Cost-Volume-Profit Analysis
Chapter 7
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Objective 1
Calculate the unit contribution
margin and the contribution
margin ratio
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Components of CVP Analysis
•
•
•
•
•
Sales price per unit
Volume sold
Variable costs per unit
Fixed costs
Operating income
3
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CVP Assumptions
1. Change in volume is only factor that
affects costs
2. 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
4
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Unit Contribution Margin
Sales price per unit
- Variable costs per unit
Contribution margin per unit
5
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Contribution Margin Ratio
Unit contribution margin
Sales price per unit
6
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Objective 2
Use CVP analysis to find
breakeven points and target profit
volumes
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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
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Income Statement Approach
Contribution Margin Income Statement
Sales
- Variable Costs
Contribution Margin
- Fixed Costs
Operating Income
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Short-Cut Approach Using the Unit
Contribution Margin
Units sold =
Fixed expenses + Operating income
Contribution margin per unit
10
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Short-Cut Approach Using the Unit
Contribution Margin Ratio
Sales in $ =
Fixed expenses + Operating income
Contribution margin ratio
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E7-15 1.
Contribution margin ratio =
Contribution margin ÷ Sales =
$187,500 ÷ $312,500 = 60%
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E7-15 1.
Aussie Travel
Contribution Margin Income Statements
Sales revenue
$250,000 $360,000
Variable expenses (40%)
100,000
144,000
Contribution margin
$150,000 $216,000
Fixed expenses
170,00
170,000
Operating income (loss)
$ (20,000)
$46,000
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E7-15 2.
Sales in $ =
Fixed expenses + Operating income
Contribution margin ratio
Sales in $ = $170,000 + $0 = $283,333
60%
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E7-16 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
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E7-16 2
Breakeven sales in units:
Fixed costs + Operating income
Contribution margin per unit
($85,000 + $0) / $0.85 = 100,000 units
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E7-16 2
Breakeven sales in dollars:
Fixed costs + Operating income
Contribution margin ratio
($85,000 + $0) / 50% = $170,000
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E7-16 3
Sales in units:
Fixed costs + Operating income
Contribution margin per unit
($85,000 + $25,000) / $0.85 = 129,412 units
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Preparing a CVP Chart
Step 1:
– Choose a sales volume.
– Plot point for total sales revenue.
– Draw sales revenue line from origin.
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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
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Preparing a CVP Chart
Step 2:
– Draw the fixed cost line
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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
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Preparing a CVP Chart
Step 3:
– Draw the total cost line ( fixed plus variable)
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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
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Preparing a CVP Chart
Step 4:
– Identify the breakeven point and the areas of
operating income and loss
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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
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Preparing a CVP Chart
Step 5:
– Mark operating income and operating loss
areas on graph
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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
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E7-20
Dollars (in thousands)
$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)
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E7-20
Dollars (in thousands)
$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)
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E7-20
Dollars (in thousands)
$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)
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E7-20
Dollars (in thousands)
$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)
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E7-20
($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
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Objective 3
Perform sensitivity analysis in
response to changing business
conditions
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Sensitivity Analysis
• “What if” analysis
• What if the sales price changes?
• What if costs change?
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E7-22
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
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E7-22
Sales needed to Breakeven =
Fixed Costs ÷ Contribution Margin Ratio
$240,000 ÷ .40 = $600,000
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E7-23
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
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Objective 4
Find breakeven and target profit
volumes for multiproduct
companies
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Multiple Product Break-Even
Point – E7-27
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
40
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Multiple Product Break-Even
Point – E7-27
Step 2: Calculate the breakeven point in units
Fixed costs + Operating income
Weighted average contribution margin per unit
($9,680 + $0) ÷ $22 = 440 composite units
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Multiple Product Break-Even
Point – E7-27
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
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E7-27
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
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Objective 5
Determine a firm’s margin of
safety and operating leverage
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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
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Margin of Safety
In units:
Expected sales in units – Breakeven sales in units
In dollars:
Margin of safety in units x Sale price per unit
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Margin of Safety As a Percentage
Margin of safety in units ÷ Expected sales in units
In dollars:
Margin of safety in $ ÷ Expected sales in $
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E7-32 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
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E7-32 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
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E7-32 1.
Margin of safety = Expected sales – breakeven sales
= $70,000 - $30,000
= $40,000
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E7-32 2.
Margin of safety as a % of target sales =
$40,000 ÷ $70,000 = 57%
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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
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Operating Leverage
• High operating leverage
– relatively more fixed costs
– relatively high contribution margin ratio
• Higher risk if volume decreases
• Higher potential for reward if volume
increases
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Operating Leverage
• Low operating leverage
– relatively more variable costs
– relatively small contribution margin ratio
• Lower risk if volume decreases
• Lower potential for reward if volume
increases
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Operating Leverage Factor
Contribution margin
Operating income
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E7-32 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
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E7-32 4.
If volume decreases 10%, income will
decrease: 10% x 1.75 = 17.5%
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End of Chapter 7
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