# CA101 Cost Accounting Estimating a Cost Function National Chengchi University

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National Chengchi University

CA101 Cost Accounting Estimating a Cost Function National Chengchi University

10-1 What two assumptions are frequently made when estimating a cost function?

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 Describe three alternative linear cost functions.

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 What is the difference between a linear and a nonlinear cost function? Give an example

of each type of cost function.

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 “High correlation between two variables means that one is the cause and the other is the

effect.” Do you agree? Explain.

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 Name four approaches to estimating a cost function.

Four approaches to estimating a cost function are

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1. Industrial engineering method.

2. Conference method.

3. Account analysis method.

4. Quantitative analysis of current or past cost relationships.

10-6 Describe the conference method for estimating a cost function. What are two advantages

of this method?

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.

10-7 Describe the account analysis method for estimating a cost function.

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 costclassification decisions.

10-8 List the six steps in estimating a cost function on the basis of an analysis of a past cost

relationship. Which step is typically the most difficult for the cost analyst?

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 When using the high-low method, should you base the high and low observations on the

dependent variable or on the cost driver?

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 highlow method.

10-10 Describe three criteria for evaluating cost functions and choosing cost drivers.

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 Define learning curve. Outline two models that can be used when incorporating learning

into the estimation of cost functions.

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 Discuss four frequently encountered problems when collecting cost data on variables

included in a cost function.

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.

10-13 What are the four key assumptions examined in specification analysis in the case of

simple regression?

Four key assumptions examined in specification analysis are

1. Linearity of relationship between the dependent variable and the independent variable

within the relevant range.

2. Constant variance of residuals for all values of the independent variable.

3. Independence of residuals.

4. Normal distribution of residuals.

10-14 “All the independent variables in a cost function estimated with regression analysis are

cost drivers.” Do you agree? Explain.

No. A cost driver is any factor whose change causes a change in the total cost of a related cost

object. A cause-and-effect relationship underlies selection of a cost driver. Some users of

regression analysis include numerous independent variables in a regression model in an attempt

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