Chap022

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22-1
Chapter
22
McGraw-Hill/Irwin1
Cost-VolumeProfit Analysis
© The McGraw-Hill Companies, Inc., 2006
22-2
Questions Addressed by
Cost-Volume-Profit Analysis
CVP analysis is used to answer questions
such as:
• How much must I sell to earn my desired income?
• How will income be affected
if I reduce selling prices to
increase sales volume?
• How will income be affected
if I change the sales mix
of my products?
McGraw-Hill/Irwin2
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22-3
Total Fixed Cost
Monthly Basic
Telephone Bill
Total fixed costs remain unchanged
when activity changes.
Number of Local Calls
McGraw-Hill/Irwin3
Your monthly basic
telephone bill probably
does not change when
you make more local calls.
© The McGraw-Hill Companies, Inc., 2006
22-4
Fixed Cost Per Unit
Your average cost per
local call decreases as
more local calls are made.
McGraw-Hill/Irwin4
Monthly Basic Telephone
Bill per Local Call
Fixed costs per unit decline
as activity increases.
Number of Local Calls
© The McGraw-Hill Companies, Inc., 2006
22-5
Total Variable Cost
Total Long Distance
Telephone Bill
Total variable costs change
when activity changes.
Minutes Talked
McGraw-Hill/Irwin5
Your total long distance
telephone bill is based
on how many minutes
you talk.
© The McGraw-Hill Companies, Inc., 2006
22-6
Variable Cost Per Unit
The cost per long distance
minute talked is constant.
For example, 7
cents per minute.
McGraw-Hill/Irwin6
Per Minute
Telephone Charge
Variable costs per unit do not change
as activity increases.
Minutes Talked
© The McGraw-Hill Companies, Inc., 2006
22-7
Cost Behavior Summary
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Changes as activity level
changes.
Remains the same over wide
ranges of activity.
Fixed
Remains the same even
when activity level changes.
Decreases as activity level
increases.
McGraw-Hill/Irwin7
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22-8
Mixed Costs
Mixed costs contain a fixed portion that is
incurred even when facility is unused, and a
variable portion that increases with usage.
Example: monthly electric utility charge
• Fixed service fee
• Variable charge per
kilowatt hour used
McGraw-Hill/Irwin8
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22-9
Total Utility Cost
Mixed Costs
Variable
Utility Charge
Fixed Monthly
Utility Charge
Activity (Kilowatt Hours)
McGraw-Hill/Irwin9
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22-10
Step-Wise Costs
Cost
Total cost remains
constant within a
narrow range of
activity.
Activity
McGraw-Hill/Irwin10
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22-11
Step-Wise Costs
Cost
Total cost increases to a
new higher cost for the
next higher range of
activity.
Activity
McGraw-Hill/Irwin11
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22-12
Curvilinear Costs
Total Cost
Costs that increase when activity increases, but
in a nonlinear manner.
Activity
McGraw-Hill/Irwin12
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22-13
Identifying and Measuring
Cost Behavior
The objective
is to classify
all costs as
either fixed or
variable.
McGraw-Hill/Irwin13
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22-14
Scatter Diagram
A scatter diagram of past cost behavior
may be helpful in analyzing mixed costs.
McGraw-Hill/Irwin14
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22-15
Scatter Diagram
Total Cost in
1,000’s of Dollars
Plot the data points on a
graph (total cost vs. activity).
20
10
* *
* *
* ** *
**
0
0
1
2
3
4
Activity, 1,000’s of Units Produced
McGraw-Hill/Irwin15
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22-16
Scatter Diagram
Total Cost in
1,000’s of Dollars
Draw a line through the plotted data points so that about
equal numbers of points fall above and below the line.
20
10
* *
* *
* ** *
**
Estimated fixed cost = 10,000
0
0
1
2
3
4
Activity, 1,000’s of Units Produced
McGraw-Hill/Irwin16
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22-17
Scatter Diagram
Total Cost in
1,000’s of Dollars
in cost
Unit Variable Cost = Slope =
in units
20
10
* *
* *
* ** *
**
Vertical
distance
is the
change
in cost.
Horizontal distance is
the change in activity.
0
0
1
2
3
4
Activity, 1,000’s of Units Produced
McGraw-Hill/Irwin17
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22-18
The High-Low Method
Exh.
22-6
The following relationships between sales
and costs are observed:
High activity level
Low activity level
Change
Sales
$ 67,500
17,500
$ 50,000
Cost
$ 29,000
20,500
$ 8,500
Using these two levels of activity, compute:
 the variable cost per unit.
 the total fixed cost.
McGraw-Hill/Irwin18
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22-19
The High-Low Method
High activity level
Low activity level
Change

Sales
$ 67,500
17,500
$ 50,000
Exh.
22-6
Cost
$ 29,000
20,500
$ 8,500
$8,500
in cost
Unit variable cost =
=
= $0.17 per $
in units $50,000
McGraw-Hill/Irwin19
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22-20
The High-Low Method
High activity level
Low activity level
Change
Exh.
22-6
Sales
$ 67,500
17,500
$ 50,000
Cost
$ 29,000
20,500
$ 8,500

$8,500
in cost
Unit variable cost =
=
= $0.17 per $
in units $50,000

Fixed cost = Total cost – Total variable
McGraw-Hill/Irwin20
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22-21
The High-Low Method
High activity level
Low activity level
Change
Exh.
22-6
Sales
$ 67,500
17,500
$ 50,000
Cost
$ 29,000
20,500
$ 8,500

$8,500
in cost
Unit variable cost =
=
= $0.17 per $
in units $50,000

Fixed cost = Total cost – Total variable cost
Fixed cost = $29,000 – ($0.17 per sales $ × $67,500)
Fixed cost = $29,000 – $11,475 = $17,525
McGraw-Hill/Irwin21
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22-22
Least-Squares Regression
Least-squares regression is usually covered
in advanced cost accounting courses. It is
commonly used with computer software
because of the large number of
calculations required.
The objective of the cost
analysis remains the
same: determination of
total fixed cost and the
variable unit cost.
McGraw-Hill/Irwin22
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22-23
Break-Even Analysis
Let’s extend our
knowledge of
cost behavior to
break-even analysis.
McGraw-Hill/Irwin23
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22-24
Computing Break-Even Point
The break-even point (expressed in units
of product or dollars of sales) is the
unique sales level at which a company
earns neither a profit nor incurs a loss.
McGraw-Hill/Irwin24
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22-25
Computing Break-Even Point
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
Unit
$ 50
30
$ 20
Contribution margin is amount by which revenue
exceeds the variable costs of producing the revenue.
McGraw-Hill/Irwin25
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22-26
Computing Break-Even Point
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
Unit
$ 50
30
$ 20
How much contribution margin must this company
have to cover its fixed costs (break even)?
Answer: $30,000
McGraw-Hill/Irwin26
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22-27
Computing Break-Even Point
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
Unit
$ 50
30
$ 20
How many units must this company sell to cover its
fixed costs (break even)?
Answer: $30,000 ÷ $20 per unit = 1,500 units
McGraw-Hill/Irwin27
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22-28
Computing Break-Even Point
Exh.
22-8
We have just seen one of the basic CVP
relationships – the break-even computation.
Break-even point in units =
Fixed costs
Contribution margin per unit
Unit sales price less unit variable cost
($20 in previous example)
McGraw-Hill/Irwin28
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22-29
Computing Break-Even Point
Exh.
22-9
The break-even formula may also be
expressed in sales dollars.
Break-even point in dollars =
Fixed costs
Contribution margin ratio
Unit contribution margin
Unit sales price
McGraw-Hill/Irwin29
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22-30
Computing Break-Even Point
ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs
are $3.00 per unit, how many units must be
sold to break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
McGraw-Hill/Irwin30
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22-31
Computing Break-Even Point
ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs
are $3.00 per unit, how many units must be
sold to break even?
a. 100,000 units
Unit contribution = $5.00 - $3.00 = $2.00
b. 40,000 units
$200,000
Fixed costs
c. 200,000 units
= $2.00 per unit
Unit contribution
d. 66,667 units
= 100,000 units
McGraw-Hill/Irwin31
© The McGraw-Hill Companies, Inc., 2006
22-32
Computing Break-Even Point
Use the contribution margin ratio formula to
determine the amount of sales revenue ABC must
have to break even. All information remains
unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
a.
b.
c.
d.
$200,000
$300,000
$400,000
$500,000
McGraw-Hill/Irwin32
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22-33
Computing Break-Even Point
Use the contribution margin ratio formula to
determine the amount of sales revenue ABC must
have to break even. All information remains
unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
Unit contribution = $5.00 - $3.00 = $2.00
a.
b.
c.
d.
$200,000
Contribution margin ratio = $2.00 ÷ $5.00 = .40
$300,000
Break-even revenue = $200,000 ÷ .4 = $500,000
$400,000
$500,000
McGraw-Hill/Irwin33
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22-34
Preparing a CVP Chart
Costs and Revenue
in Dollars
 Plot total fixed costs on the vertical axis.
Total fixed costs
Total costs
 Draw the total cost line with a slope
equal to the unit variable cost.
Volume in Units
McGraw-Hill/Irwin34
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22-35
Preparing a CVP Chart
 Starting at the origin, draw the sales line
Sales
Costs and Revenue
in Dollars
with a slope equal to the unit sales price.
Total fixed costs
Total costs
Breakeven
Point
Volume in Units
McGraw-Hill/Irwin35
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22-36
Assumptions of CVP Analysis
 A limited range of activity called the relevant
range, where CVP relationships are linear.
Unit selling price remains constant.
Unit variable costs remain constant.
Total fixed costs remain constant.
 Production = sales (no inventory changes).
McGraw-Hill/Irwin36
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22-37
Computing Income
from Expected Sales
Exh.
22-12
Income (pretax) = Sales – Variable costs – Fixed costs
McGraw-Hill/Irwin37
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22-38
Computing Income
from Expected Sales
Exh.
22-13
Rydell expects to sell 1,500 units at $100 each
next month. Fixed costs are $24,000 per
month and the unit variable cost is $70. What
amount of income should Rydell expect?
Income (pretax) = Sales – Variable costs – Fixed costs
= [1,500 units × $100] – [1,500 units × $70] – $24,000
= $21,000
McGraw-Hill/Irwin38
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22-39
Computing Sales for a Target Income
Break-even formulas may be adjusted to
show the sales volume needed to earn
any amount of income.
Unit sales =
Fixed costs + Target income
Contribution margin per unit
Fixed costs + Target income
Dollar sales =
Contribution margin ratio
McGraw-Hill/Irwin39
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22-40
Computing Sales for a Target Income
ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs
are $3.00 per unit, how many units must be
sold to earn income of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
McGraw-Hill/Irwin40
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22-41
Computing Sales for a Target Income
ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs
are $3.00 per unit, how many units must be
sold to earn income of $40,000?
Unit contribution = $5.00 - $3.00 = $2.00
a. 100,000 units
Fixed costs + Target income
b. 120,000 units
Unit contribution
c. 80,000 units$200,000 + $40,000
= 120,000 units
d. 200,000 units $2.00 per unit
McGraw-Hill/Irwin41
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22-42
Computing Sales (Dollars) for a
Target Net Income
Exh.
22-14
Target net income is income after income tax.
Dollar sales =
McGraw-Hill/Irwin42
Fixed
Target net
Income
+
+
costs
income
taxes
Contribution margin ratio
© The McGraw-Hill Companies, Inc., 2006
22-43
Computing Sales (Dollars) for a
Target Net Income
To convert target net income to before-tax
income, use the following formula:
Target net income
Before-tax income =
1 - tax rate
McGraw-Hill/Irwin43
© The McGraw-Hill Companies, Inc., 2006
22-44
Computing Sales (Dollars) for a
Target Net Income
Rydell has a monthly target net income of $18,000.
The unit selling price is $100. Monthly fixed costs are
$24,000, the unit variable cost is $70, and the tax rate
is 25 percent.
 What is Rydell’s before-tax income and
income tax expense?
McGraw-Hill/Irwin44
© The McGraw-Hill Companies, Inc., 2006
22-45
Computing Sales (Dollars) for a
Target Net Income
Rydell has a monthly target net income of $18,000.
The unit selling price is $100. Monthly fixed costs are
$24,000, the unit variable cost is $70, and the tax rate
is 25 percent.
 What is Rydell’s before-tax income and
income tax expense?
Target net income
Before-tax income =
1 - tax rate
$18,000
Before-tax income =
1 - .25
=
$24,000
Income tax = .25 × $24,000 = $6,000
McGraw-Hill/Irwin45
© The McGraw-Hill Companies, Inc., 2006
22-46
Computing Sales (Dollars) for a
Target Net Income
Rydell has a monthly target net income of $18,000.
The unit selling price is $100. Monthly fixed costs are
$24,000, the unit variable cost is $70, and the tax rate
is 25 percent.
 What monthly sales revenue will Rydell
need to earn the target net income?
McGraw-Hill/Irwin46
© The McGraw-Hill Companies, Inc., 2006
22-47
Computing Sales (Dollars) for a
Target Net Income
Rydell has a monthly target net income of $18,000.
The unit selling price is $100. Monthly fixed costs are
$24,000, the unit variable cost is $70, and the tax rate
is 25 percent.
 What monthly sales revenue will Rydell
need to earn the target net income?
Dollar sales =
Dollar sales =
McGraw-Hill/Irwin47
Fixed + Target net + Income
costs
income
taxes
Contribution margin ratio
$24,000 + $18,000 + $6,000
= $160,000
30%
© The McGraw-Hill Companies, Inc., 2006
22-48
Formula for Computing Sales (Units)
for a Target Net Income
Exh.
22-16
The formula for computing dollar sales may be
used to compute unit sales by substituting
contribution per unit in the denominator.
Unit sales =
Fixed + Target net + Income
costs
income
taxes
Contribution margin per unit
$24,000 + $18,000 + $6,000
Unit sales =
$30 per unit
McGraw-Hill/Irwin48
= 1,600 units
© The McGraw-Hill Companies, Inc., 2006
22-49
Computing the Margin of Safety
Exh.
22-17
Margin of safety is the amount by which
sales may decline before reaching breakeven sales.
Margin of safety may be expressed as a
percentage of expected sales.
Margin of safety
percentage
McGraw-Hill/Irwin49
=
Expected sales - Break-even sales
Expected sales
© The McGraw-Hill Companies, Inc., 2006
22-50
Computing the Margin of Safety
Exh.
22-17
If Rydell’s sales are $100,000 and breakeven sales are $80,000, what is the margin
of safety in dollars and as a percentage?
Margin of safety
percentage
McGraw-Hill/Irwin50
=
Expected sales - Break-even sales
Expected sales
© The McGraw-Hill Companies, Inc., 2006
22-51
Computing the Margin of Safety
Exh.
22-17
If Rydell’s sales are $100,000 and breakeven sales are $80,000, what is the margin
of safety in dollars and as a percentage?
Margin of safety = $100,000 - $80,000 = $20,000
Margin of safety
percentage
=
Expected sales - Break-even sales
Expected sales
Margin of safety
percentage
=
$100,000 - $80,000
$100,000
McGraw-Hill/Irwin51
= 20%
© The McGraw-Hill Companies, Inc., 2006
22-52
Sensitivity Analysis
The basic CVP relationships may be used to
analyze a number of situations such as
changing sales price, changing variable
cost, or changing fixed cost.
Consider the following example.
Continue
McGraw-Hill/Irwin52
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22-53
Sensitivity Analysis Example
Rydell Company is considering buying a new
machine that would increase monthly fixed costs
from $24,000 to $30,000, but decrease unit
variable costs from $70 to $60. The $100 per
unit selling price would remain unchanged.
What is the new break-even point in dollars?
McGraw-Hill/Irwin53
© The McGraw-Hill Companies, Inc., 2006
22-54
Sensitivity Analysis Example
Exh.
22-18
Rydell Company is considering buying a new
machine that would increase monthly fixed costs
from $24,000 to $30,000, but decrease unit
variable costs from $70 to $60. The $100 per
unit selling price would remain unchanged.
Revised Break-even
point in dollars
=
Revised fixed costs
Revised contribution margin ratio
Revised Break-even
point in dollars
=
$30,000
40%
McGraw-Hill/Irwin54
= $75,000
© The McGraw-Hill Companies, Inc., 2006
22-55
Computing Multiproduct
Break-Even Point
The CVP formulas may be modified for use when
a company sells more than one product.
• The unit contribution margin is replaced with the
contribution margin for a composite unit.
• A composite unit is composed of specific numbers of
each product in proportion to the product sales mix.
• Sales mix is the ratio of the volumes of the various
products.
McGraw-Hill/Irwin55
© The McGraw-Hill Companies, Inc., 2006
22-56
Computing Multiproduct
Break-Even Point
Exh.
22-19
The resulting break-even formula
for composite unit sales is:
Break-even point
in composite units
=
Fixed costs
Contribution margin
per composite unit
Consider the following example:
Continue
McGraw-Hill/Irwin56
© The McGraw-Hill Companies, Inc., 2006
22-57
Computing Multiproduct
Break-Even Point
Hair-Today offers three cuts as shown below. Annual
fixed costs are $96,000. Compute the break-even
point in composite units and in number of units for
each haircut at the given sales mix.
Selling Price
Variable Cost
Unit Contribution
Sales Mix Ratio
McGraw-Hill/Irwin57
Haircuts
Basic
Ultra
Budget
$ 10.00 $ 16.00 $ 8.00
6.50
9.00
4.00
$ 3.50 $ 7.00 $ 4.00
4
2
1
© The McGraw-Hill Companies, Inc., 2006
22-58
Computing Multiproduct
Break-Even Point
Hair-Today offers three cuts as shown below. Annual
fixed costs are $96,000. Compute the break-even
point in composite units and in number of units for
A 4:2:1
mix
thatsales
if there
are
eachsales
haircut
atmeans
the given
mix.
500 budget cuts, then there will be 1,000
ultra cuts, and 2,000 basic cuts.
Selling Price
Variable Cost
Unit Contribution
Sales Mix Ratio
McGraw-Hill/Irwin58
Haircuts
Basic
Ultra
Budget
$ 10.00 $ 16.00 $ 8.00
6.50
9.00
4.00
$ 3.50 $ 7.00 $ 4.00
4
2
1
© The McGraw-Hill Companies, Inc., 2006
22-59
Computing Multiproduct
Break-Even Point
Step 1: Compute contribution margin per
composite unit.
Selling Price
Variable Cost
Unit Contribution
Sales Mix Ratio
McGraw-Hill/Irwin59
Basic
$10.00
6.50
$3.50
×4
$ 14.00
Haircuts
Ultra
$16.00
9.00
$7.00
×2
$ 14.00
Budget
$8.00
4.00
$4.00
×1
$ 4.00
© The McGraw-Hill Companies, Inc., 2006
22-60
Computing Multiproduct
Break-Even Point
Step 1: Compute contribution margin per
composite unit.
Basic
Selling Price
$10.00
Variable Cost
6.50
Unit Contribution
$3.50
Sales Mix Ratio
×4
Weighted Contribution $ 14.00
Haircuts
Ultra
Budget
$16.00
$8.00
9.00
4.00
$7.00
$4.00
×2
×1
+ $ 14.00 + $ 4.00 = $ 32.00
Contribution margin per composite unit
McGraw-Hill/Irwin60
© The McGraw-Hill Companies, Inc., 2006
22-61
Computing Multiproduct
Break-Even Point
Exh.
22-19
Step 2: Compute break-even point in
composite units.
Break-even point
in composite units
McGraw-Hill/Irwin61
=
Fixed costs
Contribution margin
per composite unit
© The McGraw-Hill Companies, Inc., 2006
22-62
Computing Multiproduct
Break-Even Point
Exh.
22-19
Step 2: Compute break-even point in
composite units.
=
Fixed costs
Contribution margin
per composite unit
Break-even point
in composite units
=
$96,000
$32.00 per
composite unit
Break-even point
in composite units
=
3,000 composite units
Break-even point
in composite units
McGraw-Hill/Irwin62
© The McGraw-Hill Companies, Inc., 2006
22-63
Computing Multiproduct
Break-Even Point
Step 3: Determine the number of each haircut
that must be sold to break even.
Sales Composite
Product Mix
Cuts
Haircuts
Basic
4
×
3,000
= 12,000
Ultra
2
×
3,000
= 6,000
Budget
1
×
3,000
= 3,000
McGraw-Hill/Irwin63
© The McGraw-Hill Companies, Inc., 2006
22-64
Multiproduct Break-Even
Income Statement
Exh.
22-20
Step 4: Verify the results.
Basic
Selling Price
$ 10.00
Variable Cost
6.50
Unit Contribution
$
3.50
Sales Volume
×
12,000
Total Contribution
$ 42,000
Fixed Costs
Income
McGraw-Hill/Irwin64
Haircuts
Ultra
$ 16.00
9.00
$
7.00
×
6,000
$ 42,000
Budget
$
8.00
4.00
$
4.00
×
3,000
$ 12,000
Combined
$ 96,000
96,000
$
0
© The McGraw-Hill Companies, Inc., 2006
22-65
Operating Leverage
A measure of the extent to which fixed costs
are being used in an organization.
A measure of how a percentage change in
sales will affect profits.
Contribution margin
Net income
McGraw-Hill/Irwin65
= Degree of operating leverage
© The McGraw-Hill Companies, Inc., 2006
22-66
Operating Leverage
Rydell Company
Sales (1,600 units)
Less: variable expenses
Contribution margin
Less: fixed expenses
Net income
Contribution margin
Net income
$48,000
$24,000
McGraw-Hill/Irwin66
= 2.0
$160,000
112,000
48,000
24,000
$ 24,000
= Degree of operating leverage
If Rydell increases sales by 10
percent, what will the percentage
increase in income be?
© The McGraw-Hill Companies, Inc., 2006
22-67
Operating Leverage
Rydell Company
Sales (1,600 units)
Less: variable expenses
Contribution margin
Less: fixed expenses
Net income
$160,000
112,000
48,000
24,000
$ 24,000
Percent increase in sales
Degree of operating leverage
Percent increase in income
McGraw-Hill/Irwin67
10%
×
2
20%
© The McGraw-Hill Companies, Inc., 2006
22-68
Homework for Chapter 22
 Ex 22-6, 22-9, 22-11, 22-13, 22-14
 Problem 22-3A, 22-5A, 22-6A
McGraw-Hill/Irwin68
© The McGraw-Hill Companies, Inc., 2006
22-69
End of Chapter 22
McGraw-Hill/Irwin69
© The McGraw-Hill Companies, Inc., 2006
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