Chapter 5 PowerPoint

Deriving learning curves

* Mathematically, the learning curve effect can be expressed by the equation: Y=aX^b, where * Y = average number of labor hrs required per unit for X units * a = number of labor hrs required for the first unit * X = cumulative number of units produced * b = index of learning, equal to the log of the learning rate divided by the log of 2

Standard errors of the coefficients

* the standard errors of the coefficients give an idea of the confidence we can have in the fixed and variable cost coefficients * the smaller the standard error relative to its coefficient, the more precise the estimate * Such computational precision does not necessarily indicate that the estimating procedure is theoretically correct, however.

Fixed (capacity) costs are divided between

1. Committed cost Capacity costs that will continue to exist even if operations are temporarily reduced 2. Discretionary (programmed or managed) costs Need not be incurred in the short run to operate the business

The procedure for analyzing historical cost data requires two steps:

1. Make an estimate of the past relation. 2. Update this estimate so that it is appropriate for the present or future period for which management wants the estimate. This step requires adjusting costs for inflation and for changes that have occurred in the relation between costs and activity. For example, if a firm expects the production process to be more capital-intensive in the future, the accountant should reduce variable costs and increase fixed costs.

Data problems Regardless of method used, results will only be as good as the quality of the data used. Problems include

1. Missing data 2. Outliers 3. Allocated and discretionary costs 4. Inflation 5. Mismatched time periods 6. Trad-offs in choosing time period

Whatever method is used to estimate costs, the results will only be as good as the data used. Collecting appropriate data is complicated by the following problems:

1. Missing data. Misplaced source documents or failure to record a transaction can result in missing data. 2. Outliers. Observations of extreme cost-activity relations may unduly affect cost estimates. For example, a hurricane affected operations in a Florida company in August, resulting in high overhead due to one-time costs that will not be incurred every month.

We should take the following steps in analyzing cost data:

1. Review alternative cost drivers (independent variables). A cost driver ideally measures the activity that causes costs. The cost drivers, if not the sole cause of costs, should directly influence costs. Operating room hours is an example of a cost driver in a hospital; machine hours is an example in a manufacturing firm; labor hours is an example in a service firm.

Common simplifications In general, more sophisticated methods provide more accurate cost estimates than simpler ones. Methods of simplification are

1. Using only one cost driver 2. Assuming cost behavior patterns are linear within the relevant range 3. Assume cost decreases are not "sticky"

2. Analysts often assume that cost behavior patterns are linear within the relevant range. We know that costs often follow curvilinear, step, semivariable, and other patterns.

3. Analysts often assume that costs are sticky. Sticky costs are those that do not decrease proportionately with decreases in activity. A considerable body of research has developed to show that many costs are sticky.

2. Plot the data. One simple procedure involves plotting each of the observations of total costs against cost-driver activity levels. Plotting the data may make it clear that either no relation or only a nonlinear relation exists between the chosen cost driver and actual costs.

3. Examine the data and method of accumulation. Do the time periods for the cost data and the activity correspond? Occasionally, accounting systems will record costs actually incurred late on a given day as occurring on the following day. Observations collected by the month may smooth over meaningful variations of the cost driver's activity level and cost that would appear if the accountant collected weekly data.

3. Allocated and discretionary costs. Fixed costs allocated on a volume basis may appear to be variable, where the variability results from the allocation and not from a fundamental cause/effect relation. Budgeted discretionary costs appear variable (e.g., advertising expense budgeted as a percentage of revenue) when the firm allocates them to, for example, revenues.

4. Inflation. During periods of inflation, historical cost data do not accurately reflect future cost estimates. 5. Mismatched time periods. The time period for the dependent and independent variables may not match (e.g., running a machine in February but receiving and recording the energy bill in March).

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.

For example, as volume increases, the unit prices of some inputs, such as materials and power, may decrease due to volume discounts, exhibiting decreasing marginal costs.

Another example of curved cost behavior occurs when employees become more efficient with experience, as discussed in the following section.

Fixed Costs

Are costs that DO NOT change in total with change in activity levels.

Variable Costs

Are costs that change in total as the level of activity change

The managerial accountant divides fixed costs into subclassifications to explain the relation between particular types of fixed costs and current capacity. Certain fixed costs, called capacity costs, provide a firm with the capacity to produce or sell or both. A firm incurs some capacity costs, known as committed costs, even if it temporarily shuts down operations.

Committed costs result from an organization's ownership of facilities and its basic organizational structure. Production or selling capacity requires fixed capacity costs. Companies also incur fixed discretionary costs. These costs are also called programmed costs or managed costs. Examples include research, development, and advertising to generate new business.

What is an example of a curvilinear cost?

Costs become curvilinear when volume discounts are offered.

Variable costs, also known as engineered costs, change in total as the level of activity changes. An engineered cost bears a definitive physical relationship to the activity measure.

Direct materials cost is an engineered cost. It is impossible to manufacture more products without incurring greater materials costs.

Each of the cost estimation methods discussed has advantages and disadvantages. Probably the most informative estimate of cost behavior results from using several of the methods together, because each method has the potential to provide information not revealed by the others.

Exhibit 5.12 summarizes the strengths and weaknesses of these methods.

The effect of learning is often expressed as a learning curve (also known as an experience curve). 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.

Exhibit 5.6 shows the relation between volume and average labor hours in Graph A. Production time decreases as volume increases due to learning from experience.

As mentioned earlier, variable costs change in total as the level of activity changes and bear a definitive physical relationship to the activity measure.

Fixed costs remain constant over the relevant range of activity.

The total costs in the short run appear at the right side of the graph in Exhibit 5.1 on the assumption that the capacity of the existing plant is 20,000 units per year. Note that line CD represents costs for the production level of approximately 10,000 to 20,000 units only. Production levels outside this range require a different plant capacity, and the total cost line will shift up or down.

For example, if the relevant range of activity shown in Exhibit 5.1 is between 10,000 and 20,000 units, the firm assumes that certain costs are fixed while others are variable within that range. The firm would not necessarily assume that costs fixed within the relevant range will stay fixed outside the relevant range. As Exhibit 5.1 shows, for example, costs step up from point D to point E when production increases from the right side of the 10,000-to-20,000 range to the left side of the 20,000-to-30,000 range.

The ratio between an estimated regression coefficient and its standard error is known as the t-value or t-statistic.

If the absolute value of the t-statistic is approximately 2 or larger, we can be relatively confident that the actual coefficient differs from zero.

Relevant range

Is the range of activity over which the firm expects a set of cost behaviors to be consistent.

This chapter discusses methods of classifying costs into fixed and variable components.

Nearly all managerial decisions deal with choices among different activity levels; hence, the manager must estimate which costs will vary with the activity and by how much.

Simplifying cost analyses

Some costs do not vary in the short run over the relevant range (fixed costs). Some vary with volume (variable costs). Others are neither completely fixed or variable. Decision makers can simplify these variations by treating costs as either fixed or variable.

The R2 attempts to measure how well the line fits the data (that is, how closely the data points cluster about the fitted line). If all the data points were on the same straight line, the R2 would be 1.00—a perfect fit. If the data points formed a circle or disk, the R2 would be zero, indicating that no line passing through the center of the circle or disk fits the data better than any other.

Technically, R2 is a measure of the fraction of the total variance of the dependent variable about its mean that the fitted line explains. An R2 of 1 means that the regression explains all of the variance; an R2 of zero means that it explains none of the variance. R2 is sometimes known as the "coefficient of determination."

Systematic learning from experience frequently occurs, as when a firm initiates new products or processes or hires a group of new employees. As employees' experience increases, productivity improves. Labor costs per unit decrease. Learning curves illustrate how costs that are initially high for a new process, decrease over time with experience.

The relation between volume and total labor hours appears in Graph B. The relation between volume and total labor costs appears in Graph C. Total labor time and cost will decrease with increases in volume.

Costs vary with the volume of activity in several ways. Some costs do not vary in the short run over a relevant range—they are fixed. Others vary with volume—that is, they are variable. Some costs, neither strictly fixed nor strictly variable, contain both components. To simplify the analysis of cost behavior, decision makers usually assume that costs are either strictly fixed or linearly variable.

They do this because the incremental cost of analyzing the more complex data often exceeds the incremental benefits of doing so. The assumed simple linear variable-fixed cost behavior usually sufficiently approximates the reality for decision-making purposes. However, many cases require estimates and analysis of cost behavior with greater precision.

During short time periods, say, one month, the firm operates with a relatively fixed sales force, managerial staff, and set of production facilities. Consequently, many of its costs are fixed. Over long time spans, no costs are fixed because the firm can change staff size and sell or expand facilities. This fact provides the basis for the distinction drawn in economics between the long run and the short run and in accounting between fixed costs and variable costs.

To the economist, 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. Managers frequently use the notion of relevant range in estimating cost behavior. The relevant range is the range of activity over which the firm expects a set of cost behaviors to be consistent.

The total cost equation is:

Total costs = Fixed costs + (Variable costs x Activity), where fixed costs and variable costs are independent variables and total costs is the dependent variable.

Variable and fixed costs: a reminder

Variable costs change with the volume of activity. Fixed costs remain constant over the relevant range of activity.

Semivariable costs

are costs that have both fixed and variable components. Also called Mixed Costs.

Curvilinear variable costs

are costs that vary with the volume of activity but not in constant proportion

Curvilinear variable cost functions

indicate that the costs vary with the volume of activity, but not in constant proportion

Multiple regression has

more than one independent variable.

The term semivariable costs, also called mixed costs,

refers to costs that have both fixed and variable components. Repair and maintenance costs or utility costs exemplify semivariable cost behavior.

Semifixed costs change because of changes in long-term assets;

semivariable costs do not. The term semifixed costs, or step costs, refers to costs that increase in steps.

Three methods of cost estimation include

statistical regression, account analysis, and engineering estimation.