Cost Accounting (14th Edition)

NONLINEAR COST FUNCTIONS 361
Exhibit 10-12
Plots for Cumulative Average-Time Learning Model and Incremental Unit-Time Learning
Model for Rayburn Corporation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Cumulative Average Time per
Unit (Labor-Hours) (Y)
A B C D E F G H I J K L M N O P
120
100
80
60
40
20
Panel A: Cumulative Average Time per Unit
(80% Learning Curve; First Unit Takes 100 Labor-Hours)
Incremental Unit-Time
Learning Model
Cumulative Average-Time
Learning Model
0
0 16 32 48 64 80 96 112 128
Cumulative Number of Units
(X)
Cumulative Total Labor-Hours
(Y)
5000
4000
3000
2000
1000
Panel B: Cumulative Total Labor-Hours
(80% Learning Curve; First Unit Takes 100 Labor-Hours)
Incremental Unit-Time
Learning Model
Cumulative Average-Time
Learning Model
0
0 16 32 48 64 80 96 112 128
Cumulative Number of Units
(X)
The incremental unit-time learning model predicts a higher cumulative total time to produce
2 or more units than the cumulative average-time learning model, assuming the same
learning rate for both models. That is, in Exhibit 10-12, Panel B, the graph for the 80%
incremental unit-time learning model lies above the graph for the 80% cumulative averagetime
learning model. If we compare the results in Exhibit 10-10 (column D) with the results
in Exhibit 10-11 (column D), to produce 4 cumulative units, the 80% incremental unit-time
learning model predicts 314.21 labor-hours versus 256.00 labor-hours predicted by the 80%
cumulative average-time learning model. That’s because under the cumulative average-time
learning model average labor-hours needed to produce all 4 units is 64 hours; the labor-hour
amount needed to produce unit 4 is much less than 64 hours—it is 45.37 hours (see
Exhibit 10-10). Under the incremental unit-time learning model, the labor-hour amount
needed to produce unit 4 is 64 hours, and the labor-hours needed to produce the first 3 units
are more than 64 hours, so average time needed to produce all 4 units is more than 64 hours.
How do managers choose which model and what percent learning curve to use? It is
important to recognize that managers make their choices on a case-by-case basis. For example,
if the behavior of manufacturing labor-hour usage as production levels increase follows
a pattern like the one predicted by the 80% learning curve cumulative average-time learning
model, then the 80% learning curve cumulative average-time learning model should be used.
Engineers, plant managers, and workers are good sources of information on the amount and
type of learning actually occurring as production increases. Plotting this information and
estimating the model that best fits the data is helpful in selecting the appropriate model. 2
Incorporating Learning-Curve Effects into Prices
and Standards
How do companies use learning curves? Consider the data in Exhibit 10-10 for the
cumulative average-time learning model at Rayburn Corporation. Suppose variable costs
subject to learning effects consist of direct manufacturing labor, at $20 per hour, and
related overhead, at $30 per direct manufacturing labor-hour. Managers should predict
the costs shown in Exhibit 10-13.
These data show that the effects of the learning curve could have a major influence on
decisions. For example, managers at Rayburn Corporation might set an extremely low
selling price on its radar systems to generate high demand. As its production increases to
meet this growing demand, cost per unit drops. Rayburn “rides the product down the
2 For details, see C. Bailey, “Learning Curve Estimation of Production Costs and Labor-Hours Using a Free Excel Add-In,”
Management Accounting Quarterly, (Summer 2000: 25–31). Free software for estimating learning curves is available at
Dr. Bailey’s Web site, www.profbailey.com.