To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com CHAPTER 10 DETERMINING HOW COSTS BEHAVE 10-1 10-2 The two assumptions are Variations in the level of a single activity (the cost driver) explain the variations in the related total costs 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 Three alternative linear cost functions are 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 Fixed cost function––a cost function in which total costs not change with changes in the level of activity in the relevant range 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 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 telephone line where the terms are a fixed charge of $10,000 per year plus a $2 per minute charge for phone 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 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 Four approaches to estimating a cost function are Industrial engineering method Conference method Account analysis method Quantitative analysis of current or past cost relationships 10-6 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 The speed with which cost estimates can be developed The pooling of knowledge from experts across functional areas The improved credibility of the cost function to all personnel 10-1 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-7 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 The six steps are Choose the dependent variable (the variable to be predicted, which is some type of cost) Identify the independent variable or cost driver Collect data on the dependent variable and the cost driver Plot the data Estimate the cost function Evaluate the cost driver of the estimated cost function Step typically is the most difficult for a cost analyst 10-9 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 high-low method 10-10 Three criteria important when choosing among alternative cost functions are Economic plausibility Goodness of fit Slope of the regression line 10-11 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 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 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 Frequently encountered problems when collecting cost data on variables included in a cost function are The time period used to measure the dependent variable is not properly matched with the time period used to measure the cost driver(s) Fixed costs are allocated as if they are variable Data are either not available for all observations or are not uniformly reliable Extreme values of observations occur A homogeneous relationship between the individual cost items in the dependent variable cost pool and the cost driver(s) does not exist The relationship between the cost and the cost driver is not stationary Inflation has occurred in a dependent variable, a cost driver, or both 10-2 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-13 Four key assumptions examined in specification analysis are Linearity of relationship between the dependent variable and the independent variable within the relevant range Constant variance of residuals for all values of the independent variable Independence of residuals Normal distribution of residuals 10-14 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 to maximize goodness of fit, irrespective of the economic plausibility of the independent variables included Some of the independent variables included may not be cost drivers 10-15 No Multicollinearity exists when two or more independent variables are highly correlated with each other 10-16 (10 min.) Estimating a cost function Slope coefficient = Error! = $3,900 - $3,000 7,000 - 4,000 = $900 = $0.30 per machine-hour 3, 000 Constant = Total cost – (Slope coefficient Quantity of cost driver) = $3,900 – ($0.30 7,000) = $1,800 = $3,000 – ($0.30 4,000) = $1,800 The cost function based on the two observations is Maintenance costs = $1,800 + $0.30 Machine-hours The cost function in requirement is an estimate of how costs behave within the relevant range, not at cost levels outside the relevant range If there are no months with zero machinehours represented in the maintenance account, data in that account cannot be used to estimate the fixed costs at the zero machine-hours level Rather, the constant component of the cost function provides the best available starting point for a straight line that approximates how a cost behaves within the relevant range 10-3 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-17 (15 min.) Identifying variable-, fixed-, and mixed-cost functions See Solution Exhibit 10-17 Contract 1: y = $50 Contract 2: y = $30 + $0.20X Contract 3: y = $1X where X is the number of miles traveled in the day Contract Cost Function Fixed Mixed Variable SOLUTION EXHIBIT 10-17 Plots of Car Rental Contracts Offered by Pacific Corp Contract 1: Fixed Costs $160 Car Rental Co sts 140 120 100 80 60 40 20 0 50 100 Miles Travel ed per Day 150 Car Rent al Cos ts Contract 2: Mixed Costs $160 140 120 100 80 60 40 20 0 100 50 Miles Travel ed per Day 150 Car Rental Co sts Contract 3: Variable Costs $160 140 120 100 80 60 40 20 0 50 100 Miles Travel ed per Day 10-4 150 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-18 (20 min.) Various cost-behavior patterns K B G J I L F K C Note that A is incorrect because, although the cost per pound eventually equals a constant at $9.20, the total dollars of cost increases linearly from that point onward The total costs will be the same regardless of the volume level This is a classic step-cost function 10-19 (30 min.) Matching graphs with descriptions of cost and revenue behavior a b c d e f (1) (6) (9) (2) (8) (10) g h (3) (8) A step-cost function It is data plotted on a scatter diagram, showing a linear variable cost function with constant variance of residuals The constant variance of residuals implies that there is a uniform dispersion of the data points about the regression line 10-5 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-20 (15 min.) Account analysis method Variable costs: Car wash labor $240,000 Soap, cloth, and supplies 32,000 Water 28,000 Electric power to move conveyor belt 72,000 Total variable costs $372,000 Fixed costs: Depreciation Salaries Total fixed costs $ 64,000 46,000 $110,000 Some costs are classified as variable because the total costs in these categories change in proportion to the number of cars washed in Lorenzo’s operation Some costs are classified as fixed because the total costs in these categories not vary with the number of cars washed If the conveyor belt moves regardless of the number of cars on it, the electricity costs to power the conveyor belt would be a fixed cost Variable costs per car = $372,000 = $4.65 per car 80,000 Total costs estimated for 90,000 cars = $110,000 + ($4.65 × 90,000) = $528,500 10-6 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-21 (30 min.) Account analysis method Manufacturing cost classification for 2006: Account Direct materials Direct manufacturing labor Power Supervision labor Materials-handling labor Maintenance labor Depreciation Rent, property taxes, admin Total Total Costs (1) $300,000 225,000 37,500 56,250 60,000 75,000 95,000 100,000 $948,750 % of Total Costs That is Variable Fixed Variable Variable Costs Costs Cost per Unit (2) (3) = (1) (2) (4) = (1) – (3) (5) = (3) ÷ 75,000 100% 100 100 20 50 40 0 $300,000 225,000 37,500 11,250 30,000 30,000 0 $633,750 $ 0 45,000 30,000 45,000 95,000 100,000 $315,000 $4.00 3.00 0.50 0.15 0.40 0.40 0 $8.45 Total manufacturing cost for 2006 = $948,750 Variable costs in 2007: Account Direct materials Direct manufacturing labor Power Supervision labor Materials-handling labor Maintenance labor Depreciation Rent, property taxes, admin Total Unit Variable Increase in Cost per Variable Variable Cost Unit for Percentage Cost per Unit 2006 Increase per Unit for 2007 (6) (7) (8) = (6) (7) (9) = (6) + (8) $4.00 3.00 0.50 0.15 0.40 0.40 0 $8.45 5% 10 0 0 0 10-7 $0.20 0.30 0 0 0 $0.50 $4.20 3.30 0.50 0.15 0.40 0.40 0 $8.95 Total Variable Costs for 2007 (10) = (9) 80,000 $336,000 264,000 40,000 12,000 32,000 32,000 0 $716,000 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Fixed and total costs in 2007: Account Fixed Costs for 2006 (11) Direct materials $ Direct manufacturing labor Power Supervision labor 45,000 Materials-handling labor 30,000 Maintenance labor 45,000 Depreciation 95,000 Rent, property taxes, admin 100,000 Total $315,000 Percentage Increase (12) 0% 0 0 Dollar Increase in Fixed Costs (13) = (11) (12) $ Fixed Costs for 2007 (14) = (11) + (13) Variable Costs for 2007 (15) Total Costs (16) = (14) + (15) $ $336,000 $ 336,000 0 264,000 264,000 0 40,000 40,000 45,000 12,000 57,000 30,000 32,000 62,000 45,000 32,000 77,000 4,750 99,750 99,750 7,000 107,000 107,000 $11,750 $326,750 $716,000 $1,042,750 Total manufacturing costs for 2007 = $1,042,750 Total cost per unit, 2006 Total cost per unit, 2007 $948,750 = $12.65 75,000 $1,042,750 = = $13.03 80,000 = Cost classification into variable and fixed costs is based on qualitative, rather than quantitative, analysis How good the classifications are depends on the knowledge of individual managers who classify the costs Gower may want to undertake quantitative analysis of costs, using regression analysis on time-series or cross-sectional data to better estimate the fixed and variable components of costs Better knowledge of fixed and variable costs will help Gower to better price his products, to know when he is getting a positive contribution margin, and to better manage costs 10-8 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-22 (15–20 min.) Estimating a cost function, high-low method The key point to note is that the problem provides high-low values of X (annual round trips made by a helicopter) and Y X (the operating cost per round trip) We first need to calculate the annual operating cost Y (as in column (3) below), and then use those values to estimate the function using the high-low method Highest observation of cost driver Lowest observation of cost driver Difference Cost Driver: Annual RoundTrips (X) (1) 2,000 1,000 1,000 Operating Cost per Round-Trip (2) $250 $300 Annual Operating Cost (Y) (3) = (1) (2) $500,000 $300,000 $200,000 Slope coefficient = $200,000 1,000 = $200 per round-trip Constant = $500,000 – ($200 2,000) = $100,000 The estimated relationship is Y = $100,000 + $200 X; where Y is the annual operating cost of a helicopter and X represents the number of round trips it makes annually The constant a (estimated as $100,000) represents the fixed costs of operating a helicopter, irrespective of the number of round trips it makes This would include items such as insurance, registration, depreciation on the aircraft, and any fixed component of pilot and crew salaries The coefficient b (estimated as $200 per round-trip) represents the variable cost of each round trip—costs that are incurred only when a helicopter actually flies a round trip The coefficient b may include costs such as landing fees, fuel, refreshments, baggage handling, and any regulatory fees paid on a per-flight basis If each helicopter is, on average, expected to make 1,200 round trips a year, we can use the estimated relationship to calculate the expected annual operating cost per helicopter: Y = $100,000 + $200 X X = 1,200 Y = $340,000 With 10 helicopters in its fleet, Reisen’s estimated operating budget is 10 10-9 $340,000 = $3,400,000 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-23 (20 min.) Estimating a cost function, high-low method See Solution Exhibit 10-23 There is a positive relationship between the number of service reports (a cost driver) and the customer-service department costs This relationship is economically plausible Number of Customer-Service Service Reports Department Costs Highest observation of cost driver 436 $21,890 Lowest observation of cost driver 122 12,941 Difference 314 $ 8,949 Customer-service department costs = a + b (number of service reports) Slope coefficient (b) Constant (a) Customer-service department costs $8,949 = $28.50 per service report 314 = $21,890 – $28.50 436 = $9,464 = $12,941 – $28.50 122 = $9,464 = = $9,464 + $28.50 (number of service reports) Other possible cost drivers of customer-service department costs are: a Number of products replaced with a new product (and the dollar value of the new products charged to the customer-service department) b Number of products repaired and the time and cost of repairs Customer-Service Department Costs SOLUTION EXHIBIT 10-23 Plot of Number of Service Reports versus Customer-Service Dept Costs for Capitol Products $25,000 20,000 15,000 10,000 5,000 $0 100 200 300 400 Number of Service Reports 10-10 500 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com SOLUTION EXHIBIT 10-37A Overhead Costs vs Number of Minicourses 70,000 60,000 Overhead Costs ($) 50,000 Regression 40,000 Data Plot 30,000 20,000 10,000 - 10 15 20 25 30 35 40 45 50 55 Number of Minicourses SOLUTION EXHIBIT 10-37B Overhead Costs vs Number of Campers 70,000 65,000 60,000 Data Plot Overhead Costs ($) 55,000 Regression 50,000 45,000 40,000 35,000 30,000 25,000 20,000 1,000 1,500 2,000 2,500 Number of Campers 10-34 3,000 3,500 4,000 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-38 (30 min.) Evaluating multiple regression models, nonprofit (continuation of 10-37) (chapter appendix) Given the results of the simple regressions, Schonberg should ask Day to run a multiple regression model with number of minicourses and number of campers as independent variables It is economically plausible that both the number of minicourses and the number of campers affect the course overhead costs, and the multiple regression model may well provide Schonberg with an understanding of how these two factors affect costs Also, to the extent that the two independent variables are modestly correlated, the simple regressions would yield biased values for the coefficients A multiple regression would provide a better estimate of cost per minicourse and the cost per camper Yes, Schonberg should use the multiple regression model to predict course overhead instead of the two simple regression models As indicated in the table below, the multipleregression model is as good as or better than the simple regression models on all relevant criteria Criterion Economic plausibility Goodness of fit Significance of independent variable Specification analysis of estimation assumptions Multicollinearity Cost Function 1: Number of Mini-courses as Independent Variable A positive relationship between course overhead costs and each of the independent variables (number of minicourses and number of campers) is economically plausible R2 = 0.81 Excellent goodness of fit; better than any one of the simple regressions by itself The t-values of 3.54 for the coefficient on number of mini-courses and 2.06 on the number of campers indicates that each is statistically significant (its magnitude is greater than 0) Assuming linearity, constant variance and normality of residuals; reasonable independence of residuals is indicated (Durbin-Watson statistic = 1.91); however, we must be cautious when drawing inferences from only 12 observations The coefficient of correlation between the two independent variables is 0.59 This is high enough to justify running a multiple regression (as opposed to using two simple regressions), but not so high as to cause overly large standard errors Note that even if the standard errors have been inflated due to multicollinearity, each coefficient is still statistically significant 10-35 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com The multiple regression reveals that the incremental cost of each additional course offered is about $607—or, at the very least, we can say that it is several hundred dollars per course This information could be used to price the courses, or to price the camp experience, if the courses are included It could also be used to set and justify a minimum-registration requirement for each course (which, if not met, would cause the course offering to be canceled) With the number of minicourses up to 52 in the current year, there are probably a number of minicourses that are not very popular; they could be taken off the menu and a significant amount of money (approximately $607) saved with each discontinued course Each additional camper causes a $6.36 increase in costs Even if he doesn’t use the exact coefficient, this regression tells Schonberg that each extra camper seems to cause a small increase in costs Assuming that the cost structure at Fallen Leaf Summer Camp is such that each additional camper is sufficiently profitable, clearly Schonberg should focus on limiting the number of courses offered A further investigation of the components of the course overhead costs may provide additional insights 10-39 (40–50 min.) Purchasing Department cost drivers, activity-based costing, simple regression analysis The problem reports the exact t-values from the computer runs of the data Because the coefficients and standard errors given in the problem are rounded to three decimal places, dividing the coefficient by the standard error may yield slightly different t-values Plots of the data used in Regressions to are in Solution Exhibit 10-39A See Solution Exhibit 10-39B for a comparison of the three regression models Both Regressions and are well-specified regression models The slope coefficients on their respective independent variables are significantly different from zero These results support the Couture Fabrics’ presentation in which the number of purchase orders and the number of suppliers were reported to be drivers of purchasing department costs In designing an activity-based cost system, Fashion Flair should use number of purchase orders and number of suppliers as cost drivers of purchasing department costs As the chapter appendix describes, Fashion Flair can either (a) estimate a multiple regression equation for purchasing department costs with number of purchase orders and number of suppliers as cost drivers, or (b) divide purchasing department costs into two separate cost pools, one for costs related to purchase orders and another for costs related to suppliers, and estimate a separate relationship for each cost pool Guidelines presented in the chapter could be used to gain additional evidence on cost drivers of purchasing department costs Use physical relationships or engineering relationships to establish cause-and-effect links Lee could observe the purchasing department operations to gain insight into how costs are driven Use knowledge of operations Lee could interview operating personnel in the purchasing department to obtain their insight on cost drivers 10-36 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com SOLUTION EXHIBIT 10-39A Regression Lines of Various Cost Drivers on Purchasing Dept Costs for Fashion Flair Purchasing D epartment Co sts $2,500,000 2,000,000 1,500,000 1,000,000 500,000 100 50 150 Dol lar Valu e o f Merchan dise Purch ased (in mill ions) Pu rchas ing Department Cos ts $2,500,000 2,000,000 1,500,000 1,000,000 500,000 0 2,000 4,000 6,000 8,000 Number o f Pu rchase Orders Purchas ing Depart ment Cos ts $2,500,000 2,000,000 1,500,000 1,000,000 500,000 0 100 200 Number o f Su ppliers 10-37 300 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com SOLUTION EXHIBIT 10-39B Comparison of Alternative Cost Functions for Purchasing Department Costs Estimated with Simple Regression for Fashion Flair Criterion Economic Plausibility Regression PDC = a + (b MP$) Result presented at seminar by Couture Fabrics found little support for MP$ as a driver Purchasing personnel at the Miami store believe MP$ is not a significant cost driver Goodness of fit r2 = 0.08 Poor goodness of fit Significance of Independent Variables Specification Analysis A Linearity within the relevant range t-value on MP$ of 0.84 is insignificant Regression PDC = a + (b # of POs) Economically plausible The higher the number of purchase orders, the more tasks undertaken Regression PDC = a + (b # of Ss) Economically plausible Increasing the number of suppliers increases the costs of certifying vendors and managing the Fashion Flairsupplier relationship r2 = 0.42 Reasonable goodness of fit r2 = 0.39 Reasonable goodness of fit t-value on # of POs of 2.43 t-value on # of Ss of 2.28 is significant is significant Appears questionable Appears reasonable but no strong evidence against linearity Appears reasonable B Constant variance of residuals Appears questionable, Appears reasonable but no strong evidence against constant variance Appears reasonable C Independence of residuals Durbin-Watson Statistic = 2.41 Assumption of independence is not rejected Durbin-Watson Statistic = 1.97 Assumption of independence is not rejected D Normality of residuals Data base too small to Data base too small to make reliable make reliable inferences inferences Durbin-Watson Statistic = 1.98 Assumption of independence is not rejected 10-38 Data base too small to make reliable inferences To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-40 (30–40 min.) Purchasing Department cost drivers, multiple regression analysis (continuation of 10-39) (chapter appendix) The problem reports the exact t-values from the computer runs of the data Because the coefficients and standard errors given in the problem are rounded to three decimal places, dividing the coefficient by the standard error may yield slightly different t-values Regression is a well-specified regression model: Economic plausibility: Both independent variables are plausible and are supported by the findings of the Couture Fabrics study Goodness of fit: The r2 of 0.63 indicates an excellent goodness of fit Significance of independent variables: The t-value on # of POs is 2.14 while the t-value on # of Ss is 2.00 These t-values are either significant or border on significance Specification analysis: Results are available to examine the independence of residuals assumption The Durbin-Watson statistic of 1.90 indicates that the assumption of independence is not rejected Regression is consistent with the findings in Problem 10-39 that both the number of purchase orders and the number of suppliers are drivers of purchasing department costs Regressions 2, 3, and all satisfy the four criteria outlined in the text Regression has the best goodness of fit (0.63 for Regression compared to 0.42 and 0.39 for Regressions and 3, respectively) Most importantly, it is economically plausible that both the number of purchase orders and the number of suppliers drive purchasing department costs We would recommend that Lee use Regression over Regressions and Regression adds an additional independent variable (MP$) to the two independent variables in Regression This additional variable (MP$) has a t-value of –0.07, implying its slope coefficient is insignificantly different from zero The r2 in Regression (0.63) is the same as that in Regression (0.63), implying the addition of this third independent variable adds close to zero explanatory power In summary, Regression adds very little to Regression We would recommend that Lee use Regression over Regression Budgeted purchasing department costs for the Baltimore store next year are $485,384 + ($123.22 3,900) + ($2,952 10-39 110) = $1,290,662 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Multicollinearity is a frequently encountered problem in cost accounting; it does not arise in simple regression because there is only one independent variable in a simple regression One consequence of multicollinearity is an increase in the standard errors of the coefficients of the individual variables This frequently shows up in reduced t-values for the independent variables in the multiple regression relative to their t-values in the simple regression: Variables Regression 4: # of POs # of Ss Regression 5: # of POs # of Ss MP$ t-value in Multiple Regression t-value from Simple Regressions in Problem 10-39 2.14 2.00 2.43 2.28 1.95 1.84 –0.07 2.43 2.28 0.84 The decline in the t-values in the multiple regressions is consistent with some (but not very high) collinearity among the independent variables Pairwise correlations between the independent variables are: # of POs # of Ss # of POs MP$ # of Ss MP$ Correlation 0.29 0.27 0.34 There is no evidence of difficulties due to multicollinearity in Regressions and 5 are Decisions in which the regression results in Problems 10-39 and 10-40 could be useful Cost management decisions: Fashion Flair could restructure relationships with the suppliers so that fewer separate purchase orders are made Alternatively, it may aggressively reduce the number of existing suppliers Purchasing policy decisions: Fashion Flair could set up an internal charge system for individual retail departments within each store Separate charges to each department could be made for each purchase order and each new supplier added to the existing ones These internal charges would signal to each department ways in which their own decisions affect the total costs of Fashion Flair Accounting system design decisions: Fashion Flair may want to discontinue allocating purchasing department costs on the basis of the dollar value of merchandise purchased Allocation bases better capturing cause-and-effect relations at Fashion Flair are the number of purchase orders and the number of suppliers 10-40 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com 10-41 (40 min.) High-low method, alternative regression functions, accrual accounting adjustments, ethics Solution Exhibit 10-41A presents the two data plots The plot of engineering support reported costs and machine-hours shows two separate groups of data, each of which may be approximated by a separate cost function The problem arises because the plant records materials and parts costs on an ―as purchased‖ rather than an ―as used‖ basis The plot of engineering support restated costs and machine-hours shows a high positive correlation between the two variables (the coefficient of determination is 0.94); a single linear cost function provides a good fit to the data Better estimates of the cost relation result because Kennedy adjusts the materials and parts costs to an accrual accounting basis Highest observation of cost driver (August) Lowest observation of cost driver (September) Difference Cost Driver Machine-Hours 73 19 54 Reported Engineering Support Costs $ 617 1,066 $ (449) Difference between costs associated with highest and lowest observations of the cost driver Slope coefficient, b = Difference between highest and lowest observations of the cost driver = Error!= –$8.31 per machine-hour Constant (at highest observation of cost driver) = $ 617 – (–$8.31 73) = $1,224 Constant (at lowest observation of cost driver) = $1,066 – (–$8.31 19) = $1,224 The estimated cost function is y = $1,224 – $8.31X Cost Driver Restated Engineering Machine-Hours Support Costs Highest observation of cost driver (August) 73 $966 Lowest observation of cost driver (September) 19 370 Difference 54 $596 Difference between costs associated with highest and lowest observations of the cost driver Slope coefficient, b = Difference between highest and lowest observations of the cost driver $596 = = $11.04 per machine-hour 54 Constant (at highest observation of cost driver) Constant (at lowest observation of cost driver) The estimated cost function is y = $160 + $11.04 X 10-41 = = $ 966 – ($11.04 $ 370 – ($11.04 73) = $160 19) = $160 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com The cost function estimated with engineering support restated costs better approximates the regression analysis assumptions See Solution Exhibit 10-41B for a comparison of the two regressions Of all the cost functions estimated in requirements and 3, Kennedy should choose Regression using engineering support restated costs as best representing the relationship between engineering support costs and machine-hours The cost functions estimated using engineering support reported costs are mis-specified and not-economically plausible because materials and parts costs are reported on an ―as-purchased‖ rather than on an ―as-used‖ basis With respect to engineering support restated costs, the high-low and regression approaches yield roughly similar estimates The regression approach is technically superior because it determines the line that best fits all observations In contrast, the high-low method considers only two points (observations with the highest and lowest cost drivers) when estimating the cost function Solution Exhibit 10-41B shows that the cost function estimated using the regression approach has excellent goodness of fit (r2 = 0.94) and appears to be well specified Problems Kennedy might encounter include a A perpetual inventory system may not be used in this case; the amounts requisitioned likely will not permit an accurate matching of costs with the independent variable on a month-by-month basis b Quality of the source records for usage by engineers may be relatively low; e.g., engineers may requisition materials and parts in batches, but not use them immediately c Records may not distinguish materials and parts for maintenance from materials and parts used for repairs and breakdowns; separate cost functions may be appropriate for the two categories of materials and parts d Year-end accounting adjustments to inventory may mask errors that gradually accumulate month-by-month Picking the correct cost function is important for cost prediction, cost management, and performance evaluation For example, had United Packaging used Regression (engineering support reported costs) to estimate the cost function, it would erroneously conclude that engineering support costs decrease with machine-hours In a month with 60 machine-hours, Regression would predict costs of $1,393.20 – ($14.23 60) = $539.40 If actual costs turn out to be $800, management would conclude that changes should be made to reduce costs In fact, on the basis of the preferred Regression 2, support overhead costs are lower than the predicted amount of $176.38 + ($11.44 60) = $862.78––a performance that management should seek to replicate, not change On the other hand, if machine-hours worked in a month were low, say 25 hours, Regression would erroneously predict support overhead costs of $1,393.20 – ($14.23 25) = $1,037.45 If actual costs are $700, management would conclude that its performance has been very good In fact, compared to the costs predicted by the preferred Regression of $176.38 + ($11.44 25) = $462.38, the actual performance is rather poor Using Regression 1, management may feel costs are being managed very well when in fact they are much higher than what they should be and need to be managed ―down.‖ 10-42 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Since Kennedy is confident that the restated numbers are correct, he cannot change them just to please Mason If he does, he is violating the standards of integrity and objectivity for management accountants Kennedy should establish the correctness of the numbers with Mason, point out that he cannot change them, and also reason that this is a problem that could crop up each year and they should take a firm, ethical stand right away If Mason continues to apply pressure, Kennedy has no option but to escalate the problem to higher levels in the organization He should be prepared to resign, if necessary, rather than compromise his professional ethics Engineering Support Reported Costs SOLUTION EXHIBIT 10-41A Plots and Regression Lines for Engineering Support Reported Costs and Engineering Support Restated Costs $1,400 1,200 1,000 600 800 400 200 0 10 20 30 40 50 60 70 80 50 60 70 80 Engineering Support Restated Costs Machine-Hours $1,200 1,000 800 600 400 200 0 10 20 30 40 Machine-Hours 10-43 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com SOLUTION EXHIBIT 10-41B Comparison of Alternative Cost Functions for Engineering Support Costs at United Packaging Regression Dependent Variable: Engineering Support Reported Costs Negative slope relationship is economically implausible over the long run Regression Dependent Variable: Engineering Support Restated Costs Positive slope relationship is economically plausible Goodness of Fit r2 = 0.43 Moderate goodness of fit r2 = 0.94 Excellent goodness of fit Significance of Independent Variables t-statistic on machine-hours is statistically significant (t = –2.31), albeit economically implausible t-statistic on machine-hours is highly statistically significant (t=10.59) Linearity does not describe data very well Linearity describes data very well B Constant variance of residuals Appears questionable, although 12 observations not facilitate the drawing of reliable inferences Appears reasonable, although 12 observations not facilitate the drawing of reliable inferences C Independence of residuals Durbin-Watson = 2.26 Residuals serially uncorrelated Durbin-Watson = 1.31 Some evidence of serial correlation in the residuals D Normality of residuals Database too small to make reliable inferences Database too small to make reliable inferences Criterion Economic Plausibility Specification Analysis: A Linearity 10-44 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Chapter 10 Case U.S BREWING INDUSTRY: Cost Estimation (a) Using the high-low method: Highest Barrels Sold Lowest Barrels Sold Difference slope coefficient (b) constant (a) Ct = 17.037 Cost of Sales = = 5.844 Cost of Sales = 11.193 = $529.096 11.193 = $47.270 = $696.039 – ($47.270 17.037) = –$ 109.300 = –$109.300 + ($47.270 Vt) $696.039 $166.943 $529.096 A potential ambiguity in the high-low method is whether high-low is defined in terms of the dependent or independent variable In this case, the choice is important as the highest cost of sales figure is 2000, whereas the highest volume figure is 1996 The independent variable is used when determining the high and low observations as the causality runs from barrels produces to costs incurred (b) The results are reported in Regression #1 in Case Exhibit 1—see also Case Figure Evaluate the results: One approach is to use the following categorization: Economic Interpretation—Both high-low and ordinary least square (OLS) regression imply the expected positive relationship between costs and volume Statistical Specification—The major concern is with significant positive serial correlation in the residuals (the Durbin-Watson Statistic = 0.219) The consequence is that the estimated standard errors are underestimates of the underlying population values Goodness of Fit—The adjusted R2 of 0.864 for the OLS model indicates a reasonably good fit A plot of the data, however, reveals that the model does not closely fit the data in 1999 and 2000 when cost of sales increased while barrels sold decreased—see Case Figure OLS should yield more efficient (using a mean square error criterion) estimates than high-low as the technique is constructed to use all the data rather than two extreme points and to find the minimum mean square error set of estimates Concentrating on the two extreme observations may also result in ―true outliers‖ affecting the estimated costvolume relationship 10-45 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com The results are reported in Regression #2 in Case Exhibit A plot of the data is in Case Figure Relative to Regression #1, deflating by the WPIB results in several improvements in model specification: t-value of the slope coefficient (b) increases from 10.749 to 50.911, R2 increases from 0.864 to 0.993, and Durbin-Watson Statistic moves closer to (from 0.219 to 0.614) Note, however, there is still evidence of significant positive autocorrelation in the residuals—e.g., Durbin-Watson Statistic = 0.614 Problems include (a) (b) (c) (d) The Wholesale Price Index of Beer (WPIB) is an output-based index for the whole industry that need not be representative of the specific wholesale price changes for Ace One could build a firm specific index to overcome this problem The WPIB may not be a good proxy for changes in input prices to either the industry or Ace The ―Cost of Sales‖ series is an aggregate of the costs of labor, raw materials (malt, corn, barley, hops, etc.), depreciation, excise taxes, marketing, etc Deflating by the WPIB assumes that changes in the prices of the inputs can be well approximated by changes in the WPIB An alternative approach is to build a firm-specific index based on changes in prices of Ace’s inputs With any time-series index, issues of structural change arise The WPIB may reflect a nonconstant mix of beer products over time (malt, light, premium, super-premium, etc.) Moreover, even if the mix of the output was constant, the mix of the inputs may have changed in the 1986–2004 period, e.g., an increase in the capital/labor ratio through the construction of mechanized, high-volume breweries Data availability problems may arise due to the delay in publishing aggregate industry indexes Background information: Serial correlation in the residuals exists when there is a systematic pattern in the residuals such that knowledge of the residual at time t conveys information about the residuals at time t+1, t+2, etc A variety of reasons could cause serial correlation in the residuals of a linear model, e.g., (i) Underlying model is nonlinear—two possible rationales for a nonlinear model are: costs are ―sticky‖ downwards—i.e., when volume decreases by 10%, costs not decrease as much as the linear model predicts Fixed capacity costs could potentially be important for Ace in the 2000 to 2004 period when volume declined from 17.037 to 15.091 million barrels ―experience curve‖ phenomenon could result in costs increasing less than the linear model predicts (ii) Underlying model is linear but includes more than one variable and the omitted variable results in the ―residuals‖ being serially correlated Omitted variables could include the number of employees and the number of advertisements placed in various media 10-46 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com (iii) Activity levels over time have high percentage of commonality It is a common finding that models estimated in levels exhibit serial correlation—see C W J Granger and P Newbold, ―Spurious Regressions in Econometrics,‖ Journal of Econometrics (No 2, 1974) Serial correlation (in general) affects the efficiency (but not the unbiasedness) of the OLS regression estimates of a and b With positive (negative) correlation, the estimates of the standard errors will be understated (overstated) relative to the underlying population standard errors Thus, one may infer that the parameter estimates are more (less) precise than they actually are Ways to detect serial correlation in the residuals include (i) Visual inspection of the residuals (ii) Computation of the Durbin-Watson statistic which tests for first-order serial correlation The relevant values for this statistic, using a 5% significance level for one independent variable, are: Number of Observations 18 19 Positive Autocorrelation DW lower DW upper 1.03 1.26 1.06 1.28 Negative Autocorrelation DW lower DW upper 2.74 2.97 2.72 2.94 The results are reported in Regression #3 in Case Exhibit There is substantial evidence that the serial correlation problem found in question #2 has been considerably reduced, e.g., the Durbin-Watson deviates much less from than previously (2.521 in #3 versus 0.614 in #2 and 0.219 in #1) The best choice is regression #3 The Durbin-Watson statistic goes up from 219 in regression #1, and 614 in regression #2 to 2.521 in regression #3 This indicates that the serial correlation problem found in regressions #1 and #2 has been reduced The t-value of b in regression #3 is lower than that of regression #2, but higher than that of regression #1 The R2 in regression #3 falls between that of #1 and #2, indicating that there is a reasonably good fit for this model Taken together, the significantly improved Durbin-Watson statistic of regression #3, combined with a reasonable t-value for b and the R2, makes this the preferred model 10-47 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Case Exhibit Regression #1: Ct = a + bVt Ct = a + bVt Pt Ct Ct #3: Pt Pt #2: a + b(Vt – Vt-1) a t-value b t-value R2 DurbinWatson –267.10 –3.918 59.528 10.749 0.864 0.219 –30.517 –2.280 55.360 50.910 0.993 0.614 4.660 1.453 47.034 12.989 0.908 2.521 Case Figure Plot of Cost-Volume Data Case Figure Plot of Deflated Cost Versus Volume 10-48 ... overhead costs Total costs Add margin of 20% of total costs Target revenues Picking machine-hours rather than the number of batches as the cost driver will cause Chu to underestimate costs and choose... analysis, activity-based costing, choosing cost drivers Solution Exhibit 10- 33A presents the plots and regression line of machine–hours on support overhead Solution Exhibit 10- 33B presents the plots... 120,000 100 ,000 80,000 90,000 100 ,000 110, 000 Machine-Hours 10- 20 120,000 130,000 To download more slides, ebook, solutions and test bank, visit http://downloadslide.blogspot.com Solution Exhibit 10- 30