Cost-Volume-Profit Analysis
Chapter 7
7-1
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Objective 1
Calculate the unit contribution
margin and the contribution
margin ratio
7-2
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Components of CVP Analysis
•
•
•
•
•
Sales price per unit
Volume sold
Variable costs per unit
Fixed costs
Operating income
7-3
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CVP Assumptions
1. Change in volume is only factor that affects
costs
2. Managers can classify each cost as either
variable or fixed
•
These costs are linear throughout relevant range
3. Revenues are linear throughout relevant range
4. Inventory levels will not change
5. The sales mix of products will not change
7-4
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Unit Contribution Margin
Sales price per unit
- Variable costs per unit
Contribution margin per unit
Example:
Sales Price per Poster
Less: Variable Cost per poster
Contribution Margin per poster
$35
(21)
$14
7-5
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Contribution Margin Ratio
Unit contribution margin
Sales price per unit
Example:
Unit contribution margin $14 = 40%
Sales price per unit
$35
7-6
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Objective 2
Use CVP analysis to find
breakeven points and target profit
volumes
7-7
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Breakeven Point
• Sales level at which operating income is
zero
• Sales above breakeven result in a profit
• Sales below breakeven result in a loss
7-8
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Income Statement Approach
Contribution Margin Income Statement
Sales
- Variable Costs
Contribution Margin
- Fixed Costs
Operating Income
7-9
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Short-Cut Approach Using the Unit
Contribution Margin
Units sold =
Fixed expenses + Operating income
Contribution margin per unit
7-10
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Short-Cut Approach Using the Unit
Contribution Margin Ratio
Sales in $ =
Fixed expenses + Operating income
Contribution margin ratio
7-11
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E7-15 1.
Contribution margin ratio =
Contribution margin ÷ Sales =
$187,500 ÷ $312,500 = 60%
7-12
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E7-15 1.
Hint: Contribution
margin income
statements are
produced by using the
different volume
levels and the
calculated variable
Statements
expenses.
Aussie Travel
Contribution Margin Income
Sales revenue
$250,000 $360,000
Variable expenses (40%)
100,000
144,000
Contribution margin
$?
$?
Fixed expenses
170,00
170,000
Operating income (loss)
$ (20,000)
$46,000
7-13
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E7-15 2.
Sales in $ =
Fixed expenses + Operating income
Contribution margin ratio
Sales in $ = $170,000 + $0 = $283,333
60%
7-14
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E7-17 1.
Contribution margin = Sales–Variable costs
= $1.70 - $0.85
= $0.85
Contribution margin ratio:
Contribution margin per unit = $0.85 = 50%
Sales price per unit
$1.70
7-15
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E7-17 2.
Breakeven sales in units:
Fixed costs + Operating income
?
($85,000 + $0) / ? = 100,000 units
7-16
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E7-17 2.
Breakeven sales in dollars:
Fixed costs + Operating income
Contribution margin ratio
($85,000 + $0) / 50% = $170,000
7-17
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E7-17 3.
Sales in units:
Fixed costs + Operating income
Contribution margin per unit
($85,000 + $25,000) / $0.85 = 129,412 units
7-18
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Graphing the CVP Relationships
Step 1:
 Choose a sales volume
 Plot point for total sales revenue
 Draw sales revenue line from origin through
the plotted point
7-19
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Preparing a CVP Chart
$20,000
Dollars
$15,000
•
$10,000
Revenues
$5,000
$0
0
500
1,000
1,500
Volume of Units
7-20
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Preparing a CVP Chart
Step 2:
 Draw the fixed cost line
7-21
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Preparing a CVP Chart
$20,000
Dollars
$15,000
Revenues
Fixed costs
$10,000
$5,000
$0
0
500
1,000 1,500
Volume of Units
7-22
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Preparing a CVP Chart
Step 3:
 Draw the total cost line
Hint: What are
the two factors
that comprise
the Total Cost
of operations?
7-23
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Preparing a CVP Chart
$20,000
Dollars
$15,000
Revenues
Fixed costs
Total cost
$10,000
$5,000
$0
0
500
1,000 1,500
Volume of Units
7-24
Copyright © 2008 Prentice Hall All rights reserved
Preparing a CVP Chart
Step 4:
 Identify the breakeven point and
operating income and loss
Hint: When
the areas
does a of
company
“break even”?
When the
neither make
money or lose
money….
7-25
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Preparing a CVP Chart
$20,000
Breakeven point
Dollars
$15,000
$10,000
$5,000
$0
0
500
1,000
1,500
Volume of Units
7-26
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Preparing a CVP Chart
Step 5:
 Mark operating income and operating loss
areas on graph
7-27
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Preparing a CVP Chart
$20,000
Breakeven point
Dollars
$15,000
$10,000
$5,000
$0
0
500
1,000
1,500
Volume of Units
7-28
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Dollars (in thousands)
E7-24
$70,000
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
600
1,200
1,800
2,400
Tickets (in thousands)
7-29
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Dollars (in thousands)
E7-24
$70,000
$60,000
$50,000
$40,000
$30,000
Fixed Costs
$20,000
$10,000
$0
600
1,200
1,800
2,400
Tickets (in thousands)
7-30
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Dollars (in thousands)
E7-24
$70,000
$60,000
Breakeven point
$50,000
$40,000
$30,000
Fixed Costs
$20,000
$10,000
$0
600
1,200
1,800
2,400
Tickets (in thousands)
7-31
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Dollars (in thousands)
E7-24
$70,000
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
600
1,200
1,800
2,400
Tickets (in thousands)
7-32
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E7-24
($24 x units sold)-($4 x units sold)-$24,000,000 = $0
($20 x units sold) = $0 + $24,000,000
Units sold = $24,000,000 ÷ $20 = 1,200,000 tickets
1,200,000 x $24 per ticket = $28,800,000
7-33
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Objective 3
Perform sensitivity analysis in
response to changing business
conditions
7-34
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Sensitivity Analysis
•
•
•
•
“What if” analysis
What if the sales price changes?
What if costs change?
What if the sales mix changes?
7-35
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E7-25
Sales needed to Breakeven =
Fixed Costs ÷ Contribution Margin Ratio
$500,000 = Fixed Costs ÷ .40
$500,000 × .40= Fixed Costs
$200,000 = Fixed Costs
New fixed costs = $240,000
7-36
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E7-25
Sales needed to Breakeven =
Fixed Costs ÷ Contribution Margin Ratio
$240,000 ÷ .40 = $600,000
7-37
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E7-26
Sale price per scarf
Contribution margin ratio
Contribution margin per unit
$16
x.625
$10
Scarves needed to pay for extra entrance
fee cost of $150 ($1,000 x 15%):
$150 ÷ $10 = 15 scarves
7-38
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Objective 4
Find breakeven and target profit
volumes for multiproduct
companies
7-39
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Multiple Product Break-Even
Point – E7-28
Step 1: Calculate weighted-average contribution
margin
Standard
Sale price per unit
$54
Variable costs per unit
36
Contribution margin per unit
$18
Sales mix in units
x3
Contribution margin
$54
Weighted average contribution
Margin per unit ($110 / 5)
Chrome
$78
50
$28
x2
$56
Total
$110
$22
7-40
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Multiple Product Break-Even
Point – E7-28
Step 2: Calculate the breakeven point in units
Fixed costs + Operating income
Weighted average contribution margin per unit
(? + ?) ÷ ? = 440 composite units
7-41
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Multiple Product Break-Even
Point – E7-28
Step 3: Calculate the breakeven point in
units for each product line
Standard: 440 units x 3/5 = 264 units
Chrome: 440 units x 2/5 = 176 units
7-42
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E7-28
To earn $6,600
Fixed costs + Operating income
Weighted average contribution margin per unit
($9,680 + $6,600) ÷ $22 = 740 composite units
Standard: 740 x 3/5 = 444
Chrome: 740 x 2/5 = 296
7-43
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Objective 5
Determine a firm’s margin of
safety and operating leverage
7-44
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Margin of Safety
• Excess of expected sales over breakeven
sales
• Drop in sales that the company can
absorb before incurring a loss
• Used to evaluate the risk of current
operations as well as the risk of new plans
7-45
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Margin of Safety
Margin of Safety in Units =
Expected sales in units – Breakeven sales in units
Margin of Safety in Dollars =
Margin of safety in units x Sale price per unit
7-46
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Margin of Safety
Margin on safety as a percentage is the same
whether units or dollars are used
Margin of safety in units ÷ Expected sales in units
Margin of safety in dollars ÷ Expected sales in $
7-47
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E7-33 1.
Margin of safety = Expected sales – breakeven sales
Expected sales:
Sales – variable costs – fixed costs = operating income
Sales – 70% Sales - $9,000 = $12,000
30% Sales = $9,000 + $12,000
Sales = $70,000
7-48
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E7-33 1.
Margin of safety = Expected sales –
breakeven sales
Breakeven sales:
Sales – variable costs – fixed costs = operating
income
Sales - 70% x Sales - $9,000 = $0
30% Sales = $9,000
Sales = $30,000
7-49
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E7-33 1.
Margin of safety = Expected sales – breakeven sales
= $70,000 - $30,000
= $40,000
7-50
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E7-33 2.
Margin of safety as a % of target sales =
$40,000 ÷ $70,000 = 57%
7-51
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Operating Leverage
• Relative amount of fixed and variable
costs that make up total costs
• Operating leverage factor:
Contribution margin
Operating income
Indicates percentage change in operating
income that will occur from a 1% change
in volume
7-52
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Characteristics of High Operating
Leverage Firms
• High operating leverage companies have:
– Higher levels of fixed costs and lower levels of variable costs
– Higher contribution margin ratios
• For high operating leverage companies,
changes in volume significantly affect operating
income, so they also face:
– Higher risk
– Higher potential for reward
• Examples include: golf courses, hotels, rental
car agencies, theme parks, airlines, cruise lines
7-53
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Characteristics of Low Operating
Leverage companies
• Low operating leverage companies have:
– Higher levels of variable costs, and lower levels of fixed costs
– Lower contribution margin ratios
• For low operating leverage companies, changes
in volume do NOT have as significant an affect
on operating income, so they face:
– Lower risk
– Lower potential for reward
• Examples include: merchandising companies
7-54
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Operating Leverage Factor
Contribution margin
Operating income
As a general rule, the operating leverage
factor, at a given level of sales, indicates
the percentage change in operating
income that will occur from a 1% change
in volume
7-55
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E7-33 3.
Sales
Variable costs (70%)
Contribution margin
$70,000
49,000
$21,000
Operating leverage:
Contribution margin ÷ Operating income
$21,000 ÷ $12,000 = 1.75
7-56
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E7-33 4.
If volume decreases 10%, income will
decrease: 10% x 1.75 = 17.5%
7-57
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End of Chapter 7
7-58
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