ESTIMATING A COST FUNCTION USING Insert Home Page Layout B Formulas Week 1 6 UNESCO WNH . Indirect Cost Driver: Manufacturing Machine-Hours Labor Costs (X) (Y) 68 $ 1,190 88 1,211 62 1,004 72 917 60 770 96 1,456 78 1,180 46 710 82 1.316 94 1,032 68 752 48 963 862 $12,501 2 3 4 5 6 7 8 9 10 11 12 9 10 11 12 o 13 14 15 Total 16 | Dit 10-3 show the breakdown of Elegant Rugs' total machine-ho Cect manufacturing labor costs ($12,501) into weekly data for i period. Note that the data are paired; for each week, there is manufacturing labor Required: A. B. C. Using data from exhibit 10-3, run a regression program using excel. Estimate the cost function. Using the cost function, estimate cost for 90 machine hours. costs of 10-3 to illustrate how to estimate a cost function is uantitative analysis. We examine two techniques: the relatively simple high-low and as well as the more common quantitative tool used to examine and unders as regression analysis. Advantages and challenges Quantitative analysis is the most rigorous approach to estimate costs. Computer programs have made performing quantitative analysis and, in particular, regression analysis much easier. However, regression analysis requires more detailed information about costs, cost drivers, and cost functions and is therefore more time consuming to implement. Estimating a Cost Function Using Quantitative Analysis There are six steps in estimating a cost function using quantitative analysis of past data. We illustrate the steps using the Elegant Rugs example. Step 1: Choose the dependent variable. Which dependent variable (the cost to be pre- dicted and managed) managers choose will depend on the specific cost function being estimated. In the Elegant Rugs example, the dependent variable is indirect manufacturing labor costs. Step 2: Identify the independent variable, or cost driver. The independent variable (level of activity or cost driver) is the factor used to predict the dependent variable (costs). When the cost is an indirect cost, as it is with Elegant Rugs, the independent variable is also called a cost-allocation base. Although these terms are sometimes used interchangeably, we use the 380 CHAPTER 10 DETERMINING HOW COSTS BEHAVE term cost driver to describe the independent variable, Frequently, the mana ang alternative economically plausible cost drivers to identify the one that be the data tant, working with the management team, will cycle through the six steps try lationship with the dependent variable. Economic plausibility means that the relationship Recall that a cost driver should be measurable and have an economico is based on a physical relationship, a contract, or knowledge of operations and make (describing how changes in the cost driver lead to changes in the costs bens den learned in Chapter 5, all the individual items of costs included in the dependent van economic sense to the operating manager and the management Contasy should have the same cost driver, that is, the cost pool should be homogenous when items of costs in the dependent variable do not have the same cost driver, the accountant should investigate the possibility of creating homogenous cost pools ander mating more than one cost function, one for each cost item/cost driver pair As an example, consider several types of fringe benefits paid to employees and the cost drivers of the benefits: Fringe Benefit Cost Driver Health benefits Number of employeus Cafeteria meals Number of employees Pension benefits Salaries of employees Life insurance Salaries of employees The costs of health benefits and cafeteria meals can be combined into one homogenis cost pool because they have the same cost driver-the number of employees. Petsie benefits and life insurance costs have a different cost driver-the salaries of employees and, therefore, should not be combined with health benefits and cafeteria meals. Instead, pension benefits and life insurance costs should be combined into a separate homogenes cost pool. The cour pool composed of pension benefits and life insurance costs can be en mated using the salaries of employees receiving these benefits as the cost driver, Step 3: Collect data on the dependent variable and the cost driver. This is usually the most difficult step in cost analysis. Management accountants obtain data from comparty documents, from interviews with managers, and through special studies. These data may be time series data or cross-sectional data Time-series datu pertain to the same entity (such as an organization, plant, or actis ity) over successive past periods. Weekly observations of Elegant Rugs' indirect manufac turing labor costs and number of machine-hours are examples of time series data. The ideal time series database would contain numerous observations for a company whos operations have not been affected by economic or technological change. A stable econom and stable technology ensure that data collected during the estimation period represent the same underlying relationship between the cost driver and the dependent variable Moreover, the periods used to measure the dependent variable and the cost driver should be consistent throughout the observations. Cross-sectional data pertain to different entities during the same period. For example studies of loans processed and the related personnel costs at 50 individual, yet similar branches of a bank during March 2014 would produce cross-sectional data for that a month. The cross-sectional data should be drawn from entities that, within each entity have a similar relationship between the cost driver and costs. Later in this chapter, we describe the problems that arise in data collection, Step 4 Plot the data. The general relationship between the cost driver and costs be readily seen in a plot of the data once it's staphed. The plot provides insight into the relevant range of the cost function and reveals whether the relationship between the driver and costs is approximately linear. Moreover, the plot highlights extreme observations for servations outside the general pattern) that analysts should check. Was there and recording the data or an unusual event, such as a work stoppage, that makes these obser vations unrepresentative of the normal relationship between the cost driver and the Exhibit 10-4 is a plot of the weekly data from columns B and C of the Excel spread sheet in Exhibit 10-3. This graphs provides strong visual evidence of a positive at STATINGADOR Indian Laborcom 1.00 1.400 1.200 LO 600 200 mationship between Elegant Rusnumber of machine-housand ubor costs (when machine hours, p. 10 do indirect manufacturita Lubecome there do not appear to be any extreme obiervations in Excubit 104. The cleaning from 18.no 96 machine hours per week (weeks 5 and 6. respectively Step 5: Estimate the cost function. The two most common forms of quantitative analys s managers and accountants use to estimate com function are the high-low method and repression analysis. Even though computer programach as Excel make regression alysis much easier, we will describe the high-low method to provide some basic man for the idea of drawing a line to tie a number of data points. We present these berhods after Step 6. Sup & Evaluate the cost driver of the estimated cost function. In this step, we describe the criteria for evaluating the cost driver of the estimated cost function. But to do so you Sist need to understand both the high-low method and repression analysis. Identifying cost drivers is a critical aspect of managing costs and improving profitability and there fore a vital component in a manager's toolkit. High-Low Method The simplest form of quantitative analysis to "fix" a line to data points is the high-low method. It uses only the highest and lowest observed values of the cost driver within the relevant range and their respective costs to estimate the slope coefficient and the constant of the cost function. It provides a quick first look at the relationship between a cost driver ind costs. We illustrate the high-low method using data from Exhibit 10-3. Cost Driver: Indirect Manufacturing Machine-Hours Labor Costs Highest observation of cost driver (week 6) 95 $1,456 Lowest observation of cost driver (week 81 710 Difference 50 5 146 The slope coefficient, b, is calculated as follows: Difference between costs associated with highest and lowest observations of the cost driver Slope coefficient = Difference between highest and lowest observations of the cost driver = $746-50 machine-hours = $1492 per machine-hour compute the constant, we can use either the highest or the lowest observation of the Cose driver. Both calculations yield the same answer because the method solves two linear quations with two unknowns, the slope coefficient and the constant. Because 1818 To + X 3y-EX