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In pricing and yield management, airlines continually seek to estimate the variable costs of additional passengers. In doing so, United Air Lines (UAL) analysts specified the regression model by regressing the change in total costs each period against the changes in revenue passenger miles and systemwide takeoffs. The analysts concluded that about 70 percent of UAL’s costs varied with passenger traffic and takeoffs; that is, about 70 percent of UAL’s costs were variable.

This result surprised other analysts, who thought that UAL’s costs must be mostly fixed. These skeptics observed that UAL averages about 35 percent empty seats on its flights. They thought that when UAL carried a few extra passengers, these passengers would sit in

the otherwise empty seats. Then, the only incremental costs would be about 25 percent of revenues for extra credit card fees, commissions, fuel, food, check-in agents, and baggage handling. The skeptics assumed UAL would not buy new airplanes and other major assets to handle the incremental passenger traffic.

The analysts at UAL who developed the regression estimates showed that the airline responded to an increase in demand for seats by expanding its total airline capacity, not only by putting the extra passengers in otherwise empty seats.

Source: Based on the authors’ research.

Global Management

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C. W. Chow, F. J. Deng, and J. L. Ho, ‘‘The Openness of Knowledge Sharing in Organizations: A Comparative Study of the United States and the People’s Republic of China,’’ Journal of Management Accounting Research 12, 65–95.

these methods is best? In general, the more sophisticated methods will yield more accurate cost estimates than the simpler methods. However, even a sophisticated method yields only an imperfect estimate of an unknown cost behavior pattern.

Analysts often simplify all cost estimation methods. The most common simplifications are the following.

1. Analysts often assume that cost behavior depends on only one cost driver. (Multiple regression is an exception.) In reality, however, costs are affected by a host of factors, including the weather, the mood of the employees, and the quality of the raw materials used. 2. Analysts often assume that cost behavior patterns are linear within the relevant range. We

know that costs actually follow curvilinear, step, semivariable, and other patterns.

3. Analysts often assume that cost decreases are not ‘‘sticky.’’ Exhibit 5.13 shows sticky cost behavior—when costs do not decrease with activity decreases as much as they increase with activity increases. For example, managers may be reluctant to fire workers when activity decreases, so labor costs do not decrease as much as activity decreases.5

EXHIBIT 5.12 Strengths and Weaknesses of Cost Estimation Methods

Method Strengths Weaknesses

Engineering  Based on studies of what future costs should be rather than what past costs have been.

 Not particularly useful when the physical relation between inputs and outputs is indirect.  Can be costly to use.

Account Analysis  Provides a detailed expert analysis of the cost behavior in each account.

 Subjective.

Regression Method  Uses all the observations of cost data.  The line is statistically fit to the observations.  Provides a measure of the goodness of fit of the

line to the observations.

 Relatively easy to use with computers and sophisticated calculators.

 The regression model requires that several rela- tively strict assumptions be satisfied for the results to be valid.

EXHIBIT 5.13 Sticky Costs

Activity Volume Total Cost Cost behavior as

activity decreases Cost behavi or as activity in creases 5

M. C. Anderson, R. D. Banker, and S. Janakiraman, ‘‘Are Selling, General and Administrative Costs ‘Sticky’?,’’ Journal of Accounting Research, vol. 41, no. 1, pp. 47–63 shows that SG&A costs increase more when sales increase than they decrease when sales decrease by the same amount. The authors conclude that SG&A costs are ‘‘sticky.’’

You must consider on a case-by-case basis whether these assumptions are reasonable. You also must decide when it is important to use a more sophisticated, and more costly, estimation method and when it is acceptable to use a simpler approach. Like the rest of managerial accounting, you must evaluate the costs and benefits of various cost estimation techniques.

S ummar y

The following items correspond to the learning objectives presented at the beginning of the chapter

1. Distinguish between variable costs and fixed costs and between short run and long run, and define the relevant range.Total variable costs change as the level of activity changes. Total fixed costs do not change with changes in activity levels. The short run is a time period long enough to allow management to change the level of production or other activity within the constraints of current total production capacity. Management can change total production capacity only in the long run. The relevant range is the range of activity over which the firm expects a set of cost behaviors to be consistent.

2. Identify capacity costs, committed costs, and discretionary costs. Capacity costs are certain fixed costs that provide a firm with the capacity to produce or sell or both. Committed costs are costs that will continue regardless of production level. Discretionary costs need not be incurred in the short run to conduct business.

3. Describe the nature of the various cost behavior patterns. Curvilinear variable cost functions indicate that the costs vary with the volume of activity, but not in constant proportion. The learning curve function shows how the amount of time required to perform a task goes down per unit as the number of units increases. Semivariable costs have both fixed

Problem 5.4 for Self-Study

Plotting Data and Regression Analysis Output. Geoffrey Corporation, a manufacturer of stuffed animals, is interested in estimating its fixed and variable costs in the shipping department. Management has chosen the number of cartons packed as the cost driver and collected the following information for a year:

Total Overhead per Month Total Cartons Packaged per Month

$20,500 500 22,300 650 22,300 625 23,000 700 21,000 550 21,400 570 24,500 725 21,000 525 21,500 600 23,200 675 21,400 560 22,500 640

A regression analysis shows the following:

TC¼ $12,625 þ ð15:45
Number of cartonsÞ: a. Plot the data on a graph.

b. Draw the regression line.

c. What is the range of observations?

The solution to this self-study problem is at the end of the chapter on page 165.

and variable components. Semifixed costs increase in steps. A change in fixed costs usually involves a change in long-term assets, whereas a change in semifixed costs often does not. 4. Describe how managers use cost behavior patterns.Managers use cost behavior patterns to

estimate how activities affect costs. This is particularly useful in forecasting costs.

5. Explain how to use historical data to estimate costs.In analyzing cost data, (1) review alternative cost drivers, (2) plot the data, and (3) examine the data and method of accumulation. 6. Describe how analysts estimate cost behavior using regression, account analysis, and engineering methods.Regression analysis is a statistical method that estimates the relation between cost drivers and costs. Using the account analysis method, analysts review each cost account and classify it according to cost driver. The engineering method of cost estimation studies the physical relation between the quantities of inputs and outputs. The accountant assigns costs to each of the inputs to estimate the cost of the outputs.

7. Explain the costs, benefits, and weaknesses of the various cost estimation methods.A simplifying assumption is that cost behavior patterns are linear within the relevant range. The cost analyst must consider on a case-by-case basis whether assumptions made are reasonable. The analyst must also decide when it is important to use a more sophisticated, and more costly, method and when it is acceptable to use a simpler approach.

8. Identify the derivation of learning curves (Appendix 5.1).The learning curve derivation in the appendix is known as the cumulative-average-time learning model.

Ke y

E q u a t i o n

5.1

b

log Y ¼ log a þ bðlog XÞ

9. Interpret the results of regression analyses (Appendix 5.2). In regression analysis the standard errors of the coefficients measure their variation and give an idea of the confidence we can have in the fixed and variable cost coefficients. The ratio between an estimated regression coefficient and its standard error is known as the t-statistic. If the absolute value is 2 or more, we can be relatively confident that the actual coefficient differs from zero. The R2 attempts to measure how well the line fits the data; a value of 1.0 denotes a perfect fit. Some statistical problems that may affect interpretation of regression output include multicollinearity, autocorrelation, and heteroscedasticity.

Key Terms and Concepts

Account analysis method Capacity costs

Committed costs Cost behavior Cost driver Cost driver rate Cost estimation

Curvilinear variable cost Dependent variable

Discretionary costs (programmed costs, managed costs)

Engineering method of cost estimation Fixed costs

Independent variable

Learning curve (experience curve) Long run

Marginal cost R2*

Regression analysis Relevant range

Semifixed costs (step costs) Semivariable costs (mixed costs) Short run

Standard errors of the coefficients* t-statistic*

Variable costs (engineered costs)

S olutions to S elf-Study Problems