Chapter Six
BA 315- LPC UMSL
Cost-Volume-Profit Analysis
(Contribution Margin)
CURL SURFBOARDS
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
The Break-Even Point
The break-even point is the point is the volume of
activity where the organization’s revenues and
expenses are equal.
Sales
Sales
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income
Irwin/McGraw-Hill
$$250,000
250,000
150,000
150,000
100,000
100,000
100,000
100,000
$$
--
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Approach
Consider the following information developed
by the accountant at Curl, Inc.:
Sales
Sales (500
(500 surfboards)
surfboards)
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income
Irwin/McGraw-Hill
Total
Total
$$250,000
250,000
150,000
150,000
$$100,000
100,000
80,000
80,000
$$ 20,000
20,000
Per
Per Unit
Unit
$$ 500
500
300
300
$$ 200
200
Percent
Percent
100%
100%
60%
60%
40%
40%
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Approach
For each additional surf board sold, Curl
generates $200 in contribution margin.
Sales
Sales (500
(500 surfboards)
surfboards)
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income
Irwin/McGraw-Hill
Total
Total
$$250,000
250,000
150,000
150,000
$$100,000
100,000
80,000
80,000
$$ 20,000
20,000
Per
Per Unit
Unit
$$ 500
500
300
300
$$ 200
200
Percent
Percent
100%
100%
60%
60%
40%
40%
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Approach
We can calculate the break-even volume using
the following equation.
Fixed expenses
Unit contribution margin
Break-even point
=
(in units)
Let’s calculate the break-even
point in units for Curl, Inc.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Approach
Sales
Sales (400
(400 surfboards)
surfboards)
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income
$80,000
$200
Total
Total
$$200,000
200,000
120,000
120,000
$$ 80,000
80,000
80,000
80,000
$$
--
Per
Per Unit
Unit
$$ 500
500
300
300
$$ 200
200
Percent
Percent
100%
100%
60%
60%
40%
40%
= 400 surfboards
Let’s check our calculation.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Approach
Break-even Point
Sales
Sales (400
(400 surfboards)
surfboards)
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income
400 × $500 = $200,000
Irwin/McGraw-Hill
Total
Total
$$200,000
200,000
120,000
120,000
$$ 80,000
80,000
80,000
80,000
$$
--
Per
Per Unit
Unit
$$ 500
500
300
300
$$ 200
200
Percent
Percent
100%
100%
60%
60%
40%
40%
400 × $300 = $120,000
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Ratio
We can calculate the break-even point in
sales dollars rather than units by using
the contribution-margin ratio.
Contribution margin
Sales
Irwin/McGraw-Hill
= CM Ratio
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Ratio
We can calculate the break-even point in
sales dollars rather than units by using
the contribution-margin ratio.
Contribution margin
Sales
Fixed expense
CM Ratio
Irwin/McGraw-Hill
= CM Ratio
Break-even point
=
(in sales dollars)
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Ratio
Sales
Sales (400
(400 surfboards)
surfboards)
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income
$80,000
40%
Irwin/McGraw-Hill
Total
Total
$$200,000
200,000
120,000
120,000
$$ 80,000
80,000
80,000
80,000
$$
--
=
Per
Per Unit
Unit
$$ 500
500
300
300
$$ 200
200
Percent
Percent
100%
100%
60%
60%
40%
40%
$200,000 sales
© The McGraw-Hill Companies, Inc., 1999
Equation Approach
Sales revenue – Variable expenses – Fixed expenses = Profit
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Equation Approach
Sales revenue – Variable expenses – Fixed expenses = Profit
Unit
Sales
sales × volume
price in units
Unit
Sales
variable × volume
expense in units
At the break-even point profit equals zero,
and the sales volume in units is unknown.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Equation Approach
Sales revenue – Variable expenses – Fixed expenses = Profit
($500 × X) –
($300 × X)
– $80,000 = $0
($200X) – $80,000 = $0
X = 400 units
At the break-even point profit equals zero,
and the sales volume in units is unknown.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Graphing Cost-Volume-Profit
Relationships
Viewing CVP relationships in a graph gives managers a
perspective that can be obtained in no other way.
Consider the following information for Curl, Inc.:
Sales
Sales
Less:
Less: variable
variableexpenses
expenses
Contribution
Contributionmargin
margin
Less:
Less: fixed
fixedexpenses
expenses
Net
Net income
income(loss)
(loss)
Irwin/McGraw-Hill
Income
Income
300
300units
units
$$ 150,000
150,000
90,000
90,000
$$ 60,000
60,000
80,000
80,000
$$ (20,000)
(20,000)
Income
Income
400
400units
units
$$ 200,000
200,000
120,000
120,000
$$ 80,000
80,000
80,000
80,000
$$
--
Income
Income
500
500units
units
$$250,000
250,000
150,000
150,000
$$100,000
100,000
80,000
80,000
$$ 20,000
20,000
© The McGraw-Hill Companies, Inc., 1999
Cost-Volume-Profit Graph
450,000
400,000
350,000
300,000
250,000
200,000
Fixed expenses
150,000
100,000
50,000
Irwin/McGraw-Hill
100
200
300
400
Units Sold
500
600
700
800
© The McGraw-Hill Companies, Inc., 1999
Cost-Volume-Profit Graph
450,000
400,000
350,000
300,000
Total expenses
250,000
200,000
150,000
100,000
50,000
Irwin/McGraw-Hill
100
200
300
400
Units Sold
500
600
700
800
© The McGraw-Hill Companies, Inc., 1999
Cost-Volume-Profit Graph
450,000
Total sales
400,000
350,000
300,000
250,000
200,000
150,000
100,000
50,000
Irwin/McGraw-Hill
100
200
300
400
Units Sold
500
600
700
800
© The McGraw-Hill Companies, Inc., 1999
Cost-Volume-Profit Graph
450,000
Break-even
point
400,000
350,000
300,000
250,000
200,000
150,000
100,000
50,000
Irwin/McGraw-Hill
100
200
300
400
Units Sold
500
600
700
800
© The McGraw-Hill Companies, Inc., 1999
Cost-Volume-Profit Graph
450,000
400,000
350,000
300,000
250,000
200,000
150,000
100,000
50,000
Irwin/McGraw-Hill
100
200
300
400
Units Sold
500
600
700
800
© The McGraw-Hill Companies, Inc., 1999
Profit-Volume Graph
$100,000
$80,000
$60,000
$40,000
Some managers
like the profit-volume
graph because it focuses
on profits and volume.
$20,000
$$$(20,000)
$50
$100
$150
$200
$250
$300
3
4
5
6
$350
$400
7
8
$(40,000)
$(60,000)
$(80,000)
$(100,000)
Irwin/McGraw-Hill
1
2
Units sold (00s)
© The McGraw-Hill Companies, Inc., 1999
Profit-Volume Graph
$100,000
Break-even
point
$80,000
$60,000
$40,000
$20,000
$$$(20,000)
$50
$100
$150
$200
$250
$300
3
4
5
6
$350
$400
7
8
$(40,000)
$(60,000)
$(80,000)
$(100,000)
Irwin/McGraw-Hill
1
2
Units sold (00s)
© The McGraw-Hill Companies, Inc., 1999
Profit-Volume Graph
$100,000
$80,000
$60,000
$40,000
$20,000
$$$(20,000)
$50
$100
$150
$200
$250
$300
$350
$400
$(40,000)
$(60,000)
Sales revenue
$(80,000)
$(100,000)
Irwin/McGraw-Hill
1
2
3
4
5
Units sold (00s)
6
7
8
© The McGraw-Hill Companies, Inc., 1999
Profit-Volume Graph
$100,000
Profit line
$80,000
$60,000
$40,000
$20,000
$$$(20,000)
$50
$100
$150
$200
$250
$300
3
4
5
6
$350
$400
7
8
$(40,000)
$(60,000)
$(80,000)
$(100,000)
Irwin/McGraw-Hill
1
2
Units sold (00s)
© The McGraw-Hill Companies, Inc., 1999
Profit-Volume Graph
$100,000
$80,000
$60,000
$40,000
$20,000
$$$(20,000)
$50
$100
$150
$200
$250
$300
3
4
5
6
$350
$400
7
8
$(40,000)
$(60,000)
$(80,000)
$(100,000)
Irwin/McGraw-Hill
1
2
Units sold (00s)
© The McGraw-Hill Companies, Inc., 1999
Target Net Profit
We can determine the number of
surfboards that Curl must sell to earn a
profit of $100,000 using the contributionmargin approach.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Approach
We can determine the number of
surfboards that Curl must sell to earn a
profit of $100,000 using the contributionmargin approach.
Fixed expenses + Target profit
Unit contribution margin
Irwin/McGraw-Hill
Units sold to earn
=
the target profit
© The McGraw-Hill Companies, Inc., 1999
Contribution-Margin Approach
We can determine the number of
surfboards that Curl must sell to earn a
profit of $100,000 using the contributionmargin approach.
Fixed expenses + Target profit
Unit contribution margin
$80,000 + $100,000
$200
Irwin/McGraw-Hill
Units sold to earn
=
the target profit
= 900 surfboards
© The McGraw-Hill Companies, Inc., 1999
Equation Approach
Sales revenue – Variable expenses – Fixed expenses = Profit
($500 × X) –
($300 × X) – $80,000 = $100,000
($200X) = $180,00
X = 900 units
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Applying CVP Analysis
Safety Margin
The difference between budgeted sales
revenue and break-even sales revenue.
The amount by which sales can drop
before losses begin to be incurred.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Safety Margin
Curl, Inc. has a break-even point of $200,000. If
actual sales are $250,000, the safety margin is
$50,000 or 100 surfboards.
Sales
Sales
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income
Irwin/McGraw-Hill
Break-even
Break-even
sales
sales
400
400 units
units
$$ 200,000
200,000
120,000
120,000
$$ 80,000
80,000
80,000
80,000
$$
--
Actual
Actual sales
sales
500
500 units
units
$$ 250,000
250,000
150,000
150,000
$$ 100,000
100,000
80,000
80,000
$$ 20,000
20,000
© The McGraw-Hill Companies, Inc., 1999
Changes in Fixed Costs
Curl is currently selling 500 surfboards per
month.
The owner believes that an increase of $10,000
in the monthly advertising budget, would
increase bike sales to 540 units.
Should we authorize the requested increase in
the advertising budget?
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Changes in Fixed Costs
Current
Current
Sales
Sales
(500
(500 Boards)
Boards)
Sales
$$ 250,000
Sales
250,000
Less:
150,000
Less: variable
variable expenses
expenses
150,000
Contribution
$$ 100,000
Contribution margin
margin
100,000
Less:
80,000
Less: fixed
fixed expenses
expenses
80,000
Net
$$
20,000
Net income
income
20,000
Proposed
Proposed
Sales
Sales
(540
(540 Boards)
Boards)
$$ 270,000
270,000
540 units × $500 per unit = $270,000
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Changes in Fixed Costs
Current
Current
Sales
Sales
(500
(500 Boards)
Boards)
Sales
$$ 250,000
Sales
250,000
Less:
150,000
Less: variable
variable expenses
expenses
150,000
Contribution
$$ 100,000
Contribution margin
margin
100,000
Less:
80,000
Less: fixed
fixed expenses
expenses
80,000
Net
$$
20,000
Net income
income
20,000
Proposed
Proposed
Sales
Sales
(540
(540 Boards)
Boards)
$$ 270,000
270,000
162,000
162,000
$$ 108,000
108,000
90,000
90,000
$$
18,000
18,000
$80,000 + $10,000 advertising = $90,000
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Changes in Fixed Costs
Current
Current
Sales will increase by
Sales
Sales
$20,000, but net income (500 Boards)
(500 Boards)
will
decrease
by
$2,000.
Sales
$$ 250,000
Sales
250,000
Less:
150,000
Less: variable
variable expenses
expenses
150,000
Contribution
$$ 100,000
Contribution margin
margin
100,000
Less:
80,000
Less: fixed
fixed expenses
expenses
80,000
Net
$$
20,000
Net income
income
20,000
Irwin/McGraw-Hill
Proposed
Proposed
Sales
Sales
(540
(540 Boards)
Boards)
$$ 270,000
270,000
162,000
162,000
$$ 108,000
108,000
90,000
90,000
$$
18,000
18,000
© The McGraw-Hill Companies, Inc., 1999
Changes in Unit Contribution Margin
Because of increases in cost of raw materials,
Curl’s variable cost per unit has increased
from $300 to $310 per surfboard. With no
change in selling price per unit, what will be
the new break-even point?
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Changes in Unit Contribution Margin
Because of increases in cost of raw materials,
Curl’s variable cost per unit has increased
from $300 to $310 per surfboard. With no
change in selling price per unit, what will be
the new break-even point?
($500 × X) –
($310 × X) – $80,000 = $0
X = 422 units (rounded up)
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Predicting Profit Given Expected
Volume
Given:
Given:
Fixed expenses
Unit contribution margin
Target net profit
Find: {required sales volume}
Fixed expenses
Unit contribution margin
Expected sales volume
Find: {expected profit}
{
{
}
Irwin/McGraw-Hill
}
© The McGraw-Hill Companies, Inc., 1999
Predicting Profit Given Expected
Volume
In the coming year, Curl’s owner expects to sell
525 surfboards. The unit contribution margin is
expected to be $190, and fixed costs are
expected to increase to $90,000.
How much profit can we expect to earn?
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Predicting Profit Given Expected
Volume
In the coming year, Curl’s owner expects to sell
525 surfboards. The unit contribution margin is
expected to be $190, and fixed costs are
expected to increase to $90,000.
Total contribution
-
Fixed cost = Profit
($190 × 525) – $90,000 = X
X = $99,750 – $90,000
X = $9,750 profit
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
CVP Analysis with Multiple
Products
For a company with more than one product,
sales mix is the relative combination in which
a company’s products are sold.
Different products have different selling prices,
cost structures, and contribution margins.
Let’s assume Curl sells surfboards and
sailboards and see how we deal with
break-even analysis.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
CVP Analysis with Multiple
Products
Curl provides us with the following information:
Description
Surfboards
Sailboards
Total sold
Selling
Price
$
500
1,000
Unit
Unit
Variable Contribution
Cost
Margin
$ 300 $
200
450
550
Number
Description of Boards
Surfboards
500
Sailboards
300
Total sold
800
Irwin/McGraw-Hill
Number
of
Boards
500
300
800
% of
Total
62.5% (500 ÷ 800)
37.5% (300 ÷ 800)
100.0%
© The McGraw-Hill Companies, Inc., 1999
CVP Analysis with Multiple
Products
Weighted-average unit contribution margin
Contribution
Weighted
Description
Margin
% of Total Contribution
Surfboards $
200
62.5% $
125.00
Sailboards
550
37.5%
206.25
Weighted-average contribution margin $
331.25
$200 × 62.5%
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
CVP Analysis with Multiple
Products
Break-even point
Break-even
Fixed expenses
=
point
Weighted-average unit contribution margin
Break-even
=
point
$170,000
$331.25
Break-even
= 514 combined unit sales (rounded up)
point
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
CVP Analysis with Multiple
Products
Break-even point
Break-even
= 514 combined unit sales
point
Description
Surfboards
Sailboards
Total units
Irwin/McGraw-Hill
Breakeven
Sales
514
514
% of
Individual
Total
Sales
62.5%
321
37.5%
193
514
© The McGraw-Hill Companies, Inc., 1999
Assumptions Underlying
CVP Analysis
Selling price is constant throughout
the entire relevant range.
Costs are linear over the relevant
range.
In multiproduct companies, the sales
mix is constant.
In manufacturing firms, inventories
do not change (units produced =
units sold).
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Cost Structure and Operating
Leverage
The cost structure of an organization is the
relative proportion of its fixed and variable
costs.
Operating leverage is . . .


the extent to which an organization uses fixed
costs in its cost structure.
greatest in companies that have a high proportion
of fixed costs in relation to variable costs.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Measuring Operating Leverage
Operating leverage
factor
=
Contribution margin
Net income
Actual
Actual sales
sales
500
500 Board
Board
Sales
$$ 250,000
Sales
250,000
Less:
150,000
Less: variable
variable expenses
expenses
150,000
Contribution
$$ 100,000
Contribution margin
margin
100,000
Less:
80,000
Less: fixed
fixed expenses
expenses
80,000
Net
$$ 20,000
Net income
income
20,000
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Measuring Operating Leverage
Operating leverage
factor
=
Contribution margin
Net income
Actual
Actual sales
sales
500
500 Board
Board
Sales
$$ 250,000
Sales
250,000
Less:
150,000
Less: variable
variable expenses
expenses
150,000
Contribution
$$ 100,000
Contribution margin
margin
100,000
Less:
80,000
Less: fixed
fixed expenses
expenses
80,000
Net
$$ 20,000
Net income
income
20,000
$100,000
$20,000
Irwin/McGraw-Hill
= 5
© The McGraw-Hill Companies, Inc., 1999
Measuring Operating Leverage
A measure of how a percentage change in
sales will affect profits.
If Curl increases its sales by 10%, what
will be the percentage increase in net
income?
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
Measuring Operating Leverage
A measure of how a percentage change in
sales will affect profits.
Percent
Percent increase
increase in
in sales
sales
Operating
Operating leverage
leverage factor
factor ××
Percent
Percent increase
increase in
in profits
profits
Irwin/McGraw-Hill
10%
10%
55
50%
50%
© The McGraw-Hill Companies, Inc., 1999
CVP Analysis, Activity-Based Costing,
and Advanced Manufacturing Systems
An activity-based costing system can
provide a much more complete picture of
cost-volume-profit relationships and thus
provide better information to managers.
Break-even =
Fixed costs
point
Unit contribution margin
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
A Move Toward JIT and
Flexible Manufacturing
Overhead costs like setup, inspection, and
material handling are fixed with respect to
sales volume, but they are not fixed with
respect to other cost drivers.
This is the fundamental distinction
between a traditional CVP analysis and an
activity-based costing CVP analysis.
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999
End of Chapter 6 CVP Analysis
BA 315- LPC1@UMSL.EDU
We made
it!
Irwin/McGraw-Hill
© The McGraw-Hill Companies, Inc., 1999