Cost Accounting (14th Edition)

NONLINEAR COST FUNCTIONS 357
To choose the cost driver and use it to estimate the cost function in our materialshandling
example, the manager collects data on materials-handling costs and the quantities
of the two competing cost drivers over a reasonably long period. Why a long period?
Because in the short run, materials-handling costs may be fixed and, therefore, will not
vary with changes in the level of the cost driver. In the long run, however, there is a clear
cause-and-effect relationship between materials-handling costs and the cost driver.
Suppose number of loads moved is the cost driver of materials-handling costs. Increases in
the number of loads moved will require more materials-handling labor and equipment;
decreases will result in equipment being sold and labor being reassigned to other tasks.
ABC systems have a great number and variety of cost drivers and cost pools. That
means ABC systems require many cost relationships to be estimated. In estimating the
cost function for each cost pool, the manager must pay careful attention to the cost hierarchy.
For example, if a cost is a batch-level cost such as setup cost, the manager must
only consider batch-level cost drivers like number of setup-hours. In some cases, the costs
in a cost pool may have more than one cost driver from different levels of the cost hierarchy.
In the Elegant Rugs example, the cost drivers for indirect manufacturing labor costs
could be machine-hours and number of production batches of carpet manufactured.
Furthermore, it may be difficult to subdivide the indirect manufacturing labor costs into
two cost pools and to measure the costs associated with each cost driver. In these cases,
companies use multiple regression to estimate costs based on more than one independent
variable. The appendix to this chapter discusses multiple regression in more detail.
As the Concepts in Action feature (p. 356) illustrates, managers implementing ABC
systems use a variety of methods—industrial engineering, conference, and regression
analysis—to estimate slope coefficients. In making these choices, managers trade off level
of detail, accuracy, feasibility, and costs of estimating cost functions.
Decision
Point
How should a
company evaluate
and choose cost
drivers?
Nonlinear Cost Functions
In practice, cost functions are not always linear. A nonlinear cost function is a cost function
for which the graph of total costs (based on the level of a single activity) is not a straight
line within the relevant range. To see what a nonlinear cost function looks like, return to
Exhibit 10-2 (p. 344). The relevant range is currently set at 20,000 to 65,000 snowboards.
But if we extend the relevant range to encompass the region from 0 to 80,000 snowboards
produced, it is evident that the cost function over this expanded range is graphically represented
by a line that is not straight.
Consider another example. Economies of scale in advertising may enable an advertising
agency to produce double the number of advertisements for less than double the
costs. Even direct material costs are not always linear variable costs because of quantity
discounts on direct material purchases. As shown in Exhibit 10-9 (p. 358), Panel A, total
direct material costs rise as the units of direct materials purchased increase. But, because
of quantity discounts, these costs rise more slowly (as indicated by the slope coefficient)
as the units of direct materials purchased increase. This cost function has b = $25 per
unit for 1–1,000 units purchased, b = $15 per unit for 1,001 –2,000 units purchased, and
b = $10 per unit for 2,001–3,000 units purchased. The direct material cost per unit falls
at each price break—that is, the cost per unit decreases with larger purchase orders. If
managers are interested in understanding cost behavior over the relevant range from 1 to
3,000 units, the cost function is nonlinear—not a straight line. If, however, managers are
only interested in understanding cost behavior over a more narrow relevant range (for
example, from 1 to 1,000 units), the cost function is linear.
Step cost functions are also examples of nonlinear cost functions. A step cost function
is a cost function in which the cost remains the same over various ranges of the level of
activity, but the cost increases by discrete amounts—that is, increases in steps—as the
level of activity increases from one range to the next. Panel B in Exhibit 10-9 shows a
step variable-cost function, a step cost function in which cost remains the same over
narrow ranges of the level of activity in each relevant range. Panel B presents the relationship
between units of production and setup costs. The pattern is a step cost function
because, as we described in Chapter 5 on activity-based costing, setup costs are
Learning
Objective 6
Explain nonlinear cost
functions
. . . graph of cost
function is not a straight
line, for example,
because of quantity
discounts or costs
changing in steps
in particular those
arising from learning
curve effects
. . . either cumulative
average-time learning,
where cumulative
average time per unit
declines by a constant
percentage, as units
produced double
. . . or incremental unittime
learning, in which
incremental time to
produce last unit
declines by constant
percentage, as units
produced double