISCUSSION EXERCISES
1. Understand the assumptions underlying cost-volume-profit (CVP) analysis

How helpful is a model, such as CVP analysis, if the assumptions on which it is based
seem too simplistic? Even the simplest models can be helpful. Models describe known relationships
and their use can prevent errors of omission by focusing on basic concepts and interactions as well as
enable learning. From a simple checklist to the most sophisticated artificial intelligence program, models
force one to take certain steps and combine factors in particular ways. Airline pilots, even the most
experienced, use a checklist before take-off to insure that they did not forget a key item. Models or
simulations are also helpful in teaching a person to perform a task.
The CVP analysis model is a cost-effective tool that managers can use for gathering relevant information
in the process of making decisions. The simple CVP relationships are helpful in strategic and long-range
planning decisions, for example. Knowing the assumptions of the basic model, one can incorporate
changes to refine or particularize for a given situation. The need for a more complex model is recognized
after using the basic ideas of the CVP analysis. The choice of incurring additional costs is supported for
gaining significant benefit of improved decisions with a more complicated and expensive approach.
2. Explain the features of CVP analysis

Why is contribution margin such an important element in CVP analysis? Contribution

margin is an effective summary of the reasons that operating income changes as the number of units sold
changes. Variable costs increase in total as volume of output units sold increase, the same behavior as
revenue. Contribution margin is the net or summary of those two elements, revenues and variable costs.
If revenues increase due to volume increases, the contribution margin increases. A change in the selling
price will change the contribution margin as will a change in variable cost per unit. Understanding
contribution margin can enable one to quickly note that an increase in selling price without a
corresponding change in variable cost will increase the contribution to fixed cost and income. Or a
decrease in variable cost without a corresponding decrease in selling price will contribute more to
income and/or the coverage of fixed costs. Using revenues and variable costs as per unit measures, the
contribution per unit of product sold can provide a shortcut to breakeven calculations or what-if
questions. Each unit of product sold contributes that amount as it walks out the door.
Contribution margin is the connecting link between the behavior of variable cost and fixed cost. It is the
amount that contributes to covering total fixed costs and providing income. In the calculation of
number of output units or total revenues to achieve targeted operating income, contribution margin is the
pivot point. The total amount of contribution margin, fixed costs in total added to targeted operating
income as a total, is equal to an amount of contribution margin per unit multiplied by the number of units
needed to be sold to achieve that desired amount of income. Contribution margin converts total dollars to
units.

Cost-Volume-Profit Analysis

37

3. Determine the breakeven point and output level needed to achieve target operating income
using the equation, contribution margin, and graph methods

How can a company have more than one breakeven point? CVP analysis suggests only one
breakeven point because of its assumptions. The authors of the text note that there is no unique breakeven
point in the case of multiple products and multiple cost drivers. Likewise a curved, rather than a straight
line depicting the time value with the compounding of interest allows for more than one breakeven point.
The CVP analysis assumptions preclude the use of these characteristics.
Economists note at least two breakeven points in graphing revenues and costs. The revenue line is
depicted as an upward arcing curve to the right intersecting the straight diagonal line of costs, forming a
type of bow (as in archerythe bow frame as revenue and the cost line as its cord). The first or lowest
point of intersection is the CVP analysis breakeven point. The second or upper point of intersection is
determined by the relationship in demand, quantity, and price. To keep or increase demand for the
product, the economic assumption is that the price must be reduced accordingly. Reducing the price will
tend to lower total revenue even though output quantity (supply) is increasing, which concurrently causes
increasing costs. CVP analysis recognizes these assumptions by imposing the relevant range and time
period constraints.
The question may be how can a company calculate only one breakeven point when realistically the point
at which loss becomes profit, or vice versa, can exist at many turns. The value of examining the
relationships between revenues and costs enables managers to avoid pitfalls. A simple or basic
calculation is a good starting point to understanding the complex interactions.
4. Understand how income taxes affect CVP analysis

What changes to CVP analysis would have to be made if a company did have
nonoperating revenues and expenses? The presence of nonoperating revenues and expenses
would not change CVP analysis. CVP analysis is an operations concept and accordingly uses operating
income. Tax effects on operating decisions are important information for managers and can be
incorporated by using net income. The text assumes the nonoperating items to be zero for ease of
computation. Most nonoperating items are noted net of tax, causing no change to the income tax on
operations. The use of the subtotal Income before income taxes is used to compute the amount of
income taxes in arriving at net income. Income before income taxes would be defined as target
operating income + nonoperating revenues nonoperating expenses.
Target net income = (Income before income taxes) [(Income before income taxes) x (Tax rate)]
Target operating income
+Nonoperating revenue
Nonoperating expense
Income before income tax
Income tax expense (30%)
Net income (targeted)

38 Chapter 3

$440,000
80,000
20,000
$500,000
150,000
$350,000

100%
30%
70%

5. Explain CVP analysis in decision making and how sensitivity analysis can help managers
cope with uncertainty

What ethical guidelines require a management cost accountant to use sensitivity

analysis when supplying a decision maker with information obtained from CVP analysis?
The following statements taken from the IMA Standards of Ethical Conduct for Management
Accountants may be used as discussion points:
Competence
Prepare complete and clear reports and recommendations after appropriate analysis of relevant and
reliable information.
Integrity
Communicate unfavorable as well as favorable information and professional judgments or opinions.
Objectivity
Communicate information fairly and objectively.
Disclose fully all relevant information that could reasonably be expected to influence an intended
users understanding of the reports, comments, and recommendations presented.
6. Use CVP analysis to plan fixed and variable costs
Can the use of CVP analysis change a cost from variable to fixed or vice versa? The use of CVP

analysis can cause a manager to consider alternative cost structures. The analysis does not change the
cost classification for that is based upon the total cost behavior in proportion to the volume of cost driver,
a causal relationship. However, from working through several scenarios of volume levels and the impact
each would have on revenues and cost within the existing company cost structure, a manager might make
specific choices to incur costs in such a way as to change the companys cost structures. The cost
structure could be changed from predominantly variable costs to more fixed costs, for example.
One industry, in particular, has become even better known because of its accounting practices:
Hollywood. Movies that seemingly are box office hits, grossing fabulous sums of money, fail to show
any net profit. Movies such as Forrest Gump, Coming to America, and Batman are a few that
represents net profits accounting. Popular actors and actresses along with directors and producers
receive a percentage of the movies gross receipts [variable costs before contribution margin] and then
have other large costs, such as production, distribution and marketing, and interest, to deduct after that.
After all of those deductions, even with the highest-grossing films, net profit is nonexistent or the film
shows a loss. Those who are able to get a share of the gross receipts find the pictures to be highly
profitable, but those who are to share in the net profit often end up with nothing.

Cost-Volume-Profit Analysis

39

7. Apply CVP analysis to a company producing different products

In his story of Don Quixote, Cervantes stated Forewarned forearmed. How is this
quote applicable to CVP analysis? With the help of CVP analysis, a manager can develop an
understanding of trade-offs when dealing with multiple products or sales mix. The manager can be
forewarned that the downturn in sales of one product in favor of another would have unfavorable
consequences on income. Through CVP analysis the manager can know to work to boost sales of the
products with the higher contribution margins as well as work to make each product more profitable .
The manager can also consider combinations of big sale products with lesser contribution margins teamed
with products that have greater margins but do not sell as well. Perhaps as a pair or group (and higher
selling price), more amount of margin could be made with the same level of sales. Being armed with a
variety of options helps the manager to make better decisions.
8. Adapt CVP analysis to situations in which a product has more than one cost driver

Does a company have multiple cost drivers because they have multiple products?
Multiple products could create the need to recognize multiple cost drivers but production is not the sole
determinant of the need for multiple cost drivers. Cost-volume-profit analysis is primarily focused on
operating income. Any costs are candidates for analysis and the cause of what drives them.
9. Distinguish between contribution margin and gross margin

Is breakeven point calculation exclusive of the contribution margin approach to

calculating income? (See Appendix to Chapter 9) Breakeven point calculations are easier from the
perspective of classifying costs as either fixed or variable rather than mixing those behaviors through the
manufacturing/nonmanufacturing classification of the gross margin approach of cost of goods sold.
The changing of the fixed manufacturing costs from a per unit (product) cost under gross margin
emphasis to a total cost for contribution margin emphasis means that a fixed manufacturing cost changes
from a product cost to a period cost. Fixed costs as a product unit cost means that if the amount of
product inventory (work in process and finished goods) changes within a time period, the amount of fixed
cost considered an expense (CGS) would differ based on the level of inventory. Using fixed
manufacturing costs as a total for the contribution approach, and therefore unchanging, means breakeven
analysis does not need to factor in changes in product inventory. This differentiation of how to account
for fixed costs is a major difference between the gross margin and contribution margin approaches to
calculating operating income. If production is different than sales, the income amount differs from
income statement to income statement. If absorption costing is used, income is a function of both sales
and production. Therefore, changes in inventory levels can dramatically affect income. The breakeven
point is not unique. There may be several combinations of sales and production that produce an income of
zero. The breakeven formula for absorption costing is:
BEP in units Q= Total FC incurred during period + Fixed Overhead Rates (BEP in units Q Units Produced)
Unit Contribution Margin

If all units produced are sold, the amount of fixed cost included in inventory is equal to the total fixed cost
incurred. The total fixed cost incurred would then be written off as cost of goods sold for gross margin
emphasis as well as written off as total fixed manufacturing cost for contribution margin emphasis. If
some units produced are not sold, then some of the fixed manufacturing costs would be housed with the
unsold inventory for gross margin emphasis. The contribution margin emphasis would write off all of the
cost.

40 Chapter 3

DEMONSTRATION PROBLEM
Dey and Knight are the owners of the Modern Processing Company and the Oldway Manufacturing
Company, respectively. These companies manufacture and sell the same product, and competition
between the two owners has always been friendly. Cost and profit data have been freely exchanged.
Uniform selling prices have been set by market conditions.
Dey and Knight differ markedly in their management thinking. Operations at Modern are highly
mechanized, and the direct labor force is paid on a fixed-salary basis. Oldway uses manual hourly paid
labor for the most part and pays incentive bonuses. Moderns salesmen are paid a fixed salary, whereas
Oldways salesmen are paid small salaries plus commissions. Mr. Knight takes pride in his ability to
adapt his costs to fluctuations in sales volume and has frequently chided Mr. Dey on Moderns inflexible
overhead.
During 2002, both firms reported the same profit on sales of $100,000. However, when comparing results
at the end of 2003, Mr. Knight was startled by the following results:
MODERN

Sales revenue
Costs and expenses
Net income
Return on sales

2002
$100,000
90,000
$ 10,000
10%

OLDWAY

2003
$120,000
94,000
$ 26,000
21 2/3%

2002
$100,000
90,000
$ 10,000
10%

2003
$150,000
130,000
$ 20,000
13 %

On the assumption that operating inefficiencies must have existed, Knight and his accountant made a
thorough investigation of costs but could not uncover any evidence of costs that were out of line. At a
loss to explain the lower increase in profits on a much higher increase in sales volume, they have asked
you to prepare an explanation.
You find that fixed costs and expenses recorded over the two-year period were as follows:
Modern
Oldway

$70,000 each year

$10,000 each year

REQUIRED

Prepare an explanation for Mr. Knight showing why Oldways profits for 2003 were lower than those
reported by Modern despite the fact that Oldways sales had been higher.
1. Redo the income statements emphasizing contribution margin.
2. Calculate breakeven point for each company.
3. Calculate operating leverage at revenue level of $100,000.
4. Calculate the volume of sales that Oldway would have to have had in 2003 to achieve the
profit of $26,000 realized by Modern in 2003.
5. Comment on the relative future positions of the two companies when there are reductions as
well as increases in sales volume.
[SEE PAGE AFTER SOLUTION FOR GRAPH OF TWO COMPANIES]

Cost-Volume-Profit Analysis

41

SOLUTION FOR DEMONSTRATION PROBLEM:

1. Redo the income statements emphasizing contribution margin.
MODERN

Sales revenue
Variable costs
Contribution margin
Fixed costs
Operating income
2.

OLDWAY

2003
$120,000
24,000
$ 96,000
70,000
$ 26,000

2002
$100,000
80,000
$ 20,000
10,000
$ 10,000

2003
$150,000
120,000
$ 30,000
10,000
$ 20,000

Calculate breakeven point for each company.

Fixed costs/CM ratio =

3.

2002
$100,000
20,000
$ 80,000
70,000
$ 10,000

Modern: $70,000/80% = $87,500

Oldway: $10,000/20% = $50,000

Calculate operating leverage at revenue level of $100,000, the point of indifference (either approach gives same
income).

Contribution margin
Operating income
Degree of operating leverage

MODERN

OLDWAY

$80,000
$10,000
$80,000/$10,000 = 8

$20,000
$10,000
$20,000/$10,000 = 2

An increase of 20% in sales ($20,000) and contribution margin ($16,000) for Modern results in an 8.0 times that
percentage change in operating income, an increase of 160% or $16,000 increase. For Oldway, an increase of 50%
in sales ($50,000) and contribution margin ($40,000) results in a 2.0 times that percentage change in operating
income, an increase of 100% or $10,000.
4.

Calculate the volume of sales that Oldway would have to have had in 2003 to achieve the profit of $26,000
realized by Modern in 2003.
Sales Variable costs Fixed costs = $26,000
Sales - .80(Sales) - $10,000
= $26,000
.20 Sales
= $36,000
Sales
= $180,000

5.

100% Sales
80% Variable costs
20% Contribution margin
Fixed costs
Operating income

$180,000
144,000
$ 36,000
10,000
$ 26,000

Comment on the relative future positions of the two companies when there are reductions as well as increases in
sales volume.
If the companies experience reductions in sales volume, Modern will suffer loss when the sales volume drops
below $87,500, whereas Oldway will remain profitable until sales drop below $50,000. Moderns loss will be
larger in absolute amount of dollars than Oldways. Oldway has a greater margin of safety than Modern for
Oldway can watch sales drop further before experiencing a loss situation.
However, if sales volume continues to increase, Modern can use its fixed costs to leverage income to higher
levels than Oldway. If sales volume does increase by 80% to $180,000, Modern can use the fixed cost lever
to raise income by (80% x 8 = 640%) $64,000 to $74,000. As shown in #4 above, Oldway would gain only
$16,000 of income (80% x 2 = 160%) for income of $26,000.
Each company equalizes risk with reward. Modern has taken a riskier approach by investing more money in
fixed cost-type items but can experience the possibility of higher reward. Oldway, on the other hand, has
selected to take less risk and therefore forgo the possibility of greater reward. [See graphs for angles at
intersection of cost and revenue lines.]

42 Chapter 3

Operating Leverage

$
Profit
opens
up

Revenues

BEPs
OLDWAY

costs
MODERN

costs
Fixed
costs
as lever
to change
angle at
BEP

Point of Indifference

Volume

The use of fixed costs to lever open profit & expose loss possibilities
Cost-Volume-Profit Analysis

43

COMPARING INCOME STATEMENTS

USING TWO DIFFERENT COSTING METHODS
Variable Costing compared to Traditional
For each of the following independent cases, find the unknowns designated by the capital letters.
Case 1
Direct materials used
Direct manufacturing labor
Variable marketing, distribution, and customer-service costs
Fixed manufacturing overhead
Fixed marketing, distribution, and customer-service costs
Gross margin
Finished goods inventory, January 1, 2002
Finished goods inventory, December 31, 2002
Contribution margin (dollars)
Revenues
Direct materials inventory, January 1, 2002
Direct materials inventory, December 31, 2002
Variable manufacturing overhead
Work-in-process inventory, January 1, 2002
Work-in-process inventory, December 31, 2002
Purchases of direct materials
Breakeven point (in revenues)
Cost of goods manufactured
Operating income (loss)

H
H
30,000
K
I
J
25,000
0
0
30,000
100,000
12,000
5,000
5,000
0
0
15,000
66,667
G
L

Case 2
$
40,000
15,000
T
20,000
10,000
20,000
5,000
5,000
V
100,000
20,000
W
X
9,000
9,000
50,000
Y
U
(5,000)

Note to instructor [solution next page]:

This problem provides a review of Chapters 2 and 3 by comparing the traditional income statement used
for financial accounting (Chapter 2) with the variable costing income statement introduced in Chapter 3.
Because there are no changes in the amounts of beginning to ending inventory for Work-in-Process
Inventory and for Finished Goods Inventory, the amount of Cost of Goods Manufactured is the same as
the Cost of Goods Sold. The change in amount from beginning to ending of Direct Materials Inventory
affects the Direct Materials Used, a component of the manufacturing costs, but it is also a variable cost so
the total of manufacturing costs is unchanged by the change in inventory amount.
Problem 9-33 provides insight for consideration of changes in the WIP and FG inventories and the
problem of building inventory to manufacture profit under absorption (traditional) costing. A similar
problem is included in Chapter 9 of this manual, The B.E. Company.

44 Chapter 3

Solution to Cases 1 and 2

Comparing income statements using two different costing methods
Case 1 illustrated [Given numbers from problem in bold]
Revenues
$100,000
Revenues
$100,000
Variable manufacturing costs:
Cost of goods sold:
*Direct materials
22,000
*Direct materials
22,000
Direct mfg. labor
30,000
Direct mfg. labor
30,000 57,000
Var. indirect mfg.
5,000
Var. indirect mfg.
5,000
Fixed indirect mfg.*** 18,000
_
Total var. mfg. costs
57,000
Cost of goods sold
75,000 [G]
Var. nonmfg. costs:**
13,000 [K]
Total variable costs
70,000
__
Contribution margin
30,000
Gross margin
25,000
Fixed costs:
Nonmanufacturing costs:
Fixed indirect mfg.***
18,000 [I]
Var. nonmfg.**
13,000
Fixed nonmfg.
2,000 [J]
Fixed nonmfg.
2,000
Total fixed costs
20,000
Total nonmfg. costs
15,000
Operating income
$ 10,000 [L]
Operating income
$ 10,000
Breakeven point =Fixed Costs CM% of Rev.
Schedule of Cost of Goods Manuf. & Sold
66,667 = FC / .3
66,667 * 0.3 = 20,000 = FC
*Direct materials inventory:
Total FC = 20,000 Mfg. 18,000 = 2,000 Nonmfg.
Beg. $12 + Purch. $15 End $5 = Used $22 [H]
No change in WIP inventory and finished goods inventory, Cost of Goods Manufactured = Cost of Goods Sold

Case 2 illustrated [Given numbers from problem in bold]

Revenues
$100,000
Revenues
$100,000
Variable manufacturing costs:
Cost of goods sold:
Direct materials
40,000
Direct materials
40,000
Direct mfg. labor
15,000
Direct mfg. labor
15,000
Var. indirect mfg.
5,000* [X]
Var. indirect mfg.
5,000* 75,000
Fixed indirect mfg.
20,000
Total var. mfg. costs
60,000
Cost of goods sold
80,000 [U]
Var. nonmfg. costs:
15,000** [T]
Total variable costs
75,000
__
Contribution margin
25,000 [V]
Gross margin
20,000
Fixed costs:
Nonmanufacturing costs:
Fixed indirect mfg.
20,000
Var. nonmfg.
15,000**
Fixed nonmfg.
10,000
Fixed nonmfg.
10,000
Total fixed costs
30,000
Total nonmfg. costs
25,000
Operating income
$ (5,000)
Operating income
$ (5,000)
Breakeven point =Fixed Costs CM% of Rev.
Schedule of Cost of Goods Manuf. & Sold
BEP = 30,000 /CM% 120,000 = 30,000/0.25 [Y] DM: Beg20 + Purch50 Used40 =End30[W]
No change in WIP inventory and finished goods inventory, Cost of Goods Manufactured = Cost of Goods Sold

Cost-Volume-Profit Analysis

45

Chapter 3 Worksheet for Comparing Income Statements

(Note the primary cost classifications used in each income statement)
Variable or Fixed Costs

Manufacturing or Nonmanufacturing

Contribution Income Statement

Emphasizing Contribution Margin
Revenues

Financial Accounting Income Statement

Emphasizing Gross Margin
Revenues

Variable manufacturing costs:

Cost of goods sold:

Direct materials

Direct materials

Direct manufacturing labor

Direct manufacturing labor

Variable indirect manufacturing

Variable indirect manufacturing

Fixed indirect manufacturing

Total variable manufacturing costs

Cost of goods sold

Variable nonmanufacturing costs:

Total variable costs
Contribution margin

Gross margin

Fixed costs:

Nonmanufacturing costs:

Fixed indirect manufacturing

Variable nonmanufacturing

Fixed nonmanufacturing

Fixed nonmanufacturing

Operating income

Operating income

Breakeven point =Fixed Costs CM% of Rev.

Schedule of Cost of Goods Manuf. & Sold

(Note the relationship of fixed indirect manufacturing costs in calculating the margins.)

46 Chapter 3

Additional Considerations for Problem 3-28: Zapo 1-2-3

Problem 3-28 in the text asks only about units of product sold for calculating the breakeven
point. The New Customers group returns 57.14% on sales dollar ($120/$210) whereas the
Upgrade Customers group returns 66.67% on each sales dollar ($80/$120). The return on sales
dollar is maximized by selling the upgrades rather than to new customers. Many questions arise
in this situation:
Can only a certain number of units be soldmarket constraint?
Can only a certain number of units be producedcapacity constraint?
How is sales performance measurednumber of units sold, amount of revenue dollars, amount
of contribution dollars?
Why is variable advertising so high for new customers compared to upgrade customerswhen it
is essentially the same product?
What is the size of the upgrade group, and what is needed in terms of new customers to maintain
a profitable base of customers?
What is the relationship with upgrade customers? Can the same type of relationship with
upgrade customers be maintained if new customers outnumber themjeopardizing all
customer relationships?
If the problem is recast to look at sales dollars rather than units, some thought-provoking
information is available. See accompanying spreadsheet analysis of comparison of units and
sales dollars.
For every New Customer unit lost or not sold, one and three-fourths units need to be sold to
Upgrade Customers to maintain the same dollars of sales. This requires more units to be sold.
If this is possible for the company to do, then more profit is realized. [Obviously, the company
would not intentionally forgo a sale to a new customer if such a sale were possible.] The
Upgrade sold in replacement of a New is calculated as shown:
New
Sales $210
V.C.
90
C. M. $120

100.00%
42.86%
57.14%

Upgrade replacement
$120 + $90 = $210 100.00%
40 + 30 = 70
33.33%
$ 80 + $60 = $140
66.67%

The difference of $20 more for the 75% replacement ($210/$120 = 1.75%) equates to $26.67
per full replacement unit. If the company sells one unit more than the total sold using the unitsbasis, then their profit is $26.67 more than it would have been under the units-basis. The
accompanying spreadsheet shows this relationship.
A company would want to not only get the most sales dollars but also the most profit from each
of those sales dollars. Noting the relationship of margin per sales dollar for products can be
meaningful.

Cost-Volume-Profit Analysis

47

Spreadsheet for Problem 3-28 Excel spreadsheet in separate file

48 Chapter 3

SUGGESTED READINGS
Huka, S., Luft, J. & Ballow, B., Second-Order Uncertainty in Accounting Information and Bilateral
Bargaining Costs, Journal of Management Accounting Research (2000) p.115 [25p].
Maher, M., Management Accounting Education at the Millennium, Issues in Accounting Education
(May 2000) p.335 [12p].
Tambrino, P., Contribution Margin Budgeting, Community College Journal of Research and Practice
(January 2001) p.29 [8p].
Yunker, J., Stochastic CVP Analysis with Economic Demand and Cost Function, Review of
Quantitative Finance and Accounting (September 2001) p.127 [23p].

Cost-Volume-Profit Analysis

49