Transcript CHAPTER 21

21-1
CHAPTER 21
COST-VOLUME-PROFIT
ANALYSIS
21-2
Cost-Volume-Profit Analysis

You must understand the relationships
between costs, volume and “profit”
i.e., costs, volume and revenues
The concept is also known as
“Break-Even Analysis”
 Focuses on short-run decision making

i.e, time frame during which a
company can’t change effects
of certain past decisions

Long-run decision making
is covered in Chapter 26
21-3
Cost-Volume-Profit Analysis
Assumptions

Throughout the relevant range (range
of activity where cost behavior
assumptions are valid)
Unit sales price remains constant
 Unit variable cost remains constant
 Total fixed cost remains constant


All costs may be classified as either
fixed or variable
21-4
Cost Behavior Patterns
Cost behavior means
how a cost will react
to changes in the
level of business
activity.
Fixed Costs
and
Variable Costs
react differently.
21-5
Cost Behavior Patterns
Fixed Costs

Total fixed costs remain constant over
wide ranges of activity/volume.

Per unit fixed costs decrease as volume
level increases.

Example: basic monthly telephone charge

Total cost is unchanged regardless
of number of local calls.

Cost per local call decreases as
number of local calls increases.
21-6
Total Fixed Cost Example
Monthly Basic
Telephone Bill
Your monthly basic telephone bill is
probably unchanged as you make more
local calls.
Number of Local Calls
21-7
Per Unit Fixed Cost Example
Monthly Basic Telephone
Bill per Local Call
The average cost per local call decreases
as more local calls are made.
Number of Local
Calls
21-8
Cost Behavior Patterns
Variable Costs

Total variable costs increase and
decrease in proportion to increases and
decreases in volume.

Per unit variable costs remain constant
over wide ranges of volume.

Example: long distance
telephone charges
 Total
cost will increase as a
function of minutes talked.
 Cost
per minute remains unchanged.
21-9
Total Variable Cost Example
Total Long Distance
Telephone Bill
Your total long distance telephone bill
is based on how many minutes you talk.
Minutes Talked
21-10
Per Unit Variable Cost Example
Per Minute
Telephone Charge
The cost per long distance minute talked is
constant. For example, 10 cents per
minute.
Minutes Talked
21-11
Cost Behavior Patterns
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost changes
as activity level changes.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed cost remains
the same even when the
activity level changes.
Fixed cost per unit goes
down as activity level goes up.
Fixed
21-12
Cost Behavior Question
Fixed costs are usually characterized by:
a. Unit costs that remain constant.
b. Total costs that increase as activity
decreases.
c. Total costs that increase as activity
increases.
d. Total costs that remain constant.
21-13
Cost Behavior Question
Fixed costs are usually characterized by:
a. Unit costs that remain constant.
b. Total costs that increase as activity
decreases.
c. Total costs that increase as activity
increases.
d. Total costs that remain constant.
21-14
Cost Behavior Question
Variable costs are usually characterized by:
a. Unit costs that decrease as activity
increases.
b. Total costs that increase as activity
decreases.
c. Total costs that increase as activity
increases.
d. Total costs that remain constant.
21-15
Cost Behavior Question
Variable costs are usually characterized by:
a. Unit costs that decrease as activity
increases.
b.
b. Total costs that increase as activity
decreases.
c. Total costs that increase as activity
increases.
d. Total costs that remain constant.
21-16
Cost Behavior Patterns
Mixed Costs

Contains fixed portion incurred even
when facility is unused and a variable
portion which increases with usage.

Example: monthly electric utility charge

Fixed service fee

Variable charge per
kilowatt hour used
21-17
Cost Behavior Patterns
Mixed Costs
Total Cost
$
Activity/Volume Level
21-18
Cost Behavior Patterns
Mixed Costs
Total Cost
$
Variable
Portion
Fixed Portion
Activity/Volume Level
21-19
Cost Behavior Patterns
Step Costs

Definition: Constant fixed cost over a
range of activity with an increase at a
certain level to a new, higher fixed cost.

Example: A supervisor’s salary is
$30,000 for a process that produces
10,000 units. When volume increased
beyond 10,000 units, a second process
was added with a second supervisor,
increasing total salaries to $60,000.
21-20
Cost Behavior Patterns
Salaries in
Thousands of Dollars
Step Costs
60
30
0
0
10
20
Activity in Thousands
21-21
Cost Behavior Patterns
Curvilinear Costs
Total Cost
Costs that increase when activity
increases, but in a non-linear manner
Activity
21-22
Cost Behavior Patterns
Relevant Range

Definition: Range of activity where the
cost behavior assumptions are valid

Total fixed costs remain constant.

Per unit variable costs remain unchanged.

The cost behavior assumptions
discussed earlier allow us to use linear
relationships.

How does this differ from what you
learned in your economics course?
21-23
Cost Behavior Patterns
Relevant Range

Economics (Economies of Scale)
Extremely wide range assumed
 e.g., 0 to
8


Accounting
Relatively narrow range assumed
 e.g., 40,000 units to 100,000 units

The Linearity Assumption
and the Relevant Range
Total Cost
Economist’s
Curvilinear Total
Cost Function
Activity
21-24
The Linearity Assumption
and the Relevant Range
21-25
Total Cost
Economist’s
Curvilinear Total
Cost Function
Accountant’s Straight-Line
Approximation (constant
unit variable cost)
Activity
The Linearity Assumption
and the Relevant Range
21-26
Total Cost
A straight line closely approximates a
curvilinear variable cost line within the
relevant range.
Relevant
Range
Accountant’s Straight-Line
Approximation (constant
unit variable cost)
Activity
21-27
Fixed Costs and Relevant Range
Example: Office
space is available at
a rental rate of
$30,000 per year in
increments of 1,000
square feet. As the
business grows
more space is
rented, increasing
the total cost.
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Rent Cost in
Thousands of Dollars
Fixed Costs and Relevant Range
Relevant
90
Range
Relevant
60
30
00
Range
Relevant
Range
Total cost doesn’t
change for a wide
range of activity,
and then jumps to a
new higher cost for
the next higher
range of activity.
1,000
2,000
3,000
Rented Area (Square Feet)
21-29
Fixed Costs and Relevant Range
How does this type
of fixed cost differ
from a step cost?
21-30
Fixed Costs and Relevant Range
How does this type
of fixed cost differ
from a step cost?
Step costs can be
adjusted more quickly
and . . .
The width of the
activity steps is much
wider for the fixed
cost.
21-31
Methods for Analyzing Costs
We will separate
a mixed cost into
its fixed and
variable
components.
21-32
Methods for Analyzing Costs
Two methods will
be used:
Scatter Diagram
High-low method
21-33
Scatter Diagram
Total Cost in
1,000’s of Dollars
A scatter diagram of past cost behavior
is helpful in analyzing mixed costs.
20
10
* *
* *
* ** *
**
Plot the data points on a
graph (total cost vs. activity).
0
0
1
2
3
4
Activity, 1,000’s of Units Produced
21-34
Scatter Diagram
Total Cost in
1,000’s of Dollars
Draw a line through the plotted data points so that about
an equal numbers of points fall above and below the line.
20
10
* *
* *
* ** *
**
0
0
1
2
3
4
Activity, 1,000’s of Units Produced
21-35
Scatter Diagram
Total Cost in
1,000’s of Dollars
Where line intercepts with
cost axis is total fixed cost.
20
10
Review regression analysis
calculations from your statistics
class and bring your scientific
calculator to the next test.
* *
* *
* ** *
**
Estimated fixed cost = $10,000
0
0
1
2
3
4
Activity, 1,000’s of Units Produced
21-36
Methods for Analyzing Costs
Now, the
High-low method
(You are responsible
for knowing how to
use it.)
21-37
Analyzing Mixed Costs
High-Low Method
Objective: To separate total cost into
fixed and variable portions.
 Step 1 - Calculate variable cost per unit.
.

V.C./unit = in cost ÷ in units

Step 2 - Calculate total variable cost at
either high or low volume level and
subtract it from total cost at the same
volume level to determine total fixed
cost at any level.
21-38
The High-Low Method
WiseCo recorded the following production
activity and maintenance costs for two months:
High activity level
Low activity level
Change
Units
9,000
5,000
4,000
Cost
$ 9,700
6,100
$ 3,600
Using these two levels of activity, compute:
 the variable cost per unit
 the total fixed cost
21-39
The High-Low Method
High activity level
Low activity level
Change
 Unit variable cost =
Units
9,000
5,000
4,000
Cost
$ 9,700
6,100
$ 3,600
in cost
$3,600
in units = $4,000 = $.90
21-40
The High-Low Method
High activity level
Low activity level
Change
Units
9,000
5,000
4,000
Cost
$ 9,700
6,100
$ 3,600
in cost
$3,600
 Unit variable cost = in units = $4,000 = $.90
 Fixed cost = Total cost – Total variable cost
21-41
The High-Low Method
High activity level
Low activity level
Change
Units
9,000
5,000
4,000
Cost
$ 9,700
6,100
$ 3,600
in cost
$3,600
 Unit variable cost = in units = $4,000 = $.90
 Fixed cost = Total cost – Total variable cost
Fixed cost = $9,700 – ($.90 per unit × 9,000 units)
Fixed cost = $9,700 – $8,100 = $1,600
21-42
The High-Low Method
Choosing the low
activity level will
give the same
result.
21-43
The High-Low Method
High activity level
Low activity level
Change
Units
9,000
5,000
4,000
Cost
$ 9,700
6,100
$ 3,600
in cost
$3,600
 Unit variable cost =
=
= $.90
in units
$4,000
 Fixed cost = Total cost – Total variable cost
Fixed cost = $6,100 – ($.90 per unit × 5,000 units)
Fixed cost = $6,100 – $4,500 = $1,600
21-44
Cost-Volume-Profit Analysis
Now that we
understand cost
behavior, let’s
turn our
attention to
cost-volumeprofit analysis.
21-45
Cost-Volume-Profit Analysis
Objective
Determine the effects that changes in
selling prices, costs, and/or volume will
have on profits in the short run.
21-46
Costs and Revenue
in Dollars
Cost-Volume-Profit Chart
Sales
Break-even Point
Income
Total costs
Loss
Units of Activity
21-47
Profit Equations
At any point on the cost-volume-profit
chart the following relationships are valid:
Net income = Revenue – Total costs
Variable costs + Fixed costs
Contribution Margin = Revenue –
Variable costs
21-48
The Cost-Volume-Profit Chart
240
Relevant sales volume range
220 -
.
200 180 Sales
160 140 120 -
Break-even point
Total costs
100 80 Variable costs
60 -
-
-
-
-
-
-
-
1
2
3
4
5
6
7
Units (000)
8
9
10
11
-
-
0
-
20 -
Fixed
costs
-
40 -
12
21-49
Cost-Volume-Profit Analysis
Let’s look
at the OK
Company
example.
21-50
Cost-Volume-Profit Analysis
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Total
$ 100,000
60,000
$ 40,000
Unit
$ 50
30
$ 20
Contribution margin is amount by which revenue
exceeds variable costs of producing the revenue.
21-51
Cost-Volume-Profit Analysis
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Total
$ 100,000
60,000
$ 40,000
30,000
Unit
$ 50
30
$ 20
Contribution margin goes to cover fixed costs and ...
21-52
Cost-Volume-Profit Analysis
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
Unit
$ 50
30
$ 20
Contribution margin goes to cover fixed costs and …
after covering fixed costs, any remaining
contribution margin contributes to net income.
21-53
Cost-Volume-Profit Analysis
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
Unit
$ 50
30
$ 20
How much contribution margin does OK
need to cover its fixed costs (i.e., break even)?
21-54
Cost-Volume-Profit Analysis
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
Unit
$ 50
30
$ 20
How much contribution margin does OK
need to cover its fixed costs (i.e., break even)?
Answer $30,000
21-55
Cost-Volume-Profit Analysis
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
How many units must OK sell to
cover its fixed costs (break even)?
Unit
$ 50
30
$ 20
21-56
Cost-Volume-Profit Analysis
Sales Revenue (2,000 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 100,000
60,000
$ 40,000
30,000
$ 10,000
How many units must OK sell to
cover its fixed costs (break even)?
$30,000 ÷ $20 per unit = 1,500 units
Unit
$ 50
30
$ 20
21-57
Cost-Volume-Profit Analysis
Sales Revenue (1,500 units)
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Total
$ 75,000
45,000
30,000
30,000
$
0
How many units must OK sell to
cover its fixed costs (break even)?
$30,000 ÷ $20 per unit = 1,500 units
Unit
$ 50
30
$ 20
PR
O
O
F
21-58
Cost-Volume-Profit Analysis
We have just seen one of the basic costvolume-profit relationships, the
break-even computation in units.
Fixed costs
Break-even units = Contribution margin per unit
Contribution margin per unit is sales price per unit less
variable cost per unit. Conceptually, it represents the
amount of each sales dollar which “contributes” to
fixed costs and profit (net income).
21-59
Finding the Break-Even Point
Break-even (BE) Computation
BEunits =
Fixed costs
Contribution margin per unit
21-60
Cost-Volume-Profit Analysis
The break-even formula may also be
expressed in sales dollars.
Fixed costs
Break-even dollars = Contribution margin ratio rate
The contribution margin rate is computed either by
dividing contribution margin per unit by selling price
per unit or by dividing total contribution margin by
total revenues.
Conceptually, the contribution margin rate represents
the percentage of each sales dollar which
“contributes” to fixed costs and profit (net income).
21-61
Finding the Break-Even Point
The break-even formula may also be
expressed in sales dollars:
BE$ =
Fixed costs
Contribution margin rate
CMR = contribution margin
as a percentage of sales.
OK’s CMR
21-62
Finding the Break-Even Point
Sales Revenue (1,500 units)
Less: Variable costs
Contribution margin
Total
$ 75,000
45,000
30,000
Unit Percent
$ 50
100%
30
60%
$ 20
40%
OK’s contribution margin
per unit is $20.
OK’s CMR is 40%
or $20/$50.
21-63
Cost-Volume-Profit Analysis
Question
Tulip Co. sells its plant cartons at $5.00 per
unit. If fixed costs are $200,000 and variable
costs are $3.00 per unit, how many units
must be sold to break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
21-64
Cost-Volume-Profit Analysis
Question
Tulip Co. sells its plant cartons at $5.00 per
unit. If fixed costs are $200,000 and variable
costs are $3.00 per unit, how many units
must be sold to break even?
a. 100,000 units
a.
$200,000
Fixed costs
= $5.00 – $3.00
b.
b. 40,000 unitsUnit contribution
c. 200,000 units
= 100,000 units
c.
d. 66,667 units
21-65
Cost-Volume-Profit Analysis
Question
Use the CMR formula to determine the
amount of sales revenue Tulip Co. needs to
break even. Fixed costs ($200,000), unit
sales price ($5), and per unit variable cost
($3) are unchanged.
a.
b.
c.
d.
$200,000
$300,000
$400,000
$500,000
21-66
Cost-Volume-Profit Analysis
Question
Use the CMR formula to determine the
amount of sales revenue Tulip Co. needs to
break even. Fixed costs ($200,000), unit
sales price ($5), and per unit variable cost
($3) are unchanged.
a.
b.
c.
d.
$200,000
$300,000
$400,000
$500,000
CMR = ($5.00 – $3.00) ÷ $5.00 = .40
BE$ = $200,000 ÷ .40 = $500,000
Calculating Break-Even for
a Multiproduct Company
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Income
Product 1
Product 2
Amount
%
Amount
%
$ 20,000 100% $ 80,000 100%
15,000
75%
40,000
50%
4000
$ 5,000
25% $ 40,000
50%
Total
$ 100,000
55,000
$ 45,000
27,000
$ 18,000
21-67
%
100%
55%
45%
21-68
Cost-Volume-Profit Analysis
Desired Income
Break-even formulas may be adjusted to
show the sales volume needed to earn
any amount of income.
Add desired income to fixed costs in the
numerator. No other changes are needed.
BEunits
=
Fixed costs + Desired income
Contribution margin per unit
BE$
=
Fixed costs + Desired income
Contribution margin rate
21-69
Cost-Volume-Profit Analysis
Question
Tulip Co. sells its plant cartons at $5.00 per
unit. If fixed costs are $200,000 and variable
costs are $3.00 per unit, how many units
must be sold to earn income of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
21-70
Cost-Volume-Profit Analysis
Question
Tulip Co. sells its plant cartons at $5.00 per
unit. If fixed costs are $200,000 and variable
costs are $3.00 per unit, how many units
must be sold to earn income of $40,000?
Fixed costs + Desired income
a. 100,000 units Unit contribution
b. 120,000 units
$200,000 + $40,000
= 120,000 units
$5.00
–
$3.00
c. 80,000 units
d. 200,000 units
21-71
Margin of Safety
Excess of current sales over the
break-even volume of sales. (i.e., the
amount by which sales may decline
before reaching break-even sales.)
Margin of safety = Current sales – Break-even sales
Let’s calculate the margin
of safety for OK Company.
21-72
Margin of Safety
Current sales
Breakeven sales
Margin of safety
Sales Revenue
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
$ 100,000
- 75,000
$ 25,000
Break-even
Sales
1,500 Units
$ 75,000
45,000
30,000
30,000
$
0
Current
Sales
2,000 Units
$ 100,000
60,000
40,000
30,000
$ 10,000
21-73
Margin of Safety
The margin of safety may also be
expressed as a percentage of
current sales.
Sales Revenue
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Break-even
Sales
1,500 Units
$ 75,000
45,000
30,000
30,000
$
0
Current
Sales
2,000 Units
$ 100,000
60,000
40,000
30,000
$ 10,000
21-74
Margin of Safety
Margin of safety
percentage
=
=
=
Current sales - Break-even sales
Current sales
$100,000
$75,000
$100,000
25%
Sales Revenue
Less: Variable costs
Contribution margin
Less: Fixed costs
Net income
Break-even
Sales
1,500 Units
$ 75,000
45,000
30,000
30,000
$
0
Current
Sales
2,000 Units
$ 100,000
60,000
40,000
30,000
$ 10,000
21-75
THE END