Chapter 11 Cost Estimation ANSWERS TO REVIEW QUESTIONS 11.1 Companies estimate the relation between costs and cost drivers (1) for cost management, (2) for decision making, and (3) for planning and standard setting. 11.2 Engineering estimates are based more on the operations in the company and industry standards, whereas account analysis and regression are based more on company records. 11.3 True. The relevant range is often limited to the range of observations included in the data set because extrapolation beyond the observed activity levels often does not provide valid estimates. 11.4 Engineering estimates are particularly helpful when (1) attempting to compare company operations with standards, (2) trying to estimate costs for projects that have not been undertaken in the past (e.g., new construction, major special orders), and (3) considering alternatives to present operations, such as assembly line reorganization and similar changes. 11.5 The biggest problem likely to be encountered from the indiscriminate use of regression methods is that the model may not have any logical foundation. This may result in a model that appears sound on a statistical basis, but with no logical relationship between the Y and the X's. 11.6 The longer the data series used in the analysis, the easier it is to see a trend in the data. When using any method, the longer the data series, the greater the likelihood of having the widest possible range of observations. When using statistical methods, the more observations, the smaller the standard errors and the tighter the resulting estimates. On the other hand, the longer the data series, the more likely that operating conditions, technology, prices and costs have changed. Thus, the older data may not be very representative of the operations expected over the period for which the estimate is made. 11.7 Answers will vary. Examples include machine costs (e.g., copiers, automobiles, airplanes, machines in a factory), space costs (e.g., number of classrooms), and service costs. 11.8 The t-statistic indicates the statistical significance of the coefficients, or b’s. 11.9 False. Violation of the assumption that the residuals are homoscedastic means the residuals are affected by the level of the independent variable; that is , they are heteroscedastic. ANSWERS TO CRITICAL ANALYSIS 11.10 a. Direct labor would be committed if company policy or a union contract limited the company's ability to lay off unneeded personnel or if management were contemplating a change in facilities but maintaining the same labor force. b. Equipment depreciation would be a variable cost if computed on a unit-of-production basis. c. Utilities are variable above the minimum, but if the company's usage falls to the minimum or below, the costs would be committed to the minimum contracted service level. d. Supervisory salaries normally increase in steps. If the activity range is narrow, the costs are committed; but if the range is wide enough so that several "steps" would fall within the range, then the costs would appear to be variable. 11.11 All data analysis involves some subjectivity, because someone must choose the time periods, organizational units, and categories and measures of costs and activities. All of these are subjective choices, but some organizations have data guidelines that limit choices. However, multiple regression analysis appears to be more objective in how it identifies significant cost drivers. Account analysis, on the other hand, has no objective way of discriminating among cost drivers. All might appear to be important, but in most cases relatively few cost drivers explain most of total costs. 11.12 Data in the historical accounting records can be used if they are likely to reflect conditions that will occur in the future. If the impacts of future differences can be estimated, then one can modify historically based predictions to reflect future differences. 11.13 In stable environments, historical data generally are useful for making predictions about the future. In periods of organizational change, price instability or technological innovation, use of historical data without adjustment will likely give incorrect estimates. The easiest adjustment involves anticipating general price-level changes (e.g., inflation) by adjusting cost driver rates for expected general price changes. If the cost per unit for a specific activity is known to be increasing, and processes are not modified (a big if), then one can also adjust cost driver rates for specific price changes. 11.14 McDonald's moves new employees quickly down the learning curve by giving them training and by giving clear and structured work assignments. In this way, new employees work as if they are experienced soon after they are hired. 11.15 Absorption costing does require the allocation of all product costs, including “fixed” overhead, to units of product. A thorough ABC or multiple regression analysis might succeed in transforming much of the so-called fixed overhead into direct or variable costs by finding the underlying cost-drivers. It is unlikely that all product costs can be transformed and some fixed or committed product cost will remain and must be allocated. However, less total cost should be left for arbitrary cost allocations, and more of the cost should be understood and traceable. Therefore, cost estimation should be more accurate. This seems like a worthwhile gain. 11.16 Answers will vary. Our searches generated applications of regression to estimating economic growth in particular regions, estimating transportation costs, and estimating plant, human, and animal individual and population growth. 11.17 The friend's actions are not unethical as long as he or she revealed the sources of data. Ideally, the friend should also reveal the results from using both the most recent 12 months and the previous time period. The results using the older data are not likely to be of much managerial use unless they are adjusted for changes in prices and operations that have occurred since the data were recorded. 11.18 This is a hard decision and partly depends on the materiality of the error. For example, $100,000 sounds like a lot of money, but it would immaterial in an analysis of many millions. The top executive probably would not want to be bothered with minor revisions to his or her presentation. However, if the Board is going to discuss and decide an important issue that would be affected by the revision of your analysis using the correct number (that is, the error is material), then the information should be passed on to the top executive. (Better that your boss be upset now than that the error come to light later when it affects the company and many other people.) In any event, the revised analysis should be given to the top executive as soon as is practical. 11.19 You should report your observations to your superior. You may have uncovered an example of a serious data or internal control problem. 11.20 Assume the regression involves cost estimation. The relations between costs and activities may be considerably different in different parts of the world. For example, if your analysis includes data from Mexico, China, Finland and Germany, you would find that labor costs per hour are much higher in Finland and Germany. You also are likely to find that labor efficiencies vary across countries. Energy costs and transportation costs also vary across countries. The rate of inflation varies across countries making older data more problemmatic in some countries than in others. Currencies fluctuate in value. Translating (say) dollars into pesos on one date will give different values than if translated on another date. SOLUTIONS TO EXERCISES 11.21 (10 min) Cost-behavior patterns a. Mixed or Semivariable b. Step c. Variable d. Fixed 11.22 (10 min) Cost-behavior patterns a. Mixed or Semivariable cost--Graph # 1. b. Step cost--Graph # 3. c. Variable cost--Graph # 4. d. Fixed cost--Graph # 2. 11.23 (30 min) Learning curves b. Both orders meet General Electric’s margin requirement. The order of 8 units would generate a margin of $1,150,000 (= $2,500,000 - $1,350,000) which is 46% of the sales price. (46% = $1,150,000/$2,500,000) The order of 16 units would generate a margin of $1,975,000 (= $4,000,000 - $2,025,000) which is 49.375% of the sales price. (49.375% = $1,975,000/$4,000,000) 11.24 (20 min) Learning curves b. At $30 per hour, it will cost $3,686 (= $30 x 122.880 hours) to proofread 8 statements. EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE 11.25 (20 min) Learning curves Ln Y = 5.2983 – 0.2345 Ln X a. The intercept, 5.2983, is the natural log of the cost of the first unit produced. The anti-log of 5.2983 is the cost of the first unit produced, which is $200 (easily found with most calculators). The slope, - 0.2345, is the learning coefficient that represents the rate of average cost reduction for levels of X. b. The percentage rate of learning for each doubling of output is found by solving the following equation for the unknown percentage rate, L: -0.2345 = Ln(L) ÷ Ln(2) Ln(L) = -0.2345 x .6931 = - 0.1625 L = Ln-1(- 0.1625) = .85 = 85% 11.26 (10 min) Simple regression a. Insert 500 machine hours into the equation to get an estimate of the total cost of maintenance: C = $6,000 + ($5.25 x 500) = $8,625 b. Using 30 months of data to estimate this equation assumes that the underlying cost driver activities and input prices have been stable over this period. It is rare for any organization these days to be that stable, which means one should expect additional cost drivers (e.g., technology, product complexity) other than volume of machine hours. 11.27 (10 min) Simple regression a. Insert 1,000 tax returns into the equation to get an estimate of the total costs for an office that prepares 1,000 tax returns: C = $112,000 + ($154 x 1,000 ) = $266,000 b. Using observations from 24 offices for one time period assumes that the offices are quite similar (ideally, identical) in cost-driving activities and input markets. Some differences should be expected (office age, office size, population income and growth, etc.) that might drive costs in addition to the number of tax returns. 11.28 (20 min) Simple regression EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE a. Estimated total costs for a month in which 3,000 meals are sold: Total costs = $2,153 + ($2.891 x 3,000) = $10,826 b. Estimated fixed costs = the intercept of the equation = $2,153 c. Estimated total variable costs for a month in which 3,000 meals are sold: Total variable costs = $2.891 x 3,000 = $8,673 d. 7,000 meals is outside of the range of observations used to construct the cost function (that is, outside of the relevant range). Therefore, the cost function is likely to be invalid or at least will have to be modified. For example, at 7,000 meals, CC Catering may have to rent additional space and acquire additional equipment, which would step up its fixed costs. 11.29 (20 min) Simple regression a. Estimated total costs for a month in which 2,200 meals are sold: Total costs = $2,153 + ($2.891 x 2,200) = $8,513 b. Estimated fixed costs = the intercept of the equation = $2,153 c. Estimated total variable costs for a month in which 2,200 meals are sold: Total variable costs = $2.891 x 2,200 = $6,360 d. 400 meals is outside of the range of observations used to construct the cost function (that is, outside of the relevant range). Therefore, the cost function is likely to be invalid or at least will have to be modified. Perhaps CC Catering would reduce its committed resources at least temporarily. 11.30 (20 min) Simple regression a. Estimated total costs for a month in which 2,100 meals are sold: Total costs = $2,153 + ($2.891 x 2,100) = $8,224 b. Estimated fixed costs = the intercept of the equation = $2,153 c. Estimated total variable costs for a month in which 2,100 meals are sold: Total variable costs = $2.891 x 2,100 = $6,071 d. 8,000 meals is outside of the range of observations used to construct the cost function (that is, outside of the relevant range). Therefore, the cost function is likely to be invalid or at least will have to be modified. For example, at 8,000 meals, CC Catering may have to rent additional space and acquire additional equipment, which would step up its fixed costs. 11.31 (20 min) Multiple regression EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE 11.32 (20 min) Multiple regression 11.33 (30 min) High-low and simple regression a. High-low estimate Miles driven Costs Highest (limo 6) 13,200 $4,000 Lowest (limo 8) 9,200 $3,000 Variable cost estimate = (Cost at highest activity – Cost at lowest activity) / (Highest activity – Lowest activity) = ($4,000 – $3,000) / (13,200 miles - 9,200 miles) = $1,000 / 4,000 miles = $ 0.25 per mile Committed costs = Total costs – Variable costs = $4,000 – ($0.25 x 13,200 miles) = $4,000 - $3,300 = $700 The cost equation then is: Costs = $700 + $0.25 miles b. For 10,000 miles: Total costs = $0.25 x 10,000 + $700 = $3,200 c. The high-low method uses only two data points, whereas regression uses all available data points. (Also, the highest and lowest activity level may be outliers that are not representative of the data set as a whole.) EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE 11.34 (30 min) High-low compared to simple regression Abbreviated simple regression results (from Excel) are: EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE SUMMARY OUTPUT Regression Statistics R Square 0.569651316 Standard Error 272.5599779 Observations 10 Coefficients Standard Error t Stat Intercept 810.9177098 852.2320386 0.951522 Miles 0.241389527 0.074178683 3.254163 According to the regression equation, the estimated variable cost is $0.241 per mile and the estimated fixed costs is $811 per limousine. The high-low and regression results are similar in this case. (See exercise 11.33 for the high-low results.) Estimated total costs = $0.241 x 10,000 + $811 = $3,225 The following scatter graph shows that limo #9 appears to have higher than expected costs. 11.35 (30 min) High-low and simple regression a. High-low estimate Pizzas produced Costs Highest (month 6) 15,200 $ 41,100 Lowest (month 1) 8,600 $ 28,560 Variable cost estimate = (Cost at highest activity – Cost at lowest activity) / (Highest activity – Lowest activity) = ($ 41,100 – $ 28,560) / (15,200 pizzas - 8,600 pizzas) = $12,540 / 6,600 pizzas = $1.90 per pizza Fixed costs = Total costs – Variable costs = $41,100 – ($1.90 x 15,200 pizzas) = $41,100 - $28,880 = $12,220 The cost equation then is: Costs = $12,220 + $1.90 pizzas b. For 4,000 pizzas: Total costs = $ 1.90 x 4,000 pizzas + $12,220 = $ 19,820 c. The high-low method uses only two data points, whereas regression uses numerous data points. (Also, the highest and lowest activity level may be outliers that are not representative of the data set as a whole.) EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE d. 11.36 (30 min) High-low compared to simple regression EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE Abbreviated simple regression results are as follows: Regression Statistics R Square 0.661704881 Adjusted R Square 0.619417992 Standard Error 2688.918327 Observations 10 Coefficients Standard Error t Stat Intercept 16051.26625 4612.882067 3.479661 Pizzas Produced 1.476109774 0.37315508 3.955754 According to the regression equation, the estimated variable cost is $1.476 per pizza and the estimated fixed cost is $16,051 per month. The high-low results estimate a lower fixed cost and a higher variable cost per unit, probably because the high-low observations are not representative of the data set as a whole. (See exercise 11.35 for the high-low results.) Estimated total costs = $16,051 per month + $1.476 per pizza x 4,000 pizzas = $21,955 The following graph indicates no unusual data scatter. 11.37 (20 min) Interpretation of regression results a. 88.03% of the variation in overhead costs is explained by the independent variable, which is the R2 b. For 20,000 direct-labor hours, the total overhead cost estimate is: Total overhead costs = $112,153 + ($5.496 x 20,000) = $112,153 + $109,920 = $222,073 c. Charges (revenues) for using the debit card = $1,000,000 (= $1 per transaction x 1 million transactions); Costs = $722,073 (= $500,000 direct labor + $222,073 overhead) Yes, the $1 charge will cover the costs of 1 million transactions ($1,000,000 in revenues exceeds $722,073 in costs) 11.38 (15 min) Interpretation of regression results Many companies increase their advertising when sales are declining and cut back on advertising when they are operating at capacity. These phenomena make it appear as if there is a negative relationship between advertising and sales. A better model might be developed by relating this month's sales to a prior month's advertising. (Similar problems exist for repair and maintenance costs because machines are usually given routine repairs and maintenance during slow periods.) 11.39 (15 min) Interpretation of regression results; simple regression a. Costs = $1,451.784 + ($2.551 x student hours) b. Estimated cost per month = $1,452 (rounded) + ($2.551 x 250 student hours per month) = $2,089.75 11.40 (20 min) Account analysis method a. Unit-level cost per unit = $24,000/100,000 units = $0.24 b. Unit-level cost per unit = $0.24 x 1.2 = $0.288 c. Facility-level costs = $25,000 x 1.1 = $27,500 d. Estimated costs =($0.288 x 120,000 units) + ($88* x 100 batches) + ($1,980** x 12 products) + $27,500 facility costs = $34,560 + $8,800 + $23,760 + $27,500 = $94,620 * $88 = ($8,000 x 1.1) / 100 batches ** $1,980 = ($18,000 x 1.1) / 10 11.41 (20 min) Account analysis method a. Unit-level cost per unit = $160,000 / 50,000 units = $3.20 Batch-level cost per batch = $40,000 / 50 batches = $800 Product-level cost per product = $180,000 / 8 products = $22,500 b. Facility-level costs = $50,000 x 1.05 = $52,500 c. Estimated costs = ($3.36* x 60,000 units) + ($832** x 100 batches) + ($23,400*** x 12 products) + $52,500# facility costs = $201,600 + $83,200 + $280,800 + $52,500 = $618,100 * $3.36 = $3.20 x 1.05 ** $832 = $800 x 1.04 *** $23,400 = $22,500 x 1.04 # From part b 11.42 (10 min) Account analysis Forecast Expected activities Cost driver rate Expected costs Facility 1 $ 2,550.00 $ 2,550.00 Meals 3,000 1.42 4,260.00 Jobs 30 29.55 886.50 New products 4 175.00 700.00 New customers 3 225.00 2,250.00 Total costs $ 10,647 11.43 (10 min) Engineering estimates Forecast Expected activities Cost driver rate Expected costs Facility 1 $ 3,210.00 $3,210.00 Meals 3,500 1.88 6,580.00 Jobs 50 35.50 1,775.00 New products 5 168.00 840.00 New customers 2 222.00 1,776.00 Total costs $ 14,181 11.44 (20 min) Interpretation of regression data a. At 4,200 employees, the cost estimate would be: Personnel costs = $8,421 + ($492.70 x 4,200 employees) (rounded) = $8,421 + $2,069,340 = $2,077,761 b. The relation makes economic sense. The t-statistic of the coefficient for number of employees is 2.987, which is well above the t-value for a 5% significance (or 95% confidence) level. Therefore, you should feel confident that number of employees is a significant cost driver of personnel costs. SOLUTIONS TO PROBLEMS 11.45 (30 min) Interpretation of regression results EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE If you run a simple regression using Witt's data, you will find that his results are correct. However, if you prepare a scatter graph or simply examine the data carefully, you will see that observation number 5 is an outlier. Observation number 5 has a much higher cost considering the number of deliveries compared to the other observations. If you rerun the regression with observation number 5 excluded, you get the following results: Overhead = $9,776 per month + $11.686 per unit, which is closer to the controller's estimate. We suspect that the controller's staff thought about a "typical" month when deriving their estimate of $9,000 per month + $12 per unit. Comparing Witt's regression to the subjective analysis brought to light the existence of the outlier. Before tossing out the unusual cost, you should investigate its cause The problem with month 5 may be data error or there may be a problem, such as a high level of nonvalue-added costs, to be addressed by management. Abbreviated regression results and a scatter graph of the original data follow. Regression Statistics R Square 0.667356644 Standard Error 12986.21051 Observations 13 Coefficients Intercept 26501.28036 Deliveries 10.69989948 Regression analysis without the unusual cost yields the following results Regression Statistics R Square 0.984323784 Standard Error 2635.659661 Observations 12 Coefficients Intercept 9776.561937 Deliveries 11.68578345 11.46 (20 min) Interpretation of regression results a. The letter b is the cost driver rate, also known as the coefficient of the independent variable. b. The letter y is the dependent variable. In cost estimation, it represents "costs." c. The letter x is the dependent variable. In cost estimation, it is the cost driver. d. The estimated costs for 360 hours is: Costs = $684.65 + ($7.2884 x 360 hours) = $3,308.47 e. 79.724% of the total variance can be explained by the regression equation. 11.47 (40 min) Multiple regression, activity-based costing EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE a. Abbreviated multiple regression results follow: SUMMARY OUTPUT Regression Statistics R Square 0.889071361 Adjusted R Square 0.861339202 Standard Error 2397.953592 Observations 16 Coefficients Standard Error t Stat Intercept 40015.68778 3808.664173 10.50648888 Analyses 2009.385159 765.9583892 2.62336073 Customer accts 31.54960694 14.1471508 2.230103247 Paychecks 9.04684293 5.765060282 1.56925383 The monthly regression equation is Costs = $40,016 + $2,009.38 x Analyses + $31.550 x Customer Accounts + $9.047 x Paychecks Processed b. Estimated costs are as follows: Activity level Cost driver rate Estimated cost (rounded) Facility 1 $ 40,015.69 $ 40,016 Analyses 3 2,009.39 6,028 Customer accounts 200 31.55 6,310 Paychecks 1,000 9.05 9,047 Total costs $ 61,401 c. The company might save $9,047 for the month, or more if some facility cost related to processing paychecks can be eliminated. 11.48 (30 min) Account analysis a. Information needed includes cost driver activity and the cost behavior (variable, mixed, step, committed) for each of the components of cost. b. Account analysis of costs Total cost Activity* Cost-driver rate Facility $ 610,000 16 $ 38,125.00 Analyses 60,000 30 2,000.00 Customer accounts 110,000 3,650 30.13 Paychecks 180,000 15,945 11.29 Total $ 960,000 c. Forecast Activity Cost-driver rate Estimated Costs Facility 1 $ 38,125.00 $ 38,125.00 Analyses 3 2,000.00 6,000.00 Customer accounts 200 30.13 6,026.90 Paychecks 1,000 11.29 11,288.81 Total $ 61,440.71 d. Estimated cost savings $ 11,288.81 per month, without considering whether any facility or related costs could be saved. * Activity volumes are from problem 11.47. 11.49 (15 min) Engineering estimates a. Engineering analysis of costs Per unit Activity Estimated costs Facility $ 40,000.00 1 $ 40,000.00 Analyses 2,500.00 3 7,500.00 Customer accounts 50.00 200 10,000.00 Paychecks 5.00 1,000 5,000.00 Total $ 62,500.00 e. Estimated cost savings = $ 5,000.00 per month, without considering whether any facility or related costs could be saved. 11.50 (40 min) Multiple regression, activity-based costing EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE a. Abbreviated multiple regression results follow: Regression Statistics R Square 0.919250408 Adjusted R Square 0.89440438 Standard Error 92496.57637 Observations 18 Coefficients Standard Error t Stat Intercept 502713.1293 254262.3877 1.977143115 Units 9.218625234 4.058125116 2.271646381 Batches 566.1379567 512.6471965 1.104342247 Customer orders 1774.068751 644.5248619 2.752521827 New products 62939.27355 27326.92108 2.303196667 The monthly regression equation is: Costs = $502,713 + $9.2186 x Units + $566.1379 x Batches + $1,774.0687 x Customer orders + $62,939.2375 x New products b. The estimated costs of doing business given the following activity levels (i.e., cost driver volumes) are computed using the cost driver rates computed above. b. Forecast Activity Cost per unit (rounded) Estimated cost Facility 1 $ 502,713 $ 502,713 Units 30000 9.22 276,559 Batches 500 566.14 283,069 Customer orders 150 1,774.07 266,110 New products 3 62,939.27 188,818 Total cost $ 1,517,269.00 c. Cost saving Activity Cost per unit Cost saving Batches 100 $ 566.14 $ 56,613.80 , not considering any possible savings in facility costs or other costs. Note, however, that the batch coefficient is not statistically significant, so this cost savings estimate might not be reliable. Further investigation into the batch cost driver rate is warranted. 11.51 (30 min) Account analysis a. The company would have to obtain total cost data for 18 months for each of the following costs: Unit-level costs, batch-level costs, costs of processing customer orders, costs of developing new products and facility-level costs. (See part b.) b. Account analysis of costs Total cost Activity Cost per unit Facility $ 7,200,000 18 $ 400,000.00 per facility Units 6,900,000 685,750 10.06 per unit Batches 8,000,000 11,733 681.84 per batch Customer orders 6,200,000 3,337 1,857.79 per customer order New products 2,600,000 48 54,166.67 per new product Total costs $ 30,900,000 c. Forecast Activity Cost per unit Estimated cost Facility 1 $ 400,000.00 $ 400,000.00 Units 30000 10.06 301,859.28 Batches 500 681.84 340,918.78 Customer orders 150 1,857.79 278,668.38 New products 3 54,166.67 162,500.00 Total cost $ 1,483,946.44 11.52 (20 min) Engineering estimates Forecast Activity Cost per unit Estimated cost Facility 1 $ 400,000.00 $ 400,000.00 Units 30000 9.00 270,000.00 Batches 500 500.00 250,000.00 Customer orders 150 1,500.00 225,000.00 New products 3 60,000.00 180,000.00 Total cost $ 1,325,000.00 11.53 (90 min) Methods of cost estimation--account analysis Answers will vary because of the judgment and data interpretation required. Here is one approach. Use the following graphs to judge which costs are variable, step, or committed. Divide total variable activity costs by the cost driver activity. Sum the step and committed costs. EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE Variable costs per test = $0.577 + 3.251 + 0.520 + 0.434 + 0.648 = $5.430 per test Committed costs per month = $16,300 + 12,800 + 1,200 = $30,300 if tests 4,737 11.54 (45 min) Learning curves a. The basic premise of the learning curve is that efficiency increases as one gains experience, particularly in performing repetitive tasks. b. 16 units required 5,440 direct-labor hours (5,440 = 3,200 + 2,240) or an average of 340 direct-labor hours (340 hours = 5,440 / 16 units). The first 8 units required 3,200 units or an average of 400 direct-labor hours (400 hours = 3,200 / 8 units). 340 / 400 = 85% learning curve. c. Since no significant improvement is expected after the first 32 units, the standard will be set for each unit of Inexcess based on the average time for units 17 through 32. This is calculated as follows: The average time per unit for the lot of 32 units (unit numbers 1-32) = .85* x 340 hours* = 289 hours per unit. Therefore the total time to produce 32 units = 289 x 32 units = 9,248 hours. Now the total time to produce the 16 units, numbered 17-32, = 9,248 total - 5,440 hours to produce the first 16 units (see requirement b above) = 3,808 hours. The average time per unit for items 17-32 = 3,808 / 16 units = 238 hours per unit. Set the standard at 238 hours per unit. * 85% was the learning curve calculated in part b, and 340 hours was the average time per unit for units 1 through 16 as calculated in part b. EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE d. Using the direct labor standard developed above: Amount per unit: f. Answers will vary. Some uses include preparing budgets, cost estimates for bidding (as in this problem), obtaining and scheduling labor, and setting performance standards. 11.55 (30 min) Learning curves a. Ignoring learning effects, the recommendation was correct although the cost to produce gauges was overstated. That overstatement occurs because many of the costs listed will be incurred regardless of whether the gauges are purchased or produced. In fact, the total costs of producing 100 gauges should have been reported as $85,000 or $850 per gauge, which includes the materials, labor and labor related (i.e., variable) overhead. b. An 80% learning curve, gives the following labor-related and material cost for 800 gauges: This analysis indicates that Krylon should produce the gauges rather than purchase, assuming that it does not have better opportunities for its productive capacity. SOLUTIONS TO CASES 11.56 (60 min) Running regressions from published data a. Reports will vary. In addition to the sources listed, consider referring students to the SEC’s Edgar or LEXIS-NEXIS databases. b. The difference between actual and estimated costs is the "residual." c. This question requires that the student use the standard error of the coefficient, which is available from statistical software packages. d. Generally, revenue is a good predictor of cost of goods sold, although one might argue that the direction of causality should go the other direction. There are cases in which cost of goods sold may (surprisingly) not be highly correlated with revenues. We have found some such cases in high-tech companies in which virtually all of the work that generated the revenue was done long before the sale was made. 11.57 Recommended analysis steps: 1. Plot each credible independent variable (X) with the dependent variable (Y). Use scatter-plot. 2. Correct or delete obviously incorrect data, as indicated. 3. Compute pairwise correlation coefficients of all variables. 4. Compute simple and multiple regressions as appropriate. 5. Choose among regressions to find the best model(s): a. Highest R-sqd (adjusted R-sqd for multiple regressions) b. Most significant F-statistic c. X-coefficients with proper signs d. X-coefficients with suffcient statistical significance (t-statistic > 2.0) e. Parsimony and economy of use 6. Evaluate predictive ability of each model 7. Use best model to estimate costs EXCEL SOLUTIONS ARE FOUND IN EXCEL SOLUTIONS FILE a. Scattergraphs follow. Division #10’s data stand out. Division #10’s data appear to be consistently misstated. Either drop the division or restate by moving decimal point. The latter seems preferable here because the mistake seems obvious and data are scarce. b. Except for first-time pass rate, performance seems consistent across divisions with respect to cause and effect of costs. Why divisions have such varying defect rates, cycle times, and first-time pass rates is unclear. The case description implies the divisions should be more alike. Additional information about employee training, and turnover, supplier problems might help diagnose sources of problems in low performing divisions (see Chapter 7). c. Regression analyses follow. Correlation analysis with revised data Defects per month First-time pass rate, % Average cycle time per unit (minutes) Manufacturing OH Cost Defects per month 1 First-time pass rate, % 0.50108889 1 Average cycle time per unit 0.64455545 -0.18339053 1 Manufacturing OH Cost 0.82628927 0.07014691 0.869099637 1 This analysis shows that defects and cycle time are likely to be good predictors of manufacturing OH cost, but first-time pass rate is not. Defects and cycle time are fairly highly correlated, which might make interpretations of their coefficients difficult in a multiple regression. SUMMARY OUTPUT Dependent = Manufacturing overhead cost (model 1) Regression Statistics R Square 0.75027698 Adjusted R Square 0.73466929 Standard Error 2687.71798 Observations 18 Coefficients Standard Error t Stat Intercept -46376.741 18413.0191 -2.518692945 Average cycle time per unit 1560.52739 225.076359 6.933324307 SUMMARY OUTPUT Dependent = Manufacturing overhead cost (model 2) Regression Statistics R Square 0.87269245 Adjusted R Square 0.84541226 Standard Error 2051.52805 Observations 18 Coefficients Standard Error t Stat Intercept -22435.451 22079.4844 -1.016122064 Defects per month 160.778121 58.6702379 2.740369341 First-time pass rate, % -42.162075 102.806268 -0.410111911 Average cycle time per unit 1006.87142 289.31353 3.480208563 SUMMARY OUTPUT Dependent = Manufacturing overhead cost (model 3) Regression Statistics R Square 0.87116302 Adjusted R Square 0.85398475 Standard Error 1993.83421 Observations 18 Coefficients Standard Error t Stat Intercept -29144.695 14410.9815 -2.022394857 Defects per month 142.869985 38.0826864 3.75157319 Average cycle time per unit 1086.02446 209.466046 5.18472793 Model # 3 appears to be the best because of its highest adjusted R-square and significant coefficients. The negative intercept is not a concern in any of the models because this is the best parameter to describe the total costs within the relevant range. It should not be used alone or as an estimate of committed cost outside the relevant range. d. Cost prediction accuracy Prediction data (next month) Predictions Division Average defects per month First-time pass rate, % Average cycle time per unit (minutes) Actual Manufacturing OH Cost Predicted Manufacturing OH Cost (Model 1) Predicted Manufacturing OH Cost (Model 2) Predicted Manufacturing OH Cost (Model 3) 1 146 73.00 81.00 $ 78,580 $ 80,026 $ 79,517 $ 79,682 2 150 68.00 79.00 78,350 76,905 78,357 78,082 3 118 80.60 75.00 70,350 70,663 68,653 69,166 4 134 63.00 80.00 77,330 78,465 77,002 76,882 5 131 78.20 76.00 72,150 72,223 71,852 72,109 6 149 68.90 82.00 81,060 81,587 81,179 81,197 Mean absolute error $ 823.2 $ 564.3 $ 530.1 Root mean squared error $ 987.3 $ 813.1 $ 696.5 Not surprisingly, Model 3 has the lowest prediction errors. If the underlying process and activities that generate costs are stable, the statistically best regression model should also be the best out-of-sample predictor. Solution Manual for Cost Management: Strategies for Business Decisions Ronald W. Hilton, Michael W. Maher, Frank H. Selto 9780073526805, 9780072430332, 9780072830088, 9780072299021, 9780072881820, 9780072882551, 9780070874664, 9780072388404, 9780072343533
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