Chapter 15:
Cost-Volume-Profit Analysis: A
Managerial Planning Tool
Cornerstones of
Financial and Managerial Accounting, 2e
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Learning Objectives
1. Determine the break-even point in number of units and in
total sales dollars.
2. Determine the number of units that must be sold, and the
amount of revenue required, to earn a targeted profit.
3. Prepare a profit-volume graph and a cost-volume-profit
graph, and explain the meaning of each.
4. Apply cost-volume-profit analysis in a multiple-product
setting.
5. Explain the impact of risk, uncertainty, and changing
variables on cost-volume-profit analysis.
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1
Break-Even Point
in Units and Sales Dollars
►Cost-volume-profit (CVP) analysis estimates how
changes in the following three factors affect a
company’s profit.
►Costs (both variable and fixed)
►Sales volume
►Price
Profit
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1
Break-Even Point
in Units and in Sales Dollars
(continued)
► Companies use CVP analysis to help them reach important
benchmarks, like breakeven point.
► The break-even point is the point where total revenue equals
total cost (i.e., the point of zero profit).
► Put another way, the break-even point is the level of sales at
which contribution margin just covers fixed costs and
consequently operating income is equal to zero.
► Since new companies typically experience losses (negative
operating income) initially, they view their first break-even
period as a significant milestone.
$$$$$$$$
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1
Break-Even Point
in Units and in Sales Dollars
(continued)
Besides breakeven point, CVP analysis
can address many other issues as
well, including:
1 the number of units that must be
sold to break even
2 the impact of a given reduction in
fixed costs on the break-even point
3 the impact of an increase in price
on profit
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1
Using Operating Income
in Cost-Volume-Profit Analysis
For CVP analysis, it is useful to organize costs into fixed
and variable components. Below is the income
statement format that is based on the separation of
Direct
costs into fixed and variable components is called the
materials
.
Direct labor
Variable
overhead
Fixed
overhead
Variable selling and
administrative costs
Fixed selling and
administrative costs
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1
Using Operating Income
in Cost-Volume-Profit Analysis
(continued)
is the difference between
sales and variable expense. It is the amount of sales
revenue left over after all the variable expenses are
covered that can be used to contribute to fixed
expense and operating income.
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1
Cornerstone 15-1
Preparing a Contribution Margin
Income Statement
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1
Cornerstone 15-1
Preparing a Contribution Margin
Income Statement (continued)
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1
Break-Even Point
in Units
If the contribution margin income statement is
recast as an equation, it becomes more
useful for solving CVP problems.
Basic CVP
Equation
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1
Cornerstone 15-2
Calculating the Break-Even Point in Units
Information:
► Recall in Cornerstone 15-1 that Whittaker sells
mowers for $400 each and variable cost per
mower is $325. Total fixed cost equals $45,000.
Required:
1. Calculate the number of mowers that Whittier
must sell to break even.
2. Check your answer by preparing a contribution
margin income statement based on the break-even
point.
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1
Cornerstone 15-2
Calculating the Break-Even Point in Units
(continued)
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1
Break-Even Point in
Units
To recap, the break-even units are equal to the
fixed cost divided by the contribution margin
per unit.
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1
Break-Even Point
in Sales Dollars
Sometimes, managers using CVP analysis may prefer to use sales
revenue as the measure of sales activity instead of units sold. A
units sold measure can be converted to a sales revenue measure
by multiplying the unit selling price by the units sold:
For example, the break-even point for Whittier is 600 mowers;
the selling cost is $400 per mower.
So, Breakeven in Sales $’s = 600 x $400 = $240,000
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1
Variable Cost Ratio and
Contribution Margin Ratio
Any answer expressed in units sold can be easily
converted to one expressed in sales revenues.
Alternatively:
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1
Cornerstone 15-3
Calculating the Variable Cost Ratio and
the Contribution Margin Ratio
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Cornerstone 15-3
1 Calculating the Variable Cost Ratio and
the Contribution Margin Ratio (continued)
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Fixed Cost’s Relationship
with the Variable Cost Ratio and the
Contribution Margin Ratio
1
► Since the total contribution margin is the revenue remaining
after total variable costs are covered, it must be the revenue
available to cover fixed costs and contribute to profit. How
does the relationship of fixed cost to contribution margin
affect operating income?
► There are three possibilities:
► Fixed cost equals contribution margin; operating income is zero; the
company breaks even.
► Fixed cost is less than contribution margin; operating income is
greater than zero; the company makes a profit.
► Fixed cost is greater than contribution margin; operating income is
less than zero; the company makes a loss.
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1
Calculating Break-Even
in Sales Dollars
► The equation to figure the break-even sales dollars is:
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1
Cornerstone 15-4
Calculating the Break-Even Point
in Sales Dollars
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1
Cornerstone 15-4
Calculating the Break-Even Point
in Sales Dollars (continued)
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1
Cornerstone 15-4
Calculating the Break-Even Point
in Sales Dollars (continued)
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2
Units to Be Sold to
Achieve a Target Income
► While the break-even point is useful information and an
important benchmark for relatively young companies, most
companies would like to earn operating income greater than
$0.
► CVP allows us to do this by adding the target income amount
to the fixed cost.
► First, let’s look in terms of the units that must be sold to earn
a desired income.
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2
Cornerstone 15-5
Calculating the Number of Units to Be
Sold to Earn A Target Operating Income
Information:
► Whittier Company sells mowers at $400 each.
Variable cost per unit is $325, and total fixed cost
is $45,000.
Required:
1. Calculate the number of units that Whittier must
sell to earn operating income of $37,500.
2. Check your answer by preparing a contribution
margin income statement based on the number of
units calculated.
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2
Cornerstone 15-5
Calculating the Number of Units to Be Sold
to Earn A Target Operating Income (continued)
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2
Sales Revenue to
Achieve a Target Income
► How much sales revenue must Whittier generate to earn an
operating income of $37,500? This question is similar to the
one we asked earlier in terms of units but phrases the
question directly in terms of sales revenue.
► To answer the question, add the targeted operating income
of $37,500 to the $45,000 of fixed cost and divide by the
contribution margin ratio. This equation is:
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2
Cornerstone 15-6
Calculating Sales Needed to
Earn a Target Operating Income
Information:
►Whittier Company sells mowers at $400 each.
Variable cost per unit is $325, and total fixed cost is
$45,000.
Required:
1. Calculate the contribution margin ratio.
2. Calculate the sales that Whittier must make to earn
an operating income of $37,500.
3. Check your answer by preparing a contribution
margin income statement based on the sales dollars
calculated.
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2
Cornerstone 15-6
Calculating Sales Needed to
Earn A Target Operating Income (continued)
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2
Impact of Change in Revenue
on Change in Profit
► Assuming that fixed costs remain unchanged, the contribution
margin ratio can be used to find the profit impact of a change
in sales revenue.
► To obtain the total change in profits from a change in
revenues, multiply the contribution margin ratio times the
change in sales:
Change
in
Profits
Contribution
Change
=
Margin
in
x
Ratio
Sales
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Graphs of Cost-Volume-Profit
Relationships: The Profit-Volume Graph
3
A profit-volume graph visually portrays the relationship between
profits (operating income) and units sold.
► The profit-volume graph is the graph of the operating income equation:
Operating income = (Price x Units) - (Unit variable cost x Units) - Total fixed cost
► In this graph, operating income is the dependent variable, and units is the
independent variable.
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Graphs of Cost-Volume-Profit
Relationships: The Cost-Volume-Profit Graph
3
The cost-volume-profit graph depicts the relationships among cost,
volume, and profits (operating income).
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3
CVP Analysis Assumptions
Major assumptions of CVP analysis include:
1
2
Linear revenue and cost
functions remain constant
over the relevant range.
Selling prices and costs
are known with certainty.
3
4
All units produced are
sold; no finished goods
inventories remain.
Sales mix is known with
certainty for multipleproduct break-even
settings.
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4
Multiple-Product Analysis
► Cost-volume-profit analysis is fairly simple in the singleproduct setting. However, most firms produce and sell a
number of products or services.
► How do we adapt the formulas used in a single-product
setting to a multiple-product setting?
► One important distinction is to separate direct fixed expenses
from common fixed expenses.
►Direct fixed expenses are those fixed costs that can be
traced to each segment and would be avoided if the
segment did not exist.
►Common fixed expenses are the fixed costs that are not
traceable to the segments and would remain even if one
of the segments was eliminated.
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4
Break-Even Calculations
for Multiple Products
►When more than one product is produced and
sold, managers must estimate the sales mix and
calculate a package contribution margin.
is the relative combination of products
being sold by a firm.
=
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4
Cornerstone 15-7
Calculating The Break-Even Units
for a Multiple-Product Firm
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4
Cornerstone 15-7
Calculating The Break-Even Units
for a Multiple-Product Firm (continued)
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4
Cornerstone 15-7
Calculating The Break-Even Units
for a Multiple-Product Firm (continued)
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Cornerstone 15-8
4
Calculating The Break-Even Sales Dollars
for A Multiple-Product Firm
Information:
►Recall that Whittier Company sells two products that
are expected to produce total revenue next year of
$1,120,000 and total variable cost of $870,000. Total
fixed cost is expected to equal $96,250.
Required:
1. Calculate the break-even point in sales dollars for
Whittier.
2. Check your answer by preparing a contribution
margin income statement.
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4
Cornerstone 15-8
Calculating The Break-Even Sales Dollars
for A Multiple-Product Firm (continued)
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4
You Decide
Finding the Break-Even Point for a New
Business
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5
Cost-Volume-Profit Analysis
and Risk and Uncertainty
Managers must be aware of so many factors in our
dynamic world. CVP analysis is a tool that managers use to
handle risk and uncertainty.
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5
Introducing Risk and Uncertainty
An important assumption of
CVP analysis is that prices
and costs are known with
certainty.
However, risk and
uncertainty are a part of
business decision making
and must be dealt with
somehow.
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5
Methods to Deal with
Uncertainty and Risk
1
• Management must realize
the uncertain nature of
future prices, costs, and
quantities.
2
• Management must assume
a breakeven “band” rather
than a breakeven point.
3
• Managers should use
sensitivity or “what-if”
analyses.
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5
Margin of Safety and
Operating Leverage
hhhhhhhhhhhh
hhhhhhhhhhhh
HELP WANTED: Managers to
consider measures of risk, like
margin of safety and
operating leverage. MUST
HAVE knowledge of Fixed and
Variable costs.
hhhhhhhhhhhh
hhhhhhhhhhhh
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5
Margin of Safety
►The margin of safety is the units sold or the revenue
earned above the break-even volume.
►For example, if the break-even volume for a company
is 200 units and the company is currently selling 500
units, the margin of safety in units is: Sales - Breakeven units = 500 – 200 = 300 units
►If the break-even volume for a company is $200,000
and the current revenues are $500,000, the margin
of safety in sales revenue is: Revenue - Break-even
volume = $500,000 – 200,000 = $300,000
►The margin of safety as a percentage of total sales
dollars can then be expressed as: Margin of safety ÷
Revenues = $300,000 ÷ $500,000 = 60%
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5
Cornerstone 15-9
Computing the Margin of Safety
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5
Operating Leverage
►Operating leverage is use of fixed costs to
extract higher percentage changes in profits
as sales activity changes.
►Operating leverage is the measure of the
proportion of fixed costs in a company’s cost
structure.
►It is used as an indicator of how sensitive
profit is to changes in sales volume.
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5
Operating Leverage
(continued)
►The degree of operating leverage (DOL) can
be measured for a given level of sales by
taking the ratio of contribution margin to
operating income or:
Contribution margin ÷ Operating income
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5
Cornerstone 15-10
Computing the
Degree of Operating Leverage
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5
Summary of Operating
Leverage
Operating Leverage
HIGH
LOW
% profit increase with sales
increase
Large
Small
% loss increase with sales
decrease
Large
Small
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5
Cornerstone 15-11
Calculating the Impact of Increased Sales
on Operating Income Using
the Degree of Operating Leverage
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5
Sensitivity Analysis
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5
You Decide
Using Contribution Margin Income
Statements To Consider Varying Scenarios
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