6-‹#›
6-1
LEARNING OBJECTIVES
1.
2.
3.
4.
5.
6.
7.
8.
Interpret a cost-volume-profit (CVP) graph.
Use the contribution margin (CM) ratio to compute changes in
contribution margin and net operating income resulting from changes
in sales volume.
Show the effects on contribution margin of changes in variable costs,
fixed costs, selling price, and volume.
Compute the break-even point.
Determine the level of sales needed to achieve a desired target
profit with and without taxes.
Use the margin of safety and explain its significance.
Compute the degree of operating leverage at a particular level of
sales and explain how the degree of operating leverage can be used
to predict changes to net operating income.
Compute the break-even point for a multiple-product company and
explain the effects of shifts in the sales mix on contribution margin
and the break-even point.
6-2
The Contribution Margin Concept
For each additional unit Wind sells, $200 more in
contribution margin will help to cover fixed
expenses and profit.
Sales (500 bikes)
Less: variable expenses
Contribution margin
Less: fixed expenses
Net income
Total
$250,000
150,000
$100,000
80,000
$ 20,000
Per Unit
$ 500
300
$ 200
Percent
100%
60%
40%
6-3
CVP Relationships in Graphic Form
Viewing CVP relationships in a graph gives managers a perspective
that can be obtained in no other way. Consider the following
information for Wind Co.:
Sales
Sales
Less:
Less: variable
variable expenses
expenses
Contribution
Contribution margin
margin
Less:
Less: fixed
fixed expenses
expenses
Net
Net income
income (loss)
(loss)
Income
Income
300
300 units
units
150,000
150,000
90,000
90,000
$$
60,000
60,000
80,000
80,000
$$
(20,000)
(20,000)
$$
Income
Income
400
400 units
units
$$ 200,000
200,000
120,000
120,000
$$
80,000
80,000
80,000
80,000
$$
--
Income
Income
500
500 units
units
$$ 250,000
250,000
150,000
150,000
$$ 100,000
100,000
80,000
80,000
$$ 20,000
20,000
6-‹#›
6-4
CVP Graph
450,000
400,000
350,000
rea
tA
ofi
Pr
Dollars
300,000
250,000
200,000
150,000
Break-even point
ea
Ar
ss
Lo
100,000
50,000
-
100
200
300
400
500
600
700
800
Units
6-5
6-15
6-6
Contribution Margin Ratio
The contribution margin ratio is:
CM Ratio =
Contribution margin
Sales
For Wind Bicycle Co. the ratio is:
$200
$500
= 40%
6-‹#›
6-7
Break-Even: Equation Method
Profits = Sales – (Variable expenses + Fixed expenses)
OR
Sales = Variable expenses + Fixed expenses + Profits
At the break-even point
profits equal zero.
6-8
Break-Even: Contribution Margin Method
Break-even point
=
in units sold
Fixed expenses
Unit contribution margin
Break-even point in
total sales dollars =
Fixed expenses
CM ratio
6-9
Target Profit Calculations: CM Approach
Units sold to attain
=
the target profit
Fixed expenses + Target profit
Unit contribution margin
Target Profit Calculations With Taxes
Units sold to attain
=
the target profit
Fixed expenses + Target profit/(1-t)
Unit contribution margin
6-‹#›
6-10
The Margin of Safety
Excess of budgeted (or actual) sales over the
break-even volume of sales. The amount by
which sales can drop before losses begin to be
incurred.
Margin of safety = Total sales - Break-even sales
($ or units)
($ or units)
6-11
 6-6
 6-17
6-12
Operating Leverage
 A measure of how sensitive net income is to
percentage changes in sales.
 With high leverage, a small percentage increase
in sales can produce a much larger percentage
increase in net income.
Degree of
operating leverage =
Contribution margin
Net income
6-‹#›
6-13
 6-21
6-14
The Concept of Sales Mix
 Sales mix is the relative proportions in which a
company’s products are sold.
 Different products have different selling prices,
cost structures, and contribution margins.
 Break-even analysis:
 Weighted average contribution margin approach
 Product “bundling” approach
6-15
 6-11
6-‹#›
6-16
Assumptions of CVP Analysis
 Selling price is constant throughout the
entire relevant range.
 Costs are linear throughout the entire
relevant range.
 In multi-product companies, the sales mix
is constant.
 In manufacturing companies, inventories
do not change (units produced = units
sold).
6-17
 6-22