3
Cost-Volume-Profit CHAPTER Analysis
Learning Objectives
After studying this chapter, a student should be able to:
1.
Classify and summarize revenue, volume, and cost data to produce relevant
information for a cost-volume-profit analysis
2.
Distinguish among contribution margin, gross margin, and operating margin
3.
Apply cost-volume-profit analysis to determine breakeven points for a single
product company under different conditions of target operating income and net
income using the appropriate equation, contribution margin, or graph method
4.
Select the most appropriate strategy when the breakeven point is affected by
alternative planned changes to price, volume, and/or costs
5.
Analyze and select the most appropriate product mix for a two product company,
and adapt CVP analysis to multiple revenue-driver situations
6.
Analyze and select the most appropriate product mix for a two-product company,
and adapt CVP analysis to multiple cost-driver situations
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Chapter 3
CHAPTER OVERVIEW
CVP analysis help managers select the best from among many alternatives to change how
they currently do business and improve profits both in the short term and long term.
Central to CVP analysis is classifying all inventoriable and period costs as either variable
costs or fixed costs. Further, CVP analysis simplifies reality because the key assumption
is the volume of finished goods or services available for sale (Q) equals the volume of
finished goods or services sold. The ending inventory is zero in the calculations
concerning CVP thus the impact of various production and sales levels is nullified.
CVP relationships are only valid within the known or relevant range. To apply the CVP
relationships to other ranges is problematic because beyond a given range of activity new
productive or service capacity is required and any new capacity changes the variable and
fixed costs behaviour. The classification of fixed or variable costs is dependent on the
time horizon. Whether costs are fixed or variable depends on the relevant range, the
length of the time horizon, and the specific decision to be made.
Reclassification of cost data produces relevant information for CVP analysis
CVP analysis requires using a different way to classify and summarize the same set of
costs reported on a financial accounting statement of net income.
Costs are classified according to how they behave and summarized in the contribution
income statement. Where financial accounting logic focuses on gross margin (GM) and
operating margin (OM), management accounting logic focuses on the contribution
margin (TCM) in the contribution income statement.
The contribution margin relationships among revenues, costs, contribution margin, and
operating income can now be used to help answer questions such as:
What is the minimum quantity of sales in units or in dollars to ensure no losses?
What are the required sales to earn a target operating income or a target net
income?
Breakeven point (BEP) is determined using the CVP analysis when the assumption about
operating income is zero. That is the value of Q where there is neither income nor loss.
TRev = TotalVC + FC
Three methods of evaluating BEP are given: equation method; contribution margin
method; and the graph method.
The CVP analysis accommodates the determination of target operating income by
including the amount desired in the CVP formula. TRev = TotalVC + FC + Target OI
Likewise, target net income can be accommodated by including the amount of before tax
operating income in the CVP formula, Target OI = Target NI/(1 tax rate)
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Chapter 3
Using CVP with strategies of differentiation and cost leadership can help managers
execute decisions to assure survival and growth in the long term. The longer the term the
more uncertain the actual results will be.
Uncertainty can be examined under three different methods: sensitivity analysis, margin
of safety, or decision models.
CVP analysis can be adapted to multiple revenue drivers and multiple cost drivers to
select the most appropriate product mix. However, the equation, contribution margin,
and the graph methods cannot be used in the determination of the appropriate mix
because there can be more than one mix to achieve a desired outcome.
In conclusion, the major benefits of CVP analysis are improved planning and improved
actions. It has been said The success of management accounting depends on whether
decisions of managers are improved by the accounting information provided them
CVP analysis contributes to good actions and decisions. Because of uncertainty it is
possible that an unfavourable outcome could occur even when good decisions have been
made.
TEACHING TIP:
Begin the session on chapter with an overview of the chapter. Make the major points in a
three to five minute opening statement. Use the forgoing to guide your comments. At the
end of the session close with a reiteration of the same points.
TEACHING TIP: Hand out the quiz questions (quiz fits multiple 8.5 by 11 sheets) at the
beginning of the lecture so that students can write their answer and or make a correction
as necessary. The quiz paper gives the opportunity to make a note about the correct
answer as explained during feedback session. The quiz could be used as part of a
personal response system, or "clicker" technology.
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Chapter 3
CHAPTER OUTLINE
Learning Objective 1:
Classify and summarize revenue, volume, and cost data to
produce relevant information for a cost-volume-profit analysis
I.
Cost-Volume-Profit (CVP) Analysis Procedures
A. CVP analysis provides a powerful assistance to managers in all industries and
in any business function of the value chain making changes to the financial
result from their operations
B. Pricing changes can be analyzed to see if target profit can be achieved by
lowering the price with an increase in volume or raising the price with a
decrease in volume.
II.
Effect of Time Horizon
A. Costs are classified as fixed or variable depending upon a specific time
horizon.
B. Whether costs are fixed depends on the relevant range, the length of time
horizon, and the specific decision situation
C. Financial accounting relationship compared to management accounting
relationship. This is discussed in the next section but can be introduced here
to emphasize there is a difference between financial accounting logic and
management accounting logic.
Financial accounting equation (Income Statement):
Revenues minus COGS equals Gross margin
Gross margin minus operating expenses equals Operating income
Operating income minus interest expense equals Taxable Income
Taxable income minus tax expense equals Net income
D. Management accounting equation (Contribution Income Statement):
Revenues minus variable costs equals Contribution Margin
Contribution margin minus Fixed costs equals Operating income
Operating income minus interest expense equals Taxable Income
Taxable income minus tax expense equals Net Income
E. The relationship of operating income to net income is important to the CVP
analysis, because target income can be before tax or after tax. The formula
for after tax target net income is:
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Chapter 3
Revenues equal variable costs plus fixed costs plus operating income
times 1 minus the tax rate, or
Contribution margin equals fixed costs plus operating income times (1-tax
rate)
F. Assumptions made under CVP analysis:
1. Costs are either fixed or variable
2. Changes in revenue and variable costs are only because of changes in
volume
3. Behaviour of total revenues and total costs are linear or straight line as
shown in exhibit 3-2
4. Unit selling price (USP), unit variable cost (UVC), and total fixed
costs (FC) are known
5. VP assumes either a single product or a given revenue mix of several
products remains constant as the level of total units sold (Q) changes
6. All revenues and costs can be added and compared without taking
into account the time value of money
G. Cost-volume-profit relationships that are derived from the above assumptions:
1. Unit selling price (USP) minus unit variable cost (UVC) equals unit
contribution margin (UCM), this is a powerful relationship in CVP
analysis.
2. The contribution margin (TCM) can be calculated as Q(UCM) and this
can be used in many CVP analysis applications, especially in
breakeven analysis where TCM is equal to the fixed costs (FC).
3. TCM is used in target income analysis where TCM equals FC plus
target operating income (OI)
Do Chapter Quiz multiple choice question 1.
In-class exercise Mastery Questions Learning Objective 1: Question 2
Assign Exercises 3-16, and /or 3-17.
Learning Objective 2:
Distinguish among contribution margin, gross margin, and
operating margin
III.
Financial Accounting in Contrast to Management Accounting
A. Financial accounting logic has a Gross Margin (GM) and Operating Margin
(OM) focus
1. Gross Margin (GM) is Total revenues Cost of goods sold (COGS) or
Cost of sales (COS) where COGS or COS include both fixed and
variable costs.
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Chapter 3
2. Operating income (OI) is Gross margin (GM) Operating expenses
(Opex)
3. Operating margin (OM) is a ratio of Operating income (OI) / Total
revenues (TRev)
B. Management accounting logic has a Contribution Margin (TCM) focus.
1. Costs are differentiated as either fixed or variable relative to volume.
2. Revenues vary according to the volume of sales (Q).
3. Contribution margin:Total Revenues (TRev) Total Variable costs (TVC)
a.
Contribution margin per unit:
Selling price/unit (USP) Variable cost/unit (UVC)
b.
Contribution margin percentage/ratio (CM%):
Contribution Margin (TCM) divided by Sales (TRev)
4. Multiple-step Operating Income Statement:
a. Contribution Income statement:
Revenues
XXXX
Variable costs
Contribution margin
XXX
XXXX
Fixed Costs
Operating income
XXX
XX
b. Equation:
Revenue (TRev) Variable costs (TVC) = Contribution Margin (TCM)
Contribution Margin (TCM) Fixed costs (FC) = Operating income (OI)
5. Operating income versus Net income:
a. Operating income less income tax equals net income. Stated another
way Operating income is profit before income tax.
b. Chapter 3 assumes zero for nonoperating revenues and expenses.
Non-operating revenues and expenses are related to incidental
activities not related directly to the merchandising or manufacturing
activities.
Do Chapter Quiz multiple choice questions 2 and 3.
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Chapter 3
In-class exercise Mastery Questions Learning Objective 2: Question 1
Assign Exercise 3-22.
Learning Objective 3:
Apply cost-volume-profit analysis to determine breakeven points for a
single product company under different conditions of target operating
income and net income using the appropriate equation, contribution
margin, or graph method
IV.
The Breakeven Point (BEP)
A. Definition of breakeven point:
Operating income (OI) is zero
B. Breakeven point calculations:
1. Equation method:
(USP * Q) (UVC * Q) FC = OI,
where Q is the quantity or volume and OI is zero.
1. Contribution margin method
a. Per unit approach that calculates breakeven in units of output:
Fixed costs divided by contribution per unit = breakeven in units.
FC / UCM = BEP units
b. Contribution percentage/ratio approach that calculates breakeven
in dollars of revenue:
Fixed costs divided by contribution margin ratio.
FC / CM% = BEP revenue $
2. Graph method: x-axis is output units sold, y-axis is dollars; total
revenue and total cost lines intersect at breakeven point, horizontal
line projects to revenue dollars required and vertical line projects to
units of sales required. (Refer to Exhibit 3-4 on page 96).
3. Any of the three approaches for calculating breakeven may be used
Do Chapter Quiz multiple choice question 4.
C. Target Operating Income (Target OI)
Beyond breakeven the sales units or sales revenues required to achieve a
predetermined operating income. The CVP equation assumes operating
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Chapter 3
income as the measure of profit.
1. Three methods to calculate Target OI:
a) Formula method:
(USP * Q) (UVC * Q) FC = OI,
where Q is the quantity or volume
b) Contribution margin method:
Q = (Target OI + FC)/UCM
Revenues in dollars = (Target OI +FC)/CM%
c) PV Graph:
See Exhibit 3-5 page 97 for the graphical method
Do Chapter Quiz multiple choice question 5.
D. Target Net Income (Target NI) and Income Taxes
Two methods to calculate Target NI:
d) Formula method:
(USP * Q) (UVC * Q) FC = Target NI/(1 Tax rate),
where Q is the quantity or volume
e) Contribution margin method:
Q = ((Target NI/(1 Tax rate)) + FC)/UCM
Revenues in dollars = ((Target NI/(1 Tax rate)) +FC)/CM%
TEACHING TIP:
If the tax rate is 40%, the operating income required would be target net income/ (1-tax
rate). In other words for every dollar in operating income earned only (1 0.40) 60
cents contributes to net income. Taxes are 40 cents of every dollar of operating income.
Do Chapter Quiz multiple choice question 6.
In-class exercise Mastery Questions Learning Objective 3: Question 1.
Assign Problem 3-30.
Learning Objective 4:
Select the most appropriate strategy when the breakeven point is
affected by alternative planned changes to price, volume, and/or
costs
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Chapter 3
V.
Using CVP Analysis in Planning and Decision Making
Strategy is set after an analysis of how to best exploit opportunities and how best
to defend against threats in the environment given company has scarce resources
constraints. The challenge is to make decisions that assure survival and growth in
the long-term, but the longer the term, the more uncertain the actual results will
be.
A. Two strategies are available to each for profit enterprise:
1. Product Differentiation maximizing profit based on the unique and
desirable features of the good or service it sells
2. Cost Leadership maximize profit based on the best possible cost
control
B. Other changes that can be incorporated in BEP calculation:
1. calculate whether changes in total fixed costs improves profit
2. compare whether a change in selling price per unit (changes CM per
unit) improves profit
3. compare different changes in several items combinations of changes
in the fixed and variable components
4. examine uncertainty (the possibility that an actual amount will deviate
from an expected amount) using three methods:
a) sensitivity analysis,
b) margin of safety, or
c) decision models
C. Decision to Increase Discretionary Period Costs Advertising
Advertising a fixed cost and discretionary cost affects the revenue driver in a
positive way. The trade-off of higher fixed costs is for a greater increase in
revenues to produce an increase in profit overall.
D. Decision to Reduce unit selling price (USP)
1. Changes the variable costs within the relevant range. Reducing the
selling price will increase unit sales in perfect market conditions. The
relevant costs are the variable costs that will increase as a result of
greater sales and the reduction of the selling price per unit. These
changes can be compared by taking the TCM after the changes and
compare to the TCM before the changes.
2. There is not always a positive change to TCM because of the
uncertainty that sales will increase in sufficient number to produce a
positive outcome. Uncertainty is a degree of risk meaning the
likelihood of a certain outcome is less than 100% and managers must
make an estimate of the degree of probability that an outcome will
occur.
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Chapter 3
E. Three methods to deal with the issue of uncertainty:
1. Sensitivity Analysis
a) Changes in fixed costs and variable costs in the same
percentage cause a relatively small and relatively large
changes in profitability respectively.
b)
A sensitivity analysis uses percentages changes to understand
which causes the greatest effect on profit.
c)
When small changes in a cost cause large changes to profit
managers know to be careful in estimating these costs as profit
is highly sensitive to that cost.
TEACHING TIP:
Emphasize the relationship between volume and the total revenues and the total variable
costs. As volume changes total revenues and total variable costs change at the same
percentage as will the contribution margin.
Total revenues total variable costs = Total contribution margin.
As a formula:
USP * Q UVC * Q = UCM * Q ( CM% remains constant)
Total fixed costs remain constant for a given relevant range of quantity of sales or output.
Operating income is best expressed as total contribution margin less total fixed costs.
As a formula:
UCM * Q FC = OI
[See overhead/handout Cost-Volume-Profit Chart and complete it with the class]
TEACHING TIP:
When using the CVP Chart and interacting with the students, ask whether the net income
will increase of decrease before completing the questions on change. For instance the
sensitivity of a 2% change in variable and fixed costs is based on the amount of variable
and fixed costs affected. For variable costs it is a larger amount therefore the result will
be a higher net income.
2. Margin of Safety
a) A type of sensitivity analysis which is the excess of forecasted
or budgeted revenues over the breakeven revenues.
b)
Another way of expressing the margin of safety is how far
revenues can fall below the forecast or budgeted revenues
before the breakeven value is reached, thereafter losses are
incurred.
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Chapter 3
3. Decision Models and Uncertainty
a) A decision model is method of quantifying the uncertainty
surrounding future actual outcomes and the inherent
inaccuracy of estimated values.
b)
c)
The decision model can be a table with actions as rows.
Actions include choices that management can make. The
columns are events that management has no control over but
can be quantified as probable occurrences. The result of the
actions and events can be quantified as outcomes, a key
outcome is OI
d)
The events also called externalities must be quantified as to
the risk of occurrence in the form of probabilities
e)
From the probability distribution and the expected events an
expected value can be calculated. The expected
value/expected monetary value is evaluated to compare
alternatives and make a decision.
f)
II.
Choice criterion is used to make a decision which alternative
to chose. It is based on an agreed upon goal or some other
quantitative threshold, or an outcome like after tax profit.
Sometimes a good decision can result in a bad
outcome.even though the expected value was positive there
is still a probability that a bad outcome will occur.
Do Chapter Quiz multiple choice question 7.
1. Alternative Fixed-cost/Variable-cost structures
a) A high fixed cost structure means the breakeven point (BEP)
will be high in the number of units required to breakeven.
b) A lower fixed cost will reduce the required units to breakeven.
c) With an all variable cost structure, where fixed cost is zero,
there is always a positive contribution for each unit sold. A
business with all variable costs, where fixed costs are near
zero, is the best structure because it reduces risk.
d)
The fixed cost structure has an impact on operating income as
can be seen in the formula Contribution margin minus fixed
costs equals operating income. This is compared using a
measure called operating leverage.
e)
Operating leverage is calculated by dividing Contribution
margin(CM) by Operating income (OI), the result is called
Degree of Operating Leverage (DOL)
f)
High fixed costs will cause a high DOL so that a dollar of
sales will cause the operating income to increase by the
amount of the DOL
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Chapter 3
TEACHING TIP:
Knowing the degree of operating leverage at a given level of sales helps managers
determine quickly the effect of a change in sales on operating income. The leverage is in
the effect fixed costs have on operating income. A high leverage is when fixed costs are
high compared to operating income. A low leverage is when fixed costs are low
compared to operating income. The degree of operating leverage (DOL) is a measure of
this relationship. See page 108 with the accompanying table for Options 1 to 3. See that
when fixed costs are high (Option 1), the degree of operating leverage is high and
conversely, when fixed costs are low or non-existent (Option 3), the degree of operating
leverage is lower.
g) Balance risk and reward with alternate fixed cost vs. variable
cost structures
(1) The assumption is apparent that a high investment in
fixed assets and therefore high fixed costs will have a
corresponding low variable cost per unit which in turn
results in a high contribution margin. The trade-off of
high fixed costs for lower variable costs has its
rewards when the breakeven point is achieved quickly.
At the same time the opposite is true, when the
breakeven point is not achieved quickly the risk of
loss is greater.
(2) Attitude toward risk (each decision maker has their
own attitude)
(a) Risk neutral: decision maker weighs each dollar
as a full dollar, no more, no less
(b) Risk averse: decision maker weighs loss of
dollar as greater than gain of dollar
(c) Risk seeking: decision maker weighs gain of
dollar as greater than loss of dollar
III.
Do Chapter Quiz multiple choice question 8.
F. The major benefits of CVP analysis are improved planning and improved
actions.
In-class exercise Mastery Questions Learning Objective 4: Question 1
Assign Exercise 3-26.
Learning Objective 5:
Analyze and select the most appropriate product mix for a twoproduct company, and adapt CVP analysis to multiple revenuedriver situations
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Chapter 3
VI.
Multiple Revenue Drivers and Multiple Cost Drivers
A. Multiple Revenue drivers
B.
use the relative contribution of quantity of each product in the revenue mix
or sales mix that constitutes the total revenues.
1. Breakeven Point (BEP) depends on the revenue mix.
2. Q, the total number of units to be sold to breakeven can vary
depending on the revenue mix.
3. More sales of the higher revenue item will decrease the total number
of units needed to be sold.
4. More sales of a lower revenue item will increase the total number of
units needed to be sold to achieve the target income.
TEACHING TIP:
Even though there is more than one possible breakeven point this can be systematically
overcome for planning purposes. Using a constant sales mix among many products a
breakeven point can be determined. The key to establishing the sales mix is choosing one
of the products as the lowest common denominator. Say there are three products in the
sales mix each with an established denominator activity: Product A, 20,000 units;
Product B2, 40,000 units; and Product C, 80,000 units. The sales mix based on the
denominator activity would be (using Product A as the lowest common denominator)
1:2:4. Calculated by dividing Product A into the denominators of B and C respectively.
Do Chapter Quiz multiple choice question 9.
C. Service organizations have different measures of outputs, not typically units
as in merchandising sales. They are:
1. Revenue passenger miles for airlines,
2. Room-nights occupied for hotels and motels
3. Patient-days for hospitals
4. Student course credits for universities
VII. CVP Analysis in Nonprofit Organizations
A. Total revenue determines the level of service the nonprofit organization can
provide
B. Two characteristics of CVP relationships in nonprofit situation:
1. The percentage change in service is different from the percentage
change in the total revenue because of the fixed cost component.
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Chapter 3
2. Since the total revenue is a constant then there are three choices when
faced with changes to be made:
a) Reduce the number of services provided
b) Reduce the variable costs
c) Reduce the fixed costs
In-class exercise Mastery Questions Learning Objective 5: Question 1
Assign Exercise 3-29.
Learning Objective 6:
Analyze and select the most appropriate product mix for a twoproduct company, and adapt CVP analysis to multiple cost-driver
situations
VIII. Multiple Cost Drivers
A. CVP can be adapted to the general case of multiple cost drivers.
B. Just as in the case of multiple products, there is no unique breakeven point
when there are multiple cost drivers.
C. OI no longer depends solely on a single cost driver but rather on the
interaction of two cost drivers.
OI= TRev (UVC cost driver1 * Q1) - (UVC cost driver2 * Q2) - FC
D. In cases involving multiple cost drivers, the equation, contribution margin,
and graph methods described at the beginning of Chapter 3 cannot be used.
Do Chapter Quiz multiple choice question 10.
In-class exercise Mastery Questions Learning Objective 6: Question 1
Assign Exercise 3-33.
also hosts 12 Mini Case that can be assigned for
grades or just used as extra practice. The short cases
are designed to show how the chapters concepts are
applied in a real world situation. Encouraging analysis and critical thinking, they key address
the concepts covered in the chapter and have associated conceptual multiple choice
questions that feed into your gradebook.
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Chapter 3
CHAPTER 3 QUIZ
1.
Which of the following is not an assumption of cost-volume-profit analysis?
a. The behaviour of revenues and expenses is accurately portrayed as linear over
the relevant range.
b. The unit selling price, unit variable costs, and total fixed costs are known.
c. The time value of money is incorporated in the analysis.
d. Sales mix will remain constant.
2. Total contribution margin is calculated as:
a. total revenue total variable costs.
b. total revenue total manufacturing costs (CGS).
c. total revenue total fixed costs.
d. operating income + total variable costs.
3. Which of the following statements is true?
a. Gross margin can be used only in financial accounting income statements.
b. Only manufacturing-sector companies use the term gross margin in their
income statements.
c. Contribution margin can be used in place of gross margin if management
prefers that terminology in their financial statements.
d. Gross margin implies a different cost classification usage than the term
contribution margin when used in income statements.
Questions 46 are based on the following revenue and cost structure:
Selling price per unit:
Variable cost per unit:
Total fixed costs:
Tax rate on operating income:
4.
$ 100
$ 40
$12,000
40%
How many units must be sold to breakeven?
a.
150
b.
200
c.
250
d.
400
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Chapter 3
Chapter 3 Quiz continued
5. How many units must be sold to earn a target operating income of $60,000?
a. 400
b.
600 c.
1,000
d.
1,200
6. How much sales revenues must be achieved to earn a target net income of $72,000?
a. $72,000
7.
b.
$100,000
c.
$132,000
d.
$220,000
One way for managers to cope with uncertainty in profit planning is to
a. use CVP analysis because it assumes certainty.
b. recommend management hire a futurist whose work it is to predict business
trends.
c. use sensitivity analysis to explore various what-if scenarios in order to
analyze changes in revenues or costs or quantities.
d. wait to see what does happen and prepare a report based on actual amounts.
8.
Soccer Promotions sells souvenirs at games, the arrangement with the club can be
set at one of three contracts. The average sale is $7.50 and the average cost is
$2.50 and the number of sales at any given game has averaged 100. Which of the
following arrangements would you recommend, if Soccer Promotions attitude is
risk aversion?
a. $500 fixed fee
b. $250 fixed fee plus $1.50 per sale
c. 40% of sales
d. None of the above arrangements.
9. Alpha Company produces and sells two products. Product A sells for $20 and has
variable costs of $15. Product B sells for $10 and has variable costs of $6. Planned
sales for the month were 25,000 units of A and 20,000 of B. Fixed costs are $50,000
per month. At the end of the month budgeted $700,000 in sales were achieved but the
operating income was $1400,000. Which of the following descriptions of actual
results best describes what happened in the month?
a. Alpha sold 35,000 of A and no product B.
b. Alpha sold more of both products A and B than expected.
c. Alpha sold more of product A and less of product B than expected.
d. Alpha sold more of product B and less of product A than expected.
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Chapter 3
Chapter 3 Quiz continued
10. In the situation of multiple cost drivers, CVP analysis can be
a. adapted by incorporating the cost drivers into the calculation of the variable costs.
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. modified so that the various simple formulas can be used by applying them
separately to each cost driver.
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Chapter 3
CHAPTER QUIZ SOLUTIONS:
1.
[c]
2.
[a]
3.
[d]
4.
[b]
5.
[d]
6.
[a]
7.
[c]
8.
[c]
9.
[c]
10.
[a]
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Chapter 3
TEACHING TIP:
Conclude the Chapter Quiz with a review of the chapter. Reiterate the importance of this
chapter to management and management accountants.
Review of chapter upon completion of the exercises.
The importance of this chapter to managerial decisions cannot be overemphasized. In
this chapter the importance of cost structure to profitability is stressed. When sales are
uncertain, a high contribution margin percentage of sales is less risky in that fixed costs
are recovered more quickly and afterwards the contribution towards profits is the greatest.
Conversely, a low contribution margin percentage of sales is more risky when sales levels
are uncertain.
Our role as management accountants is to ensure managers are aware of their cost
structure and the degree of sensitivity these costs have towards changes in volume.
Ideally, managers will manage their operations such that every opportunity of
maximizing the total contribution margin is achieved. Achieving the maximum
contribution towards profit becomes the goal of every decision. The contribution margin
concept meets the quantitative criteria applied to each decision. Experience, maturity,
and judgment will measure the qualitative criteria.
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Chapter 3
WRITING/DISCUSSION EXERCISES
1.
Understand basic cost-volume-profit (CVP) assumptions.
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 not forget a key item. Models are
also helpful in teaching a person to perform a task. Simulations are used in various
situations.
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 then supported for gaining the benefit of
significantly improved decisions with a more complicated and expensive approach.
2.
Explain essential features of CVP assumptions.
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 behaviour 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.
Contribution margin is the connecting link between the behaviour 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
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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.
3.
Determine the breakeven point and 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
text authors note that multiple revenue drivers and multiple cost drivers will result
in multiple breakeven points. A curved, rather than a straight line depicts the time
value of money phenomenon of compounding and would allow 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.
Incorporate income tax considerations into 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 for managers to take into
consideration; this is accomplished by using net income instead of operating
income. The text assumes the nonoperating items to be zero for ease of
computation. 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
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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
$440,000
+Nonoperating revenue
80,000
Nonoperating expense
20,000
Income before income tax
$500,000
100%
Income tax expense (30%)
150,000
30%
$350,000
70%
Net income (targeted)
5.
Explain the use of 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.
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6.
Use CVP analysis to plan 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 behaviour 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 structure. The cost structure could be changed
from predominantly variable costs to more fixed costs, for example. The manager
would need to consider several factors in deciding on such a change:
Time frame: short run versus long range
Costs tend to be fixed in a compressed time span but variable given enough
time
Specific decision situation for which the cost is being incurred
7.
Risk level and attitude versus reward potential
Parameters of the relevant range
Apply CVP analysis to a multi-product company
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
tradeoffs 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. Decisions are always made about the future.
8.
Distinguish between contribution margin and gross margin.
In this chapter the same amount of costs are given for income statements
emphasizing contribution margin as for those emphasizing gross margin. Under
what circumstances would the costs differ when the emphasis was different?
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
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fixed manufacturing costs changes from a product cost to a period cost. If the
amount of inventory (work-in-process and finished goods) changes within a time
period, the total costs would differ. CVP analysis uses the phrase produced and
sold to indicate that the level of units in inventory is assumed not to change. If
production is different than sales, the income amount would differ from income
statement to income statement.
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.
9.
Adapt CVP analysis to multiple cost driver situations.
How can CVP analysis be adapted to meet the circumstance of multiple cost
drivers?
CVP analysis uses the variable - fixed cost classification. Because variable costs
stay the same per unit (within the relevant range), they are useful when used as per
unit costs for predicting. The use of multiple cost drivers requires that variable
costs be pooled by cost driver. Actual volume of cost driver can be multiplied by the
per unit variable cost for each pool. The pools are then added to equal total
variable costs. As each volume of cost driver changes, the possible combinations of
total variable cost changes, creating multiple breakeven points as well as the same
amount of income when different amount of product are sold. Fixed costs change
per unit and cannot safely be used as per unit costs for predicting. They are best
used as total costs.
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COST VOLUME PROFIT CHART
Revenues
Variable
Costs
Contribution
Margin
Fixed
Costs
Operating
Income
Taxes @
20%
Net
Income
10,000
8,000
2,000
1,500
500
100
400
Given the above revenue and cost structure as a starting point consider the following
changes:
1.
2.
3.
4.
5.
6.
Increase sales volume by 10%
Decrease sales volume by 5%
Increase variable costs by 2% and decrease fixed costs by 2%
Increase sales by 10% and the selling price by 10%
Decrease variable costs by 5% and increase fixed costs by $800
What would the sales revenues have to be to generate a net income of $700.
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Chapter 3
Completed CVP Chart
Revenues
10,000
11,000
9,500
10,000
12,100
10,000
11,875
Variable
Costs
8,000
8,800
7,600
8,160
8,800
7,600
9,500
Contribution
Margin
2,000
2,200
1,900
1,840
3,300
2,400
2,375
Fixed
Costs
1,500
1,500
1,500
1,470
1,500
2,300
1,500
Operating
Income
500
700
400
370
1,800
100
875
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Taxes @
20%
100
140
80
74
360
20
175
Net
Income
400
560
320
296
1,440
80
700
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Chapter 3
DEMONSTRATION PROBLEM
Alex Chen and Herbert Brown are the owners of Innovative Technologies Inc. and
Brown and Sons 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.
Chen and Brown differ markedly in their management thinking. Operations at Innovative
are highly mechanized, and the direct labour force is paid on a fixed-salary basis. Brown
and Sons uses manual hourly paid labour for the most part and pays incentive bonuses.
Innovatives salesmen are paid a fixed salary, whereas Brown and Sons salesmen are
paid small salaries plus commissions. Mr. Brown takes pride in his ability to adapt his
costs to fluctuations in sales volume and has frequently chided Mr. Chen on Innovatives
inflexible overhead.
During 2010, both firms reported the same profit on sales of $100,000. However, when
comparing results at the end of 2011, Mr. Brown was startled by the following results:
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Chapter 3
INNOVATIVE
BROWN AND SONS _____
2010
Sales revenue
Costs and expenses
Net income
Return on sales
2011
2010
2011
$100,000
$120,000
$100,000
$150,000
90,000
94,000
90,000
130,000
$ 10,000
$ 26,000
$ 10,000
$ 20,000
10%
21 2/3%
10%
13 %
On the assumption that operating inefficiencies must have existed, Brown and his
accountant made a thorough investigation of costs. They 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:
Innovative
$70,000 each year
Brown and Sons
$10,000 each year
REQUIRED
Prepare an explanation for Mr. Brown showing why Brown and Sons profits for 2011
were lower than those reported by Innovative despite the fact that Brown and Sons 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 Brown and Sons would have to have had in
2011 to achieve the profit of $26,000 realized by Innovative in 2011.
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]
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Chapter 3
SOLUTION FOR DEMONSTRATION PROBLEM:
1.
Redo the income statements emphasizing contribution margin.
INNOVATIVE
BROWN AND SONS___________
2010
2011
2010
2011
Sales revenue
$100,000
$120,000
$100,000
$150,000
Variable costs
20,000
24,000
80,000
120,000
$ 80,000
$ 96,000
$ 20,000
$ 30,000
70,000
70,000
10,000
10,000
$ 10,000
$ 26,000
$ 10,000
$ 20,000
Contribution margin
Fixed costs
Operating income
2.
Calculate breakeven point for each company.
Fixed costs/CM ratio =
$70,000/80% = $87,500
Brown and Sons:
3.
Innovative:
$10,000/20% = $50,000
Calculate operating leverage at revenue level of $100,000, the point of
indifference (either approach gives same income).
INNOVATIVE
BROWN AND SONS______
Contribution margin
$80,000
$20,000
Operating income
$10,000
$10,000
Degree of operating leverage $80,000/$10,000 = 8
$20,000/$10,000 = 2
An increase of 20% in sales ($20,000) and contribution margin ($16,000) for Innovative
resulted in an 8.0 times that percentage change in operating income. This is an increase of
160% or $16,000 increase. For Brown and Sons, 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.
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4. Calculate the volume of sales that Brown and Sons would have to have had in 2011 to
achieve the profit of $26,000 realized by Innovative in 2011.
Sales Variable costs Fixed costs = $26,000
Sales - .80(Sales) - $10,000 = $26,000
.20 Sales = $36,000
Sales = $180,000
100% Sales
$180,000
80%
Variable costs
144,000
20%
Contribution margin
$ 36,000
Fixed costs
Operating income
10,000
$ 26,000
5. 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, Innovative will suffer loss
when the sales volume drops below $87,500, whereas Brown and Sons will remain
profitable until sales drop below $50,000. Innovatives loss will be larger in absolute
amount of dollars than Brown and Sons. Brown and Sons has a greater margin of
safety than Innovative for Brown and Sons can watch sales drop further before
experiencing a loss situation.
However, if sales volume continues to increase, Innovative can use its fixed costs to
leverage income to higher levels than Brown and Sons. If sales volume does
increase by 80% to $180,000, Innovative can use the fixed cost lever to raise
income by (80% x 8 = 640%) $64,000 to $74,000. As shown in #4 above, Brown and
Sons would gain only $16,000 of income (80% x 2 = 160%) for income of $26,000.
Each company equalizes risk with reward. Innovative has taken a riskier approach by
investing more money in fixed cost-type items but can experience the possibility of
higher reward. Brown and Sons, 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.]
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Chapter 3
Operating Leverage
[[catch figure]]
Dollars
Revenues
Profits
Oldway
total costs
Breakeven
Points
Modern
total
Fixed
costs as
lever to
change
angle at
BE
Point of
indifference
Volume
0
the use of fixed costs to lever open profit
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Chapter 3
Worksheet for Comparing Income Statements
Contribution Income Statement
Financial Accounting Income Statement
Emphasizing Contribution Margin
Emphasizing Gross Margin
Revenues
Revenues
Variable manufacturing costs:
Cost of goods sold:
Direct materials
Direct materials
Direct manufacturing labour
Direct manufacturing labour
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 manufacturing
Variable nonmanufacturing
Fixed nonmanufacturing________
______________________________
Operating income
Operating income________________
Breakeven point = Fixed Costs CM% of Revenue
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