chapter 5 - cost estimation

©The McGraw-Hill Companies, Inc., 2008 Solutions Manual, Chapter 5 129

5 Cost Estimation

Solutions to Review Questions

5-1. Common methods of cost estimation are engineering analysis, account analysis, and statistical analysis of historical data.

5-2. Engineering estimates are based on design specifications and industry and firm cost standards.

5-3. Engineering estimates are particularly helpful when:

• Attempting to compare company operations with standards; • Trying to estimate costs for projects that have not been undertaken in the past

(e.g., new construction, major special orders such as defense items); • Considering alternatives to present operations, such as assembly line

reorganization and similar changes, where it would be too costly to carry out the change and then see if it was cost-effective.

5-4. 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 Y and X's, the model may not continue to provide good predictions. A number of spurious correlation and regression studies have been presented in the literature. For example, a simple run of correlations between average education levels in the U.S. and U.S. inflation rates might lead one to conclude that education causes inflation.

©The McGraw-Hill Companies, Inc., 2008 130 Fundamentals of Cost Accounting

5-5. The longer the data series used in the analysis, the easier it is to see a trend in the data when using the scattergraph method. 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 deviations 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 order data may not be very representative of the operations expected over the period for which the estimate is made.

5-6. Simple regression assumes a single independent variable (e.g., cost driver) and multiple regression assumes two or more independent variables.

5-7. Adjusted R2 considers the number of independent variables used in the estimation and “adjusts” the R2 to reflect the use of additional variables.

5-8. Accurate cost estimates improve decision-making. Better decisions lead to higher company value.


Solutions to Critical Analysis and Discussion Questions

5-9. a. Direct labor would be fixed if 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 fixed. d. Supervisory salaries normally increase in steps. If the activity range is narrow, the costs are fixed; but if the range is wide enough so that several "steps" would fall within the range, then the costs would appear to be variable. e. A certain level of spoilage may be a fact of life in some operations.

5-10. Account analysis incorporates the judgment of the executive where experience would be quite helpful. As a result it may include factors that are not easily captured in statistical models. The best overall cost estimate may be derived by considering both account analysis results and statistical results.

5-11. Data in the historical accounting records should only be used insofar as they are likely to continue in the future. In periods of price instability or technological innovation, use of the historical data without adjustment is likely to result in incorrect estimates. A better alternative is to use the costs that are expected to be incurred during the period for which the cost estimate is prepared.

5-12. One may:

• Adjust the data to present all costs in some common dollar measure; • Use activity measures that are expressed in dollars that move with the price

change effects in the cost to be estimated, • Use a multiple regression approach with a suitable price index as one of the

predictor variables.


5-13. The scattergraph can be useful in checking for outliers in the data—the regression model will not pick this up. Also, the scattergraph may point out changes in the data series that need to be considered when constructing the regression database.

5-14. It is possible for empirical data to show a negative intercept even though fixed costs cannot be negative. It may be that the slope of the cost curve is particularly steep over the values used in the estimation process. It may be that the operations are relatively far away from the intercept. This would be particularly likely if the company were operating close to capacity. Negative intercepts usually mean that there is some error in the specification of the cost estimate. If the company is operating close to capacity, for example, then the assumption of a linear cost function may be in error—or may only be a reasonable approximation in the range of activity close to capacity.

5-15. How well defined is the model? That is, does the one independent variable explain variation in the dependent variable? Are there any outliers? Is the relation linear?

5-16. This was probably unethical. Of course, it might be that there are legitimate reasons for dropping the observations. They might represent very unusual conditions (a strike, bad weather) that would not be expected to occur.

5-17. You should probably tell the executive about the error. If correcting the errors does not change the result (perhaps there are offsetting results or they are not significant), it might matter less when you tell the executive, but he or she needs the correct information to make good decisions.

5-18. You should report your concerns. At a minimum, the manager responsible for recording costs should be told.

5-19. Answers will vary. (1) Income tax preparers become more proficient as they learn; (2) graders on an exam can process an individual exam paper in less time as they complete more; and, (3) a travel agent will be able to book a flight in less time the more reservation requests they handle.


5-20. It is possible that material costs could be affected by learning curves. If material is difficult to work with making it subject to breakage or spoilage, employees will develop skills in working with it resulting in less scrap.

5-21. By using standardized techniques, McDonalds is able to transmit information to its employees effectively so they learn quickly.


Solutions to Exercises

5-22. (15 min.) Methods of Estimating Costs—Account Analysis: FarOut Cards. a. Cost estimate with new costs and volume.

Cost Item

Last Year’s Cost

(1)

Cost Change

(1 + Cost Increase)

(2)

This Year’s Cost

(at last year’s

volume) (1) x (2) =

(3)

Growth in Volume

(4)

This Year’s Cost

(3) x (4) = (5)

220,000 Direct materials $630,000 × 120% = $756,000 × 210,000 = $792,000

220,000 Direct labor .................. 525,000 × 104% = 546,000 × 210,000 = 572,000

220,000 Variable overhead ........... 462,000 × 100% = 462,000 × 210,000 = 484,000

Fixed Overhead .......... 720,000 × 110% = 792,000 (fixed) = 792,000

Total costs..................

$2,337,000

$2,640,000

b. Costs per unit: Last year: $11.13 (= $2,337,000 ÷ 210,000) This year: $12.00 (= $2,640,000 ÷ 220,000)


5-23. (15 min.) Methods of Estimating Costs—Account Analysis. a. Cost estimate with new costs and volume.

Cost Item

Year 1 Cost

(1)

Cost

Change (1 + Cost Increase)

(2)

Year 2 Cost (at last year’s

volume) (1) x (2) =

(3)

Growth

in Volume

(4)

Year 2 Cost (3) x (4) = (5)

130,000 Direct materials ... $120,000 × 110% = $132,000 ×

100,000 = $171,600

130,000 Direct labor .......... 860,000 × 115% = 989,000 × 100,000 = 1,285,700

130,000 Variable overhead ... 180,000a × 100% = 180,000 × 100,000 = 234,000

Fixed Overhead .. 200,000 × 105% = 210,000 (fixed) = 210,000

Total costs..........

$1,360,000

$1,901,300

a $180,000 = $380,000 total overhead – $200,000 fixed overhead. b. Costs per unit:

Last year: $13.60 (= $1,360,000 ÷ 100,000) This year: $14.63 (= $1,901,300 ÷ 130,000)


5-24. (10 min.) Methods of Estimating Costs—High-Low, Ethical Issues: Oak Island Amusements Center.

a.

Variable cost = Cost at highest activity – cost at lowest activity Highest activity – lowest activity

= $2,500,000 – $ 1,950,000 2,375,000 – 1,825,000

= $1

Fixed costs

= Total costs – variable costs

= $2,500,000 – ($1 x 2,375,000) = $125,000 or Fixed costs

= $1,950,000 – ($1 x 1,825,000)

= $125,000

b. Maintenance costs = $125,000 + ($1 x 2,600,000) = $125,000 + $2,600,000 = $2,725,000

Note that 2,600,000 visitors is outside the range of the cost observations, so this estimate may not be reliable. c. Whether this is ethical depends on the reason for dropping the observation. If you

are convinced that the higher number of visitors represents such unusual activity that this should be treated as an outlier, then you should eliminate the observation. If, however, the reason for dropping the observation is that someone does not like the result, then you should not change the analysis.


5-25. (25 min.) Methods of Estimating Costs—High-Low: Lecouvreur Corporation.

a. High-low estimate Machine

Hours Overhead

Costs Highest activity (month 12)................. 1,604 $112,842 Lowest activity (month 11).................. 1,298 $100,755 Variable cost =

Cost at highest activity – cost at lowest activity Highest activity – lowest activity

= $112,842 – $ 100,755 1,604 – 1,298

= $39.50

Fixed costs


= $112,842 – ($39.50 x 1,604) = $49,484 or Fixed costs

= $100,755 – ($39.50 x 1,298)

= $49,484

The cost equation then is: Overhead costs = $49,484 + ($39.50 per MH x Machine hours)

b. For 1,500 MH: Overhead costs = $49,484 + ($39.50 x 1,500) = $49,484 + $59,250 = $108,734


5-26. (15 min.) Methods of Estimating Costs—Scattergraph: Lecouvreur Corporation.


5-27. (15 min.) Methods of Estimating Costs—Scattergraph: Lecouvreur Corporation.


5-28. (10 min.) Methods of Estimating Costs—Simple Regression: Lecouvreur Corporation.

Simple regression estimate: Overhead = $41,293 + $45.83 x Machine-hours = $41,293 + 45.83 x 1,800 Machine-hours = $41,293 + $82,494 = $123,787

5-29. (10 min.) Estimating Costs—Simple Regression: Lecouvreur Corporation. Simple regression estimate: Overhead = $43,521 + $88.61 x Labor-hours = $43,521 + $88.61 x 600 Labor-hours = $43,521 + $53,166 = $96,687

5-30. (20 min.) Estimating Costs—Multiple Regression: Lecouvreur Corporation. Multiple regression estimate: Overhead = $24,913 + $31.93 x Labor-hours + $41.10 x Machine-hours = $24,913 + $31.93 x 600 Labor-hours + $41.10 x 1,800 Machine-hours = $24,913 + $19,158 + $73,980 = $118,051


5-31. (20 min.) Interpretation of Regression Results—Multiple Choice: Cortez Company.

a. (3) R2 = .848 (84.8%), the explanation of variation in Y from the X regressor. b. (1) $370,000. The equation resulting from this regression analysis is Total overhead

= Estimated fixed cost + estimated variable cost per labor-hour x labor-hours

= Intercept estimate + Coefficient estimate on independent variable x 50,000 DLH

= $120,000 + $5 x 50,000 DLH = $120,000 + $250,000 = $370,000

c. (2) $82 Total labor-hours = Total direct labor costs ÷ Direct labor wage rate = $640,000 ÷ $16 per hour = 40,000 direct labor-hours Labor-hours per unit = Total labor hours ÷ Total units = 40,000 ÷ 20,000 = 2 labor-hours per unit Total variable cost per unit

= Direct materials + Direct labor + Variable overhead

= ($800,000 ÷ 20,000) + ($640,000 ÷ 20,000) + $5 x 2 labor-hours

= $40 + $32 + $5 x 2 labor-hours = $82

d. (4) $14 Contribution-margin per unit = Price – variable cost per unit = $96 – $82 = $14 e. (4) Total manufacturing cost = Fixed manufacturing cost + Variable manufacturing cost = $120,000 + $82 x units

*CMA adapted


5-32. (15 min.) Interpretation of Regression Results: Brodie Company. This problem is frequently encountered when applying analytical techniques to certain costs. Quite often the advertising expenditures result in sales being generated in the following month or so. In addition, many companies increase their advertising when sales are declining and cut back on advertising when there is capacity business. A better model might be developed by relating this month's sales to last month's advertising. Similar problems exist for repair and maintenance costs since machines are usually given routine repairs and maintenance during slow periods. An inverse relationship often exists between salespersons' travel expenses and sales because the salesperson spends more time traveling when the sales are more difficult to make.

5-33. (30 min.) Interpretation of Regression Results—Simple Regression: Fred’s Fish Fry.

a. Estimation equation for nonfood kitchen costs: Nonfood kitchen costs = Fixed costs + Variable cost as a percentage of food cost = $23,400 + 250% Food cost b. Nonfood kitchen costs = $23,400 + 250% Food cost = $23,400 + 250% x $25,000 = $23,400 + $62,500 = $85,900 c. The R2 for the equation is only 23.3%, which is very low for this type of regression. Fred should consider identifying other cost drivers and using them to estimate other nonfood kitchen costs.


5-34. (20 min.) Learning Curves: General Dynamics. a. The learning rate is 80% for every doubling of output:

Unit Produced (X)

Time Required to Produce the Xth Unit

1................. 10,000 hours 2................. 8,000 hours (= 10,000 hours x 0.80) 4................. 6,400 hours (= 8,000 hours x 0.80) 8................. 5,120 hours (= 6,400 hours x 0.80)

16............... 4,096 hours (= 5,120 hours x 0.80) b. Cost of producing the first unit = $1,000,000 (= 10,000 hours x $100 per hour) Cost of producing the 16th unit = $409,600 (= 4,096 hours x $100 per hour) = 40.96% of the first unit cost (= $409,600 ÷ $1,000,000)

5-35. (20 min.) Learning Curves: Whee, Cheatham, and Howe. a. The learning rate is 90% for every doubling of output:

Financial Statements

Proofread (X)

Time Required to Proofread the Xth

Financial Statement

1................ 4.0000 hours 2 ................. 3.6000 hours (= 4.0000 hours x 0.90) 4 ................. 3.2400 hours (= 3.6000 hours x 0.90) 8 ................. 2.9160 hours (= 3.2400 hours x 0.90)

16 ............... 2.6244 hours (= 2.9160 hours x 0.90) b. Cost of proofreading the first report = $40 (= 4.0 hours x $10 per hour) Cost of proofreading the 16th report = $26.24 (= 2.6244 hours x $10 per hour) = 65.60% of the first unit cost (= $26.24 ÷ $40)


5-36. (20 min.) Learning Curves. The formula for the time to produce unit z is Y =100 z–0.3219. Substitute 5, 6, 7 for z, to obtain:

Unit (z)

Formula for Time to Produce Unit z

Time to Produce Unit z

5................ Y =100 × (5) –0.3219 59.56 6 ................. Y =100 × (6) –0.3219 56.17 7 ................. Y =100 × (7) –0.3219 53.45

Also, note that the time to produce the third unit is 70.21. Doubling production, the time to produce the sixth unit is 56.17 (= 70.21 x 0.80).

The remaining numbers can be verified easily. The cumulative time for the 5th unit is simply the cumulative time for the 4th unit (314.21) plus 59.56 (the time to produce the 5th unit), or 373.77 hours, and so on. The total cost is the cumulative time multiplied by $50 per hour. For example, the total cost for five units is $18,688.50 (=$50 x 373.77 hours) and so on. Finally, the average cost is the total cost divided by the number of units produced. So the average cost of producing five units is $3,737.70 (= $18,688.50 ÷ 5 units) and so on.


Solutions to Problems

5-37. (20 min.) Account Analysis. a.

Activity Total Cost ÷ Volume = Unit Cost Process paychecks ($180,100 ÷ 15,945 checks) = $11.30 Maintain customer accounts ($109,600 ÷ 3,650 accounts) = 30.03 Perform special analyses ($120,000 ÷ 30 analyses) = 4,000.00

b. The average fixed costs for a month are $34,391 (= $550,250 ÷ 16 months). For 1,000 checks, 200 accounts, and 3 analyses, the estimated cost is: $63,697 = $34,391 + (1,000 x $11.30) + (200 x $30.03) + (3 x $4,000).

5-38. Regressions from Published Data Answers will vary.


5-39. (30 min.) High-Low Method, Scattergraph: Cubicle Solutions. a. High-low estimate Support

Calls Call Center

Cost Highest activity (month 5)......................... 61 $720 Lowest activity (month 1).......................... 37 528


= $720 – $528 61 – 37

= $8.00 per support call

Fixed costs = Total costs – variable costs = $720 – $8.00 x 61 = $232

or Fixed costs = $528 – $8.00 x 37 = $232

The cost equation is: Overhead costs = $232 + ($8.00 per call x Support calls)


5-39 (continued) b. Scattergraph

c. The scattergraph shows a reasonably linear pattern, but the high point would lie

below a straight line that best fits the data. In fact, because the data suggest a curvilinear pattern, while the high-low method assumes a linear relation between cost and activity, you would probably not be confident in your estimate in part a.


5-40. (30 min.) High-Low Method, Scattergraph: Academy Products. a. High-low estimate Machine

Hours Overhead

Costs Highest activity (month 5)......................... 1,035,000 $3,700,000 Lowest activity (month 1).......................... 630,000 660,000


= $3,700,000 – $660,000 1,035,000 – 630,000

= $7.5062 per machine-hour (rounded)

Fixed costs = Total costs – variable costs = $3,700,000 – $7.5062 x 1,035,000 = – $4,068,889

or Fixed costs = $660,000 – $7.5062 x 630,000 = – $4,068,889

Note that the estimated fixed cost is negative. Your answer for fixed costs might differ if you use a rounded amount for the machine-hour rate.


5-40 (continued) b. Scattergraph

c. The scattergraph shows a pattern that is convex (costs are increasing faster than

machine hours), suggesting that a nonlinear cost function might provide a better estimate. This helps explain the negative estimate for fixed costs in requirement a.


5-41. (40 min.) Interpretation of Regression Results—Simple Regression Using a Spreadsheet: Lucas Plant.

a. High-low estimate Labor

Hours Overhead

Costs Highest activity (month 16)....................... 226,250 $2,079,046 Lowest activity (month 11)........................ 106,250 $1,322,535


= $2,079,046 – $1,322,535 226,250 – 106,250

= $6.30426 per labor-hour

Fixed costs


= $2,079,046 – $6.30426 x 226,250 = $652,707

or Fixed costs

= $1,322,535 – $6.30426 x 106,250

= $652,707

The cost equation is: Overhead costs = $652,707 + ($6.30426 per LH x Labor hours)


5-41. (continued) b. Scattergraph:

Note that two observations do not appear (separately) on this scattergraph. These are observations 1 and 13. The dots actually overlap. These observations have the same number of labor hours as observations 8 and 23, respectively, and the overhead costs are close to the same.


5-41. (continued) c. The results of the regression analysis are:

Regression Statistics Multiple R 0.94877977 R Square 0.90018305 Adjusted R Square 0.89564591 Standard Error 100790.077 Observations 24 Coefficients Intercept (Fixed costs) $305,062.88 Labor Hours $8.04

d. Overhead costs = $305,063 + $8.04 x 200,000 = $305,063 + $8.04 x 200,000 = $305,063 + $1,608,000 = $1,913,063


5-42. (30 min.) Interpretation of Regression Results—Simple Regression, Regression Problems

Although the correlation coefficient (or R) is 0.82, the R2, the percentage of the variation in the independent variable “explained” by the dependent variable, is about 67%. This is not low for “real,” data, but it is not as convincing as Lance would have us believe. The first thing we would look at in checking Lance’s result is a scattergraph of the data (on the next page). There we see one observation that does not seem consistent with the others. It appears to be an outlier. (This is observation 5.) If the regression is re-estimated omitting observation 5, the results are:

Regression Statistics Multiple R 0.99213093 R Square 0.98432378 Adjusted R Square 0.98275616 Standard Error 1054.26386 Observations 12 Coefficients Intercept 3910.62477 Unit Production 17.5286752 This regression has an R2 of 98%, which is much better. The cost equation with the new results is:

Overhead cost = $3,911 + $17.53 x Units. This implies a cost structure where variable costs are much more important. These results also suggest that the controller’s estimates are very reasonable.


5-42. (continued)


5-43. (30 Min.) Interpretation of Regression Results—Multiple Choice: Eastern College Business School

a. (4) Variable cost coefficient b. (2) Dependent variable c. (1) Independent variable d. (5) Some other equation Credit-

hours Administrative

Costs Highest activity (September) .................... 1,392 $228,580 Lowest activity (August) ........................... 115 $82,613


= $228,580 – $82,613 1,392 – 115

= $114.3046 per credit-hour

Fixed costs


= $228,580 – $114.3046 x 1,392 = $69,468

or Fixed costs

= $82,613 – $114.3046 x 115

= $69,468

The equation is $69,468 + $114.3046 x Number of credit hours. e. (3) Administrative costs = $96,415 + $103.56 x 1,000 credit hours = $199,975. f. (1) The correlation coefficient is the “Multiple R.” g. (2) 87.1%, the R2.


5-44. (30 Min.) Interpretation of Regression Results: Simple Regression. a. The first step in understanding the difference is to prepare a scattergraph of the

data:

Notice the one observation that appears to be unusual. (This is observation 5.)

Without knowing more about the reasons for the high cost, we might want to treat it as an “outlier” meaning we would estimate the regression without this observation. The results of that regression are:

Regression Statistics Multiple R 0.9921 R Square 0.9843 Adjusted R Square 0.9827 Standard Error 2635.7 Observations 12 Coefficients Intercept $9776.56 Number of deliveries $11.69

These results are much closer to the controller’s estimates.


5-44 (continued) b. Using the results from the “improved” regression, the cost equation for overhead

costs can be written as:

Monthly overhead = $9,777 + $11.69 x number of deliveries

This implies a contribution margin per delivery of $8.31 (= $20.00 – $11.69). To earn operating profits of $10,000, the company needs approximately 2,380 (=

[$10,000 + $9,777] ÷ $8.31) deliveries. Note, however, that this level of deliveries is outside the range of the observations

used to develop the regression estimates. Therefore, this estimate needs to be used with caution.

5-45. (30 Min.) Interpretation of Regression Results: Lerner, Inc. a. The letter b is best described as the estimate of the maintenance cost for an hour of

maintenance. b. The letter y is best described as the observed maintenance costs for a given month. c. The letter x is best described as the observed maintenance hours for a given month. d. The estimated maintenance costs for month with 360 maintenance hours is

$3,309.05 (= $684.65 + $7.29 x 360 maintenance hours). e. The total variance that can be explained by the regression is 79.7% (= R2).


5-46. (30 Min.) Cost Estimation—Simple Regression: Arnie’s Arcade & Video Palace

a. Yes. We would expect that, in general, there is a positive relation between maintenance costs and activity. Revenue seems to be a reasonable measure of activity.

b. When we estimate the regression, we obtain the following results: Regression Statistics Multiple R 0.88865726 R Square 0.78971172 Standard Error 0.3000139 Observations 24 Coefficients Intercept 3.4312 Revenues -0.0337813 These suggest that maintenance costs are negatively related to revenues. The R2 is reasonably high, suggesting a good fit. This problem is frequently encountered when applying analytical techniques to certain costs. These include maintenance and repair costs because machines are usually given routine repairs and maintenance during slow periods. Advertising is another cost that exhibits similar behavior. Many companies increase their advertising when sales are declining and cut back on advertising when there is capacity business. A better model might be developed by including seasonal variables in the regression or separating the maintenance and repair costs into routine and unscheduled costs.


5-47. (40 min.) Methods of Cost Analysis—Account Analysis, Simple and Multiple Regression Using Spreadsheets: Caiman Distribution Partners.

a. Estimating equation based on account analysis:

Cost Item Operating Cost Fixed Cost Variable Supplies ................................ $ 350,000 $ 0 $ 350,000 Supervision ........................... 215,000 150,000 65,000 Truck expense ...................... 1,200,000 190,000 1,010,000 Building leases...................... 855,000 550,000 305,000 Utilities .................................. 215,000 125,000 90,000 Warehouse labor................... 860,000 140,000 720,000 Equipment leases ................. 760,000 600,000 160,000 Data processing equipment .. 945,000 945,000 0 Other..................................... 850,000 400,000 450,000 Total...................................... $6,250,000 $3,100,000 $3,150,000

Variable cost per case = Total variable cost/Cases produced

= $3,150,000 ÷ 450,000 cases = $7.00 per case

Estimated overhead = Fixed overhead + Variable overhead per case x Number of cases

= $3,100,000 + $7.00 x Number of cases = $3,100,000 + $7.00 × 450,000 = $6,250,000


5-47. (continued) b. Cost estimate using high-low analysis.

Cases Operating Costs

Highest activity (month 12)......................... 432,000 $6,362,255 Lowest activity (month 1)............................ 345,000 $5,699,139


= $6,362,255 – $5,699,139 432,000 – 345,000

= $7.62202 per case

Fixed costs


= $6,362,255 – $7.62202 x 432,000 = $3,069,542 or Fixed costs

= $5,699,139 – $7.62202 x 345,000

= $3,069,542

The cost equation then is: Overhead costs = $3,069,542 + ($7.622 per case x Cases).

For 450,000 cases: Operating costs = $3,069,542 + $7.622 x 450,000 = $6,499,442


5-47. (continued) c. Simple regression based on cases:

Regression Statistics Multiple R 0.98034501 R Square 0.96107634 Standard Error 39850.1391 Observations 12 Coefficients Intercept $3,411,468 Cases $6.70765 Operating costs = $3,411,468 + $6.70765 x cases = $3,411,468 + $6.70765 x 450,000 $3,411,468 + $3,018,443 = $6,429,911

d. Multiple regression based on cases and price level. Regression Statistics

Multiple R 0.9905 R Square 0.9810 Adjusted R Square 0.9768 Standard Error 29315.827 Observations 12 Coefficients Intercept $3,176,995 Cases $4.41892 Price Index $8,857.73 Operating costs = $3,176,995 + $4.41892 x cases + $8,857.73 x Price level = $3,176,995 + $4.41892 x 450,000 + $8,857.73 x 145 $3,176,995 + $1,988,514 + $1,284,371 = $6,449,880


5-47. (continued) e. Recommendation. The multiple regression appears to improve the “fit” (compare the adjusted R2’s), but the rationale for the inclusion of the price level as a cost driver is unclear. There is some possibility that the price index variable is a surrogate for some other factor correlated with the growth of the business. It might be better to adjust the cost figures to real (price-level adjusted) and forecast the adjusted operating costs. Once the simple regression is complete, and it is relatively easy to do, there is no reason for the high-low estimate, because it ignores most of the information. Therefore, some combination of the controller’s account analysis estimate and the estimate from the simple regression seems most appropriate.


5-48. (40 min.) Learning Curves: Appendix 5B. a. The learning rate coefficient is -0.152004, so the table in Exhibit 5-18 would be as

follows a learning rate of 90%:

Labor Time Required to Produce the Xth Unit (i.e, the Last Cumulative

Unit Single Unit Total Time

Produced Produced)1 in Labor Total Average Cost (X) (Y) Hours2 Cost3 Per Unit4 1 ................. 100.00 100 $5,000.00 $5,000.00 2 ................. 90.00 190.00 9,500.00 4,750.00 3 ................. 84.62 274.62 13,731.02 4,577.01 4 ................. 81.00 355.62 17,781.02 4,445.25 5 ................. 78.30 433.92 21,695.95 4,339.19 6 ................. 76.16 510.08 25,503.87 4,250.64 7 ................. 74.39 584.47 29,223.60 4,174.80 8 ................. 72.90 657.37 32,868.59 4,108.57

1. Y = 100 (X-0.152004). 2. Cumulative time in labor hours for unit X is the sum of the time for each of the units

up to and including unit X. 3. Total cost is equal to the cumulative time multiplied by $50. 4. Average cost is equal to the total cost divided by the number of units produced.


5-49. (40 min.) Learning Curves–Appendix 5B: Krylon Company. Krylon should produce the tool itself. With an 80 percent learning rate (learning rate

coefficient of -0.3219), the average cost of a tool for 8 tools is $93,461, which is less than the supplier cost. This is shown in the table below, which is similar to Exhibit 5-18.

Unit Learning Total Average Total Produced Factor1 Labor Labor Cost Materials Average

(X) (Y) Cost2 Per Unit3 Cost Cost 1 1.00 $ 80,000.00 $80,000.00 $40,000.00 $120,000.00 2 0.80 144,001.25 72,000.62 40,000.00 112,000.62 3 0.70 200,171.28 66,723.76 40,000.00 106,723.76 4 0.64 251,373.27 62,843.32 40,000.00 102,843.32 5 0.60 299,026.41 59,805.28 40,000.00 99,805.28 6 0.56 343,963.31 57,327.22 40,000.00 97,327.22 7 0.53 386,724.81 55,246.40 40,000.00 95,246.40 8 0.51 427,687.20 53,460.90 40,000.00 93,460.90

1. This is the ratio of the labor time it takes to produce unit X relative to the first unit and is equal to X-0.3219

2. The total labor cost is $80,000 (the labor cost to produce the first unit) multiplied by the cumulative learning factor.

3. The average cost is the total cost divided by the number of units produced.

chapter 5 - cost estimation

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