Concept of Cost Estimation
1. Identify . . .
3. This results
in reduced . . .
Relationship
between
activities
and costs
Costs
We estimate
costs to:
manage costs
make decisions
plan & set
standards.
2. Manage . . .
Activities
1
One Cost Driver and Fixed/Variable Cost
Behavior
TC = F + VX
Where:
TC = Total Costs
F
= Fixed Costs
V
= Var. Cost Driver Rate
X
= # of Cost Driver Units
This model ignores other cost behaviors
and other cost drivers.
2
One Cost Driver and Fixed/Variable Cost
Behavior
TC = $190 + (.16 x Miles Driven)
600
510
500
Cost
400
350
300
200
$.16
190
Slope = Cost
Driver Rate
= ΔY/ΔX
100
Intercept
= Fixed
3000
Cost
0
0
1000
2000
Miles driven per month
3
Cost Estimation Methods
Regression Analysis
A statistical method used to create an
equation relating independent (or X)
variables to dependent (or Y) variables.
Past data is used to estimate relationships
between costs and activities.
Independent variables
are the cost drivers that
are correlated with the
dependent variables.
Dependent variables are
caused by the
independent variables.
4
Cost Estimation Methods
Regression Analysis
The simple cost model is actually a
regression model:
TC = F + VX
Caution: Before doing
the analysis, take time
to determine if a
logical relationship
between the variables
exists.
Click
This model will only
be useful within a
relevant range of
activity.
?
Here
5
Cost Estimation Methods
Regression Analysis
A set of data can be regressed using several
techniques:
•Manual computations
•SPSS or SAS Statistical Software
•Excel or other spreadsheet
The result of the
regression process is a
regression model:
TC = F + VX
Each regression model
has an R-square (R2)
measure of how good the
model is.
Range of R2 = 0 to 1.0
6
Cost Estimation Methods
Multiple Regression Analysis
Multiple Regression is a
regression that has more than
one independent (X) variable.
For example,
demand
Want
an
for a product may be
example?
affected
by things
such as inflation,
interest rates, and
competitors’ prices.
Can be very useful in
situations where the
dependent variable is
impacted by several
different independent
variables.
7
Cost Estimation Methods
Account Analysis
A method that looks at
past costs to estimate
current cost-driver rates.
 Break costs into categories
corresponding to each cost
driver.
 Sum total costs for each cost
driver category.
 Divide total cost for a given
cost driver category by cost
driver volume.
8
More
expensive than
regression,
and requires
more detailed
breakdown of
costs.
Cost Estimation Methods
Engineering Method
Cost estimates based on
measurement and pricing of
the work involved in the
activities that go into a
product.
Not
based on
past
costs.
9
WHY DO WE NEED TO ESTIMATE COSTS?
 CONTROL PURPOSES – STANDARD COSTS
 COST ALLOCATION-IDENTIFY SUITABLE COST DRIVERS
 DECISION MAKING-PRICING OF FUTURE PRODUCTION
 BREAK-EVEN ANALYSIS (NEXT CHAPTER)
10
REGRESSION ANALYSIS:
TC = F + VX
TC = F + V1X1 + V2X2 + V3X3 + V4X4
(1)
where TC = total cost; F = fixed costs; V = variable cost per unit; X number of units
produced; V1 = variable cost (#1) per unit of cost driver (for example, machine
hours); X1 = number of units of costs driver consumed in the total production
(machine hours).
Regression Estimation of Equation (1)
TC = α0 + α1X1 + α2X2 + α3X3 + α4X4 + (estimation error)
(2)
where TC = dependent variable; α0 = intercept (measures fixed costs); α1, etc. = regression
coefficients (estimates of V1, etc.); X1, etc. = independent variables (as in equation
1)
Standard Regression Output:
Coefficients
Estimates
Standard Errors
α0
α1
α2
α3
α4
$5.9 mill.
$2.1/mach hr.
$1.3/labr hr.
$9.1/cubic ft.
$5.5/units produced
6.1
1.0
1.1
4.2
3.9
t-statistics*
Conclusion
0.97
2.1
1.18
2.17
1.41
Not significant
Significantly > 0
Not significant
Significantly > 0
Not significant
*
t-statistics = (Estimate / Standard error) = 5.9 / 6.1 = 0.97
Rule: If -2 < t < 2 then coefficient is not significant (not different from zero)
If t < -2 or t > 2 then coefficient is significant (different from zero)
R2 (R square) is a measure of "goodness of fit". It tells us how well the regression equation
describes the actual cost generating process. R2 lies between 0 and 1.
A 0 implies a "poor" fit; a 1 implies a "perfect fit"; a 0.5 implies a
"good fit." If there are two regressions equations to choose from, the
one with the higher R2 should be selected.
11
Case Study: United Packaging
Evaluating alternative regression functions, accrual accounting adjustments
Trevor Kennedy, the cost analyst at a can manufacturing plant of United Packaging, used
a regression model to examine the relationship between total engineering support costs
reported in the plant records and machine hours. After further discussion with the
operating manager, Kennedy discovers that the materials and parts numbers reported in
the monthly records are on an “as purchased” basis and not on an “as used” or accrual
accounting basis. By examining materials and parts usage records, Kennedy is able to
restate the materials and parts costs to an “as used” basis. (No restatement of the labor
costs was necessary.) The reported and restated costs follow:(1)
(2)
(3)
(4)
(5) = (2) + (3)
(6) = (2) (4)
(7)
Total
Materials Materials Engineering
Labor: and Parts: and Parts: Support:
Reported Reported Restated
Reported
Month
Costs
Costs
Costs
Costs
March
$347
$847
$182
$1,194
April
521
0
411
521
May
398
0
268
398
June
355
961
228
1,316
July
473
0
348
473
August
617
0
349
617
September 245
821
125
1,066
October
487
0
364
487
November 431
0
290
431
Total
Engineering
Support:
Restated
Costs
$529
932
666
583
321
966
370
351
721
Machine
Hours
30
63
49
38
57
73
19
53
42
The regression results, when total engineering support reported costs (Column 5) are used
as the dependent variable, are :
Regression 1:
Engineering Support Reported Costs =f(Machine Hours)
Variable
Coefficient
Constant
1,393.20
Independent variable 1:
Machine hours
-14.23
r² = 0.43 : Durbin-Watson statistic = 2.26
Standard Error
305.68
t-Value
4.56
6.15
-2.31
The regression results, when total engineering support restated costs (Column 6) are used
as the dependent variable, are:
12
Regression 2:
Engineering Support Restated Costs = f (Machine Hours)
Variable
Coefficient
Constant
176.38
Independent variable 1:
Machine hours
11.44
r² = 0.94 : Durbin-Watson statistic = 1.31
Standard Error
53.99
t-Value
3.27
1.08
10.59
UNITED PACKAGING: DISCUSSION
Required
1. Present a plot of the date for the cost function relating the reported costs for total
engineering support to machine hours. Present a plot of the date for the cost
function relating the restated costs for totak engineering support to machine hours.
Comment on the plots.
2. Contrast and evaluate the cost function estimated with regression using restated
date for materials and parts with the cost function estimated with regression using
the date reported in the plant records.
3. Kennedy expects 50 machine hours to be worked in December. What engineering
support costs should Kennedy budget for December ?
4. What problems might Kennedy encounter when restating the materials and parts
costs recorded to an “as used” or accrual accounting basis ?
Evaluating alternative regression functions, accrual accounting adjustments.
1. Solution Exhibit 10-C1 presents the two date plots. The plot of engineering
support reported costs and machine hours shows two separate groups of date,
each of which may be approximated by a separate cost function. The problem
arises because the plant records materials and parts costs on an “as purchased”
rather than an “as used” basis. The plot of engineering support restated costs and
machine hours shows a high positive correlation between the two variables (the
coefficient of determination is 0.94) ; a single linear cost function provides a good
fit to the data. Better estimates of the cost relation result because Kennedy adjusts
the materials and parts costs to an accrual accounting basis.
2. The cost function estimated with engineering support restated costs better
approximates the regression analysis assumptions. See Solution Exhibit 10-C2
13
for a comparison of the two regressions.
3. Using the cost function estimated with restated costs, Kennedy should budget
$748.38 as engineering support costs for December calculated as follows:
Engineering support costs = $176.38 + ($11.44 per hour x 50 hours) = $748.38
4. Problem Kennedy might encounter include:
(a) A perpetual inventory system may not be used in this case; the amounts
requisitioned likely will not permit an accurate matching of costs with the
independent variable on a month-by-month basis.
(b) Quality of the source records for usage by engineers may be relatively
low; e.g., engineers may requisition materials and parts in batches, but not
use them immediately.
(c) Records may not distinguish materials and parts for maintenance from
materials and parts used for repairs and breakdowns; separate cost
functions may be appropriate for the two categories of materials and
parts.
CRITERION
1. Economic Plausibility
2. Goodness of Fit
3. Significance of
Independent Variables
Solution Exhibit 10-C2
REGRESSION 1
Dependent Variable:
Engineering Support
Reported Costs
Negative
slope
relationship
is
economically implausible
over the long run
R2 = 0.43 Moderate
goodness of fit.
t-statistic on machine
hours
is
statistically
significant (t = -2.31),
albeit
economically
implausible.
14
REGRESSION 2
Dependent Variable:
Engineering Support
Restated Costs
Positive slope
relationship is
economically plausible.
R2 = 0.94. Excellent
Goodness of fit.
t-statistic on machine
hours is highly statistically
significant (t = 10.59).