B313F Management and Cost Accounting
Lecture 6
Cost Estimation
By Charles Chiu, PhD, CFA
Introduction
Cost
estimation
Cost
behavior
Cost
prediction
Process of
determining
cost behavior,
often focusing
on historical
data.
Relationship
between
cost and
activity.
Using knowledge
of cost behavior
to forecast
level of cost at
a particular
activity. Focus
is on the future.
2
Cost Terminology



Variable Costs – costs that change in
total in relation to some chosen activity
or output
Fixed Costs – costs that do not
change in total in relation to some
chosen activity or output
Mixed Costs – costs that have both
fixed and variable components; also
called semivariable costs
3
Cost Behavior Patterns
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Fixed
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
4
Unit Variable Cost
Total Variable Cost
Total Fixed Cost
Unit Fixed Cost
5
Examples of variable costs
Merchandisers
Service Organizations
Cost of Goods Sold
Supplies and travel
Manufacturers
Merchandisers and
Manufacturers
Direct Material, Direct
Labor, and Variable
Manufacturing Overhead
Sales commissions and
shipping costs
Examples of fixed costs
Merchandisers, manufacturers, and
service organizations
Real estate taxes, Insurance, Sales salaries
Depreciation, Advertising
6
Types of Fixed Costs
Committed
Discretionary
Long-term, cannot be
reduced in the short
term.
May be altered in the
short-term by current
managerial decisions
Examples
Examples
Depreciation on
Buildings and
Equipment
Advertising and
Research and
Development
7
Trends in Cost Structure
A trend toward more fixed costs because of
• Increased automation.
• Stable workforce.
Implications
Managers are more “locked-in” with fewer decision
alternatives.
Planning becomes more crucial: fixed costs are difficult to
change with current operating decisions.
8
Cost Functions

A cost function is a mathematical
representation of how a cost changes
with changes in the level of an activity
relating to that cost (cost driver)
9
Identifying Cost Drivers
Cost Driver Examples
Activity
Cost Driver
Machining operations
Setup
Production scheduling
Inspection
Purchasing
Shop order handling
Valve assembly support
Machine hours
Setup hours
Manufacturing orders
Pieces inspected
Purchase orders
Shop orders
Customer requisitions
10
Criteria for Evaluating
Alternative Cost Drivers
1.
Economic Plausibility

2.
3.
Economic significance
Goodness of Fit
Significance of the Independent
Variable

Statistical significance
11
The Linear Cost Function
y = a + bX
The Dependent
Variable:
The cost that is
being predicted
The Intercept:
Fixed costs
The Independent
Variable:
The cost driver
The Slope of
the Line:
Variable cost
per unit
12
The total cost line can be expressed
as an equation: Y = a + bX
Where:
Y
Cost
Y = the total mixed cost
a = the total fixed cost (the
vertical intercept of the line)
b = the variable cost per unit of
activity (the slope of the line)
X = the level of activity
Variable Cost
X
Fixed Cost
Number of Units Produced
13
The Linearity Assumption and
the Relevant Range
1.
2.
Variations in the level of a single
activity (the cost driver) explain the
variations in the related total costs
Cost behavior is approximated by a
linear cost function within the
relevant range

Graphically, the total cost versus the level
of a single activity related to that cost is a
straight line within the relevant rage
14
Total Cost
A straight line
Economist’s
closely
Curvilinear Cost approximates a
Function
curvilinear
Relevant
Range
variable cost
line within the
relevant range.
Accountant’s Straight-Line
Approximation (constant
unit variable cost)
Activity
15
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.
Continue
16
Rent Cost in
Thousands of Dollars
90
60
30
00
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)
17
Criteria for Classifying Variable
and Fixed Components of a Cost
1.
2.
3.
Choice of Cost Object – different objects
may result in different classification of the
same cost
Time Horizon – the longer the period, the
more likely the cost will be variable
Relevant Range – behavior is predictable
only within this band of activity
18
Cause-and-Effect Relationship
for Cost Drivers


The most important issue in estimating a cost
function is determining whether a cause-and-effect
relationship exists between the level of an activity
and the costs related to that level of activity.
A cause-and-effect relationship might arise as a result
of:




A physical relationship between the level of activity and
costs
A contractual agreement
Knowledge of operations
Note: a high correlation (connection) between
activities and costs does not necessarily mean
causality
19
Question for Discussion 1 
Which of the following statements about cost
behavior are true?
a Fixed costs per unit vary with the level of
activity.
b Variable costs per unit are constant within
the relevant range.
c Total fixed costs are constant within the
relevant range.
d Total variable costs are constant within the
relevant range.
20
Cost Estimation Methods
1.
2.
3.
4.
Industrial Engineering Method
Conference Method
Account Analysis Method
Quantitative Analysis Methods
1.
2.
High-Low Method
Regression Analysis
21
Industrial Engineering
Method




Estimates cost functions by analyzing the
relationship between inputs and outputs in
physical terms
Includes time-and-motion studies
Very thorough and detailed, but also costly
and time consuming
Also called the Work-Measurement Method
22
Direct Labor
Direct Material
•Analyze the kind
of work performed.
•Estimate the time
required for each labor
skill for each unit.
•Material required
for each unit is
obtained from
engineering drawings
and specification sheets.
•Use local wage rates to
obtain labor cost
per unit.
•Material prices are
determined from
vendor bids.
23
Nonlinear Cost Functions
1.
2.
3.
4.
5.
Economies of Scale
Quantity Discounts
Step Cost Functions – resources increase
in “lot-sizes,” not individual units
Learning Curves – labor hours consumed
decrease as workers learn their jobs and
become better at them
Experience Curve – broader application of
learning curve that includes downstream
activities including marketing and
distribution
24
Learning Curves
There is often a systematic
relationship between experience
in performing a task and the time
required to do it.
The average time per task declines
by a constant percentage each time
the quantity of tasks done doubles.
25
Types of Learning Curves


Cumulative Average-Time Learning
Model – cumulative average time per unit
declines by a constant percentage each time
the cumulative quantity of units produced
doubles
Incremental Unit-Time Learning Model –
incremental time needed to produce the last
unit declines by a constant percentage each
time the cumulative quantity of units
produced doubles
26
Effect of Learning on Cost
Behavior
Berry Co. makes products requiring labor
that follows an 80 percent learning rate.
If the first unit of such a product requires
10 hours, what is the average time for 16
units of this product?
An 80 percent learning rate:
the average time required to make 2 units is 80 percent
of the time for 1 unit and the average time for 4 units is
80 percent of the time for 2 units, etc.
27
Cumulative Average-Time
Learning Model
Number
of Units
1
2
4
8
16
Average
Labor Time
per Unit
1 × 10 = 10
.80 × 10 = 8
.80 × 8 = 6.4
.80 × 6.4 = 5.12
.80 × 5.12 = 4.096
Total Time:
Average x Units
1 × 10 = 10
2 × 8 = 16
4 × 6.4 = 25.6
8 × 5.12 = 40.96
16 × 4.096 = 65.536
The graphic presentation of the learning
phenomenon is called the learning curve.
28
Learning Curve
Average Labor
Time per Unit
Learning effects
are large initially.
Learning effects
become smaller, eventually
reaching expected final time.
Cumulative Production Output
29
Average Labor
Time per Unit
This is used to help
determine investment required.
This is used to estimate
ongoing results.
Cumulative Production Output
30
Learning Curve Formula
Cumulative average labor time per unit
 DLH to produce unit 1
 Cumulative no. of units produced 
learning factor
ln learning rate % in decimal form 
Learning factor 
ln 2
31
Question for Discussion 2 


1.
2.
3.
Time to produce the first unit = 100
minutes
Learning factor = ln(0.80)/ln2 = -0.32193
What is the cumulative average time to
produce 5 units?
What is the total time to produce 5 units?
What is the time it took to produce the 5th
unit?
32
Incremental Unit-Time
Learning Model
Using the example of Berry Co. and using
the incremental unit-time learning model
Number
of Units
1
2
3
4
5
Individual Unit Time
for X-th Unit
1 × 10 = 10
0.80 × 10 = 8
7.02
0.80 × 8 = 6.40
5.96
Cum.
Cumulative
Ave. Time
Total Time
Per Unit
10
10
10 + 8 = 18
9
18 + 7.02 = 25.02
8.34
25.02 + 6.40 = 31.42
7.86
31.42 + 5.96 = 37.38
7.48
33
Conference Method



Estimates cost functions on the basis of
analysis and opinions about costs and
their drivers gathered from various
departments of a company
Pools expert knowledge
Reliance on opinions still makes this
method subjective
34
Account Analysis Method


Estimates cost functions by classifying
various cost accounts as variable, fixed,
or mixed with respect to the identified
level of activity
Is reasonably accurate, cost-effective,
and easy to use, but is subjective
35
Example
Account
Indirect Labor
Indirect Material
Depreciation
Property Taxes
Insurance
Utilities
Maintenance
Totals
Overhead
Total
Cost
$
450
700
1,000
200
300
400
600
$ 3,650
Costs for 1,000 Units
Variable
Fixed
Cost
Cost
$
450
700
1,000
200
300
350
50
500
100
$ 2,000
$ 1,650
Total Cost = $2 per unit + $1,650
36

Problems
what is the proper cost driver
 what is truly fixed
 changes in price
 is a history available

37
Quantitative Analysis


Uses a formal mathematical method to
fit cost functions to past data
observations
Advantage: results are objective
38
Steps in Estimating a Cost Function
Using Quantitative Analysis
1.
2.
3.
4.
5.
6.
Choose the dependent variable (the cost to
be predicted)
Identify the independent variable or cost
driver
Collect data on the dependent variable and
the cost driver
Plot the data
Estimate the cost function using the HighLow Method or Regression Analysis
Evaluate the cost driver of the estimated
cost function
39
The High-Low Method
WiseCo recorded the following production activity
and maintenance costs for two months:
High activity level
Low activity level
Change
Units
8,000
5,000
3,000
Cost
$ 9,800
7,400
$ 2,400
Using these two levels of activity, compute:
the variable cost per unit;
the fixed cost; and then
express the costs in equation form Y = a + bX. 40
The High-Low Method
High activity level
Low activity level
Change
Units
8,000
5,000
3,000
Cost
$ 9,800
7,400
$ 2,400
 Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit
 Fixed cost = Total cost – Total variable cost
Fixed cost = $9,800 – ($0.80 per unit × 8,000 units)
Fixed cost = $9,800 – $6,400 = $3,400
 Total cost = Fixed cost + Variable cost (Y = a + bX)
Y = $3,400 + $0.80X
41
Question for Discussion 3

Sales salaries and commissions are $10,000
when 80,000 units are sold, and $14,000 when
120,000 units are sold. Using the high-low
method, what is the variable portion of sales
salaries and commission?
a. $0.08 per unit
b. $0.10 per unit
c. $0.12 per unit
d. $0.125 per unit
42
Question for Discussion 4 
Sales salaries and commissions are $10,000
when 80,000 units are sold, and $14,000 when
120,000 units are sold. Using the high-low
method, what is the fixed portion of sales
salaries and commissions?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
43
Regression Analysis


Regression analysis is a statistical method
that measures the average amount of change
in the dependent variable associated with a
unit change in one or more independent
variables
Is more accurate than the High-Low
method because the regression equation
estimates costs using information from all
observations; the High-Low method uses only
two observations
44
Types of Regression


Simple – estimates the relationship between
the dependent variable and one independent
variable
Multiple – estimates the relationship
between the dependent variable and two or
more independent variables
45
Terminology


Goodness of Fit – indicates the
strength of the relationship between the
cost driver and costs
Residual Term – measures the
distance between actual cost and
estimated cost for each observation
46
The simple cost model is actually a
regression model:
TC = F + VX
This model will only
be useful within a
relevant range of
activity.
Caution: Before doing
the analysis, take time
to determine if a
logical relationship
between the variables
47
exists.
Simple Regression Method


Software can be used to
fit a regression line
through the data points.
The cost analysis
objective is the same:
Y = a + bX
Least-squares regression also provides a statistic,
called the R2, that is a measure of the goodness
of fit of the regression line to the data points.
48
R2 is the percentage of the variation in total cost
explained by the activity.
Y
Total Cost
20
* ** *
**
* *
* * R2 for this relationship is near
10
100% since the data points are
very close to the regression line.
0
0
1
2
3
Activity
4
X
49
Multiple Regression
Multiple regression includes two or
more independent variables:
TC = FC + V1X1 + V2X2
Terms in the equation have the same
meaning as in simple regression with
only one independent variable.
50
Data Problems




The time period for measuring the
dependent variable does not match the
period for measuring the cost driver
Fixed costs are allocated as if they are
variable
Some data may be missing or are not
uniformly reliable
Extreme values of observations occur from
errors in recording costs
51



There is no homogeneous relationship
between the cost driver and the individual
cost items in the dependent variable-cost
pool.
The relationship between the cost driver and
the cost is not stationary (not stable)
Inflation has affected costs, the driver, or
both
52
Data Adjustment



Corresponding numbers should be causally
related (i.e., if relating supplies to production
units, the figures should be usage of supplies
per some number of units of production NOT
supplies purchased in the same period).
Consider outliers carefully: the object is to
find the relationship that will hold in the
future.
Remember that cost relationships can change
over time (a “nonstationary” relationship). 53
The Ideal Database
1.
2.
The database should contain
numerous reliably measured
observations of the cost driver and the
costs
In relation to the cost driver, the
database should consider many values
spanning a wide range
54