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Unformatted text preview: CHAPTER 10 DETERMINING HOW COSTS BEHAVE 101 The two assumptions are 1. Variat ions in the level o f a single act ivit y (the cost driver) explain t he variat ions in the related total costs. 2. Cost behavior is approximated by a linear cost funct ion within the relevant range. A linear cost funct ion is a cost funct ion where, within the relevant range, the graph of total costs versus the level o f a single act ivit y forms a straight line. 102 Three alternat ive linear cost functions are 1. Variable cost funct ion––a cost funct ion in which total costs change in proportion to the changes in the level o f activit y in the relevant range. 2. Fixed cost funct ion––a cost funct ion in which total costs do not change wit h changes in the level o f act ivit y in the relevant range. 3. Mixed cost funct ion––a cost funct ion that has both variable and fixed elements. Total costs change but not in proportion to the changes in the level of act ivit y in the relevant range. 103 A linear cost funct ion is a cost function where, within the relevant range, the graph o f total costs versus the level of a single act ivit y related to that cost is a straight line. An example o f a linear cost funct ion is a cost funct ion for use of a telephone line where the terms are a fixed charge o f $10,000 per year plus a $2 per minute charge for phone use. A nonlinear cost funct io n is a cost funct ion where, within the relevant range, the graph o f total costs versus the level o f a single activit y related to that cost is not a straight line. Examples include econo mies o f scale in advert ising where an agency can double the number o f advertisements for less than twice the costs, stepcost funct ions, and learningcurvebased costs. 104 No. High correlat ion merely indicates that the two variables mo ve together in the data examined. It is essent ial also to consider econo mic plausibilit y before making inferences about cause and effect. Without any economic plausibilit y for a relationship, it is less likely that a hig h level of correlation observed in one set of data will be similarly found in other sets of data. 105 1. 2. 3. 4. Four approaches to estimat ing a cost funct ion are Industrial engineering method. Conference method. Account analysis method. Quant itative analysis o f current or past cost relat ionships. 106 The conference method est imates cost funct ions on the basis of analysis and opinio ns about costs and their drivers gathered fro m various departments of a co mpany (purchasing, process engineering, manufacturing, emplo yee relat ions, etc.). Advantages o f the conference method include 1. The speed with which cost estimates can be develo ped. 2. The pooling of knowledge fro m experts across functional areas. 3. The improved credibilit y o f the cost funct ion to all personnel. 101 107 The account analysis method est imates cost funct ions by classifying cost accounts in the subsidiary ledger as variable, fixed, or mixed wit h respect to the ident ified level o f activit y. Typically, managers use qualitat ive, rather than quant itative, analys is when making these cost classificat ion decisio ns. 108 The six steps are 1. Choose the dependent variable (the variable to be predicted, which is so me type of cost). 2. Ident ify the independent variable or cost driver. 3. Collect data on the dependent variable and the cost driver. 4. Plot the data. 5. Estimate the cost funct ion. 6. Evaluate the cost driver of the estimated cost functio n. Step 3 typically is the most difficult for a cost analyst. 109 Causalit y in a cost function runs fro m the cost driver to the dependent variable. Thus, choosing the highest observat ion and the lowest observat ion of the cost driver is appropriate in the highlow method. 1010 1. 2. 3. Three criteria important when choosing amo ng alternat ive cost funct ions are Economic plausibilit y. Goodness of fit. Slope of the regressio n line. 1011 A learning curve is a function that measures how laborhours per unit decline as units o f production increase because workers are learning and becoming better at their jo bs. Two models used to capture different forms of learning are 1. Cumulat ive averaget ime learning model. The cumulat ive average t ime per unit declines by a constant percentage each time the cumulat ive quant it y of unit s produced doubles. 2. Incremental unittime learning model. The incremental t ime needed to produce the last unit declines by a constant percentage each t ime the cumulat ive quantit y o f units produced doubles. 1012 Frequent ly encountered problems when co llecting cost data on variables included in a cost funct ion are 1. The time period used to measure the dependent variable is not properly matched wit h the time period used to measure the cost driver(s). 2. Fixed costs are allo cated as if they are variable. 3. Data are either not available for all observations or are not uniformly reliable. 4. Extreme values of observations occur. 5. A ho mogeneous relationship between the individual cost items in the dependent variable cost pool and the cost driver(s) does not exist. 6. The relat ionship between the cost and the cost driver is not stationary. 7. Inflat ion has occurred in a dependent variable, a cost driver, or both. 102 1013 Four key assumptions examined in specificat ion analysis are 1. Linearit y of relat ionship between the dependent variable and the independent variable within the relevant range. 2. Constant variance of residuals for all values of the independent variable. 3. Independence of residuals. 4. Normal distribut ion of residuals. 1014 No. A cost driver is any factor whose change causes a change in the total cost of a related cost object. A causeandeffect relat ionship underlies selection of a cost driver. Some users o f regression analys is include numerous independent variables in a regressio n model in an attempt to maximize goodness of fit, irrespect ive o f the econo mic plausibilit y o f the independent variables included. Some of the independent variables included may not be cost drivers. 1015 No. Mult ico llinearit y exists when two or more independent variables are highly correlated with each other. 1016 (10 min.) Estimating a cost function. 1. Difference in costs Slope coefficient = Difference in machinehours = $5, 400 - $4, 000 10, 000 - 6, 000 $1, 400 = $0.35 per machinehour 4, 000 = Constant = Total cost – (Slope coefficient ´ Quantit y of cost driver) = $5,400 – ($0.35 ´ 10,000) = $1,900 = $4,000 – ($0.35 ´ 6,000) = $1,900 The cost funct ion based on the two observations is Maintenance costs = $1,900 + $0.35 ´ Machinehours 2. The cost funct ion in requirement 1 is an est imate of how costs behave within the relevant range, not at cost levels outside the relevant range. If there are no months wit h zero machine hours represented in the maintenance account, data in that account cannot be used to estimate the fixed costs at the zero machinehours level. Rather, the constant component of the cost funct ion provides the best available starting po int for a straight line that approximates how a cost behaves within the relevant range. 103 1017 (15 min.) Identifying variable, fixed, and mixedcost functions. 1. 2. See Solut ion Exhibit 1017. 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 1 2 3 Cost Function Fixed Mixed Variable 3. SOLUTION EXHIBIT 1017 Plots of Car Rental Contracts Offered by Pacific Corp. Co n tract 1: Fi xe d C o s ts $160 Car R e n tal Co sts 140 120 100 80 60 40 20 0 0 50 100 150 M il e s Trave l e d p e r D ay Co n tract 2: M i xe d Co s ts $160 140 120 100 80 60 40 20 0 0 100 50 M il e s Trave l e d p e r D ay 150 C ar Re n t al C os ts Co n tract 3: Vari ab l e Co s ts Car R e n tal Co sts $160 140 120 100 80 60 40 20 0 0 50 100 M il e s Trave l e d p e r D ay 150 104 1018 1. 2. 3. 4. 5. 6. 7. 8. 9. (20 min.) Various costbehavior patterns. K B G J Note that A is incorrect because, alt hough the cost per pound eventually equals a constant at $9.20, the total do llars o f cost increases linearly fro m that point onward. I The total costs will be the same regardless o f the volume level. L F This is a classic stepcost function. K C 1019 (30 min.) Matching graphs with descriptions of cost and revenue behavior. a. b. c. d. e. f. (1) (6) (9) (2) (8) (10) A stepcost function. It is data plotted on a scatter diagram, showing a linear variable cost funct ion wit h constant variance of residuals. The constant variance o f residuals implies that there is a uniform dispersio n of the data points about the regression line. g. h. (3) (8) 1020 (15 min.) Account analysis method. 1. Variable costs: Car wash labor $260,000 Soap, cloth, and supplies 42,000 Water 38,000 Electric power to move conveyor belt 72,000 Total variable costs $412,000 Fixed costs: Depreciat ion $ 64,000 Salaries 46,000 Total fixed costs $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 do not vary wit h the number of cars washed. If the conveyor belt moves regardless o f the number of cars on it, the electricit y costs to power the conveyor belt would be a fixed cost. 2. Variable costs per car = $412,000 = $5.15 per car 80,000 Total costs estimated for 90,000 cars = $110,000 + ($5.15 × 90,000) = $573,500 105 1021 ( 15 min.) Account analysis 1. The electricit y cost is clearly variable since it ent irely depends on number of kilowatt hours used. The Waste Management contract is a fixed amount if the cost object is not number of quarters, since it does not depend on amount of activit y or output during the quarter. The telephone cost is a mixed cost because there is a fixed component and a component that depends on number of calls made. 2. The electricit y rate is $573 ÷ 3000 kw hour = $0.191 per kw hour The waste management fixed cost is $270 for three months, or $90 (270 ÷ 3) per month. The telephone cost is $20 + ($0.03 per call ´ 1,200 calls) = $56 Adding them together we get: Fixed cost of utilit ies = $90 (waste management) + $20 (telephone) = $110 Utilities cost = $110 + ($0.191 per kw hour kw hours used) + ($0.03 per call ´ number of calls) per month Utilit cos 3. or F ies t = $146 + ($0.191 per kw hour 4000 hours) + ($0.03 per call ´ 1,200 calls) f ebruary = $146 + $764 + $36 = $910 106 1022(30 min.) Account analysis method. 1. Manufacturing cost classification for 2009: 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 0 $300,000 225,000 37,500 11,250 30,000 30,000 0 0 $633,750 $ 0 0 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 0 $8.45 Account Direct materials Direct manufacturing labor Power Supervision labor Materialshandling labor Maintenance labor Depr eciation Rent, property taxes, admin Total Total manufacturing cost for 2009 = $948,750 Variable costs in 2010: Unit Variable Increase in Cost per Variable Variable Cost Unit for Percentage Cost per Unit Total Variable 2009 Increase per Unit for 2010 Costs for 2010 (6) (7) (8) = (6) ´ (7) (9) = (6) + (8) (10) = (9) ´ 80,000 $4.00 3.00 0.50 0.15 0.40 0.40 0 0 $8.45 5% 10 0 0 0 0 0 0 $0.20 0.30 0 0 0 0 0 0 $0.50 $4.20 3.30 0.50 0.15 0.40 0.40 0 0 $8.95 $336,000 264,000 40,000 12,000 32,000 32,000 0 0 $716,000 Account Direct materials Direct manufacturing labor Power Supervision labor Materialshandling labor Maintenance labor Depr eciation Rent, property taxes, admin. Total 107 Fixed and total costs in 2010: Dollar Fixed Increase in Fixed Costs Costs Percentage Fixed Costs for 2010 for 2009 Increase (13) = (14) = (11) (12) (11) ´ (12) (11) + (13) Variable Costs for 2010 (15) Total Costs (16) = (14) + (15) Account Direct materials $ 0 Direct manufacturing labor 0 Power 0 Supervisio n labor 45,000 Materialshandling labor 30,000 Maintenance labor 45,000 Depreciat ion 95,000 Rent, property taxes, admin. 100,000 Total $315,000 0% 0 0 0 0 0 5 7 $ 0 0 0 0 0 0 4,750 7,000 $11,750 $ 0 $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 99,750 0 99,750 107,000 0 107,000 $326,750 $716,000 $1,042,750 Total manufacturing costs for 2010 = $1,042,750 2. Total cost per unit, 2009 Total cost per unit, 2010 $948,750 = $12.65 75,000 $1,042,750 = = $13.03 80,000 = 3. Cost classificat ion into variable and fixed costs is based on qualitative, rather than quant itative, analys is. How good the classificat ions are depends on the knowledge o f individua l managers who classify the costs. Gower may want to undertake quant itative analysis o f costs, using regressio n analys is on timeseries or crosssect ional data to better estimate the fixed and variable co mponents of costs. Better knowledge of fixed and variable costs will help Gower to better price his products, to know when he is getting a posit ive contribut ion margin, and to better manage costs. 108 1023 (15–20 min.) Estimating a cost function, highlow method. 1. The key point to note is that the problem provides highlow values o f 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 co lumn (3) below), and then use those values to estimate the funct ion using the highlow method. Cost Driver: Annual Round Trips (X) (1) 2,000 1,000 1,000 Operating Cost per RoundTrip (2) $300 $350 Annual Operating Cost (Y) (3) = (1) ´ (2) $600,000 $350,000 $250,000 Highest observat ion of cost driver Lowest observat ion of cost driver Difference Slope coefficient = $250,000 ¸ 1,000 = $250 per roundtrip Constant = $600,000 – ($250 ´ 2,000) = $100,000 The est imated relat ionship is Y = $100,000 + $250 X; where Y is the annual operating cost of a helicopter and X represents the number of round trips it makes annually. 2. The constant a (estimated as $100,000) represents the fixed costs of operating a helicopter, irrespect ive o f the number o f round trips it makes. This would include items such as insurance, registration, depreciat ion on the aircraft, and any fixed co mponent of pilot and crew salaries. The coefficient b (est imated as $250 per roundtrip) 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 perflight basis. 3. 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 + $250 X X = 1,200 Y = $100,000 + $250 ´ 1,200 = $100,000 + $300,000 = $400,000 Wit h 10 helicopters in its fleet, Reisen’s est imated operating budget is 10 ´ $400,000 = $4,000,000. 109 1024 (20 min.) Estimating a cost function, highlow method. 1. See Solut ion Exhibit 1024. There is a posit ive relat ionship between the number o f service reports (a cost driver) and the customerservice depart ment costs. This relat ionship is economically plausible. 2. Number of CustomerService Service Reports Department Costs Highest observat ion of cost driver 436 $21,890 Lowest observat ion of cost driver 122 12,941 Difference 314 $ 8,949 Customerservice department costs = a + b (number of service reports) $8, 949 = $28.50 per service report 314 Constant (a) = $21,890 – $28.50 ´ 436 = $9,464 = $12,941 – $28.50 ´ 122 = $9,464 Customerservice = $9,464 + $28.50 (number of service reports) department costs Slopecoefficient (b) = 3. Other possible cost drivers of customerservice department costs are: a. Number o f products replaced wit h a new product (and the do llar value o f the new products charged to the customerservice department). b. Number of products repaired and the time and cost of repairs. SOLUTION EXHIBIT 1024 Plot of Number of Service Reports versus CustomerService Dept. Costs for Capitol Products CustomerService Department Cost s $25,000 20,000 15,000 10,000 5,000 $0 0 100 200 300 400 500 Number of Service Reports 1010 1025 (30–40 min.) Linear cost approximation. 1. Slope coefficient (b) = Difference in cost $529,000 - $400,000 = = $43.00 Difference in laborhours 7,000 - 4,000 Constant (a) = $529,000 – ($43.00 × 7,000) = $228,000 Cost funct ion = $228,000 + $43.00 ´ professio nal laborhours The linear cost funct ion is plotted in Solut ion Exhibit 1025. No, the constant component of the cost funct ion does not represent the fixed overhead cost of the Memphis Group. The relevant range o f professio nal laborhours is fro m 3,000 to 8,000. The constant component provides the best available starting po int for a straight line that approximates how a cost behaves wit hin the 3,000 to 8,000 relevant range. 2. A co mparison at various levels o f professio nal laborhours follows. The linear cost funct ion is based on the formula o f $228,000 per month plus $43.00 per professio nal laborhour. Total overhead cost behavior: Month 1 Professio nal laborhours 3,000 Actual total overhead costs $340,000 Linear approximat ion 357,000 Actual minus linear approximat ion $(17,000) Month 2 Month 3 Month 4 Month 5 Month 6 4,000 5,000 6,000 7,000 8,000 $400,000 $435,000 $477,000 $529,000 $587,000 400,000 443,000 486,000 529,000 572,000 $ 0 $ (8,000) $ (9,000) $ 0 $ 15,000 The data are shown in So lut ion Exhibit 1025. The linear cost funct ion overstates costs by $8,000 at the 5,000hour level and understates costs by $15,000 at the 8,000hour level. 3. Contribut ion before deducting incremental overhead Incremental overhead Contribut ion after incremental overhead The total contribut ion margin actually forgone is $3,000. Based on Actual $38,000 35,000 $ 3,000 Based on Linear Cost Function $38,000 43,000 $ (5,000) 1011 SOLUTION EXHIBIT 1025 Linear Cost Funct ion Plot of Professio nal LaborHours on Total Overhead Costs for Memphis Consult ing Group $700,000 Total Overhead Costs 600,000 500,000 400,000 300,000 200,000 100,000 0 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 Professional LaborHours Billed 1026 (20 min.) Costvolumeprofit and regression analysis. 1a. Average cost of manufacturing = Total manufactur ng costs i Number of bicycle frames $900,000 = $30 per frame 30,000 = This cost is greater than the $28.50 per frame that Ryan has quoted. 1b. Garvin cannot take the average manufacturing cost in 2009 of $30 per frame and mult iply it by 36,000 bicycle frames to determine the total cost of manufacturing 36,000 bicycle frames. The reason is that some o f the $900,000 (or equivalent ly the $30 cost per frame) are fixed costs and so me are variable costs. Without dist inguishing fixed fro m variable costs, Garvin cannot determine the cost of manufacturing 36,000 frames. For example, if all costs are fixed, the manufacturing costs of 36,000 frames will cont inue to be $900,000. If, however, all costs are variable, the cost of manufacturing 36,000 frames would be $30 ´ 36,000 = $1,080,000. If so me costs are fixed and so me are variable, the cost of manufacturing 36,000 frames will be somewhere between $900,000 and $1,080,000. Some students could argue that another reason for not being able to determine the cost of manufacturing 36,000 bicycle frames is that not all costs are output unitlevel costs. If so me costs are, for example, batchlevel costs, more informat ion would be needed on the number o f 1012 batches in which the 36,000 bicycle frames would be produced, in order to determine the cost of manufacturing 36,000 bicycle frames. 2. Expected cost to make = $432,000 + $15 ´ 36,000 36,000 bicycle frames = $432,000 + $540,000 = $972,000 Purchasing bicycle frames fro m Ryan will cost $28.50 ´ 36,000 = $1,026,000. Hence, it will cost Garvin $1,026,000 - $972,000 = $54,000 more to purchase the frames from Rya n rather than manufacture them inhouse. 3. Garvin would need to consider several factors before being confident that the equat ion in requirement 2 accurately predicts the cost of manufacturing bicycle frames. a. Is the relat ionship between total manufacturing costs and quant it y of bicycle frames economically plausible? For example, is the quantit y of bic ycles made the only cost driver or are there other costdrivers (for example batchlevel costs of setups, productionorders or material handling) that affect manufacturing costs? b. How good is the goodness o f fit ? That is, how well does the est imated line fit the data? c. Is the relat ionship between the number o f bicycle frames produced and total manufacturing costs linear? d. Does the slope of the regressio n line indicate that a strong relat ionship exists between manufacturing costs and the number of bicycle frames produced? e. Are there any data problems such as, for example, errors in measuring costs, trends in prices o f materials, labor or overheads that might affect variable or fixed costs over time, extreme values of observat ions, or a nonstationary relat ionship over time between total manufacturing costs and the quant it y of bicycles produced? f. How is inflat ion expected to affect costs? g. Will Ryan supply highqualit y bicycle frames on time? 1013 1027 (25 min.) Regression analysis, service company. 1. Solution Exhibit 1027 plots the relationship between laborhours and overhead costs and shows the regressio n line. y = $48,271 + $3.93 X Economic plausibility. Laborhours appears to be an econo mically plausible driver o f overhead costs for a catering company. Overhead costs such as scheduling, hiring and training o f workers, and managing the workforce are largely incurred to support labor. Goodness of fit The vert ical differences between actual and predicted costs are extremely small, indicat ing a very good fit. The good fit indicates a strong relat ionship between the labor hour cost driver and overhead costs. Slope of regression line. The regressio n line has a reasonably steep slope fro m left to right. Given the small scatterof the observat ions around the line, the posit ive slope indicates that, on average, overhead costs increase as laborhours increase. 2. The regressio n analysis indicates that, within the relevant range of 2,500 to 7,500 labor hours, the variable cost per person for a cocktail party equals: Food and beverages Labor (0.5 hrs. ´ $10 per hour) Variable overhead (0.5 hrs ´ $3.93 per laborhour) Total variable cost per person $15.00 5.00 1.97 $21.97 3. To earn a posit ive contribut ion margin, the minimum bid for a 200person cocktail part y would be any amount greater than $4,394. This amount is calculated by mult iplying the variable cost per person of $21.97 by the 200 people. At a price above the variable costs of $4,394, Bob Jones will be earning a contribut ion margin toward coverage of his fixed costs. Of course, Bob Jones will consider other factors in developing his bid including (a) an analys is of the competit ion––vigorous compet it ion will limit Jones’s abilit y to obtain a higher price (b) a determinat ion of whether or not his bid will set a precedent for lower prices––overall, the pr ices Bob Jones charges should generate enough contribution to cover fixed costs and earn a reasonable profit, and (c) a judgment of how representative past historical data (used in the regression analys is) is about future costs. SOLUTION EXHIBIT 1027 Regressio n Line of LaborHours on Overhead Costs for Bob Jones’s Catering Co mpany $90,000 80,000 70,000 Over head Costs 60,000 50,000 40,000 30,000 20,000 10,000 0 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 Cost Driver: LaborHours 1014 1028 Highlow, regression 1. Pat will pick the highest point of act ivit y, 3400 parts (August) at $20,500 of cost, and the lowest point of act ivit y, 1910 parts (March) at $11560. Cost driver: Quantity Purchased Cost 3,400 $20,500 1,910 11,560 1,490 $ 8,940 Highest observat ion of cost driver Lowest observat ion of cost driver Difference Purchase costs = a + b ´ Quantit y purchased $8, 940 Slope coefficient (b) = = $6 per part 1, 490 Constant (a) = $20,500 ─ ($6 ´ 3,400) = $100 The equation Pat gets is: Purchase costs = $100 + ($6 ´ Quant it y purchased) 2. Using the equation above, the expected purchase costs for each month will be: Purchase Quantity Expected 3,000 parts 3,200 2,500 Month October November December Formula Expected cost y = $100 + ($6 ´ 3,000) $18,100 y = $100 + ($6 ´ 3,200) 19,300 y = $100 + ($6 ´ 2,500) 15,100 3. Economic Plausibilit y: Clearly, the cost of purchasing a part is associated with the quant it y purchased. Goodness of Fit: As seen in So lut ion Exhibit 1028, the regression line fits the data well. The vert ical distance between the regressio n line and observat ions is small. Significance of the Independent Variable: The relatively steep slope of the regression line suggests that the quant it y purchased is correlated with purchasing cost for part #4599. 1015 SOLUTION EXHIBIT 1028 Serth Manufacturing Purchase Costs for Part #4599 $25,000 Cost of Purchase $20,000 $15,000 $10,000 $5,000 $0 0 1,000 2,000 Quantity Purchased 3,000 4,000 According to the regression, Pat’s original est imate of fixed cost is too low given all the data points. The original slope is too steep, but only by 16 cents. So, the variable rate is lower but the fixed cost is higher for the regression line than for the highlow cost equation. The regressio n is the more accurate estimate because it uses all available data (all nine data points) while the highlow method only relies on two data points and may therefore miss so me important informat ion contained in the other data. 4. Using the regression equat ion, the purchase costs for each month will be: Purchase Quantity Month Expected Formula Expected cost October 3,000 parts y = $501.54 + ($5.84 ´ 3,000) $18,022 November 3,200 y = $501.54 + ($5.84 ´ 3,200) 19,190 December 2,500 y = $501.54 + ($5.84 ´ 2,500) 15,102 Alt hough the two equations are different in both fixed element and variable rate, within the relevant range they give similar expected costs. In fact the estimated costs for December vary by only $2. This implies that the high and low points of the data are a reasonable representation of the total set of points within the relevant range. 1016 1029 (20 min.) Learning curve, cumulative averagetime learning model. The direct manufacturing laborhours (DMLH) required to produce the first 2, 4, and 8 units given the assumpt ion of a cumulat ive averaget ime learning curve of 90%, is as fo llows: 90% Learning Curve Cumulative Number of Units (X) (1) 1 2 3 4 5 6 7 8 Cumulative Average Time per Unit (y): Labor Hours (2) 3,000 2,700 = (3,000 ´ 0.90) 2,539 2,430 = (2,700 ´ 0.90) 2,349 2,285 2,232 2,187 = (2,430 ´ 0.90) Cumulative Total Time: LaborHours (3) = (1) ´ (2) 3,000 5,400 7,616 9,720 11,745 13,710 15,624 17,496 Alternat ively, to compute the values in co lumn (2) we could use the formula y = aXb where a = 3,000, X = 2, 4, or 8, and b = – 0.152004, which gives – when X = 2, y = 3,000 ´ 2 0.152004 = 2,700 – when X = 4, y = 3,000 ´ 4 0.152004 = 2,430 – when X = 8, y = 3,000 ´ 8 0.152004 = 2,187 Variable Costs of Producing 2 Units 4 Units 8 Units $160,000 $320,000 $ 640,000 135,000 81,000 $376,000 243,000 145,800 $708,800 437,400 262,440 $1,339,840 Direct materials $80,000 ´ 2; 4; 8 Direct manufacturing labor $25 ´ 5,400; 9,720; 17,496 Variable manufacturing overhead $15 ´ 5,400; 9,720; 17,496 Total variable costs 1017 1030 (20 min.) Learning curve, incremental unittime learning model. 1. The direct manufacturing laborhours (DMLH) required to produce the first 2, 3, and 4 units, given the assumpt ion of an incremental unittime learning curve of 90%, is as fo llows: 90% Learning Curve Cumulative Individual Unit Time for Xth Cumulative Total Time: Number of Units (X) Unit (y): Labor Hours LaborHours (1) (2) (3) 1 3,000 3,000 2 2,700 = (3,000 ´ 0.90) 5,700 3 2,539 8,239 4 2,430 = (2,700 ´ 0.90) 10,669 Values in co lumn (2) are calculated using the formula y = aXb where a = 3,000, X = 2, 3, or 4, and b = – 0.152004, which gives – when X = 2, y = 3,000 ´ 2 0.152004 = 2,700 – when X = 3, y = 3,000 ´ 3 0.152004 = 2,539 – when X = 4, y = 3,000 ´ 4 0.152004 = 2,430 Variable Costs of Producing 2 Units 3 Units 4 Units $160,000 $240,000 $ 320,000 142,500 85,500 $388,000 205,975 123,585 $569,560 266,725 160,035 $746,760 Direct materials $80,000 ´ 2; 3; 4 Direct manufacturing labor $25 ´ 5,700; 8,239; 10,669 Variable manufacturing overhead $15 ´ 5,700; 8,239; 10,669 Total variable costs 2. Incremental unittime learning model (fro m requirement 1) Cumulat ive averaget ime learning model (fro m Exercise 1028) Difference Variable Costs of Producing 2 Units 4 Units $388,000 $746,760 376,000 708,800 $ 12,000 $ 37,960 Total variable costs for manufacturing 2 and 4 units are lower under the cumulat ive averaget ime learning curve relat ive to the incremental unitt ime learning curve. Direct manufacturing laborhours required to make addit ional unit s decline more slowly in the incremental unittime learning curve relat ive to the cumulat ive averagetime learning curve when the same 90% factor is used for both curves. The reason is that, in the incremental unittime learning curve, as the number of unit s double only the last unit produced has a cost of 90% of the init ial cost. In the cumulative averagetime learning model, doubling the number o f unit s causes the average cost of all the addit ional units produced (not just the last unit) to be 90% of the init ia l cost. 1018 1031 (25 min.) Highlow method. 1. Highest observat ion of cost driver Lowest observat ion of cost driver Difference MachineHours 125,000 85,000 40,000 Maintenance Costs $250,000 170,000 $ 80,000 Maintenance costs = a + b ´ Machinehours Slope coefficient (b) = Constant (a) $80,000 = $2 per machinehour 40,000 = $250,000 – ($2 × 125,000) = $250,000 – $250,000 = $0 o r Constant (a) = $170,000 – ($2 × 85,000) = $170,000 – $170,000 = $0 Maintenance costs = $2 × Machinehours 2. SOLUTION EXHIBIT 1031 Plot and HighLow Line of MachineHours on Maintenance Costs $260,000 240,000 M aintenance Costs 220,000 200,000 180,000 160,000 140,000 120,000 100,000 80,000 90,000 100,000 110,000 120,000 130,000 MachineHours 1019 Solution Exhibit 1031 presents the highlow line. Economic plausibility.The cost funct ion shows a posit ive econo mically plausible relat ionship between machinehours and maintenance costs. There is a clearcut engineering relat ionship o f higher machinehours and maintenance costs. Goodness of fit.The highlow line appears to “fit” the data well. The vert ical differences between the actual and predicted costs appear to be quite small. Slope of highlow line.The slope of the line appears to be reasonably steep indicating that, on average, maintenance costs in a quarter vary with machinehours used. 3. Using the cost funct ion est imated in 1, predicted maintenance costs would be $2 × 90,000 = $180,000. Howard should budget $180,000 in quarter 13 because the relat ionship between machine hours and maintenance costs in So lut ion 1031 is economically plausible, has an excellent goodness o f fit, and indicates that an increase in machinehours in a quarter causes maintenance costs to increase in the quarter. 1032 (30min.) Highlow method and regression analysis. 1. See Solut ion Exhibit 1032. SOLUTION EXHIBIT 1032 Plot, Highlow Line, and Regressio n Line for Number of Customers per Week versus Weekly Total Costs for Happy Business Co llege Restaurant Weekly Total Costs $25,000 $20,000 $15,000 $10,000 $5,000 $0 0 200 400 600 800 1000 Number of Customers per Week Regression line Highlow line 1020 2. Number of Customers per week Highest observation of cost driver (Week 9) 925 Lowest obser vation of cost driver (Week 2) 745 Differ ence 180 Weekly total costs = a + b (number of customers per week) Weekly Total Costs $20,305 16,597 $ 3,708 Slope coefficient (b) = $3,708 = $20.60 per customer 180 Constant (a) = $20,305 – ($20.60 ´ 925) = $1,250 = $16,597 – ($20.60 ´ 745) = $1,250 Weekly total costs = $1,250 + $20.60 (number of customers per week) See highlow line in So lution Exhibit 1032. 3. Solut ion Exhibit 1032 presents the regressio n line. Economic Plausibility. The cost funct ion shows a posit ive econo mically plausible relat ionship between number of customers per week and weekly total restaurant costs. Number of customers is a plausible cost driver since both cost of food served and amount of time the waiters must work (and hence their wages) increase with the number of customers served. Goodness of fit. The regression line appears to fit the data well. The vert ical differences between the actual costs and the regression line appear to be quite small. Significance of independent variable. The regression line has a steep posit ive slope and increases by more than $19 for each addit ional customer. Because the slope is not flat, there is a strong relat ionship between number of customers and total restaurant costs. The regressio n line is the more accurate estimate of the relationship between number of customers and total restaurant costs because it uses all available data points while the highlow method relies only on two data points and may therefore miss some informat ion contained in the other data points. Nevertheless, the graphs of the two lines are fairly close to each other, so the cost funct ion est imated using the highlow method appears to be a good approximation o f the cost funct ion est imated using the regression method. 4. The cost estimate by the two methods will be equal where the two lines intersect. You can find the number of customers by setting the two equations to be equal and so lving for x. That is, $1,250 + $20.60x = $2,453 + $19.04x $20.60 x ─ $19.04 x = $2,453 ─ $1,250 1.56 x = 1,203 x = 771.15 or ≈ 771customers. 1021 1033 (30-40 min.) Highlow method, regression analysis. 1. Solution Exhibit 1033 presents the plots of advertising costs on revenues. SOLUTION EXHIBIT 1033 Plot and Regressio n Line of Advertising Costs on Revenues $90,000 80,000 70,000 60,000 R evenues 50,000 40,000 30,000 20,000 10,000 0 $0 $1,000 $2,000 $3,000 $4,000 $5,000 Advertising Costs 2. Solution Exhibit 1033 also shows the regressio n line o f advertising costs on revenues. We evaluate the est imated regressio n equat ion using the criteria of econo mic plausibilit y, goodness of fit, and slope of the regressio n line. Economic plausibility. Advert ising costs appears to be a plausible cost driver o f revenues. Restaurants frequent ly use newspaper advert ising to promote their restaurants and increase their patronage. Goodness of fit. The vertical differences between actual and predicted revenues appears to be reasonably small. This indicates that advertising costs are related to restaurant revenues. Slope of regression line. The slope o f the regressio n line appears to be relat ively steep. Given the small scatter of the observat ions around the line, the steep slope indicates that, on average, restaurant revenues increase wit h newspaper advertising. 1022 3. The highlow method would est imate the cost function as fo llows: Advertising Costs Highest observat ion of cost driver $4,000 Lowest observat ion of cost driver 1,000 Difference $3,000 Revenues = a + (b ´ advertising costs) Slope coefficient (b) Constant (a) = $25,000 = 8.333 $3,000 Revenues $80,000 55,000 $25,000 = $80,000 - ($4,000 ´ 8.333) = $80,000 - $33,332 = $46,668 or Constant (a) = $55,000 - ($1,000 ´ 8.333) = $55,000 - $8,333 = $46,667 Revenues 4. = $46,667 + (8.333 ´ Advertising costs) The increase in revenues for each $1,000 spent on advert ising wit hin the relevant range is a. Using the regressio n equat ion, 8.723 ´ $1,000 = $8,723 b. Using the highlow equat ion, 8.333 ´ $1,000 = $8,333 The highlow equat ion does fairly well in estimat ing the relat ionship between advertising costs and revenues. However, Martinez should use the regressio n equation because it uses informat ion fro m all observat ions. The highlow method, on the other hand, relies only on the observat ions that have the highest and lowest values o f the cost driver and these observat ions are generally not representative of all the data. 1023 1034 (30 min.) Regression, activitybased costing, choosing cost drivers. 1. Both number of units inspected and inspect ion laborhours are plausible cost drivers for inspection costs. The number of units inspected is likely related to testkit usage, which is a significant component of inspection costs. Inspection laborhours are a plausible cost driver if labor hours vary per unit inspected, because costs would be a funct ion of how much time the inspectors spend on each unit. This is particularly true if the inspectors are paid a wage, and if they use electric or electronic machinery to test the units of product (cost of operating equipment increases with t ime spent). 2. Solut ion Exhibit 1034 presents (a) the plots and regression line for number of units inspected versus inspect ion costs and (b) the plots and regressio n line for inspection labor hours and inspect ion costs. SOLUTION EXHIBIT 1034A Plot and Regressio n Line for Units Inspected versus Inspect ion Costs for Newroute Manufacturing New route Manufacturing Inspection Costs and Units Inspected $7,000 $6,000 $5,000 $4,000 $3,000 $2,000 $1,000 $0 0 500 1,000 1,500 2,000 2,500 3,000 Number of Units Inspected Inspection Costs SOLUTION EXHIBIT 1034B Plot and Regressio n Line for Inspect ion LaborHours and Inspect ion Costs for Newroute Manufacturing New route Manufacturing Inspection Costs and Inspection LaborHours $7,000 $6,000 $5,000 $4,000 $3,000 $2,000 $1,000 $0 0 50 100 150 200 250 300 Inspection LaborHours Inspection Costs Goodness of Fit. As you can see fro m the two graphs, the regression line based on number of units inspected better fits the data (has smaller vertical distances fro m the points to the line) 1024 than the regressio n line based on inspect ion laborhours. The activit y o f inspect ion appears to be more closely linearly related to the number of units inspected than inspect ion labor hours. Hence number of units inspected is a better cost driver. This is probably because the number of unit s inspected is closely related to testkit usage, which is a significant component of inspect ion costs. Significance of independent variable. It is hard to visually co mpare the slopes because the graphs are not the same size, but both graphs have steep positive slopes indicating a strong relat ionship between number of units inspected and inspect ion costs, and inspect ion labor hours and inspect ion costs. Indeed, if laborhours per inspect ion do not vary much, number of units inspected and inspection laborhours will be closely related. Overall, it is the significant cost of testkits that is driven by the number of unit s inspected (not the inspection laborhours spent on inspect ion) that makes units inspected the preferred cost driver. 3. At 150 inspect ion labor hours and 1200 units inspected, Inspect ion costs using units inspected = $1,004 + ($2.02 × 1200) = $3,428 Inspect ion costs using inspect ion laborhours = $626 + ($19.51 × 150) = $3,552.50 If Neela uses inspect ionlaborhours she will estimate inspect ion costs to be $3,552.50, $124.50 ($3,552.50 ─$3,428) higher than if she had used number of units inspected. If actual costs equaled, say, $3,500, Neela would conclude that Newroute has performed efficient ly in it s inspect ion activit y because actual inspection costs would be lower than budgeted amounts. In fact, based on the more accurate cost funct ion, actual costs of $3,500 exceeded the budgeted amount of $3,428. Neela should find ways to improve inspect ion efficiency rather than mistakenly conclude that the inspect ion act ivit y has been performing well. 1025 1035 (1520min.) Interpreting regression results, matching time periods. 1. The regressio n o f 2 years of Brickman’s mo nthly data yields the fo llowing est imated relat ionships: Maintenance costs = $21,000 – ($2.20 per machinehour ´ Number of machinehours); Sales revenue = $310,000 – ($1.80 ´ advertising expenditure) Sascha Green is comment ing about some surprising and economicallyimplausible regressio n results. In the first regression, the coefficient on machinehours has a negat ive sign. This implies that the greater the number of machinehours (i.e., the longer the machines are run), the smaller will be the maintenance costs; specifically, it suggests that each extra machine hour reduces maintenance costs by $2.20. Similarly, the second regression, with its negat ive coefficient on advert ising expenditure, implies that each extra dollar spent on advert ising will actually reduce sales revenue by $1.80! Clearly, these est imated relat ionships are not economically plausible. 2. The problem statement tells us that Brickman has four peak sales periods, each last ing two months and it schedules maintenance in the intervening mo nths, when production vo lume is low. To correctly understand the relat ionship between machinehours and maintenance costs, Brickman should est imate the regressio n equation of maintenance costs on lagged (i.e., previous mo nths’) machinehours. The greater the machine use in one mo nth, the greater is the expected maintenance costs in later months. 3. The negat ive coefficient on advert ising expenditure in the second regression can likely be explained by (1) the fact that advertising during a particular period increases sales revenues in subsequent periods (2) the possibilit y that Brickman may be increasing advert ising outlays during periods of declining sales in an attempt to clear out its endofseason merchandise. Brickman should therefore est imate the relat ionship between advert ising costs in a part icular period and sales in future periods. In fact, Brickman’s market ing and sales staff may be able to provide a good sense of what the time lag should be—how long before advertising has an effect on sales. 1026 1036 (30–40 min.) Cost estimation, cumulative averagetime learning curve. 1. Cost to produce the 2nd through the 8th troop deployment boats: Direct materials, 7 ´ $100,000 $ 700,000 1 Direct manufacturing labor (DML), 39,130 ´ $30 1,173,900 Variable manufacturing overhead, 39,130 ´ $20 782,600 Other manufacturing overhead, 25% of DML costs 293,475 Total costs $2,949,975 1 The dir ect ma nufacturing laborhours to produce the second to eighth boats can be calculated in several ways, given the assumption of a cumulative averagetime learning curve of 85%: Use of table for mat: 85% Learning Curve Cumulative Average Time per Unit (y): Labor Hours (2) 10,000.00 8,500.00 = (10,000 ´ 0.85) 7,729.00 7,225.00 = (8,500 ´ 0.85) 6,856.71 6,569.78 6,336.56 6,141.25 = (7,225 ´ 0.85) Cumulative Total Time: LaborHours (3) = (1) ´ (2) 10,000 17,000 23,187 28,900 34,284 39,419 44,356 49,130 Cumulative Number of Units (X) (1) 1 2 3 4 5 6 7 8 The direct laborhours required to produce the second thr ough the eighth boats is 49,130 – 10,000 = 39,130 hours. b Use of for mula: y = aX wher e a = 10,000, X = 8, and b = – 0.234465 – y = 10,000 ´ 8 0.234465 = 6,141.25 hours The total dir ect laborhours for 8 units is 6,141.25 ´ 8 = 49,130 hours The direct laborhours required to produce the second thr ough the eighth boats is 49,130 – 10,000 = 39,130 hours. Note: Some students will debate the exclusio n of the tooling cost. The quest ion specifies that the tooling “cost was assigned to the first boat.” Although Nautilus may well seek to ensure its total revenue covers the $725,000 cost of the first boat, the concern in this quest ion is only with the cost of producing seven more PT109s. 1027 2. Cost to produce the 2nd through the 8th boats assuming linear function for direct labor hours and units produced: Direct materials, 7 ´ $100,000 $ 700,000 Direct manufacturing labor (DML), 7 ´ 10,000 hrs. ´ $30 2,100,000 Variable manufacturing overhead, 7 ´ 10,000 hrs. ´ $20 1,400,000 Other manufacturing overhead, 25% of DML costs 525,000 Total costs $4,725,000 The difference in predicted costs is: Predicted cost in requirement 2 (based on linear cost function) Predicted cost in requirement 1 (based on 85% learning curve) Difference in favor of learningcurve based costs $4,725,000 2,949,975 $1,775,025 Note that the linear cost funct ion assumpt ion leads to a total cost that is 60% higher than the cost predicted by the learning curve model. Learning curve effects are most prevalent in large manufacturing industries such as airplanes and boats where costs can run into the millio ns or hundreds o f millio ns o f do llars, result ing in very large and mo netarily significant differences between the two models. 1028 1037 (20–30 min.) Cost estimation, incremental unittime learning model. 1. Cost to produce the 2nd through the 8th boats: Direct materials, 7 ´ $100,000 1 Direct manufacturing labor (DML), 49,358 ´ $30 Variable manufacturing overhead, 49,358 ´ $20 Other manufacturing overhead, 25% of DML costs Total costs $ 700,000 1,480,740 987,160 370,185 $3,538,085 1 he direct lab or hours to produce t he s econd thr ough t he eight h b oats can b e calcu lated via a table T for mat, given the assumption of an incr emental unittime learning curve of 85%: 85% Learning Curve Cumulative Number of Units (X) (1) 1 2 3 4 5 6 7 8 Individual Unit Time for Xth Unit (y* ): Labor Hours (2) 10,000 8,500 = (10,000 ´ 0.85) 7,729 7,225 = (8,500 ´ 0.85) 6,857 6,570 6,337 6,141 = (7,225 ´ 0.85) Cumulative Total Time: LaborHours (3) 10,000 18,500 26,229 33,454 40,311 46,881 53,217 59,358 *Calculated as y = pXq where p = 10,000, q = – 0.234465, and X = 1, 2, 3,. . .8. The direct manufacturing laborhours to produce the second through the eighth boat is 59,358 – 10,000 = 49,358 hours. 1029 2. Difference in total costs to manufacture the second through the eighth boat under the incremental unittime learning model and the cumulat ive averagetime learning model is $3,538,085 (calculated in requirement 1 of this problem) – $2,949,975 (from requirement 1 of Problem 1036) = $588,110, i.e., the total costs are higher for the incremental unittime model. The incremental unittime learning curve has a slo wer rate of decline in the time required to produce successive units than does the cumulative averagetime learning curve (see Proble m 1035, requirement 1). Assuming the same 85% factor is used for both curves: Estimated Cumulative Direct Manufacturing LaborHours Cumulative Average Incremental UnitTime Time Learning Model Learning Model 10,000 10,000 17,000 18,500 28,900 33,454 49,130 59,358 Cumulative Number of Units 1 2 4 8 The reason is that, in the incremental unittime learning model, as the number o f unit s double, only the last unit produced has a cost of 85% of the init ial cost. In the cumulat ive averaget ime learning model, doubling the number of units causes the average cost of all the addit ional unit s produced (not just the last unit) to be 85% of the init ial cost. Nautilus should examine its own internal records on past jobs and seek informat ion fro m engineers, plant managers, and workers when deciding which learning curve better describes the behavior of direct manufacturing laborhours on the production of the PT109 boats. 1030 1038 Regression; choosing among models. (chapter appendix) 1. Solution Exhibit 1038A presents the regression output for (a) setup costs and number o f setups and (b) setup costs and number of setuphours. SOLUTION EXHIBIT 1038A Regressio n Output for (a) Setup Costs and Number of Setups and (b) Setup Costs and Number o f SetupHours SU MMA RY OUTP UT R egr es sio n Statistic s Multiple R 0. 58 073 64 R Sq uar e 0. 33 725 48 Ad jus te d R Sq uare 0.24 257 69 Stan dar d Er ror 28 720 .9 95 Obs erv ations 9 AN OVA d f Reg res s ion Res idu al To ta l 1 7 8 S S MS 293 8383 589 29 383 835 89 577 4269 011 8 248 955 73 871 2652 600 F Sig nifica nc e F 3.56 2128 0.1 010 667 87 In te rc ept Num b er of Se tup s Coe ffic ients S ta nda rd Er ror t S ta t P v alu e Lo wer 9 5% U ppe r 95% L ower 9 5.0% Upp er 95 .0 % 39 05.34 82 41 439.10 166 0.094 243 07 0.92 7557 940 82.556 56 101 893 .2 5 940 82.55 66 101 893 .2 529 41 0.090 94 21 7.2 828 325 1 .8 873 600 52 0.101 0668 10 3.7 013 17 923 .8 831 9 103 .7 013 17 92 3. 883 193 Multiple R R Sq uare Ad jus te d R S qu are Stan dar d E rr or Obs erva tio ns AN OVA 0. 923 210 231 0 .85 231 713 0. 831 219 577 13 557. 86 298 9 d f Reg res s ion Res idu al To ta l 1 7 8 SS 742 594 3061 128 670 9539 871 265 2600 MS F S ignific anc e F 74 2594 306 1 40.39 8862 24 0.0 003 8302 1 8381 564 8. 5 In te rc ept Num b er of S etup Ho urs Coe ffic ients Stand ard E rro r 3 348.71 803 12 878 .6 3428 5 6.2 692 934 8 .8 529 2724 t S ta t 0 .2 6002 120 7 6. 3560 099 3 P v alue L ower 9 5% Upp er 95% L owe r 9 5.0% Upp er 95.0% 0.80 232 966 2710 4.412 9 33 801 .84 9 27 104 .4 1289 3 3801 .8 49 0.00 038 302 3 5.3 354 470 1 7 7.2031 4 35 .3 354 4701 77 .2 0313 99 1031 2. Solution Exhibit 1038B presents the plots and regressio n lines for (a) number of setups versus setup costs and (b) number of setup hours versus setup costs. SOLUTION EXHIBIT 1038B Plots and Regressio n Lines for (a) Number of Setups versus Setup Costs and (b) Number o f SetupHours versus Setup Costs Tilbert Toys Setup Costs and Number of Setups $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $0 0 50 100 150 200 250 300 Number of Setups Setup Costs Tilbert Toys Setup Costs and Number of Setup Hours $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $0 0 500 1,000 1,500 2,000 2,500 Number of Setup Hours Setup Costs 1032 3. Economic plausibilit y Number of Setups A posit ive relat ionship between setup costs and the number of setups is econo mically plausible. Number of Setup Hours A posit ive relat ionship between setup costs and the number of setup hours is also economically plausible, especially since setup time is not uniform, and the longer it takes to setup, the greater the setup costs, such as costs of setup labor and setup equipment. r2 = 85% standard error of regressio n =$13,558 Excellent goodness of fit. The tvalue of 6.36 is significant at the 0.05 level. Goodness of fit r2 = 34% standard error of regressio n =$28,721 Poor goodness of fit. The tvalue of 1.89 is not significant at the 0.05 level. Significance of Independent Variables Specificat ion analys is of estimat ion assumpt ions Based on a plot of the data, the linearit y assumpt ion ho lds, but the constant variance assumpt ion may be vio lated. The DurbinWatson statist ic of 1.12 suggests the residuals are independent. The normalit y o f residuals assumpt ion appears to hold. However, inferences drawn fro m only 9 observat ions are not reliable. Based on a plot of the data, the assumpt ions of linearit y, constant variance, independence of residuals (DurbinWatson = 1.50), and normalit y o f residuals ho ld. However, inferences drawn from only 9 observat ions are not reliable. 4. The regression model using number of setuphours should be used to estimate set up costs because number of setuphours is a more economically plausible cost driver of setup costs (compared to number of setups). The setup time is different for different products and the lo nger it takes to setup, the greater the setup costs such as costs of setuplabor and setup equipment. The regression of number of setuphours andsetup costs also has a better fit, a significant independent variable, and better satisfies the assumptions of the estimat ion technique. 1033 1039 (30min.) Multiple regression (continuation of 1038). 1. Solut ion Exhibit 1039 presents the regressio n output for setup costs using both number of setups and number of setuphours as independent variables (cost drivers). SOLUTION EXHIBIT 1039 Regressio n Output for Mult iple Regressio n for Setup Costs Using Both Number o f Setups and Number of SetupHours as Independent Variables (Cost Drivers) SU MMA RY OUTP UT Re gre ss ion S ta tis tics Multiple R 0. 92 594 047 4 R Sq uar e 0. 85 736 576 2 Ad jus te d R Squ are 0. 80 982 101 6 Stan dar d Er ror 14 391 .6 790 9 Obs erv ations 9 AN OVA df Reg res s ion Res idu al To ta l 2 6 8 S S MS F 746 9930 038 37 349 650 19 18. 032 818 124 2722 562 2 071 204 27 871 2652 600 S ignific anc e F 0 .0 029 018 26 In te rc ept Num b er of Setup s Num b er of Setup Ho urs C oefficie nts S ta nda rd E rror t S ta t P v alu e 3 894 .8 318 9 20 831 .39 503 0.186 969 33 0.8578 466 6 0. 840 273 8 13 2.0202 547 0 .4 608 404 51 0.6611 444 53 .2 993 662 1 1 1.3948 941 4 .6 774 779 79 0.0034 048 L ower 9 5% 5486 7. 419 16 262. 20 165 15 2 5. 417 064 86 U ppe r 9 5% Lo wer 9 5.0% Uppe r 95.0% 47 077 .7 553 8 548 67.41 916 4 707 7. 755 38 38 3.882 199 1 262 .2 016 515 3 83. 88 219 91 81 .1 816 675 7 25. 41 706 486 8 1. 181 667 57 2. Economic plausibilit y A posit ive relat ionship between setup costs and each of the independent variables (number of setups and number of setuphours) is econo mically plausible. r2 = 86%, Adjusted r2 = 81% Standard error of regression =$14,392 Excellent goodness of fit. The tvalue of 0.46 for number of setups is not significant at the 0.05 level. The tvalue of 4.68 for number of setuphours is significant at the 0.05 level. Assuming linearit y, constant variance, and normality of residuals, the DurbinWatson statist ic of 1.36 suggests the residuals are independent. However, we must be caut ious when drawing inferences fro m only 9 observat ions. Goodness of fit Significance of Independent Variables Specificat ion analys is of estimat ion assumpt ions 1034 3. Mult ico llinearit y is an issue that can arise with mult iple regressio n but not simple regressio n analys is. Mult ico llinearit y means that the independent variables are highly correlated. The correlat ion feature in Excel’s Data Analys is reveals a coeffic ient of correlat ion of 0.56 between number of setups and number of setuphours. Since the correlat ion is less than 0.70, the mult iple regressio n does not suffer fro m mult ico llinearit y problems. 4. The simple regressio n model using the number of setuphours as the independent variable achieves a comparable r2 to the mult iple regressio n model. However, the mult iple regressio n model includes an insignificant independent variable, number of setups. Adding this variable does not improve Williams’ abilit y to better estimate setup costs. Bebe should use the simple regression model with number of setuphours as the independent variable to estimate costs. 1040 (40–50 min.) Purchasing Department cost drivers, activitybased costing, simple regression analysis. The problem reports the exact tvalues fro m the co mputer runs o f 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 tvalues. 1. Plots of the data used in Regressio ns 1 to 3 are in Solution Exhibit 1040A. See So lut ion Exhibit 1040B for a comparison of the three regressio n models. 2. Both Regressio ns 2 and 3 are wellspecified regressio n models. The slope coefficients on their respect ive independent variables are significant ly different fro m zero. These result s support the Couture Fabrics’ presentation in which the number o f purchase orders and the number o f suppliers were reported to be drivers of purchasing department costs. In designing an act ivit ybased cost system, Fashio n Flair should use number o f purchase orders and number o f suppliers as cost drivers o f purchasing depart ment costs. As the chapter appendix describes, Fashio n Flair can eit her (a) estimate a mult iple regressio n equat ion for purchasing department costs with number o f purchase orders and number o f suppliers as cost drivers, or (b) divide purchasing depart ment costs into two separate cost pools, one for costs related to purchase orders and another for costs related to suppliers, and estimate a separate relat ionship for each cost pool. 3. Guidelines presented in the chapter could be used to gain addit ional evidence on cost drivers of purchasing department costs. 1. Use phys ical relat ionships or engineering relationships to establish causeandeffect links. Lee could observe the purchasing department operations to gain insight into how costs are driven. 2. Use knowledge of operations. Lee could interview operating personnel in the purchasing depart ment to obtain their insight on cost drivers. 1035 SOLUTION EXHIBIT 1040A Regressio n Lines of Various Cost Drivers on Purchasing Dept. Costs for Fashio n Flair Pu rc h asin g D e p artm e n t Co sts $2,500, 000 2,000, 000 1,500, 000 1,000, 000 500,000 0 0 50 100 150 D ol l ar Valu e o f M e rch an d i se Pu rch ase d (in m i ll i o n s) $2,500, 000 Pu rch as i n g D e p art m e n t Cos ts 2,000, 000 1,500, 000 1,000, 000 500,000 0 0 2,000 4,000 6,000 8,000 N u m b e r o f Pu rc h ase O rd e rs $2,500, 000 Pu rch as i n g D e p art m e n t Cos ts 2,000, 000 1,500, 000 1,000, 000 500,000 0 0 100 200 300 N u m b e r o f S u p p l ie rs 1036 SOLUTION EXHIBIT 1040B Comparison o f Alternat ive Cost Functions for Purchasing Department Costs Estimated with Simple Regressio n for Fashion Flair Criterion 1. Economic Plausibilit y Regression 1 PDC = a + (b ´ MP$) 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. Regression 2 PDC = a + (b ´ # of POs) Economically plausible. The higher the number of purchase orders, the more tasks undertaken. Regression 3 PDC = a + (b ´ # of Ss) Economically plausible. Increasing the number of suppliers increases the costs of certifying vendors and managing the Fashio n Flair supplier relat ionship. 2. Goodness of fit r2 = 0.08. Poor goodness of fit. 3. Significance of tvalue on MP$ of Independent 0.84 is insignificant. Variables r2 = 0.42. Reasonable goodness of fit. r2 = 0.39. Reasonable goodness of fit. tvalue on # of POs of 2.43 tvalue on # of Ss of 2.28 is significant. is significant. 4. Specificat ion Analys is A. Linearit y Appears questionable Appears reasonable. within the but no strong evidence relevant range against linearit y. B. Constant variance of residuals Appears questionable, Appears reasonable. but no strong evidence against constant variance. DurbinWatson Statist ic = 2.41 Assumpt ion of independence is not rejected. DurbinWatson Statist ic = 1.98 Assumpt ion of independence is not rejected. Appears reasonable. Appears reasonable. C. Independence of residuals DurbinWatson Statist ic = 1.97 Assumpt ion of independence is not rejected. Data base too small to make reliable inferences. D. Normalit y o f residuals Data base too small to Data base too small to make reliable make reliable inferences. inferences. 1037 1041 (30–40 min.) Purchasing Department cost drivers, multiple regression analysis (continuation of 1040) (chapter appendix). The problem reports the exact tvalues fro m the co mputer runs o f 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 tvalues. 1. Regressio n 4 is a wellspecified regressio n 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 tvalue on # of POs is 2.14 while the tvalue on # o f Ss is 2.00. These tvalues are either significant or border on significance. Specification analysis: Results are available to examine the independence of residuals assumpt ion. The DurbinWatson statist ic o f 1.90 indicates that the assumpt ion o f independence is not rejected. Regressio n 4 is consistent with the findings in Problem 1039 that both the number of purchase orders and the number of suppliers are drivers of purchasing department costs. Regressio ns 2, 3, and 4 all sat isfy the four criteria outlined in the text. Regressio n 4 has the best goodness o f fit (0.63 for Regressio n 4 co mpared to 0.42 and 0.39 for Regressio ns 2 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 Regressio n 4 over Regressio ns 2 and 3. 2. Regressio n 5 adds an addit ional independent variable (MP$) to the two independent variables in Regressio n 4. This addit io nal variable (MP$) has a tvalue o f –0.07, implying its slope coefficient is ins ignificant ly different from zero. The r2 in Regressio n 5 (0.63) is the same as that in Regressio n 4 (0.63), implying the addit ion o f this third independent variable adds close to zero explanatory power. In summary, Regressio n 5 adds very litt le to Regressio n 4. We would recommend that Lee use Regressio n 4 over Regression 5. 3. Budgeted purchasing depart ment costs for the Baltimore store next year are $485,384 + ($123.22 ´ 3,900) + ($2,952 ´ 110) = $1,290,662 1038 4. Mult ico llinearit y is a frequently encountered problem in cost accounting; it does not arise in simple regressio n because there is only one independent variable in a simple regressio n. One consequence o f mult icollinearit y is an increase in the standard errors of the coefficients of the individual variables. This frequently shows up in reduced tvalues for the independent variables in the mult iple regressio n relat ive to their tvalues in the simple regressio n: tvalue from Simple Regressions in Problem 1039 2.43 2.28 Variables Regression 4: # of POs # of Ss Regression 5: # of POs # of Ss MP$ tvalue in Multiple Regression 2.14 2.00 1.95 1.84 –0.07 2.43 2.28 0.84 The decline in the tvalues in the mult iple regressions is consistent with so me (but not very high) collinearit y amo ng the independent variables. Pairwise correlat ions between the independent variables are: Correlation 0.29 0.27 0.34 # of POs ¸ # of Ss # of POs ¸ MP$ # of Ss ¸ MP$ There is no evidence of difficult ies due to mult icollinearit y in Regressio ns 4 and 5. 5. are Decisio ns in which the regressio n results in Problems 1040 and 1041 could be usefu l Cost management decisions: Fashio n Flair could restructure relat ionships wit h the suppliers so that fewer separate purchase orders are made. Alternat ively, it ma y aggressively reduce the number of exist ing suppliers. Purchasing policy decisions: Fashio n Flair could set up an internal charge system for individua l retail departments within each store. Separate charges to each department could be made for each purchase order and each new supplier added to the exist ing ones. These internal charges would signal to each department ways in which their own decis io ns affect the total costs of Fashio n Flair. Accounting system design decisions: Fashio n Flair may want to discontinue allocat ing purchasing department costs on the basis o f the do llar value of merchandise purchased. Allocat ion bases better capturing causeandeffect relat ions at Fashion Flair are the number o f purchase orders and the number of suppliers. 1039 1042 (40 min.) Highlow method, alternative regression functions, accrual accounting adjustments, ethics. 1. Solution Exhibit 1042A presents the two data plots. The plot of engineering support reported costs and machinehours shows two separate groups of data, each of which may be approximated by a separate cost funct ion. 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 machinehours shows a high posit ive correlat ion between the two variables (the coefficient of determinat ion is 0.94); a single linear cost funct ion provides a good fit to the data. Better estimates of the cost relat ion result because Kennedy adjusts the materials and parts costs to an accrual account ing basis. 2. Cost Driver MachineHours 73 19 54 Reported Engineering Support Costs $ 617 1,066 $ (449) Highest observat ion of cost driver (August) Lowest observat ion of cost driver (September) Difference Slope coefficient, b Difference between costs associated with highest and lowest observations of the cost driver = Difference between highest and lowest observations of the cost driver –$449 = –$8.31 per machinehour 54 Constant (at highest observat ion of cost driver) = $ 617 – (–$8.31 ´ 73) = $1,224 Constant (at lowest observat ion of cost driver) = $1,066 – (–$8.31 ´ 19) = $1,224 The est imated cost funct ion is y = $1,224 – $8.31X = Cost Driver Restated Engineering MachineHours Support Costs Highest observat ion of cost driver (August) 73 $966 Lowest observat ion 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 machinehour 54 Constant (at highest observat ion of cost driver) = Constant (at lowest observat ion of cost driver) = The est imated cost funct ion is y = $160 + $11.04 X $ 966 – ($11.04 ´ 73) = $160 $ 370 – ($11.04 ´ 19) = $160 1040 3. The cost funct ion est imated with engineering support restated costs better approximates the regression analysis assumpt ions. See Solution Exhibit 1042B for a comparison of the two regressions. 4. Of all the cost functions est imated in requirements 2 and 3, Kennedy should choose Regressio n 2 using engineering support restated costs as best representing the relat ionship between engineering support costs and machinehours. The cost funct ions est imated using engineering support reported costs are misspecified and noteconomically plausible because materials and parts costs are reported on an “aspurchased” rather than on an “asused” basis. Wit h respect to engineering support restated costs, the highlow and regressio n approaches yield roughly similar estimates. The regression approach is technically superior because it determines the line that best fits all observat ions. In contrast, the highlow method considers only two points (observat ions wit h the highest and lowest cost drivers) when est imat ing the cost funct ion. Solution Exhibit 1042B shows that the cost function est imated using the regression approach has excellent goodness of fit (r2 = 0.94) and appears to be well specified. 5. Problems Kennedy might encounter include a. A perpetual inventory system may not be used in this case; the amounts requisit ioned likely will not permit an accurate matching o f costs with the independent variable on a monthbymo nth basis. b. Qualit y o f the source records for usage by engineers may be relat ively low; e.g., engineers may requisit ion materials and parts in batches, but not use them immediately. c. Records may not dist inguish materials and parts for maintenance fro m materials and parts used for repairs and breakdowns; separate cost funct ions may be appropriate for the two categories of materials and parts. d. Yearend account ing adjustments to inventory may mask errors that gradually accumulate monthbymo nth. 6. Picking the correct cost funct ion is important for cost predict ion, cost management, and performance evaluat ion. For example, had Unit ed Packaging used Regression 1 (engineering support reported costs) to estimate the cost funct ion, it would erroneously conclude that engineering support costs decrease with machinehours. In a month wit h 60 machinehours, Regressio n 1 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 o f the preferred Regressio n 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 machinehours worked in a month were low, say 25 hours, Regressio n 1 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 bee n very good. In fact, compared to the costs predicted by t he preferred Regressio n 2 of $176.38 + ($11.44 ´ 25) = $462.38, the actual performance is rather poor. Using Regressio n 1, management may feel costs are being managed very well when in fact they are much higher than what the y should be and need to be managed “down.” 1041 7. Because Kennedy is confident that the restated numbers are correct, he cannot change them just to please Mason. If he does, he is vio lat ing the standards o f integrit y and object ivit y for management accountants. Kennedy should establish the correctness of the numbers wit h Mason, point out that he cannot change them, and also reason that this is a problem t hat 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 organizat ion. He should be prepared to resign, if necessary, rather than co mpromise his professio nal ethics. SOLUTION EXHIBIT 1042A Plots and Regression Lines for Engineering Support Reported Costs and Engineering Support Restated Costs Engineering Support Reported Costs $1,400 1,200 1,000 600 800 400 200 0 0 10 20 30 40 50 60 70 80 MachineHours $1,200 1,000 800 600 400 200 0 0 10 20 30 40 M achineHours 50 60 70 80 Engineering Support Restated Costs 1042 SOLUTION EXHIBIT 1042B Comparison o f Alternat ive Cost Functions for Engineering Support Costs at United Packaging Regression 1 Dependent Variable: Engineering Support Reported Costs Negative slope relat ionship is economically implausible over the long run. r2 = 0.43. Moderate goodness of fit. Regression 2 Dependent Variable: Engineering Support Restated Costs Posit ive slope relationship is economically plausible. r2 = 0.94. Excellent goodness of fit. Criterion 1. Economic Plausibilit y 2. Goodness of Fit 3. Significance of Independent Variables tstatist ic on machinehours is tstatist ic on machinehours is statist ically significant highly statist ically significant (t = –2.31), albeit econo mically (t=10.59). implausible. 4. Specificat ion Analysis: A. Linearit y Linearit y does not describe data very well. Linearit y describes data very well. Appears reasonable, although 12 observat ions do not facilitate the drawing of reliable inferences. B. Constant variance of Appears questionable, although residuals 12 observat ions do not facilitate the drawing of reliable inferences. C. Independence o f residuals DurbinWatson = 2.26. DurbinWatson = 1.31. Some Residuals serially uncorrelated. evidence of serial correlat ion in the residuals. Database too small to make reliable inferences. Database too small to make reliable inferences. D. Normalit y o f residuals 1043 ...
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- Spring '10
- Cost Accounting