Module 14
Cost Behavior and Cost Estimation
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?
How can we use cost behavior to
predict future costs?
2
The Behavior of Fixed Costs
Fixed Costs remain the same in total, but may
vary 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
100
2
1.33
25
50
Volume
75
25
50
Volume
75
3
The Behavior of Variable Costs
Variable Costs vary in direct proportion to
changes in production volume, but are fixed
when expressed as per-unit
amounts.Examples: Direct material, some
direct labor, and other unit-level costs like
factory supplies.
$
Total Variable Costs
$
Variable Cost Per Unit
150
100
2
50
0
25
50
Volume
75
25
50
Volume
75
4
Curvilinear Costs and the Relevant
Range
Cost
Relevant Range
Curvilinear
Function
Straight-Line
Approximation
Volume
5
Costs Within the Relevant Range
Within the relevant range:
Total fixed costs are constant.
Fixed cost per unit decreases as units
increase.
Total variable costs increase as units
increase.
Variable cost per unit is constant.
Use the constant measures to create a
linear relationship.
6
Mixed Costs (Fixed and Variable)
Cost
Variable
Fixed
00
Volume
7
The Cost Equation
(for mixed costs)
Y = a + bX
Y = total costs.
a = total fixed costs (intercept of line).
b = variable cost per unit (slope of line).
X = units produced.
8
Cost Behavior and Decision Making
For Pizza Pete’s:
Assume that direct materials were $2 per
pizza, direct labor was $1.50 per pizza, and
variable overhead was $1.00 per pizza, and
that $6,300 is fixed overhead.
What would be the cost of goods sold
(1) for 2,600 pizzas?
(2) for 1,000 pizzas?
9
Cost Behavior and Decision Making
2,600
1,000
Direct materials
$2.00
$5,200
$ 2,000
Direct labor
$1.50
3,900
1,500
Variable OH
$1.00
2,600
1,000
6,300
6,300
$18,000
$10,800
$6.92
$10.80
Fixed OH
Total COGS
COGS per Unit
Alternative – use formula: Y = a + bX
10
Mixed Costs
Fixed and Variable Components of Pizza
Pete’s:
Fixed: lease payment each month.
Variable: pizza components, wages,
electricity, etc., that vary with the number
of deliveries made (and miles driven).
11
Separating Mixed Costs into their
Fixed and Variable Components
•High-Low Method: an algebraic technique of
solving for the slope (variable cost per unit) and
intercept (fixed costs) of a line, by using the high
and low observations (coordinates) of the line.
•Regression Analysis: A statistical technique
used to estimate the slope (VCU) and intercept
(FC) components of a mixed cost is called least
squares regression. Regression analysis uses
statistical methods to fit a cost line (regression
line) through a set of points which minimizes the
sum of the squared distance from each data
point to the line (hence the name least squares
regression).
12
Estimating Slope and Intercept 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
13
Estimating Slope and Intercept Using
the High-Low Method
4. Substitute the total cost and activity of one
of the points for “y” and “x” in the equation y =
a + bx .
5. Substitute the variable cost found using
high-low for “b” .
6. Solve for fixed costs “a” .
7. Determine the formula to use in estimating
the mixed costs at various levels .
14
Estimating Slope and Intercept Using
the High-Low Method
Example:
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
15
Estimating Slope and Intercept Using
the High-Low Method
Steps
4,5,6
Cost at high pt
Fixed Costs
Y=
a + bx
Volume at high pt
$12,450 =
a + $3.50 (2,500)
$12,450 =
a + $8,750
$3,700 =
Y=
a
Variable Costs
$3,700 + $3.50x
7. Y = $3,700 + $3.50 (X)
(formula to use to estimate costs)
16
Least Squares Regression Analysis
Regression Line =
Total Overhead Cost
Total
Costs
Slope represents the
change in $ for a 1
unit change in volume
?$
Slope of Regression
Line = Variable Cost
per unit
Fixed
Cost
1 unit
Volume
17
Regression Statistics
Benefits of regression:
Uses all of the observations, not just high and
low.
Resulting measures offer insight into the quality
of the output.
R2 (r-squared) indicates the goodness of fit for
the model. Range between 0 and 1, a high R2
indicates that the relationship between the
independent variable and the dependent variable
explains most of the change in cost.
Problem: output may indicate a relationship,
even when there is no relationship.
18
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.
19