Cost Management
ACCOUNTING AND CONTROL
HANSEN & MOWEN
17-1
17
Cost-Volume-Profit Analysis
17-2
The Break-Even Point in Units
1
Sales (72,500 units @ $40)
Less: Variable expenses
Contribution margin
$2,900,000
1,740,000
$1,160,000
Less: Fixed expenses
Operating income
800,000
$ 360,000
17-3
The Break-Even Point in Units
1
Operating Income Approach
0 = ($40 x Units) – ($24 x Units) – $800,000
0 = ($16 x Units) – $800,000
($16 x Units) = $800,000
Units = 50,000
$1,740,000 ÷
72,500
Proof
Sales (50,000 units @ $40)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$2,000,000
1,200,000
$ 800,000
800,000
$
0
17-4
The Break-Even Point in Units
1
Contribution Margin Approach
Number of units = $800,000 / ($40 - $24)
= $800,000 / $16 per unit
= 50,000 units
17-5
The Break-Even Point in Units
1
Target Income as a Dollar Amount
$424,000 = ($40 x Units) – ($24 x Units) – $800,000
$1,224,000 = $16 x Units
Units = 76,500
Proof
Sales (76,500 units @ $40)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$3,060,000
1,836,000
$1,224,000
800,000
$ 424,000
17-6
The Break-Even Point in Units
1
Target Income as a Percentage of Sales Revenue
More-Power Company wants to know the number of sanders
that must be sold in order to earn a profit equal to 15 percent
of sales revenue.
0.15($40)(Units) = ($40 x Units) – ($24 x Units) – $800,000
$6 x Units = ($40 x Units) – ($24 x Units) – $800,000
$6 x Units = ($16 x Units) – $800,000
$10 x Units = $800,000
Units = 80,000
17-7
The Break-Even Point in Units
1
After-Tax Profit Targets
Net income = Operating income – Income taxes
= Operating income – (Tax rate x Operating income)
= Operating income (1 – Tax rate)
Or
Operating income =
Net income
(1 – Tax rate)
17-8
The Break-Even Point in Units
1
After-Tax Profit Targets
More-Power Company wants to achieve net income of
$487,500 and its income tax rate is 35 percent.
$487,500 = Operating income – 0.35(Operating income)
$487,500 = 0.65(Operating income)
$750,000 = Operating income
Units = ($800,000 + $750,000)/$16
Units = $1,550,000/$16
Units = 96,875
17-9
Break-Even Point in Sales Dollars
2
Revenue Equal to Variable Cost
Plus Contribution Margin
17-10
Break-Even Point in Sales Dollars
2
The following More-Power Company
To determine the break-even in sales dollars, the contribution
contribution
income
statement
is
margin
ratio must bemargin
determined
($1,160,000
÷ $2,900,000).
shown for sales of 72,500 sanders.
Sales
Less: Variable
expenses
Contribution
margin
Less: Fixed expenses
Operating income
$2,900,000 100%
1,740,000
60%
$1,160,000
800,000
$ 360,000
40%
17-11
Break-Even Point in Sales Dollars
2
Operating income = Sales – Variable costs – Fixed Costs
0 = Sales – (Variable cost ratio x Sales) – Fixed costs
0 = Sales (1 – Variable cost ratio) – Fixed costs
0 = Sales (1 – .60) – $800,000
Sales(0.40) = $800,000
Sales = $2,000,000
17-12
Break-Even Point in Sales Dollars
2
Impact of Fixed Costs on Profit
17-13
Break-Even Point in Sales Dollars
2
Impact of Fixed Costs on Profit
17-14
Break-Even Point in Sales Dollars
2
Impact of Fixed Costs on Profit
17-15
Break-Even Point in Sales Dollars
2
Profit Targets
How much sales revenue must More-Power generate to earn a
before-tax profit of $424,000?
Sales = ($800,000) + $424,000/0.40
= $1,224,000/0.40
= $3,060,000
17-16
Multiple-Product Analysis
Regular
Sander
Sales
Less: Variable expenses
Contribution margin
Less: Direct fixed expenses
Product margin
Less: Common fixed exp.
Operating income
$3,000,000
1,800,000
$1,200,000
250,000
$ 950,000
3
MiniSander
$1,800,000
900,000
$ 900,000
450,000
$ 450,000
Total
$4,800,000
2,700,000
$2,100,000
700,000
$1,400,000
600,000
$ 800,000
17-17
Multiple-Product Analysis
3
Regular sander break-even units
= Fixed costs/(Price – Unit variable cost)
= $250,000/$16
= 15,625 units
Mini-sander break-even units
= Fixed costs/(Price – Unit variable cost)
= $450,000/$30
= 15,000 units
17-18
Multiple-Product Analysis
3
Income Statement: Break-Even Solution
17-19
Graphical Representation of
CVP Relationships
(40, $100)
Profit $100—
or Loss
80—
4
I = $5X - $100
60—
40—
20—
Break-Even Point
(20, $0)
0— |
|
| |
|
|
| |
|
|
5 10 15 20 25 30 35 40 45 50
- 20—
Units Sold
- 40— Loss
-60—
ProfitVolume
Graph
-80—
-100— (0, -$100)
17-20
Graphical Representation of
CVP Relationships
4
Cost-Volume-Profit Graph
Revenue
$500 -450 -400 -350 -300 -250 -200 -150 -100 -- Loss
50 -|
0 -- |
5 10
Total Revenue
Profit Region
Total Cost
Variable Expenses
($200, or $5 per unit)
Break-Even Point
(20, $200)
Fixed Expenses ($100)
|
|
|
15
20
25
|
|
|
30 35 40
Units Sold
|
45
|
|
50 55
|
60
17-21
Graphical Representation of
CVP Relationships
4
Assumptions of C-V-P Analysis
1. The analysis assumes a linear revenue function and a linear
cost function.
2. The analysis assumes that price, total fixed costs, and unit
variable costs can be accurately identified and remain
constant over the relevant range.
3. The analysis assumes that what is produced is sold.
4. For multiple-product analysis, the sales mix is assumed to be
known.
5. The selling price and costs are assumed to be known with
certainty.
17-22
Graphical Representation of
CVP Relationships
4
Cost and Revenue Relationships
$
Total Cost
Total
Revenue
Units
Relevant Range
17-23
Changes in the CVP Variables
5
Alternative 1: If advertising expenditures increase by
$48,000, sales will increase from 72,500 units to
75,000 units.
Summary of the Effects of the First Alternative
17-24
Changes in the CVP Variables
5
Alternative 2: A price decrease from $40 per sander
to $38 would increase sales from 72,500 units to
80,000 units.
Summary of the Effects of the Second Alternative
17-25
Changes in the CVP Variables
5
Alternative 3: Decreasing price to $38 and increasing
advertising expenditures by $48,000 will increase sales
from 72,500 units to 90,000 units.
Summary of the Effects of the Third Alternative
17-26
Changes in the CVP Variables
5
Margin of Safety
Assume that a company has a break-even volume of 200 units
and the company is currently selling 500 units.
Current sales
500
Break-even volume
200
Margin of safety (in units)
300
Break-even point in dollars:
Current revenue
Break-even volume
Margin of safety (in dollars)
$350,000
200,000
$150,000
17-27
Changes in the CVP Variables
5
Operating Leverage
Sales (10,000 units)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
Unit selling price
Unit variable cost
Unit contribution margin
Automated
System
Manual
System
$1,000,000
500,000
$ 500,000
375,000
$ 125,000
$1,000,000
800,000
$ 200,000
100,000
$ 100,000
$100
$500,00050
÷
$125,00050
=
DOL of 4
$100
$200,000
80 ÷
$200,000
20 =
DOL of 2
17-28
Changes in the CVP Variables
5
What happens to profit in
each system if sales increase
by 40 percent?
17-29
Changes in the CVP Variables
Sales (14,000 units)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
5
Automated
System
Manual
System
$1,400,000
700,000
$ 700,000
375,000
$ 325,000
$1,400,000
1,120,000
$ 280,000
100,000
$ 180,000
Automated
Manual
system—40%
system—40%
x 2 x= 480%
= 160%
$100,000
$125,000
x 80%
x 160%
= $80,000
= $200,000 increase
$100,000
$125,000
+ $80,000
+ $200,000
= $180,000
= $325,000
17-30
CVP Analysis and Activity-Based Costing
6
The ABC Cost Equation
Total cost = Fixed costs + (Unit variable cost x Number of units) +
(Setup cost x Number of setups) + (Engineering cost x Number of
engineering hours)
Operating Income
Operating income = Total revenue – [Fixed costs + (Unit variable
cost x Number of units) + (Setup cost x Number of setups) +
(Engineering cost x Number of engineering hours)]
17-31
CVP Analysis and Activity-Based Costing
6
Break-Even in Units
Break-even units = [Fixed costs + (Setup cost x Number of
setups) + (Engineering cost x Number of engineering
hours)]/(Price – Unit variable cost)
Differences Between ABC Break-Even and
Convention Break-Even

The fixed costs differ

The numerator of the ABC break-even equation has
two nonunit-variable cost terms
17-32
CVP Analysis and Activity-Based Costing
6
Example Comparing Convention and ABC Analysis
Data about Variables
Cost Driver
Unit Variable Cost
Units sold
$ 10
Setups
1,000
Engineering hours
30
Other data:
Total fixed costs (conventional)
Total fixed costs (ABC)
Unit selling price
Level of Cost Driver
-20
1,000
$100,000
50,000
20
17-33
CVP Analysis and Activity-Based Costing
6
Example Comparing Convention and ABC Analysis
Units to be sold to earn a before-tax profit of $20,000:
Units
= (Targeted income + Fixed costs)/(Price – Unit variable cost)
= ($20,000 + $100,000)/($20 – $10)
= $120,000/$10
= 12,000 units
Same data using the ABC:
Units
= ($20,000 + $50,000 + $20,000 + $30,000/($20 – $10)
= $120,000/$10
= 12,000 units
17-34
CVP Analysis and Activity-Based Costing
6
Example Comparing Convention and ABC Analysis
Suppose that marketing indicates that only 10,000 units can
be sold. A new design reduces direct labor by $2 (thus, the
new variable cost is $8). The new break-even is calculated
as follows:
Units = Fixed costs/(Price – Unit variable cost)
= $100,000/($20 – $8)
= 8,333 units
17-35
CVP Analysis and Activity-Based Costing
6
Example Comparing Convention and ABC Analysis
The projected income if 10,000 units are sold is computed
as follows:
Sales ($20 x 10,000)
Less: Variable expenses ($8 x 10,000)
Contribution margin
Less: Fixed expenses
Operating income
$200,000
80,000
$120,000
100,000
$ 20,000
17-36
CVP Analysis and Activity-Based Costing
6
Example Comparing Convention and ABC Analysis
Suppose that the new design requires a more complex
setup, increasing the cost per setup from $1,000 to $1,600.
Also, suppose that the new design requires a 40 percent
increase in engineering support. The new cost equation is
given below:
Total cost = $50,000 + ($8 x Units) + ($1,600 x Setups)
+ ($30 x Engineering hours)
17-37
CVP Analysis and Activity-Based Costing
6
Example Comparing Convention and ABC Analysis
The break-even point using the ABC equation is calculated
as follows:
Units = [$50,000 + ($1,600 x 20) + ($30 x 1,400)]/($20 – $8)
= $124,000/$12
= 10,333
This is more than the firm can sell!
17-38
End of
Chapter 17
17-39