Cost-Volume-Profit Analysis
Chapter 21
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1
Objective 1
Identify how changes in volume
affect costs
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2
Cost Behavior
• How costs change in response to changes
in a cost driver
• Cost driver - any factor whose change
makes a difference in a related total cost
• Volume (units or dollars) - most prominent
cost driver in cost-volume-profit (CVP)
analysis
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3
Cost Behavior
• Variable costs - change directly in
proportion to changes in volume
• Fixed costs - remain constant (fixed) for a
given time period despite fluctuations in
volume
• Mixed costs - have both fixed and variable
components
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Assume we pay sales
commissions of 5% on all
sales. The cost of sales
commissions increase
proportionately with increases
in sales
Total Variable Costs
Total Sales
Commissions
$2,500
$2,000
$1,500
$1,000
$500
$0
$0
$10,000 $20,000 $30,000 $40,000
Total Sales
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Variable Cost Per Unit
• Variable costs per unit do not change
as activity increases
In the previous example, sales
persons get $.05 for every
dollar of sales. If a sales
person has sales of $1,000 or
$15,000, she gets $.05 for
every dollar
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Total Sales Salaries
Total Fixed Costs
$2,500
$2,000
$1,500
$1,000
$500
Assume we
$0pay our sales staff a salary of
$2,000 per month. If a sales person makes
$10,000
$20,000
$30,000 $40,000
sales of $500,$0
she gets
paid $2,000
salary.
If she has sales of $100,000,
she gets
paid
Total
Sales
$2,000 salary
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Sales Compensation
Mixed Costs
$4,500
$4,000
$3,500
$3,000
$2,500
$2,000
$1,500
$1,000
$500
A mixed cost has elements of both fixed
$0
and variable costs. Assume we pay our
$0
$10,000 $20,000 $30,000 $40,000
sales staff, $2,000 plus 5% commission on
each sales dollar
Total Sales
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Sales Compensation
Mixed Costs
$4,500
$4,000
$3,500
$3,000
$2,500
Variable
$2,000
$1,500
$1,000
$500
$0
Fixed
$0
$10,000 $20,000 $30,000 $40,000
Total Sales
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E21-14
_____
V 1. Oil filter
_____
F 2. Building rent
_____
V 3. Oil
_____
V 4. Wages of maintenance worker
_____
F 5. Television
_____
F 6. Manager’s salary
_____
F 7. Cash register
_____
F 8. Equipment
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E21-15 a
$80,000
$60,000
$40,000
$20,000
$0
0
5,000
10,000
Units
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11
E21-15 b
$80,000
$60,000
$40,000
$20,000
$0
0
5,000
10,000
Units
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12
E21-15 c
$80,000
$60,000
$40,000
$20,000
$0
0
5,000
10,000
Units
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13
High-Low Method
• Method to separate mixed costs into
variable and fixed components
• Select the highest level and the lowest
level of activity over a period of time
In order to do CVP analysis, we have to
classify costs as to whether they are fixed
or variable. One method of doing this is the
high-low method
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14
High-Low Method – E21-16
Step 1: Calculate variable cost/unit =
Δ total cost / Δ volume of activity
($4,000-$3,600) ÷ (1,000-600)
$400 ÷ 400 = $1
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High-Low Method - E21-16
Step 2: Calculate total fixed costs =
Total mixed cost – Total variable cost
$4,000 – ($1 * 1,000) = $3,000
or
$3,600 – ($1 * 600) = $3,000
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High-Low Method – E21-16
Step 3: Create and use an equation to
show the behavior of a mixed cost
Total mixed cost = $1x + $3,000
= ($1 * 900) + $3,000
= $3,900
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Relevant Range
• Band of volume: Where total fixed costs
remain constant and variable cost per unit
remains constant
• Outside the relevant range, the cost either
increases or decreases
CVP analysis is only valid within a relevant
range, which is usually the range that
could reasonably be expected for our
business
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Objective 2
Use CVP analysis to compute
breakeven point
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Assumptions
1. Expenses can be classified as either
variable or fixed
2. The only factor that affects costs is
change in volume
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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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21
This income statement classifies
expenses accordingContribution
to behavior margin is the excess of
sales revenue over variable costs that
contributes
to covering
fixed costs and
Contribution Margin
Income
Statement
then to providing operating income
Income Statement Approach
Sales
- Variable Costs
Contribution Margin
- Fixed Costs
Operating Income
To compute breakeven point set the
equation equal to zero
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Contribution Margin Approach
Breakeven units sold =
Fixed costs + Operating income
Contribution margin per unit
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Contribution Margin Ratio
Contribution margin ÷ Sales revenue
Breakeven sales dollars =
Fixed costs + Operating income
Contribution margin ratio
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E21-17 1.
Contribution margin ÷ Sales revenue
$187,500 ÷ $312,500 = 60%
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25
E21-17 2.
Aussie Travel
Contribution Margin Income Statement
Three Months Ended March 31, 2007
Sales revenue
$250,000
$360,000
Variable Costs (40%)
(100,000)
(144,000)
Contribution Margin (60%) $150,000
$216,000
Fixed Costs
(170,000)
(170,000)
Operating Income
$(20,000)
$46,000
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E21-17 2.
Breakeven sales dollars =
Fixed costs + Operating income
Contribution margin ratio
$170,000 + $0
.60
$283,333
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E21-18
1. Contribution margin = Sales–Variable costs
= $1.70 - $0.85
= $0.85
2. Breakeven units sold =
Fixed costs + Operating income
Contribution margin per unit
($85,000 + $0) / $0.85 = 100,000 units
100,000 units x $1.70 = $170,000
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Objective 3
Use CVP analysis for profit
planning and graph relations
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Use the same techniques used for
breakeven point
Plan Profits
Example: The following information is available
for Conte Company.
Sale price per unit
Variable costs per unit
Total fixed costs
Target operating income
$30
21
$180,000
$90,000
How many units must be sold to meet the
targeted operating income?
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Plan Profits
Sales – variable costs – fixed costs = operating income
$30x – $21x - $180,000 = $90,000
$9x = $270,000
x = 30,000 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
Profit
$10,000
$5,000
Loss
$0
0
500
1,000
1,500
Volume of Units
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E21-21
Breakeven point
$70,000
$60,000
Dollars
$50,000
$40,000
Fixed Costs
$30,000
$20,000
$10,000
$0
0
100
200
300
400
500
600
700
Volume of Units
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Objective 4
Use CVP methods to perform
sensitivity analysis
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Sensitivity Analysis
• “What if” analysis
• What if the sales price changes?
• What if costs change?
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E21-22
Sale price per student
Variable costs per student
Total fixed costs
$200
120
$50,000
1. Contribution margin per unit:
$200 – 120 = $80
Breakeven point:
$50,000 ÷ $80 = 625 students
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E21-22
Sale price per student
Variable costs per student
Total fixed costs
$180
120
$50,000
2. Contribution margin per unit:
$180 – 120 = $60
Breakeven point:
$50,000 ÷ $60 = 833 students
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E21-22
Sale price per student
Variable costs per student
Total fixed costs
$200
110
$50,000
2. Contribution margin per unit:
$200 – 110 = $90
Breakeven point:
$50,000 ÷ $90 = 556 students
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45
E21-22
Sale price per student
Variable costs per student
Total fixed costs
$200
120
$40,000
1. Contribution margin per unit:
$200 – 120 = $80
Breakeven point:
$40,000 ÷ $80 = 500 students
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46
Margin of Safety
• Excess of expected sales over breakeven
sales
• Drop in sales that the company can
absorb before incurring a loss
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E21-23
Margin of safety = Expected sales – breakeven sales
Expected sales:
Sales – variable costs – fixed costs = operating income
1x - .70x - $9,000 = $12,000
.30x = $21,000
x = $70,000
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E21-23
Margin of safety = Expected sales – breakeven sales
Breakeven sales:
Sales – variable costs – fixed costs = operating income
1x - .70x - $9,000 = $0
.30x = $9,000
x = $30,000
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E21-23
Margin of safety = Expected sales – breakeven sales
= $70,000 - $30,000
= $40,000
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Objective 5
Calculate the breakeven point for
multiple product lines or services
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Multiple Product Break-Even
Point – E21-24
Use same formulas used earlier, but compute
the weighted average contribution margin of all
products.
Sales
mix = Combination
of unit
products
Multiply each
contribution
margin per
times
Step
1:
Calculate
weighted-average
contribution
that
make
up total
the sales
mix
and sales
add
them together. Divide
margin
that
number by the total number of units in the
sales mix
Standard Chrome
Sale price per unit
$54
$78
Variable costs per unit
36
50
Contribution margin per unit
$18
$28
Sales mix in units
x2
x3
Contribution margin
$36
$84
Weighted average contribution
Margin per unit ($120 / 5)
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Total
$120
$24
52
Multiple Product Break-Even
Point – E21-24
Step 2: Calculate the breakeven point in units
Fixed costs + Operating income
Weighted average contribution margin per unit
$12,000 + $0 ÷ $24 = 500 composite units
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Multiple Product Break-Even
Point – E21-24
The composite unit consists of 2 standard
scooters and 3 chrome scooters. Multiply the
Step
3:
Calculate
the
breakeven
point
breakeven units x sales mix
in
units for each product line
Standard: 500 units x 2 = 1,000
Chrome: 500 units x 3 = 1,500
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E21-24
To earn $6,600
Fixed costs + Operating income
Weighted average contribution margin per unit
($12,000 + $6,600) ÷ $24 = 775 composite units
Standard: 775 x 2 = 1,550
Chrome: 775 x 3 = 2,325
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End of Chapter 21
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