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John Wiley & Sons, Inc. 2005
Prepared by
Dan R. Ward
Suzanne P. Ward
University of Louisiana at Lafayette
Managerial Accounting
Weygandt Kieso Kimmel
CHAPTER 5
COST-VOLUME-PROFIT
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CHAPTER 5
COSTVOLUME - PROFITStudy 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.
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Study Objectives: Continued
Identify the three ways to determine the break-
even point.
Give the formulas for determining sales
required to earn target net income.Define margin of safety, and give the formulas
for computing it.
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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 makedecisions
Applies to all types of businesses and entities
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COST BEHAVIOR ANALYSISContinued
Starting point is measuring key businessactivities
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)
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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
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COST BEHAVIOR ANALYSISContinued
The activity level selected is calledtheactivity (or volume) index
Identifies the activity that causes
changes in the behavior of costs Allows costs to be classified
according to their response tochanges in activity as:
Variable Costs
Fixed Costs
Mixed Costs
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COST BEHAVIOR ANALYSISVARIABLE COSTS
Study Objective 1
Costs that varyin totaldirectly 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
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COST BEHAVIOR ANALYSISVARIABLE COSTS - Continued
Variable costs alsoremainconstant 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
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COST BEHAVIOR ANALYSISVARIABLE COSTS - Continued
Example
Damon Company manufactures radios thatcontain a $10 clock
Activity index is the number of radios produced
For each radio produced, the total cost of theclocks increases by $10
If 2,000 radios are made, the total cost of the clocksis $20,000 (2,000 X $10)
If 10,000 radios are made, the total cost of theclocks is $100,000 (10,000 X $10)
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COST BEHAVIOR ANALYSISVARIABLE COSTS - Continued
Example: Continued
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COST BEHAVIOR ANALYSISFIXED COSTS
Costs thatremain the same intotalregardless ofchanges in the activity level.
Per unit costvariesinverselywith activity:
As volume increases,
unit cost decline, and vice versa
Examples include
Property taxes
Insurance
Rent
Depreciation on buildings and equipment
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COST BEHAVIOR ANALYSISFIXED COSTS - Continued
Example
Damon Company leases its productive facilitiesfor $10,000 per month
Total fixed costs of the facilities remain constantat all levels of activity - $10,000 per month
On aper unit basis, the cost of rent decreases asactivity increases and vice versa
At 2,000 radios, the unit cost is $5 ($10,000 2,000units)
At 10,000 radios, the unit cost is $1 ($10,000
10,000 units)
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COST BEHAVIOR ANALYSISFIXED COSTS - Continued
Example:Continued
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COST BEHAVIOR ANALYSISRELEVANT RANGE
Study Objective 2
Throughout the range of possible levels of activity,astraight-line relationship usually doesnot 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 nonlinearsomefixed costs will not change over the entire range ofactivities, others may
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COST BEHAVIOR ANALYSISRELEVANT RANGE - Continued
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COST BEHAVIOR ANALYSISRELEVANT RANGE - Continued
Defined as the range of activity over which acompany expects to operate during a year
Within this range, a straight-line relationship
usually exists for both variable and fixed costs
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COST BEHAVIOR ANALYSISMIXED COSTS
Study Objective 3
Costs that haveboth a variable costelementanda fixed
cost element
Sometimes calledsemivariable cost
Change in total butnot proportionatelywith changes in
activity level
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COST BEHAVIOR ANALYSISMIXED COSTSHigh-Low Method
Mixed costs must be classified into their fixed andvariable elements
One approach to separate the costs is called thehigh-low method
Uses the total costs incurred at both the high and the lowlevels of activity to classify mixed costs
The difference in costs between the high and low levelsrepresents variable costs, since only variable costs changeas activity levels change
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COST BEHAVIOR ANALYSISMIXED COSTSHigh-Low Method - Continued
Steps in Method
STEP 1: Determine variable cost per unit using thefollowing formula:
STEP 2: Determine the fixed cost by subtractingthe total variable cost at either the high or the lowactivity level from the total cost at that level
=Change inTotal CostsHigh minus Low
Activity LevelVariable Cost
per Unit
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COST BEHAVIOR ANALYSISMIXED COSTSHigh-Low Method - Continued
ExampleData for Metro Transit Company
for the last 4-month period:
High Level of Activity: April $63,000 50,000 miles
Low Level of Activity: January 30,000 20,000 miles
Difference $33,000 30,000 miles
Step 1: Using the formula, variable costs per unit are
$33,000 30,000 = $1.10 variable cost per mile
MonthJanuaryFebruary
Miles Driven20,00040,000
Total Cost$30,000$48,000
MonthMarchApril
Miles Driven35,00050,000
Total Cost$49,000$63,000
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COST BEHAVIOR ANALYSISMIXED COSTSHigh-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
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
Activity Level
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COST BEHAVIOR ANALYSISMIXED COSTSHigh-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.
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Lets Review
Variable costs are costs that:
a. Vary in total directly and proportionately with
changes in the activity level
b. Remain the same per unit at every activity level
c. Neither of the above
d. Both (a) and (b) above
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Lets Review
Variable costs are costs that:
a. Vary in total directly and proportionately with
changes in the activity level
b. Remain the same per unit at every activity level
c. Neither of the above
d. Both (a) and (b) above
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COST-VOLUME-PROFIT
ANALYSISStudy Objective 4
Study of the effects of changes of costs and
volumeon a companys profits
A critical factor in management decisions
Important in profit planning
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COST-VOLUME-PROFIT
ANALYSIS
Considers the interrelationships among thefive
components of CVP analysis:
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ASSUMPTIONS UNDERLYINGCVP ANALYSIS
Behavior of both costs and revenues is linearthroughout the relevant range of the activity index
All costs can be classified as either variable or fixedwith reasonable accuracy
Changes in activity are the only factors that affectcosts
All units produced are sold
When more than one type of product is sold, thesales mix will remain constant
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CVP INCOME STATEMENTStudy Objective 5
A statement for internal use
Classifies costs and expenses as fixed or variable
Reportscontribution margin in the body of the
statement.
Contribution margin amount of revenueremaining after
deducting variable costs
Reports the same netincome as a traditionalincome statement
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CVP INCOME STATEMENT
Example
Vargo Video Company produces DVD players.
Relevant data for June 2005:Unit selling price of DVD player $500Unit variable costs $300Total monthly fixed costs $200,000
Units sold 1,600
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CVP INCOME STATEMENTContribution Margin Per Unit
Contribution margin is availableto cover fixed costsand to contribute to income
Formula forcontribution margin per unit:
Example: Computation for Vargo Video
=Unit Selling Price Unit VariableCosts
Contribution
Margin per Unit
=Unit Selling Price$500
Unit Variable
Costs $300
ContributionMargin per Unit
$200
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CVP INCOME STATEMENTContribution Margin Ratio
Shows the percentage of each sales dollar available
to apply toward fixed costs and profits
Example: Computation for Vargo Video
= ContributionMargin RatioUnit Selling PriceContributionMargin per Unit
=Contribution
Margin Ratio
40%
Unit Selling Price
$500
Contribution
Margin per Unit
S200
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CVP INCOME STATEMENTContribution Margin Ratio - Example
Ratio helps to determine the effect of changes in sales on net income
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BREAK-EVEN ANALYSISStudy Objective 6
Process of finding thebreak-even point
Break-even point
Level of activity at whichtotal revenues equaltotal
costs (both fixed and variable)
Can be computed or derived
from amathematical equation
by using contribution margin from a cost-volume-profit (CVP) graph
Expressed either insales units or insalesdollars
BREAK EVEN ANALYSIS
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BREAK-EVEN ANALYSISMathematical Equation
Variable Costs
$300 Q
Fixed Costs
$200,000
Net Income
$0
Sales
$500 Q = + +
Example using the Vargo Video data:
Where:
Q = sales volume; $500 = selling price; $300 = variable cost per unit; $200,000 total fixed costs
To findsales dollars required to break-even:1000 units X $500 = $500,000 (break-even sales dollars)
$200 Q $200,000
Q 1000 units
=
=
BREAK EVEN ANALYSIS
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BREAK-EVEN ANALYSISContribution Margin Technique
At the break-even point,contribution margin must equaltotal fixed costs(CM = total revenuesvariable costs)
The break-even point can be computed using eithercontribution margin per unit or contribution margin ratio
When the break even point in units is desired, contribution marginper unit is used in the following formula
When the break even point in dollars is desired, contributionmarginratio is used in the following formula
=Fixed CostsBreak-even Point
in Units
Contribution
Margin per Unit
=Fixed CostsBreak-even Point
in Dollars
Contribution
Margin Ratio
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BREAK-EVEN ANALYSISContribution Margin Technique
Example using Vargo Video data:
=Fixed Costs$200,000
Break-even Point
in Units1,000 units
Contribution
Margin per Unit$200
=Fixed Costs$200,000
Break-even Point
in Dollars
$500,000
Contribution
Margin per Unit
40%
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BREAK-EVEN ANALYSISGraphic 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 linestarting at the zero activity level
Plot the total fixed costby a horizontal line
Plot the total cost line.(Starts at the fixed cost lineat zero activity)
Determine the break-even point from the intersection ofthe total cost line and the total revenue line
BREAK EVEN ANALYSIS
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BREAK-EVEN ANALYSISCVP Graph for Vargo Video
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BREAK-EVEN ANALYSISTarget Net Income
Study Objective 7
Level of sales necessaryto achieve a specifiedincome
Can be determinedfrom each of theapproaches used todetermine break-even
sales/units
May be expressed eitherinsales dollars or salesunits
S S
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BREAK-EVEN ANALYSISTarget Net Income - Example
Using the Contribution Margin Approach
and the Vargo Video Data:
Formula forrequired sales in units:
Formula forrequired sales in dollars
=ContributionMargin Ratio
40%
Fixed Costs + TargetNet Income
$200,000 + $120,000
Required Sales inDollars
$800,000
=Contribution
Margin Per Unit
$200
Fixed Costs + TargetNet Income
$200,000 + $120,000
Required Salesin Units
1,600 units
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Lets Review
Contribution margin:
a. Is revenue remaining after deducting variable
costs
b. May be expressed as contribution margin per
unit
c. Is selling price less cost of goods sold
d. Both (a) and (b) above
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Lets Review
Contribution margin:
a. Is revenue remaining after deducting variable
costs
b. May be expressed as contribution margin per
unit
c. Is selling price less cost of goods sold
d. Both (a) and (b) above
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BREAK-EVEN ANALYSISMargin of Safety
Difference betweenactual or expected sales and salesat thebreak-even point
May be expressed in dollarsor as a ratio
Example -
To determine themargin of safety in dollars for Vargo Video
assuming that actual (expected) sales are $750,000:
=Margin of Safety
in Dollars
$250,000
Break-even
Sales
$500,000
Actual (Expected)
Sales
S750,000
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BREAK-EVEN ANALYSISMargin of Safety Ratio
Study Objective 8
Computed by dividing the margin of safety in dollarsby the actual or expected sales (using Vargo Video data)
Results indicate that Vargo Videos sales could fallby33 percent before it would be operating at a loss.
Thehigher the dollars or the percentage, the greaterthe margin of safety.
= Margin of SafetyRatio33%
Actual (Expected)Sales
$750,000
Margin of Safetyin Dollars
$250,000
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Summary of Study Objectives
Distinguish between variable and fixed costs. Variable costs:
Costs that vary in total directly and proportionately with changes
in the activity index, but remain constant on a per unit basis
Fixed costs:
Costs that remain the same in total regardless of changes in the
activity index, but, on a per unit basis, vary inversely with
changes in the activity index
Explain the significance of the relevant range.
Relevant rangeRange of activity within which the company expects to operate
Cost behavior assumed to be linear through this range
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Summary of Study Objectives
Explain the concept of mixed costs. Containsboth a variable cost and a fixed cost component
For CVP analysis, must be divided into its fixed and variableamounts
One method used to classify these costs is thehigh-low method
List the five components of CVP analysis.
Volume or level of activity
Unit selling price
Variable cost per unit
Total fixed costs
Sales mix
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Summary of Study Objectives
Indicate what contribution margin is andhow it can be expressed.
Contribution margin is the excess of revenueover all variable costs
Can be expressed either as aper unit amountor as aratio
Identify the three ways to determine thebreak-even point.
Using amathematical equation
Thecontribution margin technique
From a CVP graph
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Summary of Study Objectives Give the formulas for determining sales required to earn
target net income. General formula:
Required sales= Variable costs + Fixed costs + Target Net Income
Other formulas:Required sales in units= (Fixed costs + Target Net Income)
Contribution margin per unit
andRequired sales in dollars= (Fixed costs + Target Net Income) Contribution margin ratio
Define the margin of safety and give the formulas forcomputing it. Excess of actual or expected sales over sales at break-even
Formulas:
Actual (expected) sales Break-even sales =Margin of safety in dollars
and
Margin of safety in dollars Actual (expected) sales =Margin of safetyratio
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COPYRIGHT
Copyright 2005 John Wiley & Sons, Inc. All rights reserved. Reproduction ortranslation of this work beyond that permitted in Section 117 of the 1976 United
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