Cost Accounting (14th Edition)

STEPS IN ESTIMATING A COST FUNCTION USING QUANTITATIVE ANALYSIS 349
As an example, consider several types of fringe benefits paid to employees and the
cost drivers of the benefits:
Fringe Benefit
Health benefits
Cafeteria meals
Pension benefits
Life insurance
Cost Driver
Number of employees
Number of employees
Salaries of employees
Salaries of employees
The costs of health benefits and cafeteria meals can be combined into one homogenous
cost pool because they have the same cost driver—the number of employees. Pension benefits
and life insurance costs have a different cost driver—the salaries of employees—and,
therefore, should not be combined with health benefits and cafeteria meals. Instead, pension
benefits and life insurance costs should be combined into a separate homogenous
cost pool. The cost pool comprising pension benefits and life insurance costs can be estimated
using salaries of employees receiving these benefits as the cost driver.
Step 3: Collect data on the dependent variable and the cost driver. This is usually the
most difficult step in cost analysis. Cost analysts obtain data from company documents,
from interviews with managers, and through special studies. These data may be timeseries
data or cross-sectional data.
Time-series data pertain to the same entity (organization, plant, activity, and so on)
over successive past periods. Weekly observations of indirect manufacturing labor costs
and number of machine-hours at Elegant Rugs are examples of time-series data. The ideal
time-series database would contain numerous observations for a company whose operations
have not been affected by economic or technological change. A stable economy and
technology ensure that data collected during the estimation period represent the same
underlying relationship between the cost driver and the dependent variable. Moreover, the
periods used to measure the dependent variable and the cost driver should be consistent
throughout the observations.
Cross-sectional data pertain to different entities during the same period. For example,
studies of loans processed and the related personnel costs at 50 individual, yet similar,
branches of a bank during March 2012 would produce cross-sectional data for that
month. The cross-sectional data should be drawn from entities that, within each entity,
have a similar relationship between the cost driver and costs. Later in this chapter, we
describe the problems that arise in data collection.
Step 4: Plot the data. The general relationship between the cost driver and costs can be
readily observed in a graphical representation of the data, which is commonly called a
plot of the data. The plot provides insight into the relevant range of the cost function, and
reveals whether the relationship between the driver and costs is approximately linear.
Moreover, the plot highlights extreme observations (observations outside the general pattern)
that analysts should check. Was there an error in recording the data or an unusual
event, such as a work stoppage, that makes these observations unrepresentative of the
normal relationship between the cost driver and the costs?
Exhibit 10-4 is a plot of the weekly data from columns B and C of the Excel spreadsheet
in Exhibit 10-3. This graph provides strong visual evidence of a positive linear relationship
between number of machine-hours and indirect manufacturing labor costs (that
is, when machine-hours go up, so do indirect manufacturing labor costs). There do not
appear to be any extreme observations in Exhibit 10-4. The relevant range is from 46 to
96 machine-hours per week (weeks 8 and 6, respectively).
Step 5: Estimate the cost function. We will show two ways to estimate the cost function
for our Elegant Rugs data. One uses the high-low method, and the other uses regression
analysis, the two most frequently described forms of quantitative analysis. The widespread
availability of computer packages such as Excel makes regression analysis much
more easy to use. Still, we describe the high-low method to provide some basic intuition
for the idea of drawing a line to “fit” a number of data points. We present these methods
after Step 6.