CHAPTER 4
Cost-Volume-Profit Analysis
Common Cost Behavior Patterns
 Variable Costs
 Fixed Costs
 Mixed Costs
 Step Costs
Variable Costs
 Costs that change in proportion to
changes in volume or activity
 At restaurants, food costs vary with the
number of customers served
 For airlines, fuel costs vary with the
number of miles flown
 Example
 Activity increases by 10%
 Cost increases by 10%
Variable Costs
Fixed Costs
 Do not change in response to changes
in activity level
 Typical fixed costs are depreciation,
supervisory salaries, and building
maintentance
 Example
 Activity increases by 10%
 Costs remain unchanged
Fixed Costs
Fixed Costs
 Discretionary Fixed Costs
 Management can easily change
 Advertising, Research and Development
 Committed Fixed Costs
 Cannot be easily changed
 Rent, Insurance
Fixed Costs
Mixed Costs
 Contain variable and fixed cost
elements
 Example
 Salesperson with base salary (fixed)
 Receives commission on sales (variable)
Mixed Costs
Step Costs
 Fixed cost for a specific range
 Increases to higher level when upper
bound of range is exceeded
 Example
 Company adds third production shift
 Costs increase to include supervisory costs
Step Costs
Direct Labor
Cost Estimation Methods
 Account Analysis
 Scattergraphs
 High-Low Method
 Regression Analysis
Account Analysis
 Most common approach
 Requires professional judgment of
management
 Management classifies costs as fixed
and variable
Account Analysis
 Costs are then estimated
 Variable cost per unit
 Total fixed costs
Account Analysis
 Estimates used to find total production
costs at various production levels
Scattergraphs
 Utilization of cost information from
previous periods
 Weekly, monthly, or quarterly cost
reports
 Plot the costs at specific activity levels
Scattergraphs
High-Low Method
 Utilization of cost information from
previous periods
 Connect straight line from lowest
activity level to highest activity level
High-Low Method
High-Low Method
 Cost Estimations
 Variable cost equals the slope of the line
 Fixed cost equals the intercept of cost
axis
 Estimates used to find total production
costs at various production levels
Regression Analysis
 Statistical technique
 Estimates the slope and intercept of
a cost equation
 Typically spreadsheet programs are
utilized
Regression Analysis
The Relevant Range
 Limitation of estimates
 Accuracy expected only for
production levels within range
 Difficult to assess costs outside the
relevant range
The Relevant Range
Cost-Volume-Profit Analysis
 Equation Abbreviations
x = Quantity of units produced and sold
SP = Selling price per unit
VC = Variable cost per unit
TFC = Total fixed cost
Cost-Volume-Profit Analysis
 The Profit Equation
Profit = SP(x) – VC(x) – TFC
 Fundamental to CVP analysis
Cost-Volume-Profit Analysis
 Break-Even Point
 Number of units sold that allow the
company to neither a profit nor a loss
 $0 = SP(x) – VC(x) – TFC
 Margin of Safety
 Difference between expected sales and
break-even sales
Break-Even Point
Cost-Volume-Profit Analysis
 Contribution Margin (CM)
 Difference between selling price and
variable cost per unit
Profit = (SP – VC)(x) – TFC
OR
Profit = CM per unit(x) - TFC
Cost-Volume-Profit Analysis
 Contribution Margin Ratio
 Contribution of every sales dollar to covering
fixed cost
CM Ratio = SP – VC
SP
 Profit Equation (utilizing CM Ratio)
Sales($) = Profit + TFC
CM Ratio
Cost-Volume-Profit Analysis
 “What If” Analysis
 Utilize profit equation to determine
impact of managerial decisions
 Change in Fixed and Variable Costs
 Change in Selling Price
Cost-Volume-Profit Analysis
 Taxes in CVP Analysis
 Profit Formula without Tax Considerations
Before Tax Profit = SP(x) – VC(x) – TFC
 Profit Formula with Tax Considerations
After Tax Profit = [SP(x) – VC(x) – TFC](1-t)

Gabby’s Wedding Cakes creates
elaborate wedding cakes. Each cake
sells for $500. The variable cost of
baking the cakes is $200 and the fixed
cost per month is $6,000
1. Calculate the break-even point for a
month.
2. How many cakes must be sold to earn a
monthly profit of $9,000?
 Break-Even Point
x = (Profit + TFC) / CM per Unit
x = ($0 + $6,000) / $300
x = 20 cakes
 What if monthly profit is $9,000?
x = ($9,000 + $6,000) / $300
x = 50 cakes
Multiproduct Analysis
 Contribution Margin Approach
 Used if products are similar
 Identify number of units needed to be
sold to break even
 Calculate weighted average contribution
margin based on expected units sold
Multiproduct Analysis
 Contribution Margin Ratio Approach
 Products are substantially different
 Identify dollar amount of sales needed
to break even
 Calculate total CM Ratio and use to
determine break-even point
Assumptions in CVP Analysis
 Costs can be accurately separated
into fixed and variable components
 Fixed costs remain fixed
 Variable costs per unit do not change
Operating Leverage
 Level of fixed versus variable costs
in a company
 High level of fixed costs has a high
operating leverage
 Typically have large fluctuations in
profit when sales fluctuate
Outsourcing
Constraints
 Constraints on how many items can
be produced
 Shortage of space, equipment, or
labor
 Utilize contribution margin per unit
to analyze situations

Rhetorix, Inc. produces stereo speakers.
The selling price per pair of speakers is
$800. The variable cost of production is
$300 and the fixed cost per month is
$50,000.
1. Calculate the contribution margin
associated with a pair of speakers.
2. Calculate the contribution margin ratio
for Rhetorix associated with a pair of
speakers.
 Contribution Margin
CM = SP – VC
CM = $800 - $300
CM = $500
 If the company sells five more speakers
than planned, what is the expected effect
on profit of selling the additional
speakers?
Expected Effect = $500 * 5 units
= $2,500
 Contribution Margin Ratio
CM Ratio = (SP – VC)/SP
= ($800 - $300)/$800
= 62.5%
 If the company has sales that are
$5,000 higher than expected, what
is the expected effect on profit?
Expected Effect = 62.5% * $5,000
= $3,125
1. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Contribution
Margin per unit is?
a. $65
b. $75
c. $175
d. $30
1. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Contribution
margin per unit is?
a. $65
b. $75
c. $175
d. $30
2. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Break-Even
Point is?
a. 1,000 units
b. 1,083 units
c. 2,000 units
d. None of these
2. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Break-Even
Point is?
a. 1,000 units
b. 1,083 units
c. 2,000 units
d. None of these
3. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Expected sales
are 4,200 units. The Margin of
Safety is?
a. $264,000
b. $384,000
c. $143,000
d. $121,000
3. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Expected sales
are 4,200 units. The Margin of
Safety is?
a. $264,000
b. $384,000
c. $143,000
d. $121,000
4. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Expected sales
are 4,200 units. What is profit
expected to be?
Answer here: _________________
4. At Winford Corp., the selling price
per unit for lawn mowers is $120,
variable cost per unit is $55. Fixed
costs are $130,000. Expected sales
are 4,200 units. What is profit
expected to be?
Answer here: $143,000