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Problem 10-36 The Nautilus Company, which is under contract to the U.S. Navy, assembles troop deployment boats. As part of its research program, it completes the assembly of the first of a new model (PT109) of deployment boats. The Navy is impressed with the PT109. It requests that Nautilus submit a proposal on the cost of producing another 6 PT109s. Nautilus reports the following cost information for the first PT109 assembled and uses an 90% cumulative average-time learning model as a basis for forecasting direct manufacturing labor-hours for the next 6 PT109s. (An 90% learning curve means b = -0.152004.) Direct materials $200,000 Direct manufacturing labor time for first boat 15,000 labor-hours Direct manufacturing labor rate $40 per direct manufacturing labor-hour Variable manufacturing overhead cost $25 per direct manufacturing labor-hour Other manufacturing overhead 20% of direct manufacturing labor costs Tooling costs (1) $280,000 Learning curve for manufacturing labor time per boat 90% cumulative average time (2) (1) Tooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat. (2) Using the formula (p. 359), for an 90% learning curve, b = ln.90/ln2 = (-0.105361/.693147) = -0.152004 Required: 1. Calculate predicted total costs of producing the six PT109s for the Navy. (Nautilus will keep the first deployment boat assembled, costed at $1,575,000, as a demonstration model for potential customers.) Calculation of the direct manufacturing labor-hours b= -0.152003093 to produce the 2nd to 8th boats can be calculated as follows: y = aX to the power of b where Cumulative y = cumulative average time per unit in labor-hours # of a = labor hours required for first unit Units X = cumulative number of units 1 b = ln(learning-curve % in decimal form) / ln2 2 b = ln 0.90 / ln2 = -0.152003093 3 -0.105360516 4 0.693147181 5 -0.152003093 6 7 Extra unit 8 The DLHs required to produce the 2nd through the 7th boats Cumulative Average-time Cost to produce the 2nd through 7th boats Learning Model Direct materials, 6 X $200,000 $1,200,000.00 Direct manufacturing labor (DML) $2,524,580.90 Variable mfg. Overhead $1,577,863.06 Other mfg. Overhead (20% of DML$) $504,916.18 Total costs for boats 2 through 7 $5,807,360.15 2. What is the dollar amount of the difference between (a) the predicted total costs for producing the six PT109s in requirement 1, and (b) the predicted total costs for producing the six PT109s, assuming that there is no learning curve for direct manufacturing labor? That is, for (b) assume a linear function for units produced and direct manufacturing labor-hours. Assumption Cost to produce the 2nd through 7th boats (a) Direct labor hours required based on assumption 63,114.52 Learning Curve Direct materials, 6 X $200,000 $1,200,000.00 Direct manufacturing labor (DML) $2,524,580.90 Variable mfg. Overhead $1,577,863.06 Other mfg. Overhead (25% of DML$) $504,916.18 Total costs for boats 2 through 7 $5,807,360.15 Difference Learning curve effects are most prevalent in large manufacturing industries such as airplanes and boats where costs can run into the millions or hundreds of millions of dollars, resulting in very large and monetarily significant differences between the two methods. Problem 10-37 Assume the same information for the Nautilus Company as in Problem 10-36 with one exception. This exception is th Nautilus uses an 90% incremental unit-time learning model as a basis for predicting direct manufacturing labor-hours in its assembling operations. 1. Calculate predicted total costs of producing the 6 additional PT109s for the Navy. (Nautilus will keep the first deployment boat assembled, costed at $1,575,000, as a demonstration model for potential customers.) Calculation of the direct manufacturing labor-hours b= -0.15200309 to produce the 2nd to 7th boats can be calculated as follows: y = aX to the power of b where Cumulative y = Time (in labor-hours) to produce the most recent unit # of a = labor hours required for first unit Units X = cumulative number of units 1 b = ln(learning-curve % in decimal form) / ln2 2 b = ln 0.90 / ln2 = -0.152003093 3 -0.105360516 4 0.693147181 5 -0.152003093 6 7 Extra unit 8 The DLHs required to produce the 2nd through the 7th boats Incremental Unit-time Learning Cost to produce the 2nd through 7th boats Model Direct materials, 6 X $100,000 $1,200,000.00 Direct manufacturing labor (DML) $2,906,835.56 Variable mfg. Overhead $1,816,772.22 Other mfg. Overhead (20% of DML$) $581,367.11 Total costs for boats 2 through 7 $6,504,974.89 Difference 2. Compare the cost of the 2nd - 7th boats using the "Incremental Unit-time Learning Model" with the costs of the 2nd boats using the "Cumulative Average-time Learning Model: Incremental Unit-time Learning Cost to produce the 2nd through 7th boats Model Direct materials, 6 X $200,000 $1,200,000.00 Direct manufacturing labor (DML) $2,906,835.56 Variable mfg. Overhead $1,816,772.22 Other mfg. Overhead (20% of DML$) $581,367.11 Total costs for boats 2 through 7 $6,504,974.89 Difference Why are the predictions different? The incremental unit-time learning curve has a slower rate of decline in the time required to produce successive un than does the cumulative average-time learning curve even though the same 90% factor is used for both curves. The reason is that, in the incremental unit-time learning model, as the number of units double, only the last unit produced has a time of 90% of the initial time. In the cumulative average-time learning model, doubling the numbe of units causes the average time of all the additional units produced (not just the last unit) to be 90% of the initial ti Cumulative # of Units 1 2 3 4 5 6 7 8 How should Nautilus decide which model it should use? The company should examine its own internal records on past jobs and seek information from engineers, plant managers, and when deciding which learning curve better describes the behavior of direct manufacturing labor-hours on the production of the boats. deployment boats. del (PT109) of s submit a proposal uring labor-hours manufacturing labor-hour manufacturing labor-hour manufacturing labor costs ve average time (2) d to the first deployment boat. .693147) = -0.152004 us will keep the first r potential customers.) 90% LC 90% LC Average Average Time per Time per Cumulative Unit (y): Unit (y): Total Time: Labor-Hrs. Labor-Hrs. Labor-Hrs. 15,000.00 15,000.00 15,000.00 13,500.00 13,500.00 27,000.00 12,693.09 38,079.27 12,150.00 12,150.00 48,600.00 11,744.80 58,724.00 11,423.78 68,542.68 11,159.22 78,114.52 10,935.00 10,935.00 87,480.00 63,114.52 s for producing the six PT109s, s, for (b) assume a Assumption (b) 90,000.00 No Learning Curve $1,200,000.00 3,600,000.00 2,250,000.00 720,000.00 Proof $7,770,000.00 $7,770,000.00 $1,962,639.85 h as airplanes and esulting in very large ne exception. This exception is that g direct manufacturing labor-hours y. (Nautilus will keep the first r potential customers.) 90% LC 90% LC Incremental Incremental Unit Time for Unit Time for Cumulative Xth Unit (y) Xth Unit (y) Total Time: Labor-Hrs. Labor-Hrs. Labor-Hrs. 15,000.00 15,000.00 15,000.00 13,500.00 13,500.00 28,500.00 12,693.09 41,193.09 12,150.00 12,150.00 53,343.09 11,744.80 65,087.89 11,423.78 76,511.67 11,159.22 87,670.89 10,935.00 10,935.00 98,605.89 72,670.89 ng Model" with the costs of the 2nd - 7th Cumulative Average-time Learning Model $1,200,000.00 $2,524,580.90 $1,577,863.06 $504,916.18 $5,807,360.15 ($697,614.75) required to produce successive units % factor is used for both curves. f units double, only the last unit arning model, doubling the number e last unit) to be 90% of the initial time. Cumulative Incremental Average-time Unit-time Learning Learning Model Model Cumulative Cumulative Total Time: Total Time: Labor-Hrs. Labor-Hrs. 15,000.00 15,000.00 27,000.00 28,500.00 38,079.27 41,193.09 48,600.00 53,343.09 58,724.00 65,087.89 68,542.68 76,511.67 78,114.52 87,670.89 87,480.00 98,605.89 n from engineers, plant managers, and workers ng labor-hours on the production of the PT109 Problem 10-31 Ken Howard, financial analyst at KMW Corporation, is examining the behavior of quarterly maintenance costs for budgeting purposes. Howard collects the following data on machine-hours worked and maintenance costs for the past 12 quarters: Machine Maintenance Quarter Hours Costs 1 100,000 $205,000 2 120,000 $240,000 3 110,000 $220,000 4 130,000 $260,000 5 95,000 $190,000 6 115,000 $235,000 7 105,000 $215,000 8 125,000 $255,000 9 105,000 $210,000 10 125,000 $245,000 11 115,000 $200,000 12 140,000 $280,000 1. Estimate the cost function for the quarterly data using the high-low method. Machine Total Cost Hours $280,000 140,000 $190,000 95,000 $90,000 45,000 $2 VC per Machine Hour Total Total Total Cost Variable Costs Fixed Costs $280,000 $280,000 $0 No fixed costs $190,000 $190,000 $0 No fixed costs Cost Function: Y = $2 (Machine Hours) 2. Plot and comment on the estimated cost function. Actual Estimated Machine Maintenance Maintenance Quarter Hours ACosts ECosts 1 100,000 $205,000 $200,000 2 120,000 $240,000 $240,000 3 110,000 $220,000 $220,000 4 130,000 $260,000 $260,000 5 95,000 $190,000 $190,000 6 115,000 $235,000 $230,000 7 105,000 $215,000 $210,000 8 125,000 $255,000 $250,000 9 105,000 $210,000 $210,000 10 125,000 $245,000 $250,000 11 115,000 $200,000 $230,000 12 140,000 $280,000 $280,000 See P10-31(Chart) There appears to be a clear-cut relationship between machine hours and maintenance costs. The high-low line appears to "fit" the data well. The vertical differences between the actual and predicted costs appear to be quite small. 3. Howard anticipates that KMW will operate machines for 100,000 hours in quarter 13. Calculate the predicted maintenance costs in quarter 13 using the cost function estimated in requirement 1. Estimated maintenance costs = 100,000 X $2 = $200,000 90,000 hours? aintenance costs aintenance costs Estimated Cost Function & Actual Costs $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $0 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 ACosts Machine Hours ECosts Linear (ECosts) Exercise 10-40 Fashion Bling operates a chain of 10 retail department stores. Each department store makes its own purchasing deci Fashion Bling, is interested in better understanding the drivers of purchasing department costs. For many years, Fas costs to products on the basis of the dollar value of merchandise purchased. A $100 item is allocated 10 times as ma department as a $10 item. Barry Lee recently attended a seminar titled "Cost Drivers in the Retail Industry." In a presentation at the seminar, a le system reported that "number of purchase orders" and "number of suppliers" were the two most important cost drive value of merchandise purchased in each purchase order was not found to be a significant cost driver. Barry Lee inter Department at Fashion Bling's Miami store. They believed that the competitors conclusions regarding cost drivers fo Department. Mr. Barry Lee collects the following data for the most recent year for Fashion Bling's 10 retail departmen $ Value of Number of Merchandise Purchase Number of Department Purchased Orders Suppliers Store (MP$) (# of PO) (# of S) Baltimore $68,307,000 4,345 125 Chicago 33,463,000 2,548 230 LA 121,800,000 1,420 8 Miami 119,450,000 5,935 188 NYC 33,575,000 2,786 21 Phoenix 29,836,000 1,334 29 Seattle 102,840,000 7,581 101 St. Louis 38,725,000 3,623 127 Toronto 139,300,000 1,712 202 Vancouver 130,110,000 4,736 196 Lee decides to use simple regression analysis to examine whether one or more of three variables are reasonable cost Summary results for these regressions are as follows: Regression 1: PDC = a + (b X MP$) SUMMARY OUTPUT Regression 1 (MP$) $2,500,000 Regression Statistics Multiple R 0.651131304 R Square 0.423971975 Adjusted R Square 0.351968472 Standard Error 401027.6454 $2,000,000 Observations 10 ANOVA df SS MS Purchase Dept. Dollars Regression 1 9.46961E+11 9.46961E+11 $1,500,000 Residual 8 1.28659E+12 1.60823E+11 Total 9 2.23355E+12 Coefficients Standard Error t Stat Intercept $1,000,000 730715.82 265418.8246 2.753067048 (# of PO) 156.9660646 64.68655284 2.426564065 Purchase Dept. Do $500,000 $0 $0 $20,000,000 $40,000,000 $60,000,000 $80,000,000 Dollar Value of Merchandise SUMMARY OUTPUT Regression 1: PDC = a + (b X MP$) PDC = $1,041,421.37 + .003126704 (MP$) Regression Statistics: Regression 1 Multiple R 0.282507267 R Square 0.079810356 Adjusted R Square -0.03521335 Standard Error 510550.3505 Observations 10 2.60662E+11 ANOVA df SS MS Regression 1 1.80863E+11 1.80863E+11 Residual 8 2.08529E+12 2.60662E+11 Total 9 2.26616E+12 Coefficients Standard Error t Stat Intercept 1041421.366 346708.5474 3.003737214 (MP$) 0.003126704 0.003753624 0.832982632 From a t-table for df=8 and one tail equal to .025 (95% confidence interval), the t-value is: Therefore the intercept confidence intervals are: And the b-coefficient confidence intervals are: For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval. For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval. Evaluation of the information: Regression 1: MP$ Criterion 1. Economic Plausibility A leading competitor found little support for MP$ as a significa Purchasing personnel at the Miami store also believe MP$ is n 2. Goodness of fit r2 = 0.0798 indicates a poor fit. 3. Significance of "X" Variable t-value of 0.832982632 is insignificant; the larger the t-value the From a t-table for df=8 and one tail equal to .025 (95% confidence inte 4. Specification Analysis: The testing of the assumptions of regression analysis pg. 369 A. Linearity within the relevant range Appears questionable (See Scatter diagram) B. Constant variance of residuals Appears questionable, but no strong evidence against constant varia C. Independence of residuals Durbin-Watson Statistic = 2.41 (Assumption of independence is not r For samples of 10-20 observations, a D/W statistic in the range of 1.1 that the residuals are independent. D. Normality of residuals Too few data points to make reliable inferences. Regression 2: PDC = a + (b X (# of PO)) $2,500,000 Regression 2 (Number of Purchase Orders) $2,000,000 Purchase Dept. Dollars $1,500,000 $1,000,000 $500,000 $0 0 1,000 2,000 3,000 Number of Purchase Orders SUMMARY OUTPUT Regression 2: PDC = a + (b X (# of PO)) PDC = $722,537.85 + $159.48 (# of PO) Regression Statistics: Regression 2 Multiple R 0.656228523 R Square 0.430635874 Adjusted R Square 0.359465358 Standard Error 401601.1595 Observations 10 1.61283E+11 ANOVA df SS MS Regression 1 9.75888E+11 9.75888E+11 Residual 8 1.29027E+12 1.61283E+11 Total 9 2.26616E+12 Coefficients Standard Error t Stat Intercept 722537.851 265834.6274 2.717997494 (# of PO) 159.4842168 64.83547006 2.459829731 From a t-table for df=8 and one tail equal to .025 (95% confidence interval), the t-value is: Therefore the intercept confidence intervals are: And the b-coefficient confidence intervals are: For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval. For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval. Evaluation of the information: Regression 2: # of PO Criterion 1. Economic Plausibility Economically plausible. Increasing the number of purchase or 2. Goodness of fit r2 = 0.430635874 indicates a reasonable fit. 3. Significance of "X" Variable t-value of 2.459829731 is significant; the larger the t-value the b 4. Specification Analysis: The testing of the assumptions of regression analysis pg. 369 A. Linearity within the relevant range Appears reasonable (See Scatter diagram) B. Constant variance of residuals Appears reasonable C. Independence of residuals Durbin-Watson Statistic = 1.97 (Assumption of independence is not r For samples of 10-20 observations, a D/W statistic in the range of 1.1 that the residuals are independent. D. Normality of residuals Too few data points to make reliable inferences. Regression 3: PDC = a + (b X (# of S)) $2,500,000 Regression 3 (Number of Suppliers) $2,000,000 hase Dept. Dollars Purchase Dept. Dollars $1,500,000 $1,000,000 $500,000 $0 0 50 100 Number of Suppliers SUMMARY OUTPUT Regression 3: PDC = a + (b X (# of S)) PDC = $828,814.24 + $3,815.69 (# of S) Regression Statistics Multiple R 0.621971696 R Square 0.386848791 Adjusted R Square 0.310204889 Standard Error 416757.7672 Observations 10 1.73687E+11 ANOVA df SS MS Regression 1 8.7666E+11 8.7666E+11 Residual 8 1.3895E+12 1.73687E+11 Total 9 2.26616E+12 Coefficients Standard Error t Stat Intercept 828814.2417 246570.4694 3.361368633 (# of S) 3815.694852 1698.407173 2.24663138 From a t-table for df=8 and one tail equal to .025 (95% confidence interval), the t-value is: Therefore the intercept confidence intervals are: And the b-coefficient confidence intervals are: For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval. For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval. Evaluation of the information: Regression 3: # of Suppliers Criterion 1. Economic Plausibility Economically plausible. Increasing the number of suppliers in the Fashion Bling-supplier relationships. 2. Goodness of fit r2 = 0.386848791 indicates a reasonable fit. 3. Significance of "X" Variable t-value of 2.24663138 is significant. 4. Specification Analysis A. Linearity within the Appears reasonable (See Scatter diagram) relevant range B. Constant variance of residuals Appears reasonable. C. Independence of residuals Durbin-Watson Statistic = 2.01 (Assumption of independence For samples of 10-20 observations, a D/W statistic in the range that the residuals are independent. D. Normality of residuals Too few data points to make reliable inferences. 2. Do the regression results support the competitor's presentation about the purchasing department's cost drivers? Fashion Bling can either (a) develop a multiple regression equation for estimating purchasing departme suppliers as cost allocation bases, or (2) divide the purchasing department cost pool into two separate and another for costs related to suppliers, and estimate a separate simple regression equation for each 3. How might Lee gain additional evidence on drivers of Purchasing Department costs at each store? a. 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. b. Use knowledge of operations. Lee could interview operating personnel in the purchasing department to obtain their insight on cost Exercise 10-41 Barry Lee decides that the simple regression analysis used in P10-40 could be extended to a multiple regression analy Regression 4: PDC = a + (b1)(# of PO) + (b2)(# of S) SUMMARY OUTPUT PDC = $484,521.6364 + $126.6639997 (# of PO) + $2903.2977 Regression Statistics: Regression 4 Multiple R 0.797723096 R Square 0.636362138 Adjusted R Square 0.532465606 Standard Error 343107.6721 Observations 10 7.21048E+11 1.17723E+11 ANOVA df SS MS Regression 2 1.4421E+12 7.21048E+11 Residual 7 8.2406E+11 1.17723E+11 Total 9 2.26616E+12 Coefficients Standard Error t Stat Intercept 484521.6346 256684.0955 1.887618451 (# of PO) 126.6639997 57.7952084 2.191600362 (# of S) 2903.297788 1458.922564 1.99002871 From a t-table for df=7 and one tail equal to .025 (95% confidence interval), the t-value is: Therefore the intercept confidence intervals is: And the b-coefficient confidence intervals are: Number of purchase orders Number of Suppliers For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval. For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval. Evaluation of the information: Regression 4: PDC = a + (b1)(# of PO) + (b2)(# of S) Criterion 1. Economic Plausibility Economically plausible. Both independent variables are plaus the findings of the competitor's research and Bling's own rese 2. Goodness of fit r2 = 0.636362138 indicates an excellent fit. 3. Significance of "X" Variables t-value of 2.19 is significant for the (# of PO) variable t-value of 1.99 is nearly significant for the (# of S) variable 4. Specification Analysis A. Linearity within the Appears reasonable. relevant range B. Constant variance of residuals Appears reasonable. C. Independence of residuals Durbin-Watson Statistic = 1.91 (Assumption of independence D. Normality of residuals Too few data points to make reliable inferences. 1. Compare regression 4 with regression 2 and 3 in Problem 10-40. Which model would you recommend that Lee use Regression 4 is economically feasible and has the highest r2 value. Lee should use the results from regression 4 to predict PDC. Regression 5: PDC = a + (b1 X (# of PO)) + (b2 X (# of S)) + (b3 X MP$) SUMMARY OUTPUT PDC = $483,559.95 + $126.5778427 (# of PO) + $2,900.7309 (# of S) + -.000194148 (M Regression Statistics: Regression 5 Multiple R 0.797724783 R Square 0.63636483 Adjusted R Square 0.454547245 Standard Error 370597.2708 Observations 10 4.80701E+11 1.37342E+11 ANOVA df SS MS Regression 3 1.4421E+12 4.80701E+11 Residual 6 8.24054E+11 1.37342E+11 Total 9 2.26616E+12 Coefficients Standard Error t Stat Intercept 483559.9493 312554.2588 1.547123214 (MP$) 0.0000194148 0.002913205 0.006664422 (# of PO) 126.5778427 63.75031137 1.985525089 (# of S) 2900.7309 1622.198995 1.788147391 From a t-table for df=6 and one tail equal to .025 (95% confidence interval), the t-value is: Therefore the intercept confidence intervals is: And the b-coefficient confidence intervals are: Dollars of Merchandise Purchased Number of purchase orders Number of Suppliers For a normal curve: "+/-" 1.96 standard errors for 95% confidence interval. For a normal curve: "+/-" 2.58 standard errors for 99% confidence interval. 2. Compare regression 5 with regression 4. Which model would you recommend that Lee use? Regression 4 should be used. It is slightly less complicated (and therefore less costly), has about the same r 2, and the standard errors regression variables are slightly smaller. 3. Lee estimates the following data for the Baltimore store for next year: Dollar value of merchandise purchased $75,000,000 Number of purchase orders 4,000 Number of suppliers 95 Regression 4: PDC = a + (b1)(# of PO) + (b2)(# of S) PDC = $484,521.6364 + $126.6639997 (# of PO) + $2903.297788 (# of S) PDC = $1,266,990.92 Slightly preferred -- see above. Regression 5: PDC = a + (b1)(# of PO) + (b2)(# of S) + (b3)(MP$) PDC = $483,559.95 + $126.5778427 (# of PO) + $2,900.7309 (# of S) + .000194148 (MP$) PDC = $1,266,896.87 More complicated, more costly, not much improvement. 4. What difficulties do not arise in simple regression analysis that may arise in multiple regression analysis? Multicollinearity is a frequently encountered problem in cost accounting; it does not arise in simple reg because there is only one independent variable in a simple regression. Multicollinearity exists when tw more independent variables are highly correlated with each other. One consequence of multicollinearity is an increase in the standard errors of the coefficients of the indi variables. This frequently shows up in reduced t-values for the independent variables in the multiple regression relative to their t-values in the simple regression. t-value t-value Multiple Simple Variables Regression Regression Regression 4 # of PO 2.191600362 2.459829731 # of S 1.99002871 2.24663138 Regression 5 # of PO 1.985525089 2.459829731 # of S 1.788147391 2.24663138 MP$ 0.006664422 0.832982632 The decline in the t-values in the multiple regressions is consistent with some (but not very high) collinearity among the independent variables. Generally, users of regression analysis believe that a coefficient of correlation between independent va greater than 0.70 indicates multicollinearity. The coefficients of correlation between the potential independent variables for Fashion Bling are: Pair-wise Correlation Values # of PO # of PO / # of S 0.285358 # of Suppliers # of PO / MP$ 0.270157 # of S / MP$ 0.296190 MP$ # of PO No values are near the .70 benchmark. MP$ # of Suppliers 5. Give examples of decisions in which the regression results reported here could be informative. Cost management decisions: Fashion Bling could restructure relationships with suppliers so that fewer separate purchase orders are made. Alternatively, it may aggressively reduce the number of existing suppliers. Purchasing policy decisions: Fashion Bling 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 Bling. Account system design decisions: Fashion Bling may want to discontinue allocating purchasing department costs on the basis of dollar value of merchandise purchased. Allocation bases better capturing cause-and-effect relations at Fashion Bling are the number of purchase orders and the number of suppliers. ent store makes its own purchasing decisions. Barry Lee, assistant to the president of g department costs. For many years, Fashion Bling has allocated purchasing department A $100 item is allocated 10 times as many overhead costs associated with the purchasing ry." In a presentation at the seminar, a leading competitor that has implemented an ABC " were the two most important cost drivers of purchasing department costs. The dollar a significant cost driver. Barry Lee interviewed several members of the Purchasing ors conclusions regarding cost drivers for purchasing costs also applied to their Purchasing ar for Fashion Bling's 10 retail department stores: Purchasing $ Value of Department Merchandise Number of Costs Purchased Suppliers (PDC) (MP$) (# of S) $1,522,000 $68,307,000 125 1,095,000 33,463,000 230 542,000 121,800,000 8 2,053,000 119,450,000 188 1,068,000 33,575,000 21 517,000 29,836,000 29 1,544,000 102,840,000 101 1,761,000 38,725,000 127 1,605,000 139,300,000 202 1,263,000 130,110,000 196 ore of three variables are reasonable cost drivers of purchasing department costs. Regression 1 (MP$) F Significance F 5.888213164 0.041423692 P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 0.024940453 118658.5171 1342773.123 118658.5171 1342773.123 0.041423692 7.798509836 306.1336195 7.798509836 306.1336195 $80,000,000 $100,000,000 $120,000,000 $140,000,000 $160,000,000 Dollar Value of Merchandise ession 1: PDC = a + (b X MP$) = $1,041,421.37 + .003126704 (MP$) R2 0.079810356 Slope 0.003126704 Intercept 1041421.366 0.693860065 F Significance F 0.693860065 0.429019986 3.003737214 0.832982632 P-value Lower 95% Upper 95% 0.016974731 241910.0229 1840932.71 0.429019986 -0.005529169 0.011782576 5 (95% confidence interval), the t-value is: 2.306004133 241,910.0229 1,840,932.710 (0.005529169) 0.011782576 or 95% confidence interval. or 99% confidence interval. found little support for MP$ as a significant driver. l at the Miami store also believe MP$ is not a significant driver. (r2 >.30 passes). 0.079810356 2 is insignificant; the larger the t-value the better nd one tail equal to .025 (95% confidence interval), the t-value is: 2.306004133 egression analysis See Scatter diagram) but no strong evidence against constant variance. = 2.41 (Assumption of independence is not rejected.) servations, a D/W statistic in the range of 1.10 - 2.90 range indicates make reliable inferences. sion 2 (Number of Purchase Orders) 4,000 5,000 6,000 7,000 8,000 Number of Purchase Orders ession 2: PDC = a + (b X (# of PO)) = $722,537.85 + $159.48 (# of PO) R2 0.430635874 Slope 159.4842168 Intercept 722537.851 6.050762303 F Significance F 6.050762303 0.039329201 2.717997494 2.459829731 P-value Lower 95% Upper 95% 0.026330178 109522.1014 1335553.6 0.039329201 9.973354903 308.9950788 5 (95% confidence interval), the t-value is: 2.306004133 109,522.1014 1,335,553.6 9.973354903 308.9950788 or 95% confidence interval. or 99% confidence interval. le. Increasing the number of purchase orders increases the purchasing tasks to be undertaken. ates a reasonable fit. (r2 >.30 passes). 0.430635874 1 is significant; the larger the t-value the better egression analysis e Scatter diagram) = 1.97 (Assumption of independence is not rejected.) servations, a D/W statistic in the range of 1.10 - 2.90 range indicates make reliable inferences. ression 3 (Number of Suppliers) 150 200 250 Number of Suppliers ession 3: PDC = a + (b X (# of S)) = $828,814.24 + $3,815.69 (# of S) R2 0.386848791 Slope 3815.694852 Intercept 828814.2417 5.047352558 F Significance F 5.047352558 0.054854897 3.361368633 2.24663138 P-value Lower 95% Upper 95% 0.00991164 260221.7201 1397406.763 0.054854897 -100.8391101 7732.228814 5 (95% confidence interval), the t-value is: 2.306004133 260,221.7201 1,397,406.763 (100.8391101) 7,732.228814 or 95% confidence interval. or 99% confidence interval. le. Increasing the number of suppliers increases the costs of certifying vendors and managing pplier relationships. ates a reasonable fit. (r2 >.30 passes). 0.386848791 is significant. See Scatter diagram) tic = 2.01 (Assumption of independence is not rejected.) observations, a D/W statistic in the range of 1.10 - 2.90 range indicates independent. o make reliable inferences. purchasing department's cost drivers? Yes. (See above analysis.) ation for estimating purchasing department costs with the # of purchasee orders and the # of g department cost pool into two separate cost pools, one for costs related to purchase orders rate simple regression equation for each pool using the appropriate cost drive. ment costs at each store? stablish cause-and-effect links. o gain insight into how costs are driven. department to obtain their insight on cost drivers. e extended to a multiple regression analysis. 64 + $126.6639997 (# of PO) + $2903.297788 (# of S) 6.124960342 F Significance F 6.124960342 0.02899625 1.887618451 2.191600362 1.99002871 P-value Lower 95% Upper 95% 0.10102841 -122439.8024 1091483.072 0.064526149 -9.999951709 263.327951 0.08688758 -546.5058866 6353.101463 5 (95% confidence interval), the t-value is: 2.364624251 confidence intervals is: (122,439.8024) 1,091,483.072 nfidence intervals are: ber of purchase orders (9.999951709) 263.327951 ber of Suppliers (546.505886596) 6,353.101463 or 95% confidence interval. or 99% confidence interval. a + (b1)(# of PO) + (b2)(# of S) le. Both independent variables are plausible and are supported by mpetitor's research and Bling's own research. ates an excellent fit. (r2 >.30 passes). ficant for the (# of PO) variable y significant for the (# of S) variable tic = 1.91 (Assumption of independence is not rejected.) o make reliable inferences. odel would you recommend that Lee use? alue. Lee should use the results from PO) + $2,900.7309 (# of S) + -.000194148 (MP$) 3.500018051 F Significance F 3.500018051 0.089598866 1.547123214 0.006664422 1.985525089 1.788147391 P-value Lower 95% Upper 95% 0.172797006 -281232.7692 1248352.668 0.994898658 -0.007108942 0.007147771 0.094299047 -29.41354943 282.5692348 0.123970458 -1068.647038 6870.108839 5 (95% confidence interval), the t-value is: 2.446911846 confidence intervals is: (281,232.7692) 1,248,352.668 nfidence intervals are: rs of Merchandise Purchased (0.007108942) 0.007147771 ber of purchase orders (29.413549432) 282.5692348 ber of Suppliers (1,068.647038) 6,870.108839 or 95% confidence interval. or 99% confidence interval. mend that Lee use? bout the same r2, and the standard errors around the of S) + .000194148 (MP$) ore costly, not much improvement. in multiple regression analysis? ccounting; it does not arise in simple regression ression. Multicollinearity exists when two or ndard errors of the coefficients of the individual e independent variables in the multiple stent with some (but not very high) nt of correlation between independent variables ent variables for Fashion Bling are: # of PO # of Suppliers 1 0.285358146 0.285358146 1 MP$ # of PO 1 0.270157066 0.270157066 1 MP$ # of Suppliers 1 0.296190300 0.296190300 1 could be informative. relationships with suppliers so that y aggressively reduce the number ternal charge system for individual h department could be made for each nes. These internal charges would affect the total costs of Fashion Bling. discontinue allocating purchasing purchased. Allocation bases better umber of purchase orders and the Observation X 1 6 2 10 3 8 4 11 5 5 6 12 7 9 Hi-Low Method 8 7 Y 9 4 48 10 14 18 Total 86 310 30 Mean 31 Hi-Low Regression b-value 3 3.268398268 3.268398268 Intercept 6 2.891774892 2.891774892 Formula y = 6 + 3X y=2.891774892+ 3.268398268(X) SUMMARY OUTPUT (Shadded Yellow) Regression Statistics Multiple R 0.988576473 R Square 0.977283443 0.977283443 0.977283443 Adjusted R Square 0.974443873 Standard Error 1.693506825 Observations 10 ANOVA df SS MS F Regression 1 987.0562771 987.0562771 344.1660377 Residual 8 22.94372294 2.867965368 Total 9 1010 Coefficients Standard Error t Stat P-value Intercept 2.891774892 1.606987982 1.799500011 0.109636756 X 3.268398268 0.176177712 18.55171253 7.34874E-08 1.799500011 18.55171253 Hi-Low Actual value of Y when X is equal to 12 = 45 Best quess of Y, with knowledge of X equal to 12, is 42 Best quess of Y, with no knowledge of X, is the mean 31 Total Variation from the mean when X is = to 12 45 - 31 = 14 Explained Variation by knowing X is equal to 12 42 - 31 = 11 Unexplained Variation when X is equal to 12 45 - 42 = 3 RESIDUAL OUTPUT (Regression) Regression Explained by X Observation # X Y Predicted Y Residuals 1 6 22 22.5021645 -8.497835498 2 10 34 35.57575758 4.575757576 3 8 29 29.03896104 -1.961038961 4 11 40 38.84415584 7.844155844 5 5 19 19.23376623 -11.76623377 6 12 45 42.11255411 11.11255411 7 9 30 32.30735931 1.307359307 8 7 25 25.77056277 -5.229437229 9 4 18 15.96536797 -15.03463203 10 14 48 48.64935065 17.64935065 Total 310 0.000000000 60 50 Hi-Low Method X 14 4 40 10 30 y 20 10 0 0 2 Significance F 7.34874E-08 344.1660377 987.0562771 2.867965368 Lower 95% Upper 95% 2.306004133 = T-value for df =8 -0.813946037 6.597495821 -0.813946037 6.597495821 2.862131736 3.674664801 2.862131736 3.674664801 Regression 45 42.11255411 31 14 11.11255411 42.11233411 - 31 2.887445887 45 - 42.11255411 Unexplained Squared Residuals Squared Total Variation Total Variation Squared 72.21320815 -0.502164502 0.252169187 -9 -9 81 20.93755739 -1.575757576 2.483011938 3 3 9 3.845673807 -0.038961039 0.001517963 -2 -2 4 61.53078091 1.155844156 1.335975713 9 9 81 138.444257 -0.233766234 0.054646652 -12 -12 144 123.4888589 2.887445887 8.337343753 14 14 196 1.709188359 -2.307359307 5.323906973 -1 -1 1 27.34701374 -0.770562771 0.593766983 -6 -6 36 226.0401604 2.034632035 4.139727516 -13 -13 169 311.4995783 -0.649350649 0.421656266 17 17 289 987.0562771 0.000000000 22.94372294 0 0 1010 0.977283443 1010 0.977283443 0.977283443 0.977283443 r= 0.988576473 Graph -- Data 4 6 8 10 12 x Y 14 16 Anna Martinez is checking to see if there is any relationship between newspaper advertising and sales revenue at the Casa Real restaurant where she is the financial manager. She has obtained the following data for the past 10 months: Advertising Month Revenues Costs March $50,000 $2,000 April $70,000 $3,000 May $55,000 $1,500 June $65,000 $3,500 July $56,000 $1,000 August $65,000 $2,000 September $45,000 $1,500 October $80,000 $4,000 November $55,000 $2,500 December $60,000 $2,500 Using the high-low method, determine the cost function which could be used to estimate restaurant revenues based on advertising costs. Revenues Costs 2 $80,000 $4,000 2 $56,000 $1,000 2 $24,000 $3,000 $8.00 2 $80,000 $32,000 $48,000 $56,000 $8,000 $48,000 2 Y = $48,000 + ($8.00 X Advertising Costs)