Chapter 15
Cost-Volume-Profit Relationships
• Cost-Volume-Profit (CVP) Analysis - the study of the
interrelationships between costs and volume and how
they impact profit.
• Surveys suggest that over 50 percent of responding
firms use some form of CVP analysis.
• Useful in answering such questions as:
• How will revenues and costs be affected if we sell
1,000 more units? If we raise or lower our selling
prices? If we cut fixed costs by 20 percent?
• How many units must we sell in order to break
even?
• How might changes in product mix affect our
profits?
1
A New Income Statement Format
• Traditional income statement mixes fixed and
variable costs.
• Examples
– COGS has fixed and variable components.
– Selling and administrative has fixed and
variable components.
• This has been the form we used in external
financial reporting.
• Your text calls this a functional income statement.
• For internal analysis, we may restructure the
income statement to arrange fixed and variable
components into separate categories.
2
A New Income Statement Format
The new format will be:
Sales
- Variable Costs
= Contribution margin
- Fixed Costs
= Profit
Note that all amounts above are total dollar
amounts (as they are in the traditional income
statement). We will abbreviate:
S - VC = CM
S - VC - FC = P
3
A New Income Statement Format
The Contribution Margin activity may also be
expressed in other formats:
Per unit: Selling price per unit (SPU)
Variable cost per unit (VCU)
Contribution margin per unit (CMU)
Percentage: where sales are defined as 100%, the
VC and CM may be defined as a percentage of
sales.
Summary (note that Fixed Costs are always/only
expressed in total):
Dollars
Per Unit
Percentage
Sales
SPU
100%
-VC
-VCU
- VC%
=CM
=CMU
= CM%
4
“What-if” Decisions using CM Statement
• Analyze the effect of changing various
components:
Selling price per unit
Variable cost per unit
Fixed costs
• Changes in cost, price or volume usually
affects other components as well.
• CVP analysis examines the effects of these
changes.
5
CVP Analysis
CVP analysis arises from manipulation of the
fundamental CM Income Statement:
Sales - Variable Cost – Fixed Costs = Net Income
Substitute “per unit” components, and indicate “X”
as the number of units:
SPU (X) - VCU (X) - FC = P
(SPU – VCU) (X)
CMU (X)
CMU (X) =
X =
- FC = P
- FC = P
FC + P
(FC + P)/CMU
6
Some Useful Formulas
Target units to achieve a particular target profit (P):
X = (FC + P) / CMU
Target units required to break-even
(target profit = 0):
X = (FC + 0) / CMU
For target revenues (sales activity in dollars)
(1) take target units x selling price per unit, or
(2) Substitute CM%(CM Ratio) for CMU in the
above formulas when you do not know the units.
7
Graph of Break-Even
$
Revenues
Cost
BE
.
Units
Treatment of After-Tax Profit
CVP analysis is based on before-tax profit, as tax
laws have more effect than unit activity on cash
paid for taxes.
To convert from after-tax profit to before-tax profit,
use the following formula:
Before-tax Profit = After-tax Profit/(1- Tax Rate)
One you have Before-tax Profit, just use it as “P” in
all the formulas.
9
Operating Leverage
• The extent to which a firm’s cost structure is
made up of fixed costs is called operating
leverage.
• Everything else being equal, the higher a firm’s
operating leverage, the higher its break-even
point.
• Higher leverage is associated with more rapidly
increasing losses if demand is less than that
required to break even.
• Higher leverage is associated with more rapidly
increasing profits after reaching the break-even
point.
• Firms with lower leverage tend to have greater
flexibility in reacting to changes in demand.
10
Graph of Break-Even for High and Low
Leverage Firms
$
Revenues
Lower Leverage
Higher Leverage
BE1
BE2
Intersection
Units
Operating Leverage
• Operating leverage indicates the sensitivity of
net operating income to percentage changes
in sales.
• Degree of operating leverage =
Contribution margin in dollars
Net operating income
• This formula yields a factor change in income
for every percentage change in sales.
• Higher factor indicates a higher sensitivity to
change in sales.
• Higher factors "better" when sales go up, but
more problematic when sales drop.
12
Example of Operating Leverage
Given the following two companies:
Company A
Company B
CM
$120,000
CM
$180,000
Fixed Cost
90,000
Fixed
150,000
Net Inc.
$30,000
Net Inc. $ 30,000
Calculate operating leverage:
Co. A
Co. B
CM/NI
120/30 = 4
180/30 =6
Interpretation:
For A: 1% increase in sales = 4% increase in NI
For B: 1% increase in sales = 6% increase in NI
If sales increase 2%, NI :
A incr. 2% x 4 = 8% x 30,000 = $2,400
B incr. 2% x 6 = 12% x 30,000 = $3,600
Class Problem
Assume that a company is considering a change in
its cost structure, and would like to automate
some of its production activities.
The current fixed costs are $60,000 per year and the
current variable cost per unit is $20.
This decision would add $42,000 per year to the
fixed costs, but reduce variable cost per unit by $6
per unit (reduced labor costs).
1. Calculate the Break even for the current cost
structure.
2. Calculate the Break Even in units if the new cost
structure is implemented.
3. Calculate the point at which the new cost
structure is more profitable than the old cost
structure, i.e., at what point do the two cost
functions intersect?
Graph for Class Problem
$
Revenues
Part 1
Part 2
Units
Multiple Products and Sales Mix
• Sales mix is the relative proportion in which a
company’s products are sold.
• Changes in sales mix will cause a change in
profit.
• Changing to a high profit margin item may
decrease sales revenue but increase profit.
• Changing to a low profit margin item may
increase sales revenue but decrease profit.
• Changes in sales mix complicates the breakeven analysis.
• Multiple products must be analyzed with a
“weighted average” contribution margin, based
on the proportional contribution if each product.
16