Prepared by
Debby Bloom-Hill
CMA, CFM
CHAPTER 4
Cost-Volume-Profit Analysis
Slide 4-2
Management Questions
 Planning
 What level of profit should be in the
budget for the coming year?
 Control
 Did the manager responsible for
production costs do a good job of
controlling costs?
 Decision making
 Should the price be increased?
Slide 4-3
Learning objective 1:
Identify common cost behavior patterns
Common Cost Behavior Patterns
 Variable Costs
 Costs which change directly in
proportion to changes in quantity or
activity
 Fixed Costs
 Costs which do not change when
quantity or activity volume changes
Slide 4-4
Learning objective 1: Identify common cost behavior patterns
Common Cost Behavior Patterns
 Mixed Costs
 Costs that have both variable and fixed
elements
 Step Costs
 Fixed for a range of output, but
increase when upper bound of range
is exceeded
Slide 4-5
Learning objective 1: Identify common cost behavior patterns
Variable Costs
 Costs that change in proportion to
changes in volume or activity
 An automobile manufacturer will need
400 tires to make 100 cars, but 4,000
tires to make 1,000 cars
 A bakery will need 2 eggs to make 1 cake
and 20 eggs to make 10 cakes
 If activity increases by a certain
percentage, cost increases by that same
percentage
Slide 4-6
Learning objective 1: Identify common cost behavior patterns
A company has decided that direct labor
costs are 100% variable. Last month total
direct labor costs were $125,000 and total
direct labor hours worked were 10,000.
1. What is the direct labor cost per hour?
$125,000 / 10,000 hours = $12.50 per hour
2.Predict labor costs in a month when 12,000
labor hours are worked
$12.50 per hour × 12,000 hours = $150,000
Slide 4-7
Learning objective 1: Identify common cost behavior patterns
Variable Costs
Total Variable Cost = $91 × Units produced
Slide 4-8
Learning objective 1: Identify common cost behavior patterns
Fixed Costs
 Do not change in response to changes in
activity level
 Typical fixed costs are depreciation,
supervisory salaries, and building
maintenance
• Rent for a bakery will not double if
output increases from 100 to 200 cakes
 If activity increases by a certain
percentage, costs remain unchanged
Slide 4-9
Learning objective 1: Identify common cost behavior patterns
Fixed Costs
Total fixed cost = $94,000
Slide 4-10
Learning objective 1: Identify common cost behavior patterns
Fixed Costs
 Discretionary fixed costs
 Management can easily change, e.g.
advertising, research & development
 Many companies cut back on these costs
when sales drop. This can be shortsighted
 A cut in research & development can have a
negative effect on long run profitability
 A cut in repair and maintenance can have a
negative effect on the life of valuable assets
 Committed fixed costs
 Cannot be easily changed, e.g. rent,
insurance
Slide 4-11
Learning objective 1: Identify common cost behavior patterns
Mixed Costs
 Contain both variable and fixed cost
elements
 Can separate mixed costs into variable
and fixed components
 Salesperson with base salary (fixed) and
commission on sales (variable)
 Base salary included with fixed costs
 Commission included with variable
costs
Slide 4-12
Learning objective 1: Identify common cost behavior patterns
Mixed Costs
Total cost = ($91 × Units produced) + $94,000
Slide 4-13
Learning objective 1: Identify common cost behavior patterns
Step Costs
 Fixed cost for a specific range of volume
 Increases to higher level when upper bound
of range is exceeded
 At that point, costs again remain fixed until
another upper bound is exceeded
 Step costs are often classified as either:
 Step variable costs, if the range of activity
where the cost is fixed is small, or
 Step fixed costs, if the range of activity where
the cost is fixed is large
Slide 4-14
Learning objective 1: Identify common cost behavior patterns
Step Costs
Total step costs =
$7,000 for relevant range 0 – 3,000 units produced
$14,000 for relevant range 3,001 – 6,000 units
$21,000 for relevant range 6,001 – 9,000 units
Slide 4-15
Learning objective 1: Identify common cost behavior patterns
Relevant Range
 The relevant range is the range of activity for
which assumptions as to how costs behave are
reasonably valid
 If it is known that production is going to be
within the relevant range, we can use
assumptions about the fixed and variable
costs
 Making assumptions about fixed and
variable costs at production levels well
above or below this range would not be
valid
Slide 4-16
Learning objective 1: Identify common cost behavior patterns
The Relevant Range
Slide 4-17
Learning objective 3: Perform cost-volume profit analysis for single products
Cost Estimation Methods
 Account Analysis
 Classify costs into variable and fixed pools
 Scattergraphs
 Can see cost relationships visually
 High-Low Method
 Linear estimation connects high and low
volume observations
 Regression Analysis
 Linear estimation is best fit to observed
values
Slide 4-18
Learning objective 2: Estimate the relation between cost and activity using account analysis
and the high-low method
Account Analysis
 Most common approach
 Requires professional judgment of
management
 Management classifies costs as fixed,
variable, or mixed
 Total variable costs divided by activity
equals variable cost per unit
 Variable cost per unit and total fixed
costs can be used in cost equation
Slide 4-19
Learning objective 2: Estimate the relation between cost and activity using account analysis
and the high-low method
Account Analysis
Slide 4-20
Learning objective 2: Estimate the relation between cost and activity using account analysis
and the high-low method
Scattergraphs
 Utilization of cost information from
several previous periods
 Weekly, monthly, or quarterly cost
reports are useful
 Plot the actual costs at the observed
activity levels
 Look for relationship between cost and
activity, linear is ideal
 Use relationship to predict future costs
Slide 4-21
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
Scattergraphs
Is there a relationship between units produced and
production costs? Describe the relationship.
Slide 4-22
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
High-Low Method
 Utilization of cost information from
previous periods
 Fits a straight line from lowest activity
level to highest activity level
 Slope of the line is the estimate of the unit
variable cost
 The slope measures the change in cost
per unit change in activity level
 Total cost at lowest or highest activity level
minus variable cost at that level equals
fixed cost
Slide 4-23
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
High-Low Method
Total cost
at high
activity
level
Total cost at
low activity
level
Slide 4-24
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
High-Low Method
Slide 4-25
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
High-Low Method
Slide 4-26
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
During the past year, Island Air flew 15,000 miles in
August (its busiest month) and had total costs of
$300,000. In November (its least busy month) the
company flew 5,000 miles and had $200,000 of
costs. Using the high-low method, estimate variable
cost per mile and fixed cost per month.
a.
b.
c.
d.
$20 of variable cost and $100,000 fixed
$15 of variable cost and $250,000 fixed
$10 of variable cost and $150,000 fixed
$5 of variable cost and $250,000 fixed
Answer: c
Slide 4-27
Learning objective 1: Identify common cost behavior patterns
During the past year, Island Air flew 15,000 miles in
August (its busiest month) and had total costs of
$300,000. In November (its least busy month) the
company flew 5,000 miles and had $200,000 of costs.
Using the high-low method, estimate variable cost per
mile and fixed cost per month.
Estimate of variable cost =
(𝟑𝟎𝟎,𝟎𝟎𝟎 −𝟐𝟎𝟎,𝟎𝟎𝟎)
(𝟏𝟓,𝟎𝟎𝟎 −𝟓,𝟎𝟎𝟎)
=
𝟏𝟎𝟎,𝟎𝟎𝟎
𝟏𝟎,𝟎𝟎𝟎
= $10
Variable cost at low level = $10 * 5,000 miles = $50,000
Fixed cost = $200,000 total – $50,000 variable = $150,000
Slide 4-28
Learning objective 1: Identify common cost behavior patterns
Regression Analysis
 Statistical technique
 Estimates the slope and intercept of a cost
equation
 Finds the best straight line fit to the
observations
 Typically statistical software packages are
utilized
 Spreadsheet applications like Excel®
typically include statistical operations
 See appendix fox Excel® example
Slide 4-29
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
Cost-Volume-Profit Analysis
 The Profit Equation
Profit = SP(x) – VC(x) – TFC
Where:
x = Quantity of units produced and sold
SP = Selling price per unit
VC = Variable cost per unit
TFC = Total fixed cost
 Fundamental to CVP analysis
Slide 4-30
Learning objective 3: Perform cost-volume profit analysis for single products
Cost-Volume-Profit Analysis
 Break-Even Point
 Number of units sold that allow the company
to neither earn a profit nor incur a loss
 $0 = SP(x) – VC(x) – TFC
 CodeConnect has the following cost
structure
 Selling price $200.00 per unit
 Variable cost $90.83 per unit
 Total fixed cost $160,285
 Find CodeConnect’s break-even point
Slide 4-31
Learning objective 3: Perform cost-volume profit analysis for single products
Cost-Volume-Profit Analysis
 Break-Even Point
$0 = SP(x) – VC(x) – TFC
$0 = $200.00 (x) – $90.83(x) – $160,285
$0 = $109.17(x) – $160,285
$109.17(x) = $160,285
x = $160,285 / $109.17
x = 1,468.21 units
Break-even point is 1,469 units (always round up)
Slide 4-32
Learning objective 3: Perform cost-volume profit analysis for single products
Break-Even Point
Slide 4-33
Learning objective 3: Perform cost-volume profit analysis for single products
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. What is the
break-even point in number of units?
a. 200
b. 20
c. 12
d. 100
Answer: b
Slide 4-34
Learning objective 3: Perform cost-volume profit analysis for single products
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. What is the
break-even point in number of units?
0 = SP(x) – VC(x) – TFC
0 = (SP – VC)(x) – TFC
0 = (500 – 200)(x) – 6,000
0 = 300(x) – 6,000
300(x) = 6,000
x = 6,000 / 300 = 20
Slide 4-35
Learning objective 3: Perform cost-volume profit analysis for single products
Margin of Safety
 The margin of safety is the difference
between the expected level of sales and
break-even sales
 If breakeven sales for Model DX375 is
$293,600 and expected sales are
$350,000, calculate the margin of safety
 The margin of safety is:
$350,000 - $293,600 = $56,400
Slide 4-36
Learning objective 3: Perform cost-volume profit analysis for single products
Margin of Safety Ratio
 The margin of safety can also be
expressed as a ratio
 Called the margin of safety ratio
 Equal to the margin of safety divided by
expected sales
 Shows what percentage sales would have
to drop before the product shows a loss
Margin of
safety ratio
=
𝐌𝐚𝐫𝐠𝐢𝐧 𝐨𝐟 𝐬𝐚𝐟𝐞𝐭𝐲
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐬𝐚𝐥𝐞𝐬
=
$𝟓𝟔,𝟒𝟎𝟎
$𝟑𝟓𝟎,𝟎𝟎𝟎
= 0.16
Slide 4-37
Learning objective 3: Perform cost-volume profit analysis for single products
Contribution Margin
 Difference between revenue and
variable costs
 Contribution margin = total revenue
minus total variable costs
 Contribution margin per unit = selling
price minus variable cost per unit
 For CodeConnect’s Model DX375, the
contribution margin is the $200.00
selling price less the variable cost of
$90.83
Slide 4-38
$200.00 – $90.83
= $109.17
Learning objective 3: Perform cost-volume profit analysis for single products
Contribution Margin
 The contribution margin per unit measures
the amount of incremental profit generated
by selling an additional unit
 For CodeConnect, how much incremental
profit would be generated by selling 100
more units?
Incremental profit = number of units sold *
contribution margin per unit
Incremental profit = 100 * $109.17 =
$10,917
Slide 4-39
Learning objective 3: Perform cost-volume profit analysis for single products
Contribution Margin
 The profit equation in terms of the
contribution margin
Profit = SP(x) – VC(x) – TFC
Profit = (SP – VC)(x) – TFC
Profit = Contribution margin per unit(x) - TFC
Slide 4-40
Learning objective 3: Perform cost-volume profit analysis for single products
Units Needed for Target Profit
 Solve the profit equation for the sales
quantity in units
 Unit sales (x) needed to attain a specified
profit =
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂
𝐒𝐏 −𝐕𝐂
=
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂
𝐂𝐨𝐧𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐦𝐚𝐫𝐠𝐢𝐧 𝐩𝐞𝐫 𝐮𝐧𝐢𝐭
Slide 4-41
Learning objective 3: Perform cost-volume profit analysis for single products
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 in units
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂
𝐒𝐏 −𝐕𝐂
=
𝟎+𝟔,𝟎𝟎𝟎
𝟓𝟎𝟎 −𝟐𝟎𝟎
=
𝟔,𝟎𝟎𝟎
= 20 cakes
𝟑𝟎𝟎
2. How many cakes must be sold to earn a profit
of $9,000?
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐅𝐂
𝐒𝐏 −𝐕𝐂
=
𝟗,𝟎𝟎𝟎 +𝟔,𝟎𝟎𝟎
𝟓𝟎𝟎 −𝟐𝟎𝟎
=
𝟏𝟓,𝟎𝟎𝟎
= 50 cakes
𝟑𝟎𝟎
Slide 4-42
Learning objective 3: Perform cost-volume profit analysis for single products
Contribution Margin Ratio
 The unit contribution margin ratio
measures the amount of incremental
profit generated by an additional dollar of
sales
 Two methods to calculate the
contribution margin ratio
1. Contribution margin divided by sales
revenue (Sales – TVC) / Sales
2. Unit contribution margin divided by
selling price (SP – VC) / SP
Slide 4-43
Learning objective 3: Perform cost-volume profit analysis for single products
Contribution Margin Ratio
 For the Model DX375 bar code reader, the
contribution margin ratio is
$𝟐𝟎𝟎.𝟎𝟎 −$𝟗𝟎.𝟖𝟑
= 0.54585
$𝟐𝟎𝟎.𝟎𝟎
 This indicates that the company earns an
incremental $0.54585 for every dollar of
sales
 If sales increase $10,000 the incremental
profit is 0.54585 * $10,000 = $5,458.50
Slide 4-44
Learning objective 3: Perform cost-volume profit analysis for single products
“What If” Analysis
 “What if” analysis examines what will
happen if an action is taken
 The profit equation can show how profit
will be affect by various options under
consideration
 CodeConnect is selling 3,000 units at
$200, with variable cost of $90.83 and
fixed cost of $160,285
 Management is considering a change to
$80.00 variable cost and fixed cost of
$210,285
Slide 4-45
Learning objective 3: Perform cost-volume profit analysis for single products
“What If” Analysis
 Change in fixed and variable costs
 Without the change, the profit is
$200(3,000) - $90.83(3,000) - $160,285 = $167,225
 If the price and quantity stay the same, the
profit assuming the alternative is selected
would be
$200(3,000) - $80(3,000) - $210,285 = $149,715
 The alternative would hurt profitability
Slide 4-46
Learning objective 3: Perform cost-volume profit analysis for single products
“What If” Analysis
 Change in selling price
 Any one of the variables in the profit
equation can be considered
 For example, if CodeConnect sells 3,000
units, what selling price is required to
earn a profit of $200,000?
$200,000 = SP(3,000) - $90.83(3,000) - $160,285
SP(3,000) = $632,775
SP = $210.93
Slide 4-47
Learning objective 3: Perform cost-volume profit analysis for single products
Matthews Consulting expects to work 5,000
hours next month. It has variable costs of $100
per hour and fixed costs of $600,000. What
price must the company charge to earn a monthly
profit of $900,000?
a. $500
b. $350
c. $400
d. $200
Answer: c
Slide 4-48
Learning objective 3: Perform cost-volume profit analysis for single products
Matthews Consulting expects to work 5,000
hours next month. It has variable costs of $100
per hour and fixed costs of $600,000. What
price must the company charge to earn a monthly
profit of $900,000?
$900,000 = SP(5,000) - $100(5,000) - $600,000
$900,000 = SP(5,000) - $1,100,000
SP(5,000) = $2,000,000
SP = $2,000,000 / 5,000 = $400
Slide 4-49
Learning objective 3: Perform cost-volume profit analysis for single products
Multiproduct Analysis
 Contribution margin approach
 Used if the items sold are similar
 Calculate a weighted average contribution
margin per unit
 Use the weighted average contribution
margin in the profit formula to calculate
breakeven point and target sales
 The relative product mix is then used to
calculate the required sales of individual
items
Slide 4-50
Learning objective 3: Perform cost-volume profit analysis for single products
Multiproduct Analysis
 The company has fixed costs of $3,500,000
Slide 4-51
Learning objective 4: Perform cost-volume profit analysis for multiple products
Multiproduct Analysis
 Break-even sales in units
𝐏𝐫𝐨𝐟𝐢𝐭+𝐓𝐨𝐭𝐚𝐥 𝐟𝐢𝐱𝐞𝐝 𝐜𝐨𝐬𝐭𝐬
=
𝐖𝐞𝐢𝐠𝐡𝐭𝐞𝐝 𝐚𝐯𝐞𝐫𝐚𝐠𝐞 𝐜𝐨𝐧𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧 𝐦𝐚𝐫𝐠𝐢𝐧 𝐩𝐞𝐫 𝐮𝐧𝐢𝐭
𝟎+$𝟑,𝟓𝟎𝟎,𝟎𝟎𝟎
= 2,500 units
$𝟏,𝟒𝟎𝟎
 The 2,500 units is made up of the 2:1 mix, so Rohr
must sell 1,667 Model A (2/3 of 2,500) and 833
Model B units (1/3 0f 2,500)
Slide 4-52
Learning objective 4: Perform cost-volume profit analysis for multiple products
Multiproduct Analysis
 Contribution Margin Ratio Approach
 Products are substantially different
 Calculate total company contribution
margin ratio
 Use total company contribution margin
ratio to compute required sales in dollars
 Total company fixed costs (common costs)
are not included for contribution margin
approach but used for contribution margin
ratio approach
Slide 4-53
Learning objective 4: Perform cost-volume profit analysis for multiple products
Multiproduct Analysis
A company with 4 divisions has the
following information available:
Total sales
$6,450,000
Total variable costs
$4,706,000
Total direct fixed costs
$484,000
Total common fixed costs
$1,120,000
1. Calculate total contribution margin ratio
($6,450,000 – $4,706,000) / $6,450,000 = .2704
2.Calculate total company break-even sales in
dollars
($484,000 + $1,120,000) / .2704 = $5,931,953
Slide 4-54
Learning objective 4: Perform cost-volume profit analysis for multiple products
Assumptions in CVP Analysis
 Assumptions can affect the validity of
the analysis
1. Costs can be separated into fixed and
variable components
2. Total fixed cost and unit variable cost
do not change over the levels of interest
3. Multiproduct analysis assumes the
product mix does not change
 Despite assumptions, CVP is useful
Slide 4-55
Learning objective 4: Perform cost-volume profit analysis for multiple products
Operating Leverage
 Level of fixed versus variable costs in a
company
 A company with a high level of fixed costs
has a high operating leverage
 Companies with high operating leverage
have large fluctuations in profit when
sales increase or decrease
 These companies are seen as more risky
 High operating leverage is better when
sales are expected to increase
Slide 4-56
Learning objective 5: Discuss the effect of operating leverage
Constraints
 Due to shortages of space, equipment or
labor there can be constraints on how many
items can be produced
 Utilize contribution margin per unit to
analyze situations
 Calculate contribution margin per unit of
constraint
 Produce product with highest contribution
margin per unit of constraint
 Linear programming can solve multiple
constraints
Slide 4-57
Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint
Constraints
A company can produce Product A or
Product B using the same machinery. Only
1,000 machine hours are available
Selling price
Variable cost
Contribution margin
Machine hours to
produce one unit
Contribution margin
per machine hour
Product A Product B
$500
$300
300
200
$200
$100
10 hours
$20
2 hours
$50
Slide 4-58
Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint
Constraints
 With the 1,000 available machine hours,
 Product A generates $20,000 of
contribution margin
 Product B generates $50,000 of
contribution margin
 Although Product A has the higher
contribution margin per unit, Product B
has the higher contribution margin per
unit of constraint
Slide 4-59
Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint
CHAPTER 4
Cost-Volume-Profit Analysis
Appendix
Slide 4-60
Regression Analysis
Slide 4-61
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
Regression Analysis
Slide 4-62
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
Regression Analysis
Slide 4-63
Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method
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Slide 4-64