CHAPTER 5
COST – VOLUME - PROFIT
Study Objectives
Distinguish between variable and fixed costs.
Explain the significance of the relevant range.
Explain the concept of mixed costs.
List the five components of cost-volume-profit
analysis.
Indicate what contribution margin is and how it
can be expressed.
Study Objectives: Continued
Identify the three ways to determine the breakeven point.
Give the formulas for determining sales
required to earn target net income.
Define margin of safety, and give the formulas
for computing it.
COST BEHAVIOR ANALYSIS
 Definition: The study of how specific costs
respond to changes in the level of
business activity
 Some costs change; others remain the same
 Helps management plan operations and make
decisions
 Applies to all types of businesses and entities
COST BEHAVIOR ANALYSIS
Continued
 Starting point is measuring key business
activities
 Activity levels may be expressed in terms of
 Sales dollars (in a retail company)
 Miles driven (in a trucking company)
 Room occupancy (in a hotel)
 Dance classes taught (by a dance studio)
COST BEHAVIOR ANALYSIS
Continued
 Many companies use more
than one measurement base
 For an activity level
to be useful:
Changes in the level or volume of activity should be
correlated with changes in cost
COST BEHAVIOR ANALYSIS
Continued
 The activity level selected is called
the activity (or volume) index
 Identifies the activity that causes
changes in the behavior of costs
 Allows costs to be classified
according to their response to
changes in activity as:
Variable Costs
Fixed Costs
Mixed Costs
COST BEHAVIOR ANALYSIS
VARIABLE COSTS
Study Objective 1
 Costs that vary in total directly and proportionately
with changes in the activity level
 If the activity level increases 10 percent, total
variable costs increase 10 percent
 If the activity level decreases by 25 percent, total
variable costs will decrease by 25 percent
COST BEHAVIOR ANALYSIS
VARIABLE COSTS - Continued
 Variable costs also remain constant per unit at
every level of activity
Examples of variable costs include
 Direct material and direct labor for a manufacturer
 Sales commissions for a merchandiser
 Gasoline in airlines and trucking companies
COST BEHAVIOR ANALYSIS
VARIABLE COSTS - Continued
Example
 Damon Company manufactures radios that
contain a $10 clock
 Activity index is the number of radios produced
 For each radio produced, the total cost of the
clocks increases by $10
 If 2,000 radios are made, the total cost of the clocks
is $20,000 (2,000 X $10)
 If 10,000 radios are made, the total cost of the
clocks is $100,000 (10,000 X $10)
COST BEHAVIOR ANALYSIS
VARIABLE COSTS - Continued
Example: Continued
COST BEHAVIOR ANALYSIS
FIXED COSTS
 Costs that remain the same in total regardless of
changes in the activity level.
 Per unit cost varies inversely with activity:
As volume increases,
unit cost decline, and vice versa
 Examples include




Property taxes
Insurance
Rent
Depreciation on buildings and equipment
COST BEHAVIOR ANALYSIS
FIXED COSTS - Continued
Example
 Damon Company leases its productive facilities
for $10,000 per month
 Total fixed costs of the facilities remain constant
at all levels of activity - $10,000 per month
 On a per unit basis, the cost of rent decreases as
activity increases and vice versa
 At 2,000 radios, the unit cost is $5 ($10,000 ÷ 2,000
units)
 At 10,000 radios, the unit cost is $1 ($10,000 ÷
10,000 units)
COST BEHAVIOR ANALYSIS
FIXED COSTS - Continued
Example: Continued
COST BEHAVIOR ANALYSIS
RELEVANT RANGE
Study Objective 2
 Throughout the range of possible levels of activity,
a straight-line relationship usually does not exist for
either variable costs or fixed costs
 The relationship between variable costs and changes in
activity level is often curvilinear
 For fixed costs, the relationship is nonlinear – some
fixed costs will not change over the entire range of
activities, others may
COST BEHAVIOR ANALYSIS
RELEVANT RANGE - Continued
COST BEHAVIOR ANALYSIS
RELEVANT RANGE - Continued
 Defined as the range of activity over which a
company expects to operate during a year
 Within this range, a straight-line relationship
usually exists for both variable and fixed costs
COST BEHAVIOR ANALYSIS
MIXED COSTS
Study Objective 3
 Costs that have
both a variable cost
element and a fixed
cost element
 Sometimes called
semivariable cost
 Change in total but
not proportionately
with changes in
activity level
COST BEHAVIOR ANALYSIS
MIXED COSTS – High-Low Method
 Mixed costs must be classified into their fixed and
variable elements
 One approach to separate the costs is called the
high-low method
 Uses the total costs incurred at both the high and the low
levels of activity to classify mixed costs
 The difference in costs between the high and low levels
represents variable costs, since only variable costs change
as activity levels change
COST BEHAVIOR ANALYSIS
MIXED COSTS – High-Low Method - Continued
Steps in Method
 STEP 1: Determine variable cost per unit using the
following formula:
Change in
Total Costs
÷
High minus Low
Activity Level
=
Variable Cost
per Unit
 STEP 2: Determine the fixed cost by subtracting
the total variable cost at either the high or the low
activity level from the total cost at that level
COST BEHAVIOR ANALYSIS
MIXED COSTS – High-Low Method - Continued
Example
Data for Metro Transit Company
for the last 4-month period:
Month
January
February
Miles Driven
20,000
40,000
Total Cost
$30,000
$48,000
High Level of Activity:
Low Level of Activity:
Month
March
April
April
January
Difference
Miles Driven
35,000
50,000
$63,000
30,000
$33,000
Total Cost
$49,000
$63,000
50,000 miles
20,000 miles
30,000 miles
Step 1: Using the formula, variable costs per unit are
$33,000  30,000 = $1.10 variable cost per mile
COST BEHAVIOR ANALYSIS
MIXED COSTS – High-Low Method - Continued
Example: Continued
Step 2: Subtract total variable costs at either the high or low
activity level from the total cost at that same level
Activity Level
Total Cost
Less: Variable costs
(50,000 x $1.10)
(20,000 x $1.10)
Total fixed costs
High
$63,000
55,000
$ 8,000
Low
$30,000
22,000
$ 8,000
COST BEHAVIOR ANALYSIS
MIXED COSTS – High-Low Method - Continued
Example: Continued
 Maintenance costs: $8,000 per month plus $1.10 per mile
 To determine maintenance costs at a particular activity level:
 multiply the activity level times the variable cost per unit
 then add that total to the fixed cost
EXAMPLE: If the activity level is 45,000 miles, the estimated
maintenance costs would be $8,000 fixed and $49,500
variable ($1.10 X 45,000 miles) for a total of $57,500.
COST-VOLUME-PROFIT
ANALYSIS
Study Objective 4
 Study of the effects of changes of costs and
volume on a company’s profits
 A critical factor in management decisions
 Important in profit planning
COST-VOLUME-PROFIT
ANALYSIS
 Considers the interrelationships among the five
components of CVP analysis:
ASSUMPTIONS UNDERLYING
CVP ANALYSIS
 Behavior of both costs and revenues is linear
throughout the relevant range of the activity index
 All costs can be classified as either variable or fixed
with reasonable accuracy
 Changes in activity are the only factors that affect
costs
 All units produced are sold
 When more than one type of product is sold, the
sales mix will remain constant
CVP INCOME STATEMENT
Study Objective 5
 A statement for internal use
 Classifies costs and expenses as fixed or variable
 Reports contribution margin in the body of the
statement.
 Contribution margin –
amount of revenue
remaining after
deducting variable costs
 Reports the same net
income as a traditional
income statement
CVP INCOME STATEMENT
Example
 Vargo Video Company produces DVD players.
 Relevant data for June 2005:
Unit selling price of DVD player
Unit variable costs
Total monthly fixed costs
Units sold
$500
$300
$200,000
1,600
CVP INCOME STATEMENT
Contribution Margin Per Unit
 Contribution margin is available to cover fixed costs
and to contribute to income
 Formula for contribution margin per unit:
Unit Selling Price
–
Unit Variable
Costs
=
Contribution
Margin per Unit
 Example: Computation for Vargo Video
Unit Selling Price
$500
–
Unit Variable
Costs $300
=
Contribution
Margin per Unit
$200
CVP INCOME STATEMENT
Contribution Margin Ratio
 Shows the percentage of each sales dollar available
to apply toward fixed costs and profits
Contribution
Margin per Unit
÷
Unit Selling Price
=
Contribution
Margin Ratio
 Example: Computation for Vargo Video
Contribution
Margin per Unit
S200
÷
Unit Selling Price
$500
=
Contribution
Margin Ratio
40%
CVP INCOME STATEMENT
Contribution Margin Ratio - Example
Ratio helps to determine the effect of changes in sales on net income
BREAK-EVEN ANALYSIS
Study Objective 6
 Process of finding the break-even point
 Break-even point
 Level of activity at which total revenues equal total
costs (both fixed and variable)
 Can be computed or derived
• from a mathematical equation
• by using contribution margin
• from a cost-volume-profit (CVP) graph
 Expressed either in sales units or in sales dollars
BREAK-EVEN ANALYSIS
Mathematical Equation
Example using the Vargo Video data:
Sales
$500 Q
=
Variable Costs
$300 Q
+
Fixed Costs
$200,000
$200 Q
=
$200,000
Q
=
1000 units
+
Net Income
$0
Where:
Q = sales volume; $500 = selling price; $300 = variable cost per unit; $200,000 total fixed costs
To find sales dollars required to break-even:
1000 units X $500 = $500,000 (break-even sales dollars)
BREAK-EVEN ANALYSIS
Contribution Margin Technique
 At the break-even point, contribution margin must equal
total fixed costs (CM = total revenues – variable costs)
 The break-even point can be computed using either
contribution margin per unit or contribution margin ratio
 When the break even point in units is desired, contribution margin
per unit is used in the following formula
Fixed Costs
÷
Contribution
Margin per Unit
=
Break-even Point
in Units
 When the break even point in dollars is desired, contribution
margin ratio is used in the following formula
Fixed Costs
÷
Contribution
Margin Ratio
=
Break-even Point
in Dollars
BREAK-EVEN ANALYSIS
Contribution Margin Technique
Example using Vargo Video data:
Fixed Costs
÷
Contribution
Margin per Unit
=
Break-even Point
in Units
$200,000
$200
1,000 units
Fixed Costs
Contribution
Margin per Unit
Break-even Point
in Dollars
$200,000
÷
40%
=
$500,000
BREAK-EVEN ANALYSIS
Graphic Presentation
 A cost-volume-profit (CVP) graph shows costs,
volume, and profits
 Used to visually find the break-even point
 To construct a CVP graph,
 Plot the total revenue line
starting at the zero activity level
 Plot the total fixed cost
by a horizontal line
 Plot the total cost line.
(Starts at the fixed cost line
at zero activity)
 Determine the break-even point from the intersection of
the total cost line and the total revenue line
BREAK-EVEN ANALYSIS
CVP Graph for Vargo Video
BREAK-EVEN ANALYSIS
Target Net Income
Study Objective 7
 Level of sales necessary
to achieve a specified
income
 Can be determined
from each of the
approaches used to
determine break-even
sales/units
 May be expressed either
in sales dollars or sales
units
BREAK-EVEN ANALYSIS
Target Net Income - Example
Using the Contribution Margin Approach
and the Vargo Video Data:
 Formula for required sales in units:
Fixed Costs + Target
Net Income
÷
$200,000 + $120,000
Contribution
Margin Per Unit
Required Sales
in Units
=
1,600 units
$200
 Formula for required sales in dollars
Fixed Costs + Target
Net Income
$200,000 + $120,000
÷
Contribution
Margin Ratio
40%
=
Required Sales in
Dollars
$800,000
BREAK-EVEN ANALYSIS
Margin of Safety
 Difference between actual or expected sales and sales
at the break-even point
 May be expressed in dollars or as a ratio
 Example To determine the margin of safety in dollars for Vargo Video
assuming that actual (expected) sales are $750,000:
Actual (Expected)
Sales
S750,000
–
Break-even
Sales
$500,000
=
Margin of Safety
in Dollars
$250,000
BREAK-EVEN ANALYSIS
Margin of Safety Ratio
Study Objective 8
 Computed by dividing the margin of safety in dollars
by the actual or expected sales (using Vargo Video data)
Margin of Safety
in Dollars
$250,000
÷
Actual (Expected)
Sales
$750,000
=
Margin of Safety
Ratio
33%
 Results indicate that Vargo Video’s sales could fall by
33 percent before it would be operating at a loss.
 The higher the dollars or the percentage, the greater
the margin of safety.