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Chapter Four
Cost-Volume-Profit Analysis:
A Managerial Planning Tool
COPYRIGHT © 2012 Nelson Education Ltd.
Learning Objectives
1. Determine the break-even point in units and 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
4-2
COPYRIGHT © 2012 Nelson Education Ltd.
OBJECTIVE 1
Determine the break-even point
in units and sales dollars
4-3
COPYRIGHT © 2012 Nelson Education Ltd.
Cost-Volume-Profit Analysis
A powerful tool for planning and decision making
It can be used to calculate:
The number of units
that must be sold to
break-even
The impact of an
increase in price on
profit
The impact of a given
reduction in fixed
costs on the breakeven point
4-4
COPYRIGHT © 2012 Nelson Education Ltd.
Break-Even Point
Total Revenue = Total Cost
Or put it another way:
Total Revenue
- Total Costs
Zero Profit
4-5
COPYRIGHT © 2012 Nelson Education Ltd.
Using Operating Income in
Cost-Volume-Profit Analysis
Contribution Margin
Sales
-
Variable
Expense
Contribution
=
Margin
Contribution Margin is then used to cover
Fixed Costs and Operating Income
4-6
COPYRIGHT © 2012 Nelson Education Ltd.
Contribution Margin Income
Statement
• Divides costs based on behaviour
• Costs are divided into variable and fixed
components
• Important subtotal is contribution margin
– Sales revenue minus variable expenses
4-7
COPYRIGHT © 2012 Nelson Education Ltd.
Using Operating Income in
Cost-Volume-Profit Analysis
Contribution Margin
Sales
-
Variable
Costs
Contribution
Margin
-
Fixed
Costs
=
Contribution
Margin
=
Operating
Income
Break-even point is when
Operating Income = 0
4-8
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-1
How to Prepare a Contribution Margin
Income Statement
Information:
• Whittier Co. plans to sell 1,000 mowers at $400 each in the
coming year. Product costs include:
–
–
–
–
Direct materials per mower $180
Direct labour per mower $100
Variable overhead per mower $25
Total fixed factory overhead $15,000
• Variable selling expense is a commission of $20 per
mower; fixed selling and administrative expense totals
$30,000
4-9
COPYRIGHT © 2012 Nelson Education Ltd.
Example
Required:
• Calculate the total variable cost per unit
• Calculate the total fixed expense for the year
• Prepare a contribution margin income statement
for Whittier Co. for the coming year
4-10
COPYRIGHT © 2012 Nelson Education Ltd.
Variable Cost
Variable
Cost Per
unit
Direct
Variable
Direct
+
+
+
=
Labour
Overhead
Materials
Variable
Selling
Expense
Variable
Cost Per
unit
=
+ $100 +
$20
Variable
Cost Per
unit
=
$180
$25
+
$325
4-11
COPYRIGHT © 2012 Nelson Education Ltd.
Fixed Expenses
=
Fixed
Overhead
+
Fixed Selling &
Administrative
Expense
Total Fixed
Expenses
=
$15,000
+
$30,000
Total Fixed
Expenses
=
$45,000
Total Fixed
Expenses
4-12
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year
Total
Sales ($400 × 1,000 mowers)
Total variable expense ($325 × 1,000)
Total contribution margin
Total fixed expense
Operating income
Per Unit
$400,000
$400
325,000
325
$ 75,000
$ 75
45,000
$ 30,000
Each unit contributes $75
to cover fixed costs
4-13
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-2
How to Solve for the Break-Even Point in Units
Information:
• Whittier Co. plans to sell 1,000 mowers at $400 each in
the coming year. Product costs include:
– Direct materials per mower $180
– Direct labour per mower $100
– Variable overhead per mower $25
– Total fixed factory overhead $15,000
• Variable selling expense is a commission of $20 per
mower; fixed selling and administrative expense totals
$30,000
4-14
COPYRIGHT © 2012 Nelson Education Ltd.
Example
Required:
• Calculate the total variable cost per unit
• Calculate the total fixed expense for the year
• Calculate the number of mowers that Whittier Co. must
sell to break-even
• Check the answer by preparing a contribution margin
income statement based on the break-even point
4-15
COPYRIGHT © 2012 Nelson Education Ltd.
Variable & Fixed Costs
These were computed in Cornerstone 4-1
Variable
Cost Per = $180 + $100 + $25 + $20 = $325
unit
Total Fixed
=
Expenses
$15,000 + $30,000 = $45,000
4-16
COPYRIGHT © 2012 Nelson Education Ltd.
Break-Even Number of
Mowers
Formula can be simplified down to:
Break-even
units
Total Fixed Cost
=
Contribution Margin per unit
Selling Price – Variable cost per unit
Break-even
units
=
Break-even
units
=
$45,000
($400 – $325)
600 mowers
4-17
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year based on sales of 600 mowers
Total
Sales ($400 × 600 mowers)
Total Variable Expense ($325 × 600)
Total Contribution Margin
Total Fixed Expense
Operating Income
Per Unit
$240,000
$400
195,000
325
$ 45,000
$ 75
45,000
$
0
Operating income is zero when 600 units are sold.
The break-even calculation is correct!
4-18
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-3
How to Calculate the Variable Cost Ratio and the
Contribution Margin Ratio
Information:
• Whittier Co. plans to sell 1,000 mowers at $400 each
in the coming year
• Variable cost per unit is $325
• Total fixed cost is $45,000
4-19
COPYRIGHT © 2012 Nelson Education Ltd.
Example
Required:
• Calculate the variable cost ratio
• Calculate the contribution margin ratio using unit
figures
• Prepare a contribution margin income statement
based on the budgeted figures for next year
– In a column next to the income statement, show the
percentages based on sales for:
• Sales
• Total variable costs
• Total contribution margin
4-20
COPYRIGHT © 2012 Nelson Education Ltd.
Variable Cost Ratio
Variable
Cost Ratio
=
Variable Cost
Sales
Variable
Cost Ratio
=
$325
$400
Variable
Cost Ratio
=
81.25%
4-21
COPYRIGHT © 2012 Nelson Education Ltd.
Contribution Margin Ratio
Contribution
Margin per unit
=
Sales
Contribution
Margin per unit
=
$75 per unit
Contribution
Margin Ratio
=
Contribution
Margin Ratio
=
-
Variable Cost
Contribution Margin
Sales
$75
= 18.75%
$400
4-22
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year
$400,000
% of
Sales
100.00
325,000
81.25
$ 75,000
18.75
Total
Sales ($400 ×1,000 mowers)
Total Variable Exp. (0.8125 × $400,000)
Total Contribution Margin
Total Fixed Expense
Operating Income
45,000
$ 30,000
4-23
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-4
How to Solve for the Break-Even
Point in Sales Dollars
Information:
• Whittier Co. plans to sell 1,000 mowers at $400 each
in the coming year
• Variable cost per unit is $325
• Total fixed cost is $45,000
4-24
COPYRIGHT © 2012 Nelson Education Ltd.
Example
Required:
• Calculate the contribution margin ratio
• Calculate the sales revenue that Whittier Co. must make
to break-even by using the break-even point in sales
equation
• Prepare a contribution margin income statement based on
the break-even point in sales dollars
4-25
COPYRIGHT © 2012 Nelson Education Ltd.
Contribution Margin Ratio
Contribution
Margin per unit
=
Contribution
Margin Ratio
=
$400 – $325 =
$75
$400
$75 per unit
= 18.75%
These were computed in Cornerstone 4-1
4-26
COPYRIGHT © 2012 Nelson Education Ltd.
Break-Even Point in
Sales Dollars
Break-even
sales
Total fixed expenses
=
Break-even
sales
=
$45,000
0.1875
Break-even
sales
=
$240,000
Contribution margin ratio
4-27
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year
Sales
$240,000
Total Variable Exp. (0.8125 × $240,000)
Total Contribution Margin
Total Fixed Expense
Operating Income
195,000
$ 45,000
45,000
$
0
Operating Income is zero when sales are $240,000
The break-even calculation is correct!
4-28
COPYRIGHT © 2012 Nelson Education Ltd.
OBJECTIVE 2
Determine the number of units
that must be sold and the
amount of revenue required to
earn a targeted profit
COPYRIGHT © 2012 Nelson Education Ltd.
Units to Be Sold to
Achieve a Target Income
Two Ways:
1. Using Operating Income equation
2. Using the Basic Break-even equation
Cornerstone 4-5 will walk us through
these computations
4-30
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-5
How to Solve for the Number of Units to Be Sold to
Earn a Target Operating Income
Information:
• Whittier Co. sells mulching mowers at $400 each
• Variable cost per unit is $325 and total fixed cost is $45,000
Required:
• Calculate the number of units that Whittier Co. must sell
to earn operating income of $37,500
• Prepare a contribution margin income statement based
on the number of units calculated
4-31
COPYRIGHT © 2012 Nelson Education Ltd.
Units to Be Sold to
Achieve a Target Income
Number of
units to earn
target income
=
Number of
units to earn
target income
=
$45,000 + $37,500
$400 - $325
Number of
units to earn
target income
=
1,100
Total fixed expense + Target income
Price – Variable cost per unit
4-32
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year
Sales ($400 ×1,100)
$440,000
Total variable expense ($325 × 1,100)
Total contribution margin
Total fixed expense
Operating income
357,500
$ 82,500
45,000
$ 37,500
The calculation is correct!
The operating income is $37,500
4-33
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-6
How to Solve for the Sales Needed to Earn
a Target Operating Income
Information:
• Whittier Co. sells mulching mowers at $400 each
• Variable cost per unit is $325 and Total fixed cost is $45,000
Required:
• Calculate the contribution margin ratio
• Calculate the sales that Whittier Co. must make to earn an
operating income of $37,500
• Prepare a contribution margin income statement based on
the sales dollars calculated
4-34
COPYRIGHT © 2012 Nelson Education Ltd.
Sales Revenue to Achieve a
Target Income
Sales dollars
to earn target
income
=
Sales dollars to
earn target
income
=
Sales dollars
to earn target
income
=
Fixed Cost + Target Income
Contribution margin ratio
$45,000 + $37,500
0.1875
$440,000
4-35
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year
Sales
$440,000
Total variable exp. (0.8125 × $440,000)
Total contribution margin
Total fixed expense
Operating income
357,500
$ 82,500
45,000
$ 37,500
The calculation is correct!
The operating income is $37,500
4-36
COPYRIGHT © 2012 Nelson Education Ltd.
OBJECTIVE 3
Prepare a profit-volume graph
and a cost-volume-profit graph
and explain the meaning of each
COPYRIGHT © 2012 Nelson Education Ltd.
Profit-Volume Graph
• Visually portrays the relationship between
profits and units sold
• Operating Income is the dependent variable
• Units sold is the independent variable
4-38
COPYRIGHT © 2012 Nelson Education Ltd.
Cost-Volume-Profit Graph
• Depicts relationship among cost volume and
profits
• Graph two separate lines:
– Total revenue
– Total cost
• Vertical axis: measured in dollars
• Horizontal axis: measured in units sold
4-39
COPYRIGHT © 2012 Nelson Education Ltd.
Assumptions of CostVolume-Profit Analysis
• Revenue and cost functions are linear
• Price, total fixed costs, and unit variable costs
can be identified and remain constant over
relevant range
• All units produced are sold –no changes in
inventory levels
• Sales mix is constant
• Selling prices and costs are known with certainty
4-40
COPYRIGHT © 2012 Nelson Education Ltd.
Linear Cost and Revenue
Functions
Cost-Volume-Profit assumes that cost and
revenue functions are linear
In other words they are straight lines
4-41
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Production Equal to Sales
• Cost-Volume-Profit assumes that what is
produced is actually sold
• Inventory levels do not change over period
• CVP focuses on current costs by excluding
inventory costs of previous periods
4-42
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Constant Sales Mix
Multiple product break-even analysis
requires a constant sales mix
Relative combination of
products being sold by a firm
Sales mix is difficult to predict with
certainty
4-43
COPYRIGHT © 2012 Nelson Education Ltd.
Linear Cost and Revenue
Functions
Firms seldom know prices, variable costs, and
fixed costs with certainty
There are formal ways of explicitly building
uncertainty into the Cost-Volume-Profit model
4-44
COPYRIGHT © 2012 Nelson Education Ltd.
OBJECTIVE 4
Apply cost-volume-profit analysis
in a multiple-product setting
COPYRIGHT © 2012 Nelson Education Ltd.
Multiple-Product Analysis
Cost-Volume-Profit analysis becomes
more complex with multiple products
We need to adapt the singleproduct formulas
4-46
COPYRIGHT © 2012 Nelson Education Ltd.
Direct & Common Fixed
Expenses
Direct
Fixed Expenses
Common
Fixed Expenses
Fixed costs that can
be traced to each
segment and would
be avoided if the
segment did not exist
Fixed costs that are
not traceable to the
segments and would
remain even if one of
the segments was
eliminated
4-47
COPYRIGHT © 2012 Nelson Education Ltd.
Multiple-Product Analysis
Break-even point in units
Key: identify expected sales mix
Sales Mix:
• Measured in units sold
• Reduced to the smallest possible whole numbers
• Required in order to determine break-even point in
units
4-48
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-7
How to Calculate the Break-Even Units
for a Multiple-Product Firm
Information:
• Whittier Co. sells two products:
– Mulching mowers priced at $400
– Riding mowers priced at $800
• The variable costs per unit are:
– $325 per mulching mower
– $600 per riding mower
• Total fixed expense is $96,250
• Whittier’s expected sales mix is three mulching mowers to
two riding mowers
4-49
COPYRIGHT © 2012 Nelson Education Ltd.
Example
Required:
• Form a package of mulching and riding mowers,
based on the sales mix, and calculate the
package contribution margin
• Calculate the break-even point in units for
mulching mowers and for riding mowers
• Check calculations by preparing a contribution
margin income statement
4-50
COPYRIGHT © 2012 Nelson Education Ltd.
Package Contribution Margin
Product
Price
Mulching
$400
Unit
Variable
Cost
$325
800
600
Riding
Unit
Contrib.
Margin
$ 75
3
$225
200
2
400
Package Total
Sales Pkg. Unit
Contrib.
Mix
Margin
$625
4-51
COPYRIGHT © 2012 Nelson Education Ltd.
Break-Even Point in Units
Break-even
packages
Fixed Cost
=
Break-even
packages
=
$96,250
$625
Break-even
packages
=
154
Package contribution margin
4-52
COPYRIGHT © 2012 Nelson Education Ltd.
Break-Even Point in Units
154 Break-even packages
Each package contains:
3 mulching mowers, 2 riding mowers
Mulching mowers
break-even units
= 154 × 3 = 462
Riding mowers
break-even units
= 154 × 2 = 308
4-53
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year
Mulching
462 × $400
Riding
Total
$184,800 $246,400 $431,200
Sales
Total Variable Expense
150,150
184,800
334,950
Total Contribution Margin $ 34,650 $ 61,600 $ 96,250
$ 96,250
Total Fixed Expense
Operating Income
462 × $325
$
0
308 × $800
4-54
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-8
How to Calculate the Break-Even Sales Dollars for a
Multiple-Product Firm
Information:
• Whittier Co. sells two products that are expected to produce:
– Total revenue next year of $1,120,000
– Total variable costs of $870,000
• Total fixed costs are expected to equal $96,250
Required:
• The break-even point in sales dollars for Whittier Co.
• Check calculations by preparing a contribution margin
income statement
4-55
COPYRIGHT © 2012 Nelson Education Ltd.
CVP Analysis
Break-even point in sales dollars
Contribution
Margin
Ratio
=
Contribution
Margin
Ratio
=
Contribution
Margin
Ratio
=
Expected Contribution Margin
Total Sales Revenue
$250,000
$1,120,000
0.22*
*Rounded
4-56
COPYRIGHT © 2012 Nelson Education Ltd.
CVP Analysis
Break-even sales
Fixed Cost
Break-Even
Sales
=
Break-Even
Sales
=
$96,250
0.22
Break-Even
Sales
=
$437,500
Contribution Margin Ratio
4-57
COPYRIGHT © 2012 Nelson Education Ltd.
Whittier Company
Contribution Margin Income Statement
For the Coming Year
Sales
$437,500
Total Variable Exp. (0.78 × 437,500)
Total Contribution Margin
Total Fixed Expense
Operating Income
341,250
$ 96,250
96,250
$
0
Operating income is zero when sales are $437,500
The break-even calculation is correct!
4-58
COPYRIGHT © 2012 Nelson Education Ltd.
OBJECTIVE 5
Explain the impact of risk,
uncertainty, and changing variables
on cost-volume-profit analysis
COPYRIGHT © 2012 Nelson Education Ltd.
CVP Analysis:
Risk and Uncertainty
• The break-even point can be affected by
changes in:
– Price
– Unit Contribution Margin
– Fixed Cost
Changes in any of the above
will affect the sales mix
4-60
COPYRIGHT © 2012 Nelson Education Ltd.
Risk and Uncertainty Effects
on Managers
• Must realize the uncertain nature of future
prices, costs, and quantities
• Move from consideration of a break-even point
to what might be called a “break-even band”
• May engage in sensitivity or what-if analysis
4-61
COPYRIGHT © 2012 Nelson Education Ltd.
Margin of Safety
• Units sold or revenue earned above break-even
volume
• Crude measure of risk
– When there is a downturn in sales, the risk of
suffering losses will be less if the firm’s margin of
safety is large than if the margin of safety is small
4-62
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-9
How to Compute the Margin of Safety
Information:
• This year, Whittier Co. plans to sell 1,000 mowers at $400 ea.
• Variable costs are $325
• Fixed costs are $45,000
• Break-even units were previously calculated as 600
Required:
• Calculate the margin of safety for Whittier Co. in units
• Calculate the margin of safety for Whittier Co. in sales
revenue
4-63
COPYRIGHT © 2012 Nelson Education Ltd.
Margin of Safety in Units
Margin of
safety in units
=
Sales in
units
-
Break-even
units
Margin of
safety in units
=
1,000
-
600
Margin of
safety in units
=
400
4-64
COPYRIGHT © 2012 Nelson Education Ltd.
Margin of Safety in Sales
Revenue
Margin of safety in
sales revenue
=
Sales
Margin of safety
in sales revenue
=
$400(1,000)
Margin of safety
in sales revenue
=
-
Break-even
units
- $400(600)
$160,000
4-65
COPYRIGHT © 2012 Nelson Education Ltd.
Operating Leverage
• Relative mix of fixed costs to variable costs
• Higher proportions of fixed costs to the amount of
variable costs create higher operating leverage
• The greater the degree of operating leverage, the
larger the effect on operating income when sales
change
Degree of
operating
leverage
=
Contribution margin
Operating income
4-66
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-10
How to Compute the Degree of Operating Leverage
Information:
• This year, Whittier Co. plans to sell 1,000 mowers at $400 ea.
• Variable costs are $325
• Fixed costs are $45,000
• Operating Income at 1,000 units is $30,000
Required:
• Calculate the degree of operating leverage for Whittier Co.
4-67
COPYRIGHT © 2012 Nelson Education Ltd.
Operating Leverage
Degree of operating leverage (DOL) can be
measured for a given level of sales
Degree of
operating leverage
=
Degree of
operating leverage
=
Degree of
operating leverage
=
Contribution Margin
Operating Income
($400 - $325)(1,000 units)
$30,000
2.5
4-68
COPYRIGHT © 2012 Nelson Education Ltd.
Cornerstone 4-11
How to Compute the Impact of Increased Sales
on Operating Income Using the DOL
Information:
• Whittier Co. plans to sell 1,000 mowers and earn operating
income equal to $30,000 next year
• Whittier’s degree of operating leverage is equal to 2.5
• Now, the company plans to increase sales by 20 percent
next year
4-69
COPYRIGHT © 2012 Nelson Education Ltd.
Example
Required:
• Calculate the percent change in operating income
expected by Whittier Co. for the next year using the
degree of operating leverage
• Calculate the operating income expected by Whittier Co.
next year using the percent change in operating income
calculated in the above requirement
4-70
COPYRIGHT © 2012 Nelson Education Ltd.
Percentage Change in
Operating Leverage
Percent change in
operating leverage
DOL
×
Percent change
in sales
=
Percent change in
operating leverage
=
2.5
×
20%
Percent change in
operating leverage
=
50%
4-71
COPYRIGHT © 2012 Nelson Education Ltd.
Expected Operating Income
Expected
operating
income
Original
= operating +
income
Expected
operating
income
= $30,000 + (0.50 × $30,000)
Expected
operating
income
= $45,000
(percent change × original
operating income)
4-72
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