Cost Chapter 3

discretionary fixed expenses

- costs incurred for the acquisition of short-term capacity or services, usually as the result of yearly planning. - EX: use of contingent workers

Mixed costs

- costs that have both a fixed and a variable component.

Non-unit-level drivers

- explain the changes in cost as factors other than units change. - Examples of non-unit-based output measures include the number of setups, work orders, engineering change orders, inspection hours, and material moves.

If the nonlinear view more accurately portrays reality, what should we do?

- ne possibility is to determine the actual cost function—but every activity could have a different cost function, and this approach could be very time consuming and expensive (if it can even be done). It is much simpler to assume a linear relationship.

When a firm acquires the resources needed to perform an activity, it obtains activity capacity.

- the ability to perform activities or the number of times an activity can be performed. - Usually, the amount of activity capacity needed corresponds to the level where the activity is performed efficiently.

Similarly, if resource usage can be reduced, bringing about unused capacity, managers must carefully consider what to do with the excess capacity.

Eliminating the excess capacity may decrease resource spending and thus improve overall profits. Alternatively, using the excess capacity to increase output could increase revenues without a corresponding increase in resource spending.

The high-low method has two advantages

First, it is objective. That is, any two people using the high-low method on a particular data set will arrive at the same answer. Second, it is simple to calculate. The high-low method allows a manager to get a quick fix on a cost relationship using only two data points.

The high-low method is usually not as good as the other methods for two reasons.

First, the high or low points can be what are known as outliers, representing atypical cost-activity relationships. If so, the cost formula computed using these two points will not represent what usually takes place - Second, even if these points are not outliers, other pairs of points may clearly be more representative.

The fifth column, labeled "P-value," is the level of significance achieved.

Generally, a P-value of 0.05 or less is needed for significance (to feel comfortable that the independent variable is indeed strongly associated with the dependent variable). The fixed cost parameter, the intercept, is significant at the 0.172 level.

one purpose of a scattergraph is to assess the validity of the assumed linear relationship. Additionally, inspecting the scattergraph may reveal several points that do not seem to fit the general pattern of behavior. Upon investigation, it may be discovered that these points (the outliers) were due to some irregular occurrences. This knowledge can provide justification for their elimination and perhaps lead to a better estimate of the underlying cost function.

Keep in mind that the scattergraph and the other statistical aids are tools that help managers improve their judgment. Using the tools does not prevent the manager from using his or her own judgment to alter any of the estimates produced by formal methods.

Can fixed costs change?

Of course they can, but this does not make them variable. They are fixed at a new higher (or lower) level.

The Anderson Company regression results in Exhibit 3.12 show a standard error of the regression of $771 (rounded). What does this mean?

On average, the actual cost of moving materials and the predicted cost differ by $771. The average monthly cost of moving materials is $4,510. Thus, a standard error of $771 seems large. A smaller standard error would give Anderson Company more confidence in the predicted value of moving costs. This may encourage the company to search for more and/or better independent variables.

To use the account analysis method, the accountant uses judgment and experience to separate the accounts into two categories—fixed and variable

Once the fixed categories are known, the average monthly cost can be computed and this is the fixed amount. The variable categories need to be further separated into categories according to the driver the accountant wishes to associate with the account.

So far, we have assumed that the cost function is continuous. In reality, some cost functions may be discontinuous

One such discontinuous function, a step function

The activity-based resource usage model just described can improve both managerial control and decision making.

Operational control information systems encourage managers to pay more attention to controlling resource usage and spending. A well-designed operational system would allow managers to assess the changes in resource demands that will occur from new product mix decisions. Adding new, customized products may increase the demand for various overhead activities; if sufficient unused activity capacity does not exist, then resource spending must increase.

Goodness of fit can be further analyzed using the standard error of the regression and the standard errors of the estimates.

Put simply, the standard error of the regression tells how tightly the data points cluster around the regression line. A smaller standard error indicates that the regression line more closely approximates the data. A larger standard error indicates the opposite and may be cause to search for more and better independent variables.

The industrial engineering method and the account analysis method are judgment-based methods of determining cost behavior

Quantitative methods also exist that rely on past data to generate a linear model that describes the variable and fixed portions of a cost.

The high-low method preselects the two points that are used to compute the parameters F and V.

The high point is defined as the point with the highest output or driver level. The low point is defined as the point with the lowest output or driver level.

A number of cost behavior patterns do not follow a linear pattern An important type of nonlinear cost curve is the learning curve.

The learning curve shows how the labor hours worked per unit decrease as the number of units produced increases. The basis of the learning curve is almost intuitive—as we perform an action over and over, we improve, and each additional performance takes less time than the preceding ones.

Managers can see that the ideas behind the learning curve can extend to the service industry as well as to manufacturing firms When used in this way, the learning curve is often called the experience curve.

relates cost to increased efficiency, such that the more often a task is performed, the lower will be the cost of doing it.

activity rate

the average unit cost, obtained by dividing the resource expenditure by the activity's practical capacity.

The learning curve model takes two common forms:

the cumulative average-time learning curve model and the incremental unit-time learning curve model. The difference between the two lies in the assumption made about the speed of learning.

goodness of fit

the degree of association between Y and X (cost and activity). It is measured by how much of the total variability in Y is explained by X. - This measure is important because the method of least squares identifies the best-fitting line, but it does not reveal how good the fit is.

deviation

the difference between the cost predicted by a cost formula and the actual cost. It measures the distance of a data point from the cost line.

This efficient level of activity performance is called practical capacity.

the efficient level of activity performance.

The three widely used quantitative methods of separating a mixed cost into its fixed and variable components are

the high-low method, the scatterplot method, and the method of least squares. - Each method requires us to make the simplifying assumption of a linear cost relationship

coefficient of determination (R2)

the percentage of total variability in a dependent variable (e.g., cost) that is explained by an independent variable (e.g., activity level). It assumes a value of between 0 and 1.

relevant range,

the range over which the assumed cost relationship is valid for the normal operations of a firm.

Activity drivers explain changes in activity costs by measuring changes in activity output (usage). The two general categories of activity drivers are

unit-level drivers and non-unit-level drivers. Recall that drivers are factors that cause changes in resource usage, activity usage, costs, and revenues

If all of the activity capacity acquired is not used, then there is unused capacity,

which is the difference between the acquired capacity and the actual amount of the activity used. The relationship between resource spending and resource usage can be used to define variable and fixed cost behavior.

Since the measure of closeness is the sum of the squared deviations of the points from the line, the smaller the measure, the better the line fits the points.

The line that fits the points better than any other line is called the best-fitting line. It is the line with the smallest (least) sum of squared deviations. The method of least squares identifies the best-fitting line. We rely on statistical theory to obtain the formulas that produce the best-fitting line.

The activity-based resource usage model also allows managers to better calculate the changes in resource supply and demand resulting from decisions such as make or buy, accept or reject special orders, and keep or drop product lines.

The model increases the power of a number of traditional management accounting decision-making models.

A significant advantage of the scatterplot method is that it allows a cost analyst to inspect the data visually

The scatterplot method suffers from the lack of any objective criterion for choosing the best-fitting line. The quality of the cost formula depends on the quality of the subjective judgment of the analyst. The high-low method removes the subjectivity in the choice of the line. Regardless of who uses the method, the same line will result.

At a 95 percent confidence level, the range is 854 ± (2.306 × 570) or -460.42 to 2,168.42. This range does include zero, and we cannot be reasonably confident that the coefficient on the intercept term, fixed cost, is significantly different from zero.

These t statistics are used to test the hypothesis that the parameters are different from zero. The fifth column presents the level of significance achieved. All parameters are significant at the 0.0001 level.

When resources are acquired in advance, there may be a difference between the resources supplied and the resources used (demanded).

This can only occur for costs that display fixed cost behavior (resources acquired in advance of usage). The traditional cost management system provides information only about the cost of the resources supplied. A contemporary cost management system, on the other hand, tells how much of the activity is used and the cost of its usage, based on the activity rate.

An advantage of engineering methods is that they can be applied to new processes and designs. Industrial engineers determine the amount of each direct material needed and the amount of labor time each process will take. Then accountants and purchasing specialists can apply the appropriate unit costs.

While this method is useful in determining the cost of manufactured items, where the process stays the same from unit to unit, it is less useful in services where different customers or circumstances may require varying amounts of time and types of service.

step-cost function

a cost function in which cost is defined for ranges of activity usage rather than point values. The function has the property of displaying constant cost over a range of activity usage and then changing to a different cost level as a new range of activity usage is encountered.

The industrial engineering method

a forward-looking method of determining through physical observation and analysis, just what activities, in what amounts, are needed to complete a process. - Time and motion studies may be used in conjunction with this method. Industrial engineers may literally stand behind production workers with a stop watch to determine precisely how many minutes it takes to produce a unit of product.

The account analysis method

a method used to estimate costs by classifying accounts in the general ledger as fixed, variable, or mixed. -In practice, accounts are usually put into either the fixed or variable category based on the predominant nature of the costs in the individual account. This method is often used in practice because it is simple and straightforward to apply.

hypothesis test of cost parameters

a statistical assessment of a cost formula's reliability that indicates whether the parameters are different from zero.

step-variable costs

a step-cost function in which cost remains constant over relatively narrow ranges of activity.

step-fixed costs

a step-cost function in which cost remains constant over wide ranges of activity usage. - In reality, many so-called fixed costs may be best described by a step-cost function. Many committed resources—particularly those that involve implicit contracting—follow a step-cost function.

dependent variable

a variable whose value depends on the value of another variable. For example, Y in the cost formula Y = F + VX depends on the value of X.

independent variable

a variable whose value does not depend on the value of another variable. For example, in the cost formula Y = F + VX, the variable X is an independent variable.

Flexible resources

acquired as used and needed, these are a strictly variable cost. The quantity supplied equals quantity demanded, so there is no excess capacity. - Since the cost of flexible resources equals the cost of resources used, the total cost of the resource increases as demand for the resource increases. - resource supply and usage are measured by an output measure, or driver.

Variable costs

are defined as costs that, in total, vary in direct proportion to changes in an activity driver. - Variable costs can also be represented by a linear equation. - Here, total variable costs depend on the level of activity driver. - Note that total variable cost increases in direct proportion to increases in the number of voice coils produced (the activity driver); the rate of increase is measured by the slope of the line.

Unit-level drivers

are factors that measure the demands placed on unit-level activities by products and, therefore, may explain changes in cost as units produced change. - Pounds of direct materials, kilowatt-hours used to run production machinery, and direct labor hours are examples of unit-based activity drivers. While none of these drivers is equal to the number of units produced, each does vary proportionately with the number of units produced.

Committed resources

are supplied in advance of usage. An explicit or implicit contract is used to obtain a given quantity of resource, regardless of whether that amount is fully used or not. Because the amount of committed resource supplied may exceed the firm's demand for it, unused capacity is possible.

The incremental unit-time learning curve model

decreases by a constant percentage each time the cumulative quantity of units produced doubles. The same general assumptions for the learning curve hold; however, the learning rate is assumed to apply to the last unit produced, not to the cumulative average of all units to date

The vertical distance measures the closeness of a single point to the line, but we really need a measure of closeness of all points to the line.

each single measure of closeness is first squared, and then these squared deviations are summed as the overall measure of closeness. Squaring the deviations avoids the cancellation problem caused by a mix of positive and negative numbers.

learning rate

expressed as a percent, it gives the percentage of time needed to make the next unit, based on the time it took to make the previous unit. - The learning rate is determined through experience and must be between 50 and 100 percent. A 50 percent learning rate would eventually result in no labor time per unit—an absurd result. A 100 percent learning rate implies no learning (since the amount of decrease is zero). An 80 percent learning curve is often used to illustrate this model, possibly because the original learning curve work with the aircraft industry found an 80 percent learning curve.

he high-low method

gives managers a quick way of estimating cost behavior. Only two data points are needed, the high and low activity points, so this method is especially easy for companies without a long history.

hree statistical assessments concerning the cost formula's reliability:

hypothesis test of cost parameters, goodness of fit, and confidence intervals.

Cost behavior

is the term used to describe whether a cost changes when the level of output changes. A cost that does not change as output changes is a fixed cost. A variable cost, on the other hand, increases in total with an increase in output and decreases in total with a decrease in output.

Since accounting records typically show only the total cost and the associated output of a mixed cost item

it is necessary to separate the total cost into its fixed and variable components. Only through a formal effort to separate costs can they be classified into the appropriate cost behavior categories.

Resources can be categorized as

(1) flexible and (2) committed

nonlinear behavior

- Economists usually assume that variable costs increase at a decreasing rate up to a certain volume, at which point they increase at an increasing rate. - Here, variable costs increase as the number of units increases, but not in direct proportion.

Scatterplot Method

- The first step in applying the scatterplot method is to plot the data points so that the relationship between materials handling costs and activity output can be seen - This plot is referred to as a scattergraph - The vertical axis is total activity cost (materials handling cost), and the horizontal axis is the driver or output measure (number of moves)

we use the Adjusted R Square because this value has been adjusted for the number of variables included in the equation

- The value for Adjusted R Square is 0.85 (rounded), which means that 85 percent of the variability in the materials handling cost is explained by the number of moves. - the closer is to 1.00, the better

Determining whether a cost is fixed or variable depends on the time horizon.

- According to economics, in the long run, all costs are variable; in the short run, at least one cost is fixed. But how long is the short run? Different costs have short runs of different lengths. Direct materials, for example, are relatively easy to adjust. - The length of the short-run period depends to some extent on management judgment and the purpose for which cost behavior is being estimated.

An alternative measure of goodness of fit is the coefficient of correlation (r)

- the square root of the coefficient of determination, which is used to express not only the degree of correlation between two variables but also the direction of the relationship. - the value of the coefficient of correlation can range between −1 and +1. If the coefficient of correlation is positive, then the two variables move together in the same direction; they are positively correlated. - A coefficient of correlation value close to zero indicates no correlation.

cumulative average-time learning curve model

-the model stating that the cumulative average time per unit decreases by a constant percentage, or learning rate, each time the cumulative quantity of units produced doubles.

In practice, companies use a variety of methods of estimating costs.

Among these methods are the industrial engineering method, the account analysis method, and a variety of quantitative and statistical methods.

Resources are economic elements that enable one to perform activities.

Common resources of a manufacturing plant include direct materials, direct labor, electricity, equipment, and so on. When a company spends money on resources, it is acquiring the ability or capacity to perform an activity.

committed fixed expenses.

costs incurred for the acquisition of long-term activity capacity, usually as the result of strategic planning.

A confidence interval provides a range of values for the actual cost with a prespecified degree of confidence.

onfidence intervals allow managers to predict a range of values instead of a single prediction. Of course, if the degree of association is perfect, then the confidence interval will consist of a single point and the actual cost will always coincide with the predicted cost. Thus, goodness of fit and confidence intervals are related, and they provide cost analysts some idea of how reliable the resulting cost equation is.