CHAPTER 10

DETERMINING HOW COSTS BEHAVE

10-1 Three alternative linear cost functions are

1. Variable cost function––a cost function in which total costs change in proportion to the cost driver in the relevant range.

2. Fixed cost function––a cost function in which total costs do not change with changes in the cost driver in the relevant range.

3. Mixed cost function––a cost function that has both variable and fixed elements. Total costs change but not in proportion to the changes in the cost driver in the relevant range.

10-2 The two assumptions are:

1. Variations in the total costs of a cost object are explained by variations in a single cost driver.

2. A linear cost function adequately approximates cost behavior within the relevant range of the cost driver. A linear cost function is a cost function where, within the relevant range, the graph of total costs versus a single cost driver forms a straight line.

10-3 A linear cost function is a cost function, where within the relevant range, the graph of total costs versus a single cost driver forms a straight line. An example of a linear cost function is a cost function for use of a telephone line where the terms are a fixed charge of $10,000 per year plus a $2 per minute charge for phone use. A nonlinear cost function is a cost function where, within the relevant range, the graph of total costs versus a single cost driver does not form a straight line. Examples include economies of scale in advertising where an agency can double the number of advertisements for less than twice the costs, step-function costs, and learning-curve-based costs.

10-4 No. High correlation merely indicates that the two variables move together in the data examined. It is essential to also consider economic plausibility before making inferences about cause and effect. Without any economic plausibility for a relationship, it is less likely that a high level of correlation observed in one set of data will be similarly found in other sets of data.

10-5 Four approaches to estimating a cost function are:

1. Industrial engineering method.

2. Conference method.

3. Account analysis method.

4. Quantitative analysis of current or past cost relationships.

10-6 The conference method develops cost estimates on the basis of analysis and opinions gathered from various departments of an organization (purchasing, process engineering, manufacturing, employee relations, etc.). Advantages of the conference method include:

1. The speed with which cost estimates can be developed.

2. The pooling of knowledge from experts across functional areas.

3. The improved credibility of the cost function to all personnel.

10-7 The account analysis method estimates cost functions by classifying cost accounts in the ledger as variable, fixed, or mixed with respect to the identified cost driver. Typically, managers use qualitative, rather than quantitative analysis when making these cost-classification decisions.

10-8 The six steps are:

1. Choose the dependent variable (the variable to be predicted, which is some type of cost).

2. Identify the cost driver(s) (independent variables).

3. Collect data on the dependent variable and the cost driver(s).

4. Plot the data.

5. Estimate the cost function.

6. Evaluate the estimated cost function.

 

Step 3 typically is the most difficult for a cost analyst.

10-9 Causality in a cost function runs from the cost driver to the dependent variable. Thus, choosing the highest observation and the lowest observation of the cost driver is appropriate in the high-low method.

10-10 Criteria important when choosing among alternative cost functions are:

1. Economic plausibility.

2. Goodness of fit.

3. Slope of the regression line.

10-11 Frequently encountered problems when collecting cost data on variables included in a cost function are:

1. The time period used to measure the dependent variable is not properly matched with the period used to measure the cost driver(s).

2. Fixed costs are allocated as if they are variable.

3. Data are either not available for all observations or are not uniformly reliable.

4. Extreme values of observations occur.

5. A homogeneous relationship between the individual cost items in the dependent variable and the cost driver(s) does not exist.

6. The relationship between cost and the cost driver is not stationary.

7. Inflation has occurred in a dependent variable, a cost driver, or both.

10-12 A learning curve is a function that shows how labor hours per unit decline as units of output are increased. Two models used to capture different forms of learning are:

1. Cumulative average-time learning model. The cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced is doubled.

2. Incremental unit-time learning model. The incremental unit time (the time needed to produce the last unit) declines by a constant percentage each time the cumulative quantity of units produced is doubled.

10-13 Four key assumptions examined in specification analysis are:

1. Linearity between the dependent variable and the independent variable within the relevant range.

2. Constant variance of residuals for all values of the independent variable.

3. Residuals are independent of each other.

4. Residuals are normally distributed.

10-14 No. A cost driver is any factor whose change causes a change in the total cost of a related cost object. A cause-and-effect relationship underlies selection of a cost driver. Some users of regression analysis include numerous independent variables in a regression model in an attempt to maximize goodness of fit, irrespective of the economic plausibility of the independent variables included. Some of the independent variables included may not be cost drivers.

10-15 No. Multicollinearity exists when two or more independent variables are highly correlated with each other.

10-16 (10 min.) Estimating a cost function.

1. Slope coefficient =  

=  

=  = $0.30 per machine hour

Constant = Total cost – (Slope coefficient ´ Quantity of cost driver)

= $3,900 – ($0.30 ´ 7,000) = $1,800

= $3,000 – ($0.30 ´ 4,000) = $1,800

The cost function based on the two observations is:

Maintenance costs = $1,800 + $0.30 (machine-hours)

2. The cost function in requirement 1 is an estimate of how costs behave within the relevant range, not at cost levels outside the relevant range. If there are no months with zero machine-hours represented in the maintenance account, data in that account cannot be used to estimate the fixed costs at the zero machine-hours level. Rather, the constant component of the cost function provides the best available starting point for a straight line that approximates how a cost behaves within the relevant range.

10-17 (15 min.) Identifying variable, fixed, and mixed cost functions.

1. See Solution Exhibit 10-17.

2. Contract 1 : y= $50

Contract 2 : y= $30 + $0.20

Contract 3 : y = $1

where D is the number of miles traveled in the day.

Solution Exhibit 10-17

Plots of Car Rental Contracts Offered by Pacific Corp.

10-18 (20 min.) Various cost-behavior patterns.

 

1. K

2. B

3. G

4. J Note that A is incorrect because although the cost per pound eventually equals a constant at $9.20, the total dollars of cost increases linearly from that point onward.

5. I The total costs will be the same regardless of the volume level.

6. L

7. F This is a classic step-function cost.

8. K

9. C

10-19 (40-50 min.) Matching graphs with descriptions of cost behavior.

1. (1)

2. (7) A step-cost function rather than a fixed cost.

3. (11)

4. (2)

5. (9)

6. (12)

7. (3)

8. (9)

 

10-20 (20 min.) Account analysis method.

1. Variable costs:

Car wash labor $240,000

Soap, cloth, and supplies 32,000

Water 28,000

Power to move conveyor belt 72,000

Total variable costs $372,000

Fixed costs:

Depreciation $ 64,000

Supervision 30,000

Cashier 16,000

Total fixed costs $110,000

2. Variable costs per car =  = $4.65 per car

Total costs estimated for 90,000 cars = $110,000 + ($4.65 ´ 90,000) = $528,500

3. Average cost in 19_8 =  =  = $6.025

Average cost in 19_9 =  = $5.87

Some students may assume that power costs of running the continuously moving conveyor belt is a fixed cost. In this case the variable costs in 19_8 will be $300,000 and the fixed costs $182,000.

The variable costs per car in 19_8 = $300,000 Ö 80,000 cars = $3.75 per car

Total costs for 90,000 cars in 19_9 = $182,000 + ($3.75 ´ 90,000) = $519,500

The average cost of washing a car in 19_9 = $519,500 Ö 90,000 = $5.77.

10-21 (30 min.) Account analysis method.

1. Manufacturing cost classification for 19_8:

Total manufacturing cost for 19_8 = $948,750

Variable costs in 19_9:

10-21 (Cont'd.)

Fixed and total costs in 19_9:

Total manufacturing costs for 19_9 = $1,042,750

2. Total unit costs 19_8 =  = $12.65

Total unit costs 19_9 =  = $13.03

3. Cost classification into variable and fixed costs is based on qualitative rather than quantitative analysis. How good the classifications are depends on the knowledge of individual managers who classify the costs. Gower may want to undertake quantitative analysis of costs, using regression analysis on time-series or cross-sectional data to better estimate the fixed and variable components of costs. Better knowledge of fixed and variable costs will help Gower to better price his products, know when he is getting a positive contribution margin, and better manage costs.

10-22 (20 min.) Estimating a cost function, high-low method.

1. See Solution Exhibit 10-22. There is a positive relationship between the number of service reports (a cost driver) and the customer-service department costs. This relationship is economically plausible.

2. Number Of Customer-Service

Service Reports Department Costs

Highest observation of cost driver 436 $21,890

Lowest observation of cost driver 122 12,941

Difference 314 $ 8,949

Customer-service department costs = a + b (number of service reports)

Slope coefficient (b) =  = $28.50 per service report

Constant (a) = $21,890 – $28.50 (436) = $9,464

= $12,941 – $28.50 (122) = $9,464

Customer-service

department costs = $9,464 + $28.50 (number of service reports)

3. Other possible cost drivers of customer-service department costs are:

(a) Number of products replaced with a new product (and the dollar value of the new products charged to the customer-service department).

(b) Number of products repaired and the time and cost of repairs.

 

 

10-22 (Cont'd.)

Solution Exhibit 10-22

Plot of Number of Service Reports Versus

Customer-Service Costs for Capitol Products

10-23 (30-40 min.) Linear cost approximation.

1. Slope coefficient (b) =  

=  = $43.00

Constant (a) = $529,000 – $43.00 (7,000)

= $228,000

Cost function = $228,000 + $43.00 (professional labor-hours)

The linear cost function is plotted in Solution Exhibit 10-23.

No, the constant component of the cost function does not represent the fixed overhead cost of the Memphis Group. The relevant range of professional labor-hours is from 3,000 to 8,000. The constant component provides the best available starting point for a straight line that approximates how a cost behaves within the 3,000 to 8,000 relevant range.

2. A comparison at various levels of professional labor-hours follows. The linear cost function is based on the formula of $228,000 per month plus $43.00 per professional labor-hour:

Total overhead cost behavior:

The data are shown in Solution Exhibit 10-23. The linear cost function overstates costs by $8,000 at the 5,000-hour level and understates costs by $15,000 at the 8,000-hour level.

3. Based on Based on linear

actual cost function

Contribution before deducting incremental overhead $38,000 $38,000

Incremental overhead 35,000 43,000

Contribution after incremental overhead $ 3,000 $ (5,000)

The total contribution margin actually forgone is $3,000.

10-23 (Cont'd.)

Solution Exhibit 10-23

Linear Cost Function Plot of Professional Labor-Hours

on Total Overhead Costs For Memphis Consulting Group

10-24 (25 min.) Regression analysis, service company.

1a. Solution Exhibit 10-24 plots the relationship between labor hours and overhead costs and shows the regression line.

y = $48,271 + $3.93 X

1b. Economic plausibility. Labor hours appears to be an economically plausible driver of overhead costs for a catering company. Overhead costs such as scheduling, hiring, and training of workers, and managing the workforce are largely incurred to support labor.

Goodness of fit. The vertical differences between actual and predicted costs are extremely small, indicating a very good fit. The good fit indicates a strong relationship between the labor hour cost driver and overhead costs.

Slope of regression line. The regression line has a reasonably steep slope from left to right. The positive slope indicates that, on average, overhead costs increase as labor hours increase.

2. The regression analysis indicates that, within the relevant range of 2,500 to 7,500 labor hours, the variable cost per person for a cocktail party equals:

Food and beverages $15.00

Labor (0.5 hrs. ´ $10 per hour) 5.00

Variable overhead (0.5 hrs ´ $3.93 per labor hour) 1.97

Total variable cost per person $21.97

3. To earn a positive contribution margin, the minimum bid for a 200-person cocktail party would be any amount greater that $4,394. This amount is calculated by multiplying the variable cost per person of $21.97 by the 200 people. At a price above the variable costs of $4,394, Bob Jones will be earning a contribution margin toward coverage of his fixed costs.

Of course, Bob Jones will consider other factors in developing his bid including (a) an analysis of the competition––vigorous competition will limit Jones's ability to obtain a higher price (b) a determination of whether or not his bid will set a precedent for lower prices––overall, the prices Bob Jones charges should generate enough contribution to cover fixed costs and earn a reasonable profit (c) a judgment of how representative past historical data (used in the regression analysis) is about future costs.

10-24 (Cont'd.)

Solution Exhibit 10-24

Regression Line of Labor Hours on Overhead Costs

for Bob Jones's Catering Company

10-25 (30-35 min.) Regression analysis, activity-based costing, choosing
cost drivers.

1. Solution Exhibit 10-25A presents the plots and regression line of machine hours on support overhead. Solution Exhibit 10-25B presents the plots and regression line of number of batches on support overhead. As described below, evaluating the three criteria of economic plausibility, goodness of fit, and slope of regression line, from the plots, I would choose number of batches as the cost driver of support overhead costs.

Economic plausibility. Number of batches appears to be a more plausible cost driver of support overhead costs than machine hours. Support staff indicate that they spend a good portion of their time at the start of each batch ensuring that the equipment is setup correctly and checking that the first units of production in each batch are of good quality. Once the machine is working properly, support staff are not needed to supervise the actual running of the machines. Consequently support staff resources are more likely to vary with the number of batches rather than the total number of machine hours worked.

Goodness of fit. Compare Solution Exhibits 10-25A and 10-25B. The vertical differences between actual and predicted costs are much smaller for number of batches than for machine hours. This indicates that number of batches has as better fit and a stronger relationship with support overhead costs.

Slope of regression line. Again compare Solution Exhibits 10-25A and 10-25B. The slope of the regression line of number of batches on support overhead is relatively steep while the regression line of machine hours on support overhead is relatively flat (small slope). A relatively steep regression line for number of batches indicates that, on average, support overhead costs increase as number of batches increase. On the other hand, the relatively flat regression line for machine hours indicates a weak or no relationship between support overhead costs and machine hours––on average, changes in machine hours appear to have a minimal effect on support overhead costs.

2. As described in requirement 1, number of batches is the preferred cost driver. Using this cost driver and the regression equation y = $16,031 + $197.30 ´ number of batches, Chu should budget the following support overhead costs for the 300 batches tht will be run next month: y = $16,031 + $197.30 ´ 300 = $16,031 + $59,190 + $75,221.

3a Using machine hours as the cost driver and the regression equation y = $28,089 + $10.23 ´ machine hours, Chu would budget support overhead costs for the 2,600 machine hours that will be worked next month as

y = $28,089 + $10.23 ´ 2,600 = $28,089 + $26,598 = $54,687

10-25 (Cont'd.)

Picking machine hours rather than the number of batches as the cost driver will cause Chu to underestimate costs and choose lower target revenues and prices. Support overhead costs, however, will vary with number of batches rather than machine hours. Using information from the preceding table, actual costs will be closer to $200,221 against target revenues of $215,624. Target profitability is unlikely to be met. With better cost driver information Chu would probably have priced products higher and earned greater revenues, assuming, of course, that customers are willing to pay the higher prices.

3b. Choosing the "wrong" cost driver and estimating the incorrect cost function will also have repercussions for cost management and cost control. Suppose Roban Plastics budgets support overhead costs of $54,687 for next month using the machine hour regression. Suppose actual support overhead costs, driven by number of batches, are $74,000 next month. Management of Roban Plastics would regard this as unsatisfactory performance and begin to explore ways to cut costs to bring it more in line with budgeted support overhead costs. In fact, on the basis of the preferred cost driver, number of batches, the plant's actual costs are lower than the predicted amount ($75,221)––a performance that management should seek to replicate rather than change. Using "wrong" cost drivers misleads management in cost planning, cost management and cost control besides resulting in inappropriate product pricing decisions.

10-25 (Cont'd.)

Solution Exhibit 10-25a

Regression line of Machine Hours on Support Overhead Costs

for Rohan Plastics

Solution Exhibit 10-25b

Regression line of Number of Batches on Support Overhead Costs

For Rohan Plastics

10-26 (25-30 min.) High-low method, cost estimation, cost management.

1a. The high-low method estimates the cost function on the basis of only the highest and lowest observed values of the cost driver within the relevant range.

Slope coefficient, b =  

= $27,000 Ö 203 = $133.00 per batch

The constant a = y - bX

At the highest observation of the cost driver,

Constant a = $84,000 – ($133 ´ 309) = $84,000 – $41,097 = $42,903

Alternatively, subject to rounding differences, the constant a could be computed using the lowest observation of the cost driver

Constant a = $57,000 – ($133 ´ 106) = $57,000 – 41,098 = $42,902)

The high-low estimate of the cost function is

y = a + bX

y = $42,903 + $133 ´ Number of batches

1b. Solution Exhibit 10-26 plots the monthly data and the cost function estimated using the high-low method for support overhead costs and the number of batches.

1c. Solution Exhibit 10-26 also plots the regression line for support overhead costs and the number of batches. Solution Exhibit 10-26 indicates clearly that the cost function represented by the regression line dominates the cost function estimated using the high low method. The high-low cost function is not representative of and does not "fit" the data––the high-low cost function line is on one side of the data with all data points lying below the high-low line. In contrast the regression line goes through the data minimizing the vertical differences between actual and predicted costs.

10-26 (Cont'd.)

The high-low cost function line exposes the obvious danger of relying on only two observations to estimate the cost relationship between number of batches and support overhead costs. For one thing, the highest and lowest cost driver value observations are not representative. Even if representative high and representative low observations are chosen the high-low method suffers from the limitation of ignoring information from all but two observations when estimating the cost function.

I would definitely choose the regression line-based cost function y = $16,031 + $197.30 ´ Number of batches to estimate, manage and control costs.

2. Using the high-low cost function line y = $42,903 + $133 ´ Number of batches, for 300 batches, Chu would budget costs of

y = $42,903 + $133 ´ 300 = $42,903 + $39,900 = $82,803

Using the regression cost function line y = $16,031 + $197.03 ´ Number of batches for 300 batches, Chu would budget costs of

y = $16,031 + $197.30 ´ 300 = $16,031 + $59,190 = $75,221

 

 

Estimating costs using the high-low cost function rather than the regression cost function will cause Chu to overestimate costs and choose higher target revenues and prices. If these markets are competitive, higher prices could cause Roban Plastics to lose business. The regression cost function, which is a more accurate predictor of support overhead cost behavior, suggests that Roban Plastics could charge lower prices, earn less revenue and still achieve the desired margin.

10-26 (Cont'd.)

3b. Choosing the "wrong" cost function––the high-low cost function––will also have repercussions for cost management and cost control. Suppose Roban Plastics budgets support overhead costs of $82,803 for next month using the high-low cost function. Supposse actual support overhead costs are $78,000. Based on the high-low prediction of $82,803, Roban Plastics would conclude it has performed well, and would probably prompt the company to adopt similar practices in the future. But comparing the $78,000 performance with the $75,221 prediction of the regression model indicates poor control of costs that would instead cause Roban Plastics to search for ways to improve its cost performance. Using the wrong cost function gives management misleading signals about how well it is managing and controlling costs.

Solution Exhibit 10-26

Regression and High-Low Lines of Number of Batches

on Support Overhead Costs for Rohan Plastics

10-27 (20 min.) Learning curve, cumulative average-time learning curve.

The direct manufacturing labor-hours (DMLH) required to produce the first 2,4 and 8 units given the assumption of a cumulative average-time learning curve of 90% is as follows:

Alternatively, to compute the values in column (2) we could use the formula

y = pXq

where p = 3,000, X = 2, 4 or 8 and q = –0.1520, which gives

when X = 2, y = 3,000 ´ 2–0.1520 = 2,700

when X = 4, y = 3,000 ´ 4–0.1520 = 2,430

when X = 8, y = 3,000 ´ 8–0.1520 = 2,187

 

10-28 (20 min.) Learning curve, incremental unit-time learning curve

1. The direct manufacturing labor hours (DMLH) required to produce the first 2, 3 and 4 units given the assumption of an incremental unit-time learning curve of 90% is as follows:

Values in column 2 are calculated using the formula y = pXq

where p = 3,000, X = 2, 3 or 4 and q = –0.1520, which gives

when X = 2, y = 3,000 ´ 2–0.1520 = 2,700

when X = 3, y = 3,000 ´ 3–0.1520 = 2,539

when X = 4, y = 3,000 ´ 4–0.1520 = 2,430

 

10-28 (Cont'd.)

Total variable costs for manufacturing 2 and 4 units are lower under the cumulative average-time learning curve relative to the incremental unit-time learning curve. Direct manufacturing labor hours required to make additional units declines more slowly in the incremental unit-time learning curve relative to the cumulative average-time learning curve assuming the same 90% factor is used for both curves. The reason is that in the incremental unit-time learning curve, as the number of units double, only the last unit produced has a cost of 90% of the initial cost. In the cumulative average-time model, doubling the number of units causes the average cost of all the additional units produced (not just the last unit) to be 90% of the initial cost.

10-29 (30-40 min.) Cost estimation, cumulative average-time learning

curve.

1. Cost to Produce the Second through the Eighth Troop Deployment Boats:

Direct materials, 7 ´ $100,000 $ 700,000

Direct manufacturing labor, 39,130* ´ $30 1,173,900

Variable manufacturing overhead, 39,130 ´ $20 782,600

Other manufacturing overhead, 25% of $1,173,900 293,475

Total costs $2,949,975

 

*The direct manufacturing labor-hours to produce the second to eighth boats can be calculated in several ways, given the assumption of a cumulative average-time learning curve of 85%:

(a) Use of Table Format:

 

The direct-labor-hours required to produce the second through the eight boats is 49,130 – 10,000 = 39,130 hours.

 

10-29 (Cont'd.)

(b) Use of Formula:

y = pXq

where p = 10,000, X = 8, and q = -.2345.

y = 10,000 ´ 8 -.2345 = 6,141 hours (rounded)

The total direct labor hours for 8 units is 6,141 ´ 8 = 49,128 hours

The direct labor hours required to produce the second through the eighth boats is 49,128 – 10,000 = 39,128 hours. (By taking the q factor to 6 decimal digits, an estimate of 49,130 hours would result.)

 

Note: Some students will debate the exclusion of the tooling cost. The question specifies that the tooling "cost was assigned to the first boat." Although Nautilus may well seek to ensure its total revenue covers the $725,000 cost of the first boat, the concern in this question is only with the cost of producing seven more PT109s.

2. Cost to Produce the Second through the Eighth Boats Assuming Linear Function for Direct Labor Hours and Units Produced:

 

Direct materials, 7 ´ $100,000 $ 700,000

Direct manufacturing labor, 7 ´ 10,000 hours ´ $30 2,100,000

Variable manufacturing overhead, 7 ´ 10,000 hours ´ $20 1,400,000

Other manufacturing overhead, 25% of $2,100,000 525,000

Total costs $4,725,000

The difference in predicted costs is:

• Predicted cost in requirement 2

(based on linear cost function) $4,725,000

• Predicted cost in requirement 1

(based on an 85% learning curve) 2,949,975

Difference $1,775,025

 

10-30 (20-30 min.) Cost estimation, incremental unit-time learning curve.

1. Cost to Produce the Second through the Eighth Boats:

Direct materials, 7 ´ $100,000 $ 700,000

Direct manufacturing labor, 49,356* ´ $30 1,480,680

Variable overhead, 49,356 ´ $20 987,120

Other overhead, 25% of $1,480,680 370,170

Total costs $3,537,970

*The direct labor hours to produce the second through the eighth boats can be calculated via a table format given the assumption of an incremental unit-time learning curve of 85%:

*Calculated as m = pXq where p = 10,000, q = -.2345, and X = 1, 2, 3,..., 8.

The direct manufacturing labor-hours to produce the second through the eighth boat is 59,356 - 10,000 = 49,356 hours.

10-30 (Cont'd.)

2. Difference in total costs to manufacture the second through the eighth boat under the incremental unit-time learning model and the cumulative average-time learning model is $3,537,970 (calculated in requirement 1 of this problem) – $2,949,975 (from requirement 1 of Problem 10-26) = $587,995.

The incremental unit-time learning curve has a slower decline in the reduction in time required to produce successive units than does the cumulative average-time learning curve (see Problem 10-26, requirement 1). Assuming the same 85% factor is used for both curves:

Nautilus should examine its own internal records on past jobs and seek information from engineers, plant managers, and workers when deciding which learning curve better describes the behavior of direct manufacturing labor-hours on the production of the PT109 boats.

10-31 (30 min.) Cost estimation, cumulative average-time learning

model.

1. The experience curve is on a per lot basis. The manufacturing labor cost per unit in the first lot is $40,000.

The average cost per unit for 240 units in 8 lots = $40,000 ´ 8 – 0.1520

= $29,160

2. Total variable costs of producing 240 units of new telecommunication equipment:

Direct materials, 240 units ´ $60,000 $14,400,000

Direct manufacturing labor, 240 units ´ $29,160 6,998,400

Variable manufacturing overhead, 60% of $6,998,400 4,199,040

Total variable manufacturing costs $25,597,440

 

3. The average cost per unit for the last round of learning when going from 4 lots to 8 lots (120 units to 240 units) is the change in cumulative total costs divided by 120 units (240 units for 8 lots – 120 units for 4 lots):

 = $25,920

This is Cooper's average manufacturing cost per unit for each additional unit after 240 units.

Hence Cooper's bid price per unit on the 240 units of additional telecommunication equipment should be:

Direct materials $ 60,000

Direct manufacturing labor 25,920

Variable manufacturing overhead, 60% of $25,920 15,552

Total variable manufacturing costs 101,472

Markup at 25% of total variable manufacturing costs 25,368

Bid price per unit $126,840

 

10-32 (30 min.) Cost estimation, incremental unit-time learning curve

* Calculated as m = pXq where p = $40,000, q = –0.1520, and X= 1,2,3, ..., 8.

Total variable costs of producing 240 units of new telecommunication equipment

Direct materials, 240 units ´ $60,000 $14,400,000

Direct manufacturing labor 7,888,560

Variable manufacturing overhead, 60% of $7,888,560 4,733,136

Total variable manufacturing costs $27,021,696

 

Difference in predicted costs:

Predicted cost under incremental unit-time

learning curve model $27,021,696

Predicted cost under cumulative average-time

learning curve model (requirement 2 of Problem 10-28) 25,597,440

Difference in favor of cumulative average-time

learning curve model $ 1,424,256

 

When the same learning rate is assumed (90% in our example), the cumulative average learning curve model gives lower costs because the average time and cost per unit declines by 90% each time the cumulative quantity of units produced is doubled. In contrast, under the incremental unit learning curve model, only the time and cost to produce the last unit at the 2X production level is 90% of the time and cost needed to produce the last unit at the X production level.

10-33 (40-50 min.) Data collection issues, use of high-low method.

1. Solution Exhibit 10-33 presents the three plots.

(a) Increases in operating costs are associated with increases in track miles hauled. This relationship is economically plausible. It is reasonable to assume that the costs included in operating costs (for example, fuel and labor) would be driven (in part) by track miles hauled. There is one extreme observation (September). Apart from this observation, a linear relationship appears reasonable.

(b) Decreases in maintenance costs are associated with increases in track miles hauled. Over a long time horizon (say, ten years) this relationship appears not to be economically plausible. However, it can arise in the short-run because maintenance may be deferred from periods of high demand to periods of low demand. Alternative explanations are:

• Winter months require higher maintenance due to the adverse effects of weather on equipment.

• Low months of track miles hauled arise from trains being taken out of operation for maintenance.

(c) Increases in total transportation costs are associated with increases in track miles hauled. This series is the aggregate of the (a) and (b) series, which exhibit markedly different patterns. There is less evidence of linearity than with the (a) series. The positive slope is due to the absolute amounts of the operating costs exceeding those of the maintenance costs.

 

2. The high and low observations on track miles hauled are used in the high-low method:

Operating costs = a+ b (track miles hauled):

Slope coefficient (b) =  = $0.075

Constant (a) = $986 – $0.075 (10,980) = $162.50

= $386 – $0.075 (2,980) = $162.50

Operating costs = $162.50 + $0.075 (track miles hauled)

The positive slope coefficient is consistent with the pattern observed in the graph of requirement 1 (a ) in Solution Exhibit 10-33.

10-33 (Cont'd.)

Maintenance costs = a+ b (track miles hauled):

Slope coefficient (b) =  =–$0.038

Constant (a) = $210 – (–$0.038)(10,980) = $627.24

= $514 – (–$0.038)(2,980) = $627.24

Maintenance costs = $627.24 - $0.038 (track miles hauled)

The negative slope coefficient is consistent with the pattern observed in the graph of requirement 1(b). (From a long-run viewpoint, a negative slope is not economically plausible. However, it is economically plausible in the short-run for a discretionary cost such as maintenance.)

Total transportation costs = a+ b (track miles hauled):

Slope coefficient =  = $0.037

Constant = $1,196 – $0.037(10,980) = $789.74

= $ 900 – $0.037(2,980) = $789.74

Total transportation costs = $789.74 + $0.037 (track miles hauled)

The positive slope coefficient is consistent with the pattern observed in the graph of requirement 1(c).

3. Total transportation costs next year are [$789.74 + (0.037 ´ 6, 000)] ´ $12 = $12,140.88

4. Limitations of the high-low method for estimating a cost function include:

(a) One or both of the high and low points may be an outlier, which would result in an unrepresentative cost function.

(b) Information in all observations except the two data points is ignored.

(c) High-low imposes a linear cost function on what may be a nonlinear relationship.

(d) High-low cannot capture systematic patterns (like seasonality) that occur within the high and low observations.

 

Students with knowledge of regression analysis may also mention the following:

(e) High-low does not provide diagnostic information (such as a measure of goodness of fit or r2) that is available with the regression method.

 

 

10-33 (Cont'd.)

Solution Exhibit 10-33

Plots of Transportation Costs Versus Track Miles Hauled for Central Railroaad

10-34 (30-40 min.) High-low and regression approaches.

1. Solution Exhibit 10-34 plots the relationship between machine-hours and power costs.

Solution Exhibit 10-34

Plot of Machine Hours Versus Power Costs

2(i)

Difference

Slope coefficient =  = $0.667 per machine-hour

Constant = $500 – ($0.667 ´ 400) = $233.20

= $300 – ($0.667 ´ 100) = $233.30

(difference in values are due to rounding errors)

Cost function estimated with high-low approach is:

y = $233.20 + $0.667X

(ii) One approach to computing a and b under the regression approach is to use the equations given in the chapter appendix.

SY = na + b(SX)

SXY = a (SX) + b(SX)2

That is, 1,600 = 4a + 1,000b R1

435,000 = 1,000a + 300,000 b R2

400,000 = 1,000a + 250,000 b R3 = 250(R1)

35,000 = 50,000 b R4 = R2 – R3

b =  = $0.70

1,600 = 4a + 1,000 (0.70)

900 = 4a

a =  = $225

Cost function estimated with the regression approach is:

y = $225 + $0.70 (machine-hours)

Alternatively, we can substitute directly by reexpressing into the normal equations symbolically as follows:

a =  

and b =  

Substituting we get

a =  =  = $225

Another approach is to use a computer software package. Results are:

r2 = 0.98; Durbin-Watson Statistic = 2.20

In this simple illustration, the high-low estimate using only two observations closely approximates the least squares regression approach that minimizes the sum of squares of the vertical deviations from the observations to the estimated regression line. The regression equation indicates that variable power costs are $0.70 per machine hour against the high-low estimate of $0.667. The fixed component of power costs within the relevant range equals $225, while the high-low method estimates this component as $233.20. The high-low method gives good results in this case because all the data points fall very close to the regression line.

a =  =  = $$0.70

10-34 (Cont'd.)

3.   = SY Ö 4 = $1,600 Ö 4 = $400

S(Y –   = (350 – 400)2 + (450 – 400)2 + (300 – 400)2 + (500 – 400)2

= 2,500 + 2,500 + 10,000 + 10,000 = 25,000

Period Y y = $225 + $0.70 X Y – y (Y – y)2

1 350 365 –15 225

2 450 435 +15 225

3 300 295 + 5 25

4 500 505 – 5 25

Total 1,600 500

r2 = 1 –  = 1 –  = 1 –  = 0.98

An r2 of ).98 indicates excellent goodness of fit. Only 2% of the varialtion in power costs is not explained by machine hours. Since the relation between machine hours and power costs is also economically plausible, Campi Corporation can be very confident of using the regression results to set its flexible budget for power costs. Machine hours is a cost driver of power costs.

10-35 (30-40 min.) Evaluating alternative regression model not for
profit.

1.a Solution Exhibit 10-35A plots the relationship between number of academic programs and overhead costs.

1b. Solution Exhibit 10-35B plots the relationship between number of enrolled students and overhead costs.

2. Solution Exhibit 10-35C compares the two simple regression models estimated by Hanks. Both regression models appear to perform well when estimating overhead costs. Cost function 1 using number of academic programs as the independent variable appears to perform slightly better than csot function 2 which uses number of enrolled students as the independent variable. Cost function 1 has a high r2 and goodness of fit, a high t-value indicating a significant relationship between number of academic programs and overhead costs, and meets all the specification assumptions for ordinary least squares regression. Cost function 2 has a lower r2 than cost function 1 and exhibits positive autocorrelation among the residuals as indicated by a low Durbin-Watson statistic.

3. The analysis indicates that overhead costs are related to the number of academic programs and the number of enrolled students. If Southwestern has pressures to reduce and control overhead costs, it may need to look hard at closing down some of its academic programs and reducing its intake of students. Reducing enrolled students may cut down on overhead costs but it also cuts down on revenues (tuition payments), hurts the reputation of the school, and reduces its alumni base, which is a future source of funds. For these reasons, Southwestern may prefer to downsize its academic programs, particularly those programs that attract few students. Of course Southwestern should continue to reduce costs by improving the efficiency of the delivery of its programs.

10-35 (Cont'd.)

Solution Exhibit 10-35a

Plot of Number of Academic Programs Versus Overhead Costs (in thousands)

Solution Exhibit 10-35b

Lot of Number of Enrolled Students Versus Overhead Costs (in thousands)

10-35 (Cont'd.)

Solution Exhibit 10-35c

Comparison of Alternative Cost Functions for Overhead Costs Estimated with Simple Regression for Southwestern University

10-36 (30 min.) Evaluating multiple regression models, not for profit.

1. It is economically plausible that the correct form of the model of overhead costs includes both number of academic programs and number of enrolled students as cost drivers. The findings in Problem 10-35 indicate that each of the independent variables affects overhead costs. (Each regression has a significant r2 and t-value on the independent variable.) Hanks could choose to divide overhead costs into two cost pools, (i) those overhead costs that are more closely related to number of academic program and (ii) those overhead costs more closely related to number of enrolled students and rerun the simple regression analysis on each overhead cost pool. Alternatively, Hanks could run a multiple regression analysis with total overhead costs as the dependent variable and the number of academic programs and number of enrolled students as the two independent variables.

2. Solution Exhibit 10-36A evaluates the multiple regression model using the format of Exhibit 10-21. Hanks should use the multiple regression model over the two simple regression models of Problem 10-35. The multiple regression model appears economically plausible and the regression model performs very well when estimating overhead costs. It has an excellent goodness of fit, significant t-values on both independent variables and meets all the specification assumptions for ordinary least squares regression.

There is some correlation between the two independent variables but multi-collinearity does not appear to be a problem here. The significance of both independent variables (despite some correlation between them) suggests that each variable is a driver of overhead cost. Of course, as the chapter describes, even if the independent variables exhibited multicollinearity, Hanks should still prefer to use the multiple regression model over the simple regression models of Problem 10-35. Omitting any one of the variables will cause the estimated coefficient of the independent variable included in the model to be biased away from its true value.

3. Possible uses for the multiple regression results include:

a. Planning and budgeting at Southwestern University. The regression analysis indicates the variables (number of academic programs and number of enrolled students) that help predict changes in overhead costs.

b. Cost control and performance evaluation. Hanks could compare actual performance with budgeted or expected numbers and seek ways to improve the efficiency of the University operations, and evaluate the performance of managers responsible for controlling overhead costs.

c. Cost management. If, cost pressures increase, the University could save costs by closing down academic programs that have few students enrolled.

10-36 (Cont'd.)

Solution Exhibit 10-36A

Evaluation of Cost Function for Overhead Costs Estimated with Multiple Regression for Southwestern University

10-37 (40-50 min.) Purchasing department cost drivers, simple regression analysis.

 

The problem reports the exact t-values from the computer runs of the data. Because the coefficients and standard errors given in the problem are rounded to three decimal places, dividing the coefficient by the standard error may yield slightly different t-values.

Plots of the data used in Regressions 1 to 3 are in Solution Exhibit 10-37A.

1. See Solution Exhibit 10-37B for a comparison of the three regression models.

2. Both Regressions 2 and 3 are well-specified regression models. The slope coefficient on their respective independent variables are significantly different from zero. These results support the Couture Fabric's presentation in which the number of purchase orders and the number of suppliers were reported to be drivers of purchasing department costs.

3. Guidelines 1 and 2 presented in the chapter could be used to gain additional evidence on cost drivers of purchasing department costs.

Guideline 1: 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.

Guideline 2: Use knowledge of operations. Lee could interview operating personnel in the purchasing department to obtain their insight on cost drivers.

10-37 (Cont'd.)

Solution Exhibit 10-37A

Regression Lines of Various Cost Drivers on Purchasing Dept. Costs for Fashion Fair

10-37 (cont'd.)

Solution Exhibit 10-37B

Comparison of Alternative Cost Functions for Purchasing Department

Costs Estimated with Simple Regression for Fashion Fair

10-38 (30-40 min.) Purchasing department cost drivers, multiple

regression analysis.

The problem reports the exact t-values from the computer runs of the data. Because the coefficients and standard errors given in the problem are rounded to three decimal places, dividing the coefficient by the standard error may yield slightly different t-values.

1. Regression 4 is a well-specified regression model:

Economic plausibility: Both independent variables are plausible and are supported by the findings of the Couture Fabrics study.

Goodness of fit: The r2 of 0.63 indicates an excellent goodness of fit.

Significance of independent variables: The t-value on # of POs is 2.14 while the t-statistic on # of Ss is 2.00. These t-values are either significant or border on significance.

Specification analysis: Results are available to examine the independence of residuals assumption. The Durbin-Watson statistic of 1.90 indicates that the assumption of independence is not rejected.

Regression 4 is consistent with the findings in Problem 10-34 that both the number of purchase orders and the number of suppliers are drivers of purchasing department costs. Regressions 2, 3, and 4 all satisfy the four criteria outlined in the text. Regression 4 has the best goodness of fit (0.63 for Regression 4 compared to 0.42 and 0.39 for Regressions 2 and 3, respectively). Most importantly, it is economically plausible that both the number of purchase orders and the number of suppliers drive purchasing department costs. We would recommend that Lee use Regression 4 over Regressions 2 and 3.

2. Regression 5 adds an additional independent variable (MP$) to the two independent variables in Regression 4. This additional variable (MP$) has a t-value of –0.07, implying its slope coefficient is insignificantly different from zero. The r2 in Regression 5 (0.63) is the same as that in Regression 4 (0.63), implying the addition of this third independent variable adds close to zero explanatory power. In summary, Regression 5 adds very little to Regression 4. We would recommend that Lee use Regression 4 over Regression 5.

3. Budgeted purchasing department costs for the Baltimore store next year are:

$485,384 + ($123.22 ´ 3,900) + ($2,952 ´ 110) = $1,290,662

10-38 (Cont'd.)

4. Multicollinearity is a frequently encountered problem in cost accounting; it does not arise in simple regression because there is only one independent variable in a simple regression. One consequence of multicollinearity is an increase in the standard errors of the coefficients of the individual variables. This frequently shows up in reduced t-values in the multiple regression relative to their t-values in the simple regression:

The decline in the t-values in the multiple regressions are consistent with some (but not very high) collinearity among the independent variables. Pairwise correlations between the independent variables are:

Correlation

# of POs / # of Ss 0.29

# of POs / MP$ 0.27

# of Ss / MP$ 0.34

5. Decisions in which the regression results in Problems 10-34 and 10-35 could be used are:

Cost management decisions: Fashion Flair could restructure relationships with the suppliers so that fewer separate purchase orders are made. Alternatively, it may aggressively reduce the number of existing suppliers.

Purchasing policy decisions: Fashion Flair could set up an internal charge system for individual retail departments within each store. Separate charges to each department could be made for each purchase order and each new supplier added to the existing ones. These internal charges would signal to each department ways in which their own decisions affect the total costs of Fashion Flair.

Accounting system design decisions: Fashion Flair may want to discontinue allocating purchasing department costs on the basis of the dollar value of merchandise purchased. Allocation bases better capturing cause-and-effect relations at Fashion Flair are the number of purchase orders and the number of suppliers.

10-39 (20 min.) Data analysis and ethics.

1(a) Average annual labor costs over the last ten years $1,200,000

Expected annual labor costs if robots introduced 550,000

Expected annual savings $ 650,000

1(b) Average annual labor costs over the last three years $ 800,000

Expected annual labor costs if robots introduced 550,000

Expected annual savings $ 250,000

Yes, it makes a difference in terms of justifying the robot investment. Using a 10-year average, the expected annual savings exceed the desired amount of $400,000 per year. Using average annual labor costs over the last three years, expected annual savings in labor costs falls short of the $400,000 target needed to justify the robot investment.

2. One explanation for average labor costs over the most recent three-year period being less than the average labor costs over the past ten years is learning curve effects. Learning-by-doing has caused workers to become more efficient. Alternatively, Comdex may have changed the VCR design to simplify manufacturing and reduce costs. Comdex may also have introduced new equipment that reduced labor costs.

3. The behavior of both Helen Gibbs and Joan Hansen to deliberately overestimate savings in labor costs to justify investments in robots is unethical. In assessing the situation, the specific "Standards of Ethical Conduct for Management Accountants," described in Exhibit 1-5 that Joan Hansen, the management accountant, should consider are listed below.

Competence

Clear reports using relevant and reliable information should be prepared. Reports prepared on the basis of overestimating savings in direct and indirect manufacturing labor (by considering older costs that are much higher than current costs) violate the management accountant's responsibility for competence. It is unethical for Gibbs to suggest that Hansen overestimate the cost savings that were computed for the robot investment and for Hansen to change the numbers to justify the investment in robots.

Integrity

The Standards of Ethical Conduct require the management accountant to communicate favorable as well as unfavorable information. In this regard both Gibbs's and Hansen's behavior of inflating manufacturing labor cost savings to justify the investment in robots could be viewed as unethical.

10-39 (Cont'd.)

Objectivity

The management accountant's Standards of Ethical Conduct require that information should be fairly and objectively communicated and that all relevant information should be disclosed. From a management accountant's standpoint, overestimating manufacturing labor cost savings to justify the robot investment violates objectivity. For the various reasons cited above, we should take the position that the behavior of Gibbs and Hansen is unethical.

4. Hansen should indicate to Gibbs that the savings in manufacturing labor costs alone are not large enough to justify the robot investment. She should also indicate to Gibbs her concern about inflating cost savings to justify the robot investment, quite independent of how important she thinks it is for the company to invest in the robots. She may wish to point out that part of the problem is the excessive focus on cost savings alone to justify the robot investment. An important benefit of the robot investment is the ability to generate higher revenues by producing superior products. If Gibbs still insists on inflating costs to justify the investment, Hansen should raise the matter with Gibbs's superior. If, after taking all these steps, there is continued pressure to overstate cost savings, Hansen should consider resigning from the company, rather than engage in unethical behavior.

10-40 (40 min.) Evaluating alternative regression functions, accrual

accounting adjustments

1. Solution Exhibit 10-40A presents the two data plots. The plot of engineering support reported costs and machine hours shows two separate groups of data, each of which may be approximated by a separate cost function. The problem arises because the plant records materials and parts costs on an "as purchased" rather than an "as used" basis. The plot of engineering support restated costs and machine hours shows a high positive correlation between the two variables (the coefficient of determination is 0.94); a single linear cost function provides a good fit to the data. Better estimates of the cost relation result because Kennedy adjusts the materials and parts costs to an accrual accounting basis.

2.

Slope coefficient, b =  

=  = –$8.31 per machine hour

Constant (at highest observation of cost driver) = $ 617 – (–$8.31)(73) = $1,224

Constant (at lowest observation of cost driver) = $1,066 – (–$8.31)(19) = $1,224

Slope coefficient, b =  

=  = $11.04 per machine hour

Constant (at highest observation of cost driver) = $ 966 – ($11.04)(73) = $160

Constant (at lowest observation of cost driver) = $ 370 – ($11.04)(19) = $160

10-40 (Cont'd.)

3. The cost function estimated with engineering support restated costs better approximates the regression analysis assumptions. See Solution Exhibit 10-40B for a comparison of the two regressions.

4. Of all the cost functions estimated in requirements 2 and 3, I would choose Regression 2 using engineering support restated costs as best representing the relationship between engineering support costs and machine hours. The cost functions estimated using engineering support reported costs are mispecified and not-economically plausible because materials and parts costs are reported on an "as purchased" rather than on an "as used" basis. With respect to engineering support restated costs, the high-low and regression approaches yield roughly similar estimates. The regression approach is technically superior because it determines the line that best fits all observations. In contrast the high-low method only considers two points (observations with the highest and lowest cost drivers) when estimating the cost function. Solution Exhibit 10-40B shows that the cost function estimated using the regression approach has excellent goodness of fit (r2 = 0.94) and appears to be well specified.

5. Using the regression cost function estimated with restated costs, Kennedy should budget $748.38 as engineering support costs for December calculated as follows:

Engineering support costs = $176.38 + ($11.44 per hour ´ 50 hours) = $748.38

6. Problems Kennedy might encounter include:

(a) A perpetual inventory system may not be used in this case; the amounts requisitioned likely will not permit an accurate matching of costs with the independent variable on a month-by-month basis.

(b) Quality of the source records for usage by engineers may be relatively low; e.g., engineers may requisition materials and parts in batches, but not use them immediately.

(c) Records may not distinguish materials and parts for maintenance from materials and parts used for repairs and breakdowns; separate cost functions may be appropriate for the two categories of materials and parts.

(d) Year-end accounting adjustments to inventory may mask errors that gradually accumulate month-by-month.

 

10-40 (Cont'd.)

7. Picking the correct cost function is important for cost prediction, cost management and performance evaluation. For example had United Packaging used Regression 1 (engineering support reported costs) to estimate the cost function, it would erroneously conclude that engineering support costs decrease with machine hours. In a month with 60 machine hours regression 1 would predict costs of $1,393.20 – ($14.23 ´ 60) = $539.40. If actual costs turn out to be $800, management would conclude that changes should be made to reduce costs. In fact on the basis of the preferred regression 2, support overhead costs are lower than the predicted amount of $176.38 + ($11.44 ´ 60) = $862.78––a performance that management should seek to replicate, not change.

On the other hand, if machine hours worked in a month were low, say 25 hours, regression 1 would erroneously predict support overhead costs of $1,393.20 – ($14.23 ´ 25) = $1,037.45. If actual costs are $700, management would conclude that its performance has been very good. In fact, compared to the costs predicted by the preferred regression 2 of $176.38 + ($11.44 ´ 25) = $462.38, the actual performance is rather poor. Using regression 1 management may feel costs are being managed very well when in fact they are much higher than what they should be and need to be managed "down."

10-40 (Cont'd.)

 

SOLUTION EXHIBIT 10-40A

Plots and Regression Lines for Engineering Support

Reported Costs and Engineering Support Restated Costs

Engineering Support Report Costs

Machine Hours

Engineering Support Restated Costs

Machine Hours

10-40 (cont'd)

SOLUTION EXHIBIT 10-40B

Comparison of Alternative Cost Functions for Engineering Support Costs

at United Packaging