0
CHAPTER 4
Cost Behavior and
Relevant Costs
© 2009 Cengage Learning
1
Introduction
What is the nature of costs and
how are they used in decision
making?
Do they increase or decrease as
production volume changes?
Do they remain stable?
1
2
Introduction
The concept of predictable cost
behavior based on volume is very
important to the effective use of
accounting information for managerial
decision making.
As production volume changes, costs
may
•Increase
•Decrease
•Remain the same
2
3
Introduction
Key Concept
Costs behave in
predictable ways.
3
4
The Behavior of Fixed Costs
Fixed costs remain the same in total, but
change per unit when production
volume changes.
Examples: Rent, Depreciation, Salary of a
Plant Manager, Insurance, Property Taxes
$
Total Fixed Costs
$
Fixed Cost Per Unit
4
10
2
1.33
25
50
Volume
75
25
50
Volume
4
75
The Behavior of Variable
Costs
5
Variable costs stay the same per unit but change in
total as volume changes.
Examples: Direct material, direct labor, and
other unit-level costs like factory supplies
$
Total Variable Costs
$
150
100
Variable Cost Per
Unit
20
50
25
50
Volume
75
25
50
75
5
Volume
6
Curvilinear Costs and the
Relevant Range
Cost
Relevant Range
Curvilinear
Function
Straight-Line
Approximation
Volume
6
7
Relevant Range
Key Concept
Within the relevant range, fixed costs
are constant in total and vary per unit,
and variable costs vary in total and
are constant per unit.
7
8
The Cost Equation
y = a + bx
y = total direct material costs
a = total fixed costs
b = slope of line (variable costs
per unit)
x = volume of units produced
8
Cost Behavior and Decision
Making
9
Last month, 2,100 pizzas cost $15,750
Amount
Direct materials $4,200
Per Unit
$2.00
Direct labor
3,150
1.50
Overhead
8,400
4.00
$15,750
$7.50
Total
If all costs are variable, how much would
2,600 pizzas cost?
9
Cost Behavior and Decision
Making
Cost of Goods Sold for 2,600
pizzas:
2,600 x $7.50 = $19,500
Assume that direct materials
were $2, direct labor was
$1.50, and variable overhead
was $1.00 per pizza, and that
$6,300 is a fixed cost. What
would be the cost of goods
sold for 2,600 pizzas? 10
10
Cost Behavior and Decision
Making
Direct materials
$2.00 x 2,600 =
$5,200
Direct labor
$1.50 x 2,600 =
3,900
Variable overhead
$1.00 x 2,600 =
2,600
=
6,300
Fixed costs
Total cost of goods
sold
$18,000
Which do you think is more
representative of the real cost??
11
11
12
Step Costs
Step Costs remain constant within a
relevant range of production.
Example: Janitorial services within a
company that manufactures desks
0-7,500 desks
7,501-15,000 desks
1 Janitor
2 Janitors
$25,000
$50,000
12
13
Mixed Costs
Fixed and Variable Components of
Delivery Van Expense
Fixed: Lease payment each month
Variable: Gas, oil, maintenance and
other costs that vary with the
number of deliveries made (and
miles driven)
13
14
Separating Mixed Costs into their Fixed
and Variable Components
Regression Analysis: A statistical technique
used to estimate the fixed and variable
components of a mixed cost. Is referred to as
least squares regression.
Regression analysis uses statistical methods
to fit a cost line (regression line) through a
set of data points which minimizes the sum
of the squared distance from each data point
to the line (hence the name least squares
regression).
14
Least Squares Regression
Analysis
Regression Line =Total Overhead Cost
Slope represents the
change in cost for a 1
unit change in volume
Costs
?$
Slope of Regression Line =
Variable Cost per unit
Fixed Cost
1 unit
Volume 15
15
16
Using a Spreadsheet Program to
Perform Regression Analysis
Using the actual values of the mixed
costs (dependent variable) and the
volume of production (independent
variable) and a spreadsheet program
such as Excel, you can compute a
regression line using least squares
regression.
See Exhibits 4-10--4-13 in the text.
16
17
Regression Statistics
Exhibit 4-13 shows R2 of less than 1.0
(.883), which implies that other
independent variables may help explain
the change in overhead costs.
Examples: Outside temperature and
other environmental factors might
impact overhead costs incurred.
17
18
Regression Statistics
Other uses in managerial decision-making
situations.
Marketing Managers predicting changes in
sales based on changes in advertising
expenditures.
Production Managers interested in quality
control might collect data on overtime worked
in a factory vs. the number of defective items
produced.
18
Estimating Regression Results Using the
High/Low Method
1. Use only two data points, the high and low
levels of activity and their related total
overhead costs.
2. Subtract the smallest from the largest for
each and use the changes in the following
formula.
3.
Change in Cost
Change in volume
= Variable cost per unit
19
19
Estimating Regression Results Using the
High/Low Method
4. Substitute the total cost of one of the points
for “y” in the equation y = a + bx
5. Substitute the variable cost found using
high-low for “b”
6. Substitute the number of activity units for the
data point chosen for “x”
7. Solve for fixed costs “a”
8. Determine the formula to use in estimating
the mixed costs at various levels
20
20
21
Estimating Regression Results
Using the High/Low Method
If the high point of activity was 2,500
units with $12,450 of overhead costs
and the low point of activity was 1,950
units with $10,525 of overhead costs,
what would be the estimated total
costs at 2,435 units of activity?
21
Estimating Regression Results Using the
High/Low Method
1. High Point = 2,500 units at $12,450
Low Point = 1,950 units at $10,525
2. 2,500 - 1,950 = 550 units (change in
units)
$12,450 - $10,525 = $1,925 (change in
cost)
3. $1,925 / 550 units = $3.50 variable
cost/unit
22
22
23
Estimating Regression Results Using the
High/Low Method
Steps
4,5,6,7.
Y=
a + bx
Volume at high pt
$12,450 =
a + $3.50 (2,500)
$12,450 =
a + $8,750
Cost at high pt
Fixed Costs
$3,700 =
Y=
a
Variable Costs
$3,700 + $3.50x
8. Y = $3,700 + $3.50 (2,435)
Projected volume
Y = $12,222.50 which is total projected
23
overhead costs at 2,435 units.
24
Relevant Costs and Cost
Behavior
Step Costs
It can be misleading to
always view variable costs
as relevant and fixed costs
as not relevant.
24
25
Taxes and Decision Making
Three Tax Considerations:
1. Costs of operating businesses are
deductible for income tax and revenues are
taxable.
2. Form of a transaction may impact the
amount of tax paid or whether cost is tax
deductible
3. Payment of tax requires cash outflow, thus
reducing the amount of cash available for other
purposes.
25
26
Taxes and Decision
Making
Key Concept
Managers must
consider the impact
of taxes when making
decisions.
26
27
After-Tax Costs and Revenues
After-Tax Cost of a tax deductible cash
expenditure:
After-tax cost = Pretax cost X (1-tax rate)
After-Tax Benefit of a taxable cash receipt:
After-tax benefit = Pretax receipts X (1-tax
rate)
27
28
Before- and After-Tax Income
After-tax income = Pretax income X (1tax rate)
$700 = $1,000 x (1 -.30)
28