CHAPTER 10
DETERMINING HOW COSTS BEHAVE
10-1 The two assumptions are
1. Variations in the level of a single activity (the cost driver) explain the variations in the
related total costs.
2. Cost behavior is approximated by a linear cost function within the relevant range. A
linear cost function is a cost function where, within the relevant range, the graph of total
costs versus the level of a single activity forms a straight line.
10-2 Three alternative linear cost functions are
1. Variable cost function––a cost function in which total costs change in proportion to the
changes in the level of activity in the relevant range.
2. Fixed cost function––a cost function in which total costs do not change with changes in
the level of activity in the relevant range.
3. Mixed cost function––a cost function that has both variable and fixed elements. Total
costs change but not in proportion to the changes in the level of activity in the relevant
range.
10-3 A linear cost function is a cost function where, within the relevant range, the graph of
total costs versus the level of a single activity related to that cost is a straight line. An example of
a linear cost function is a cost function for use of a videoconferencing line where the terms are a
fixed charge of $10,000 per year plus a $2 per minute charge for line use. A nonlinear cost
function is a cost function where, within the relevant range, the graph of total costs versus the
level of a single activity related to that cost is not a straight line. Examples include economies of
scale in advertising where an agency can double the number of advertisements for less than twice
the costs, step-cost functions, and learning-curve-based costs.
10-4 No. High correlation merely indicates that the two variables move together in the data
examined. It is essential also to consider economic plausibility before making inferences about
cause and effect. Without any economic plausibility for a relationship, it is less likely that a high
level of correlation observed in one set of data will be similarly found in other sets of data.
10-5 Four approaches to estimating a cost function are
1. Industrial engineering method.
2. Conference method.
3. Account analysis method.
4. Quantitative analysis of current or past cost relationships.
10-6 The conference method estimates cost functions on the basis of analysis and opinions
about costs and their drivers gathered from various departments of a company (purchasing,
process engineering, manufacturing, employee relations, etc.). Advantages of the conference
method include
1. The speed with which cost estimates can be developed.
2. The pooling of knowledge from experts across functional areas.
3. The improved credibility of the cost function to all personnel.
10-1
, 10-7 The account analysis method estimates cost functions by classifying cost accounts in the
subsidiary ledger as variable, fixed, or mixed with respect to the identified level of activity.
Typically, managers use qualitative, rather than quantitative, analysis when making these cost-
classification decisions.
10-8 The six steps are
1. Choose the dependent variable (the variable to be predicted, which is some type of cost).
2. Identify the independent variable or cost driver.
3. Collect data on the dependent variable and the cost driver.
4. Plot the data.
5. Estimate the cost function.
6. Evaluate the cost driver of the estimated cost function.
Step 3 typically is the most difficult for a cost analyst.
10-9 Causality in a cost function runs from the cost driver to the dependent variable. Thus,
choosing the highest observation and the lowest observation of the cost driver is appropriate in
the high-low method.
10-10 Three criteria important when choosing among alternative cost functions are
1. Economic plausibility.
2. Goodness of fit.
3. Slope of the regression line.
10-11 A learning curve is a function that measures how labor-hours per unit decline as units of
production increase because workers are learning and becoming better at their jobs. Two models
used to capture different forms of learning are
1. Cumulative average-time learning model. The cumulative average time per unit declines
by a constant percentage each time the cumulative quantity of units produced doubles.
2. Incremental unit-time learning model. The incremental time needed to produce the last
unit declines by a constant percentage each time the cumulative quantity of units
produced doubles.
10-12 Frequently encountered problems when collecting cost data on variables included in a
cost function are
1. The time period used to measure the dependent variable is not properly matched with the
time period used to measure the cost driver(s).
2. Fixed costs are allocated as if they are variable.
3. Data are either not available for all observations or are not uniformly reliable.
4. Extreme values of observations occur.
5. A homogeneous relationship between the individual cost items in the dependent variable
cost pool and the cost driver(s) does not exist.
6. The relationship between the cost and the cost driver is not stationary.
7. Inflation has occurred in a dependent variable, a cost driver, or both.
10-2
DETERMINING HOW COSTS BEHAVE
10-1 The two assumptions are
1. Variations in the level of a single activity (the cost driver) explain the variations in the
related total costs.
2. Cost behavior is approximated by a linear cost function within the relevant range. A
linear cost function is a cost function where, within the relevant range, the graph of total
costs versus the level of a single activity forms a straight line.
10-2 Three alternative linear cost functions are
1. Variable cost function––a cost function in which total costs change in proportion to the
changes in the level of activity in the relevant range.
2. Fixed cost function––a cost function in which total costs do not change with changes in
the level of activity in the relevant range.
3. Mixed cost function––a cost function that has both variable and fixed elements. Total
costs change but not in proportion to the changes in the level of activity in the relevant
range.
10-3 A linear cost function is a cost function where, within the relevant range, the graph of
total costs versus the level of a single activity related to that cost is a straight line. An example of
a linear cost function is a cost function for use of a videoconferencing line where the terms are a
fixed charge of $10,000 per year plus a $2 per minute charge for line use. A nonlinear cost
function is a cost function where, within the relevant range, the graph of total costs versus the
level of a single activity related to that cost is not a straight line. Examples include economies of
scale in advertising where an agency can double the number of advertisements for less than twice
the costs, step-cost functions, and learning-curve-based costs.
10-4 No. High correlation merely indicates that the two variables move together in the data
examined. It is essential also to consider economic plausibility before making inferences about
cause and effect. Without any economic plausibility for a relationship, it is less likely that a high
level of correlation observed in one set of data will be similarly found in other sets of data.
10-5 Four approaches to estimating a cost function are
1. Industrial engineering method.
2. Conference method.
3. Account analysis method.
4. Quantitative analysis of current or past cost relationships.
10-6 The conference method estimates cost functions on the basis of analysis and opinions
about costs and their drivers gathered from various departments of a company (purchasing,
process engineering, manufacturing, employee relations, etc.). Advantages of the conference
method include
1. The speed with which cost estimates can be developed.
2. The pooling of knowledge from experts across functional areas.
3. The improved credibility of the cost function to all personnel.
10-1
, 10-7 The account analysis method estimates cost functions by classifying cost accounts in the
subsidiary ledger as variable, fixed, or mixed with respect to the identified level of activity.
Typically, managers use qualitative, rather than quantitative, analysis when making these cost-
classification decisions.
10-8 The six steps are
1. Choose the dependent variable (the variable to be predicted, which is some type of cost).
2. Identify the independent variable or cost driver.
3. Collect data on the dependent variable and the cost driver.
4. Plot the data.
5. Estimate the cost function.
6. Evaluate the cost driver of the estimated cost function.
Step 3 typically is the most difficult for a cost analyst.
10-9 Causality in a cost function runs from the cost driver to the dependent variable. Thus,
choosing the highest observation and the lowest observation of the cost driver is appropriate in
the high-low method.
10-10 Three criteria important when choosing among alternative cost functions are
1. Economic plausibility.
2. Goodness of fit.
3. Slope of the regression line.
10-11 A learning curve is a function that measures how labor-hours per unit decline as units of
production increase because workers are learning and becoming better at their jobs. Two models
used to capture different forms of learning are
1. Cumulative average-time learning model. The cumulative average time per unit declines
by a constant percentage each time the cumulative quantity of units produced doubles.
2. Incremental unit-time learning model. The incremental time needed to produce the last
unit declines by a constant percentage each time the cumulative quantity of units
produced doubles.
10-12 Frequently encountered problems when collecting cost data on variables included in a
cost function are
1. The time period used to measure the dependent variable is not properly matched with the
time period used to measure the cost driver(s).
2. Fixed costs are allocated as if they are variable.
3. Data are either not available for all observations or are not uniformly reliable.
4. Extreme values of observations occur.
5. A homogeneous relationship between the individual cost items in the dependent variable
cost pool and the cost driver(s) does not exist.
6. The relationship between the cost and the cost driver is not stationary.
7. Inflation has occurred in a dependent variable, a cost driver, or both.
10-2
