5. What 6. D is the relationship between committed resources and cost behavior?

Question

5. What 6. D is the relationship between committed resources and cost behavior? escribe ble to the difference between a variable cost and a step-variable cost. When is treat step-variable costs as if they were variable costs? 7. Why do mixed costs pose a problem when it comes to classifying costs into fixed and 8. Why is a scattergraph a good first step in separating mixed costs into their fixed and va 9. What are the advantages of the scatterplot method over the high-low method? The highn 10. Describe the method of least squares. Why is this method better than either the highlo 11. What is meant by the best-fitting line? Is the best-fitting line necessarily a good-itting line able categories? components? method over the scatterplot method? method or the scatterplot method? Explain. riabe 12. When is multiple regression required to explain cost behavior? 13. Explain the meaning of the learning curve. How do managers determine the appropriate learning curve percentage to use? 14. Assume you are the manager responsible for implementing a new service. The time to pr form the service is subject to the learning curve. Would you prefer that the new service have a learning rate of 85 percent or 80 percent? Why? 15. Some firms assign mixed costs to either the fixed or variable cost categories without using any formal methodology to separate them. Explain how this practice can be defended.

Explanation / Answer

5)

Committed Resources Committed resources are supplied in advance of usage. They are acquired by the use of either an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the quantity of the resource available is fully used or not. Committed resources may exceed the demand for their usage; thus, unused capacity is possible. Many resources are acquired before the actual demands for the resource are realized. There are two examples of this category of resource acquisition. First, organizations acquire many multiperiod service capacities by paying cash up front or by entering into an explicit contract that requires periodic cash payments. Buying or leasing buildings and equipment are examples of this form of advance resource acquisition. The annual expense associated with the multiperiod category is independent of actual usage of the resource. Often, these expenses are referred to as committed fixed expenses. They essentially correspond to committed resources—costs incurred that provide long-term activity capacity. A second and more important example concerns organizations that acquire resources in advance through implicit contracts—usually with their employees. These implicit contracts require an ethical focus, since they imply that the organization will maintain employment levels even though there may be temporary downturns in the quantity of activity used. Companies may manage the difficulties associated with maintaining this fixed level of expense by using contingent, or temporary, workers when needed. Many companies have indicated that the key reason for the use of contingent workers is flexibility— in meeting demand fluctuations, in controlling downsizing, and in buffering core workers against job loss.

Resource spending for this category corresponds to discretionary fixed expenses— costs incurred for the acquisition of short-term activity capacity. Hiring three sustaining engineers for $150,000 who can supply the capacity of processing 7,500 change orders is an example of implicit contracting (change orders is the driver used to measure resource capacity and usage).3 Certainly, none of the three engineers would expect to be laid off if only 5,000 change orders were actually processed—unless, of course, the downturn in demand is viewed as being permanent.

In our discussion of cost behavior, we have assumed that the cost function (either linear or nonlinear) is continuous. This type of cost function is known as a step function. A step-cost function displays a constant level of cost for a range of activity output and then jumps to a higher level of cost at some point, where it remains for a similar range of activity. In Exhibit 3-4, the cost is $100, as long as activity output is between 0 and 20 units. If the volume is between 20 and 40 units, the cost jumps to $200.

6)

A step variable cost is a cost that generally varies with the level of activity, but which tends to be incurred at certain discrete points and to involve large changes in amounts when such a point is reached. Conversely, a truly variable cost will vary continually and directly in concert with the level of activity.

An example of a step variable cost is the compensation of a quality assurance (QA) worker in the assembly area of a production department. Each QA worker is capable of reviewing a certain number of parts per day. Once the production process exceeds that volume level, another quality assurance worker must be hired. Thus, the cost of the QA person generally varies with the level of activity, but only changes at discrete points - when the existing QA staff can no longer handle the work load, forcing another person to be hired.

The example shows a common characteristic of a step variable cost, which is that there tends to be a relatively wide activity range within which the existing cost can be incurred without incurring any additional cost, and after which a large additional cost must be incurred. To return to the example, this means that the QA person could be more efficient or work somewhat longer hours in order to avoid incurring the large incremental cost of an additional person. In such a situation, it may be more cost-effective for the employer to offer overtime to the existing staff than to pay the more substantial cost of a new hire.

Because a step variable cost can remain approximately the same while activity levels change, this step effect can impact the allocated cost per manufactured unit. The allocated amount per unit decreases as the number of units produced increases, until such time as the higher volume level triggers the incurrence of a new step variable cost, after which the cost per unit increases due to the higher total variable cost

A variable cost is a corporate expense that changes in proportion with production output. Variable costs increase or decrease depending on a company's production volume; they rise as production increases and fall as production decreases.

The total expenses incurred by any business consist of fixed costs and variable costs. Fixed costs are expenses that remain the same regardless of production output. Whether a firm makes sales or not, it must pay its fixed costs, as these costs are independent of output. Examples of fixed costs are rent, employee salaries, insurance, and office supplies. A company must still pay its rent for the space it occupies to run its business operations irrespective of the volume of product manufactured and sold. Although, fixed costs can change over a period of time, the change will not be related to production.

Variable costs, on the other hand, are dependent on production output. The variable cost of production is a constant amount per unit produced. As volume of production and output increases, variable costs will also increase. Conversely, when fewer products are produced, the variable costs associated with production will consequently decrease. Examples of variable costs are sales commissions, direct labor costs, cost of raw materials used in production, and utility costs. The formula for variable cost is given as:

Total variable cost = Quantity of output x Variable cost per unit of output.

7)

A mixed cost is a cost that contains both a fixed cost component and a variable cost component. It is important to understand the mix of these elements of a cost, so that one can predict how costs will change with different levels of activity. Typically, a portion of a mixed cost may be present in the absence of all activity, in addition to which the cost may also increase as activity levels increase. As the level of usage of a mixed cost item increases, the fixed component of the cost will not change, while the variable cost component will increase. The formula for this relationship is:

Y = a + bx

Y = Total cost

a = Total fixed cost

b = Variable cost per unit of activity

x = Number of units of activity

For example, if a company owns a building, the total cost of that building in a year is a mixed cost. The depreciation associated with the asset is a fixed cost, since it does not vary from year to year, while the utilities expense will vary depending upon the company's usage of the building. The fixed cost of the building is $100,000 per year, while the variable cost of utilities is $250 per occupant. If the building contains 100 occupants, then the mixed cost calculation is:

$125,000 Total cost = $100,000 Fixed cost + ($250/occupant x 100 occupants)

As another example of a mixed cost, a company has a broadband contract with the local cable company, which it pays $500 per month for the first 500 megabytes of usage per month, after which the price increases by $1 per megabyte used. The following table shows the mixed cost nature of the situation, where there is a baseline fixed cost, and above which the cost increases at the same pace as usage:

Mixed costs are common in a corporation, since many departments require a certain amount of baseline fixed costs in order to support any activities at all, and also incur variable costs to provide varying quantities of services above the baseline level of support. Thus, the cost structure of an entire department can be said to be a mixed cost. This is also a key concern when developing budgets, since some mixed costs will vary only partially with expected activity levels, and so must be properly accounted for in the budget.

The best way to deal with mixed costs in a budget is to use a formula in place of a single number for a mixed cost, with the cost automatically varying based on a designated activity level (such as sales). This approach is more complicated, but yields budget figures that are more likely to match actual results.

8)

The scattergraph method is a visual representation of the cost and activity data associated with an expense. The resulting chart is used to identify and separate the fixed and variable components of a cost. The method is most useful for gaining insight into the nature of mixed costs, which can then be used to project costs in a company forecast or budget, based on expected activity levels. A cost that has both fixed and variable components is considered a mixed cost.

Use the following steps to create a scattergraph and glean costing information from it:

Ideally, the result of a scattergraph analysis should be a formula that states the total amount of fixed cost and the variable cost per unit of activity. Thus, if an analyst finds that the fixed cost associated with a mixed cost is $1,000 per month and the variable cost component is $3.00 per unit, then it is easy to project that an activity level of 500 units in an accounting period will result in a total mixed cost of $2,500 (calculated as $1,000 fixed cost + ($3.00/unit x 500 units)).

The scattergraph method is not an overly precise method for determining cost levels, since it does not factor in the impact of step costingpoints, where costs change dramatically at certain activity levels. For example, reaching a certain number of units produced might require outsourcing some work or opening a new production shift, either of which will alter the variable cost incurred per unit and/or the fixed cost level.

The scattergraph method is also not useful in situations where there is little correlation between the cost incurred and the related activity level, since this makes it difficult to project costs into the future. Actual costs incurred in future periods might vary substantially from what the scattergraph method projects will happen.

9)

Scatter Diagrams

Merits

Demerits

HIGH LOW METHOD

Ease of Use

A major advantage of the high-low method of cost estimation is its ease of use. By only requiring cost information from the highest and lowest activity level and some simple algebra, managers can get information about cost behavior in just a few minutes. In addition to being easy to use, because the method doesn't require any kind of tools or programs, it is also inexpensive to implement.

Accuracy Under Stable Costs

If costs are relatively stable over time, and the high and low activity level are representative of the company's cost behavior over time, the high-low method can be extremely accurate. However, an interesting conundrum occurs if the endpoints are not representative. Even if costs are very stable throughout the rest of the range of activity, if the lowest of highest level of activity are systematically different, then managers will have inaccurate information. To guard against this, managers may want to plot activity levels vs. costs for a subset of the data that the company has. This way, managers may be able to see if the points they have selected for the high-low method really are representative of normal costs.

Inaccuracy with Variation

A problem with the high-low method is that if costs are relatively unstable, this method could produce inaccurate results. Because the high-low method uses only two points to calculate a cost estimate, monthly variation in costs is not captured in the estimate, even if the points are representative of normal cost behavior. If managers plot the activity level vs. cost and see high variability, they have a decision to make. If timeliness is more important than accuracy, then the high-low method is probably good enough. However, if accuracy is tantamount, then another method should be consulted.

Least-Squares Regression

Perhaps the biggest drawback of the high-low method is not inherent within the method itself. With the prevalence of spreadsheet software, least-squares regression, a method that takes into consideration all of the data, can be easily and quickly employed to obtain estimates that may be magnitudes more accurate than high-low estimates. Least-squares regression uses statistics to mathematically optimize the cost estimate. Further, because this method uses all of the data available, small idiosyncrasies in cost behavior have less effect on the estimate as the amount of data increases.

10)

The least squares method provides the overall rationale for the placement of the line of best fit among the data points being studied. The most common application of the least squares method, referred to as linear or ordinary, aims to create a straight line that minimizes the sum of the squares of the errors generated by the results of the associated equations, such as the squared residuals resulting from differences in the observed value and the value anticipated based on the model.

This method of regression analysis begins with a set of data points to be graphed. An analyst using the least squares method will seek a line of best fit that explains the potential relationship between an independent variable and a dependent variable. In regression analysis, dependent variables are designated on the vertical Y axis and independent variables are designated on the horizontal X-axis. These designations will form the equation for the line of best fit, which is determined from the least squares method.

Example of Least Squares Method

For example, an analyst may want to test the relationship between a company’s stock returns and the returns of the index for which the stock is a component. In this example, the analyst seeks to test the dependence of the stock returns on the index returns. To do this, all of the returns are plotted on a chart. The index returns are then designated as the independent variable, and the stock returns are the dependent variable. The line of best fit provides the analyst with coefficients explaining the level of dependence.

11)

ine of best fit is one of the most important outputs of regression analysis. Regression refers to a quantitative measure of the relationship between one or more independent variables and a resulting dependent variable. Regression is of use to professionals in a wide range of fields from science and public service to financial analysis.

To perform a regression analysis, a statistician collects a set of data points, each including a complete set of dependent and independent variables. For example, the dependent variable could be a firm’s stock price and the independent variables could be the Standard and Poor’s 500 index and the national unemployment rate, assuming that the stock is not listed in the S&P 500. The sample set could be each of these three data sets for the past 20 years. On a chart, these data points would appear as scatter plot, a set of points that may or may not appear to be organized along any line. If a linear pattern is apparent, it may be possible to sketch a line of best fit that minimizes the distance of those points from that line. If no organizing axis is visually apparent, regression analysis can generate a line based on the least squares method. This method builds the line which minimizes the squared distance of each point from the line of best fit.

To determine the formula for this line, the statistician enters these three results for the past 20 years into a regression software application. The software produces a linear formula that expresses the causal relationship between the S&P 500, the unemployment rate, and the stock price of the company in question. This equation is the formula for the line of best fit. It is a predictive tool, providing analysts and traders with a mechanism to project the firm’s future stock price based on those two independent variables.

The Line of Best Fit Equation and Its Components

A regression with two independent variables such as the example discussed above will produce a formula with this basic structure:

y= c + b1(x1) + b2(x2)

In this equation, y is the dependent variable, c is a constant, b1 is the first regression coefficient and x1 is the first independent variable. The second coefficient and second independent variable are b2 and x2. Drawing from the above example, the stock price would be y, the S&P 500 would be x1 and the unemployment rate would be x2. The coefficient of each independent variable represents the degree of change in y for each additional unit in that variable. If the S&P 500 increases by one, the resulting y or share price will go up by the amount of the coefficient. The same is true for the second independent variable, the unemployment rate. In a simple regression with one independent variable, that coefficient is the slope of the line of best fit. In this example or any regression with two independent variables the slope is a mix of the two coefficients. The constant c is the y-intercept of the line of best fit.

13)

The learning curve also is referred to as the experience curve, the cost curve, the efficiency curve or the productivity curve. This is because the learning curve provides measurement and insight into all the above aspects of a company. The idea behind this is any employee, regardless of position, takes time to learn how to carry out a specific task or duty. The amount of time needed to produce the associated output is high. Then, as the task is repeated, the employee learns how to complete it quickly and that reduces the amount of time needed for a unit of output.

That is why the learning curve is downward sloping in the beginning with a flat slope toward the end, with the cost per unit depicted on the Y-axis and total output on the X-axis. As learning increases, it decreases the cost per unit of output initially before flattening out, as it becomes harder to increase the efficiencies gained through learning.

Benefits of Using the Learning Curve

The learning curve does a good job of depicting the cost per unit of output over time. Companies know how much an employee earns per hour and can derive the cost of producing a single unit of output based on the amount of hours needed. A well-placed employee who is set up for success should decrease the company's costs per unit of output over time. Businesses can use the learning curve to conduct production planning, cost forecasting and logistic schedules.

The slope of the learning curve represents the rate in which learning translates into cost savings for a company. The steeper the slope, the higher the cost savings per unit of output. This standard learning curve is known as the 80% learning curve. It shows that for every doubling of a company's output, the cost of the new output is 80% of the prior output. As output increases, it becomes harder and harder to double a company's previous output, depicted using the slope of the curve, which means cost savings slow over time.

12)

Multiple regression is an extension of simple linear regression. It is used when we want to predict the value of a variable based on the value of two or more other variables. The variable we want to predict is called the dependent variable (or sometimes, the outcome, target or criterion variable). The variables we are using to predict the value of the dependent variable are called the independent variables (or sometimes, the predictor, explanatory or regressor variables).

For example, you could use multiple regression to understand whether exam performance can be predicted based on revision time, test anxiety, lecture attendance and gender. Alternately, you could use multiple regression to understand whether daily cigarette consumption can be predicted based on smoking duration, age when started smoking, smoker type, income and gender.

Multiple regression also allows you to determine the overall fit (variance explained) of the model and the relative contribution of each of the predictors to the total variance explained. For example, you might want to know how much of the variation in exam performance can be explained by revision time, test anxiety, lecture attendance and gender "as a whole", but also the "relative contribution" of each independent variable in explaining the variance.

This "quick start" guide shows you how to carry out multiple regression using SPSS Statistics, as well as interpret and report the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for multiple regression to give you a valid result. We discuss these assumptions next.

Megabytes Variable Cost Fixed Cost Total Cost 500 $0 $500 $500 600 100 500 600 700 200 500 700 800 300 500 800 900 400 500 900

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