Assignment Material

Questions

1. 10-1. What two assumptions are frequently made when estimating a cost function?
2. 10-2. Describe three alternative linear cost functions.
3. 10-3. What is the difference between a linear and a nonlinear cost function? Give an example of each type of cost function.
4. 10-4. “High correlation between two variables means that one is the cause and the other is the effect.” Do you agree? Explain.
5. 10-5. Name four approaches to estimating a cost function.
6. 10-6. Describe the conference method for estimating a cost function. What are two advantages of this method?
7. 10-7. Describe the account analysis method for estimating a cost function.
8. 10-8. List the six steps in estimating a cost function on the basis of an analysis of a past cost relationship. Which step is typically the most difficult for the cost analyst?
9. 10-9. When using the high-low method, should you base the high and low observations on the dependent variable or on the cost driver?
10. 10-10. Describe three criteria for evaluating cost functions and choosing cost drivers.
11. 10-11. Define learning curve. Outline two models that can be used when incorporating learning into the estimation of cost functions.
12. 10-12. Discuss four frequently encountered problems when collecting cost data on variables included in a cost function.
13. 10-13. What are the four key assumptions examined in specification analysis in the case of simple regression?
14. 10-14. All the independent variables in a cost function estimated with regression analysis are cost drivers.” Do you agree? Explain.
15. 10-15. Multicollinearity exists when the dependent variable and the independent variable are highly correlated.” Do you agree? Explain.

Multiple-Choice Questions

1. 10-16. HL Co. uses the high-low method to derive a total cost formula. Using a range of units produced from 1,500 to 7,500, and a range of total costs from $21,000 to $45,000, producing 2,000 units will cost HL:
   
   1. a. $8,000
   2. b. $12,000
   3. c. $23,000
   4. d. $29,000
2. 10-17. A firm uses simple linear regression to forecast the costs for its main product line. If fixed costs are equal to $235,000 and variable costs are $10 per unit, how many units does it need to sell at $15 per unit to make a $300,000 profit?
   
   1. a. 21,400
   2. b. 47,000
   3. c. 60,000
   4. d. 107,000
3. 10-18. In regression analysis, the coefficient of determination
   
   1. a. Is used to determine the proportion of the total variation in the dependent variable (Y) explained by the independent variable (X).
   2. b. Ranges between negative one and positive one.
   3. c. Is used to determine the expected value of the net income based on the regression line.
   4. d. Becomes smaller as the fit of the regression line improves.
4. 10-19. A regression equation is set up, where the dependent variable is total costs and the independent variable is production. A correlation coefficient of 0.70 implies that
   
   1. a. The coefficient of determination is negative.
   2. b. The level of production explains 49% of the variation in total costs
   3. c. There is a slightly inverse relationship between production and total costs.
   4. d. A correlation coefficient of 1.30 would produce a regression line with better fit to the data.
5. 10-20. What would be the approximate value of the coefficient of correlation between advertising and sales where a company advertises aggressively as an alternative to temporary worker layoffs and cuts off advertising when incoming jobs are on backorder?
   
   1. a. 1.0
   2. b. 0
   3. c. $-1.0$
   4. d. $-100$

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Exercises

1. 10-21. ESTIMATING A COST FUNCTION. The controller of the Blade Company is preparing the budget for 2021 and needs to estimate a cost function for delivery costs. Information regarding delivery costs incurred in the prior 2 months are

Required

1. Estimate the cost function for delivery.

2. Can the constant in the cost function be used as an estimate of fixed delivery cost per month? Explain.

1. 10-22.  IDENTIFYING VARIABLE-, FIXED-, AND MIXED-COST FUNCTIONS. The Rolling Hills Corporation operates car rental agencies at more than 20 airports. Customers can choose from one of three contracts for car rentals of 1 day or less:
   1. • Contract 1: $50 for the day
   2. • Contract 2: $30 for the day plus $0.20 per mile traveled
   3. • Contract 3: $1.00 per mile traveled
   4. Required
   5. 1. Plot separate graphs for each of the three contracts, with costs on the vertical axis and miles traveled on the horizontal axis.
   6. 2. Express each contract as a linear cost function of the form $y=a+bX$.
   7. 3. Identify each contract as a variable-, fixed-, or mixed-cost function.
2. 10-23. VARIOUS COST-BEHAVIOR PATTERNS. (CPA, adapted) The vertical axes of the graphs below represent total cost, and the horizontal axes represent units produced during a calendar year. In each case, the zero point of dollars and production is at the intersection of the two axes.

1. Select the graph that matches the numbered manufacturing cost data (requirements 1–9). Indicate by letter which graph best fits the situation or item described. The graphs may be used more than once or not at all.

1. Annual depreciation of equipment, where the amount of depreciation charged is computed by the machine-hours method.

2. Electricity bill—a flat fixed charge, plus a variable cost after a certain number of kilowatt-hours are used, in which the quantity of kilowatt-hours used varies proportionately with quantity of units produced.

3. City water bill, which is computed as follows:

The gallons of water used vary proportionately with the quantity of production output.

4. Cost of direct materials, where direct material cost per unit produced decreases with each pound of material used (for example, if 1 pound is used, the cost is $10; if 2 pounds are used, the cost is $19.98; if 3 pounds are used, the cost is $29.94), with a minimum cost per unit of $9.20.

5. Annual depreciation of equipment, where the amount is computed by the straight-line method. When the depreciation schedule was prepared, it was anticipated that the obsolescence factor would be greater than the wear-and-tear factor.

6. Rent on a manufacturing plant donated by the city, where the agreement calls for a fixed-fee payment unless 200,000 labor-hours are worked, in which case no rent is paid.

7. Salaries of repair personnel, where one person is needed for every 1,000 machine-hours or less (that is, 0 to 1,000 hours requires one person, 1,001 to 2,000 hours requires two people, and so on).

8. Cost of direct materials used (assume no quantity discounts).

9. Rent on a manufacturing plant donated by the county, where the agreement calls for rent of $100,000 to be reduced by $1 for each direct manufacturing labor-hour worked in excess of 200,000 hours, but a minimum rental fee of $20,000 must be paid.

1. 10-24. MATCHING GRAPHS WITH DESCRIPTIONS OF COST AND REVENUE BEHAVIOR. (D. Green, adapted) Given here are a number of graphs.

1. The horizontal axis of each graph represents the units produced over the year, and the vertical axis represents total cost or revenues.
2. Required
3. Indicate by number which graph best fits the situation or item described (a–h). Some graphs may be used more than once; some may not apply to any of the situations.
   1. a. Direct material costs
   2. b. Supervisors’ salaries for one shift and two shifts
   3. c. A cost–volume–profit graph
   4. d. Mixed costs—for example, fixed charge plus a rate per unit produced
   5. e. Depreciation of plant, computed on a straight-line basis
   6. f. Data supporting the use of a variable-cost rate, such as manufacturing labor cost of $14 per unit produced
   7. g. Incentive bonus plan that pays managers $0.10 for every unit produced above some level of production
   8. h. Interest expense on $2 million borrowed at a fixed rate of interest 
4. 10-25. ACCOUNT ANALYSIS, HIGH-LOW. Smith Corporation wants to find an equation to estimate some of their monthly operating costs for the operating budget for 2021. The following cost and other data were gathered for 2020: 

Required

1. Which of the preceding costs is variable? Fixed? Mixed? Explain.

2. Using the high-low method, determine the cost function for each cost.

3. Combine the preceding information to get a monthly operating cost function for the Smith Corporation.

4. Next month, Smith expects to use 350 machine hours, have 90 employees, and ship 8,600 units. Estimate the total operating cost for the month.

1. 10-26. ACCOUNT ANALYSIS METHOD. Hamwey, Inc., a manufacturer of plastic products, reports the following manufacturing costs and account analysis classification for the year ended December 31, 2020.

1. Hamwey, Inc., produced 75,000 units of product in 2020. Hamwey’s management is estimating costs for 2021 on the basis of 2020 numbers. The following additional information is available for 2021.
   1. a. Direct materials prices in 2021 are expected to increase by 8% compared with 2020.
   2. b. Under the terms of the labor contract, direct manufacturing labor wage rates are expected to increase by 8% in 2021 compared with 2020.
   3. c. Power rates and wage rates for supervision, materials handling, and maintenance are not expected to change from 2020 to 2021.
   4. d. Depreciation costs are expected to increase by 10%, and rent, property taxes, and administration costs are expected to increase by 9%.
   5. e. Hamwey expects to manufacture and sell 82,500 units in 2021.
   6. Required
   7. 1. Prepare a schedule of variable, fixed, and total manufacturing costs for each account category in 2021. Estimate total manufacturing costs for 2021.
   8. 2. Calculate Hamwey’s total manufacturing cost per unit in 2020, and estimate total manufacturing cost per unit in 2021.
   9. 3. How can you obtain better estimates of fixed and variable costs? Why would these better estimates be useful to Hamwey?

1. 10-27.  ESTIMATING A COST FUNCTION, HIGH-LOW METHOD. Roy Travel offers helicopter service from suburban towns to John F. Kennedy International Airport in New York City. Each of its nine helicopters makes between 1,350 and 2,100 round-trips per year. The records indicate that a helicopter that has made 1,350 round-trips in the year incurs an average operating cost of $450 per round-trip, and one that has made 2,100 round-trips in the year incurs an average operating cost of $350 per round-trip.
   1. Required
   2. 1. Using the high-low method, estimate the linear relationship $y=a+bX\mathrm{,}$  where y is the total annual operating cost of a helicopter and X is the number of round-trips it makes to JFK airport during the year.
   3. 2. Give examples of costs that would be included in a and in b.
   4. 3. If Roy Travel expects each helicopter to make, on average, 1,700 round-trips in the coming year, what should be its estimated operating budget for the helicopter fleet?

1. 10-28. ESTIMATING A COST FUNCTION, HIGH-LOW METHOD. Lynsay Detz is examining customer-service costs in the southern region of Clancey Products. Clancey Products has more than 200 separate electrical products that are sold with a 6-month guarantee of full repair or replacement with a new product. When a product is returned by a customer, a service report is prepared. This service report includes details of the problem and the time and cost of resolving the problem. Weekly data for the most recent 8-week period are as follows:

1. Required

1. Plot the relationship between customer-service costs and number of service reports. Is the relationship economically plausible?

2. Use the high-low method to compute the cost function relating customer-service costs to the number of service reports.

3. What variables, in addition to number of service reports, might be cost drivers of weekly customer-service costs of Clancey Products?

1. 10-29. LINEAR COST APPROXIMATION. Dr. Young, of Young and Associates, LLP, is examining how overhead costs behave as a function of monthly physician contact hours billed to patients. The historical data are as follows:

1. Required

1. Compute the linear cost function, relating total overhead costs to physician contact hours, using the representative observations of 200 and 300 hours. Plot the linear cost function. Does the constant component of the cost function represent the fixed overhead costs of Young and Associates? Why?

2. What would be the predicted total overhead costs for (a) 150 hours and (b) 400 hours using the cost function estimated in requirement 1? Plot the predicted costs and actual costs for 150 and 400 hours.

3. Dr. Young had a chance to do some school physicals that would have boosted physician contact hours billed to patients from 200 to 250 hours. Suppose Dr. Young, guided by the linear cost function, rejected this job because it would have brought a total increase in contribution margin of $9,000, before deducting the predicted increase in total overhead cost, $10,000. What is the total contribution margin actually forgone?

1. 10-30. COST–VOLUME–PROFIT AND REGRESSION ANALYSIS. Grant Corporation manufactures a drink bottle, model CL24. During 2020, Grant produced 240,000 bottles at a total cost of $1,080,000. Wren Corporation has offered to supply as many bottles as Grant wants at a cost of $4.40 per bottle. Grant anticipates needing 255,000 bottles each year for the next few years. 
   1. Required
   2. 1.  
      1. a. What is the average cost of manufacturing a drink bottle in 2020? How does it compare to Wren’s offer?
      2. b. Can Grant use the answer in requirement 1a to determine the cost of manufacturing 255,000 drink bottles? Explain. 
   3. 2. Grant’s cost analyst uses annual data from past years to estimate the following regression equation with total manufacturing costs of the drink bottle as the dependent variable and drink bottles produced as the independent variable:

During the years used to estimate the regression equation, the production of bottles varied from 229,000 to 265,000. Using this equation, estimate how much it would cost Grant to manufacture 255,000 drink bottles. How much more or less costly is it to manufacture the bottles than to acquire them from Wren?

3. What other information would you need to be confident that the equation in requirement 2 accurately predicts the cost of manufacturing drink bottles?

1. 10-31. REGRESSION ANALYSIS, SERVICE COMPANY. (CMA, adapted) Linda Olson owns a professional character business in a large metropolitan area. She hires local college students to play these characters at children’s parties and other events. Linda provides balloons, cupcakes, and punch. For a standard party the cost on a per-person basis is as follows:

1. Linda is quite certain about the estimates of the materials and labor costs but is not as comfortable with the overhead estimate. The overhead estimate was based on the actual data for the past 9 months, which are presented here. These data indicate that overhead costs vary with the direct labor-hours used. The $40 estimate was determined by dividing total overhead costs for the 9 months by total labor-hours.

1. Linda has recently become aware of regression analysis. She estimated the following regression equation with overhead costs as the dependent variable and labor-hours as the independent variable:

1. Required

1. Plot the relationship between overhead costs and labor-hours. Draw the regression line and evaluate it using the criteria of economic plausibility, goodness of fit, and slope of the regression line.

2. Using data from the regression analysis, what is the variable cost per person for a standard party?

3. Linda Olson has been asked to prepare a bid for a 20-child birthday party to be given next month. Determine the minimum bid price that Linda would be willing to submit to recoup variable costs.

1. 10-32. HIGH-LOW, REGRESSION. May Blackwell is the new manager of the materials storeroom for Clayton Manufacturing. May has been asked to estimate future monthly purchase costs for part #696, used in two of Clayton’s products. May has purchase cost and quantity data for the past 9 months as follows:

1. Estimated monthly purchases for this part based on expected demand of the two products for the rest of the year are as follows:

1. Required

1. The computer in May’s office is down, and May has been asked to immediately provide an equation to estimate the future purchase cost for part #696. May grabs a calculator and uses the high-low method to estimate a cost equation. What equation does she get?

2. Using the equation from requirement 1, calculate the future expected purchase costs for each of the last 3 months of the year.

3. After a few hours, May’s computer is fixed. May uses the first 9 months of data and regression analysis to estimate the relationship between the quantity purchased and purchase costs of part #696. The regression line May obtains is as follows:

Evaluate the regression line using the criteria of economic plausibility, goodness of fit, and significance of the independent variable. Compare the regression equation to the equation based on the high-low method. Which is a better fit? Why?

4. Use the regression results to calculate the expected purchase costs for October, November, and December. Compare the expected purchase costs to the expected purchase costs calculated using the high-low method in requirement 2. Comment on your results.

1. 10-33. LEARNING CURVE, CUMULATIVE AVERAGE-TIME LEARNING MODEL. Global Defender manufactures radar systems. It has just completed the manufacture of its first newly designed system, RS-32. Manufacturing data for the RS-32 follow:

1. Required
2. Calculate the total variable costs of producing 2, 4, and 8 units. 
3. 10-34. LEARNING CURVE, INCREMENTAL UNIT-TIME LEARNING MODEL. Assume the same information for Global Defender as in Exercise 10-33, except that Global Defender uses an 85% incremental unit-time learning model as a basis for predicting direct manufacturing labor-hours. $(\text{An} 85\%\hspace{0.17em}\text{learning curve means} b=-0.234465\mathrm{.})$ 
   1. Required
   2. 1. Calculate the total variable costs of producing 2, 3, and 4 units. 
   3. 2. If you solved Exercise 10-33, compare your cost predictions in the two exercises for 2 and 4 units. Why are the predictions different? How should Global Defender decide which model it should use? 
4. 10-35. HIGH-LOW METHOD. Wayne Mueller, financial analyst at CELL Corporation, is examining the behavior of quarterly utility costs for budgeting purposes. Mueller collects the following data on machine-hours worked and utility costs for the past 8 quarters:

1. Required

1. Estimate the cost function for the quarterly data using the high-low method.

2. Plot and comment on the estimated cost function.

3. Mueller anticipates that CELL will operate machines for 125,000 hours in quarter 9. Calculate the predicted utility costs in quarter 9 using the cost function estimated in requirement 1.

Problems

1. 10-36.  HIGH-LOW METHOD AND REGRESSION ANALYSIS. Market Thyme, a cooperative of organic family-owned farms, has recently started a fresh produce club to provide support to the group’s member farms and to promote the benefits of eating organic, locally produced food. Families pay a seasonal membership fee of $100 and place their orders a week in advance for a price of $40 per order. In turn, Market Thyme delivers fresh-picked seasonal local produce to several neighborhood distribution points. Five hundred families joined the club for the first season, but the number of orders varied from week to week. 
2. Tom Diehl has run the produce club for the first season. Tom is now a farmer but remembers a few things about cost analysis from college. In planning for next year, he wants to know how many orders will be needed each week for the club to break even, but first he must estimate the club’s fixed and variable costs. He has collected the following data over the club’s first season of operation:

1. Required

1. Plot the relationship between number of orders per week and weekly total costs.

2. Estimate the cost equation using the high-low method, and draw this line on your graph.

3. Tom uses his computer to calculate the following regression formula:

Draw the regression line on your graph. Use your graph to evaluate the regression line using the criteria of economic plausibility, goodness of fit, and significance of the independent variable. Is the cost function estimated using the high-low method a close approximation of the cost function estimated using the regression method? Explain briefly.

4. Did Market Thyme break even this season? Remember that each of the families paid a seasonal membership fee of $100.

5. Assume that 500 families join the club next year and that prices and costs do not change. How many orders, on average, must Market Thyme receive each of 10 weeks next season to break even?

1. 10-37. HIGH-LOW METHOD; REGRESSION ANALYSIS. (CIMA, adapted) Amy Mendenhall, sales manager of Fitzsimmons Arenas, is checking to see if there is any relationship between promotional costs and ticket revenues at the sports stadium. She obtains the following data for the past 9 months:

1. She estimates the following regression equation:

1. Required

1. Plot the relationship between promotional costs and ticket revenues. Also draw the regression line and evaluate it using the criteria of economic plausibility, goodness of fit, and slope of the regression line.

2. Use the high-low method to compute the function relating promotional costs and revenues.

3. Using (a) the regression equation and (b) the high-low equation, what is the increase in revenues for each $10,000 spent on promotional costs within the relevant range? Which method should Amy use to predict the effect of promotional costs on ticket revenues? Explain briefly.

1. 10-38.  REGRESSION, ACTIVITY-BASED COSTING, CHOOSING COST DRIVERS. Sleep Late, a large hotel chain, has been using activity-based costing to determine the cost of a night’s stay at their hotels. One of the activities, “Inspection,” occurs to ensure the room is in good condition. Sleep Late has been using “number of rooms inspected” as the cost driver for inspection costs. A significant component of inspection costs is the cost of replacing cutlery, crockery, and furnishings as a result of an inspection. 
2. Mary Adams, the chief inspector, is wondering whether inspection labor-hours might be a better cost driver for inspection costs. Adams gathers information for weekly inspection costs, rooms inspected, and inspection labor-hours as follows:

1. Adams runs regressions on each of the possible cost drivers and estimates these cost functions:

1.  Required

1. Explain why rooms inspected and inspection labor-hours are plausible cost drivers of inspection costs.

2. Plot the data and regression line for rooms inspected and inspection costs. Plot the data and regression line for inspection labor-hours and inspection costs. Which cost driver of inspection costs would you choose? Explain.

3. Adams expects inspectors to inspect 300 rooms and work for 105 hours next week. Using the cost driver you chose in requirement 2, what amount of inspection costs should Adams budget? Explain any implications of Adams choosing the cost driver you did not choose in requirement 2 to budget inspection costs.

1. 10-39. INTERPRETING REGRESSION RESULTS. Spirit Freightways is a leader in transporting agricultural products in the western provinces of Canada. Reese Brown, a financial analyst at Spirit Freightways, is studying the behavior of transportation costs for budgeting purposes. Transportation costs at Spirit are of two types: (1) operating costs (such as labor and fuel) and (2) maintenance costs (primarily overhaul of vehicles). 
2. Brown gathers monthly data on each type of cost, as well as the total freight miles traveled by Spirit vehicles in each month. The data collected are shown below (all in thousands):

1.  Required

1. Conduct a regression using the monthly data of operating costs on freight miles. You should obtain the following result:

Regression: $\text{Operating costs}=a+(b\times \text{Number of freight miles})$

$$r^2=0.86\text{;\hspace{0.05em}\hspace{0.05em}Durbin‐Watsonstatistic}=2.18$$

2. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of economic plausibility, goodness of fit, and slope of the regression line.

3. Brown expects Spirit to generate, on average, 3,600 freight miles each month next year. How much in operating costs should Brown budget for next year?

4. Name three variables, other than freight miles, that Brown might expect to be important cost drivers for Spirit’s operating costs.

5. Brown next conducts a regression using the monthly data of maintenance costs on freight miles. Verify that she obtained the following result:

Regression: $\text{Maintenance costs}=a+(b\times \text{Number of freight miles})$

6. Provide a reasoned explanation for the observed sign on the cost driver variable in the maintenance cost regression. What alternative data or alternative regression specifications would you like to use to better capture the above relationship?

1. 10-40 COST ESTIMATION, CUMULATIVE AVERAGE-TIME LEARNING CURVE. The WLJ Boat Company, which is under contract to the U.S. Navy, assembles troop deployment boats. As part of its research program, it completes the assembly of the first of a new model (PT109) of deployment boats. The Navy is impressed with the PT109. It requests that WLJ Boat submit a proposal on the cost of producing another six PT109s. 
2. WLJ Boat reports the following cost information for the first PT109 assembled and uses a 90% cumulative average-time learning model as a basis for forecasting direct manufacturing labor-hours for the next six PT109s. (A 90% learning curve means $\mathrm{b}=-0.152004.$)

1.  Required

1. Calculate predicted total costs of producing the six PT109s for the Navy. (WLJ Boat will keep the first deployment boat assembled, costed at $1,493,200, as a demonstration model for potential customers.)

2. What is the dollar amount of the difference between (a) the predicted total costs for producing the six PT109s in requirement 1 and (b) the predicted total costs for producing the six PT109s, assuming that there is no learning curve for direct manufacturing labor? That is, for (b) assume a linear function for units produced and direct manufacturing labor-hours.

1. 10-41. COST ESTIMATION, INCREMENTAL UNIT-TIME LEARNING MODEL. Assume the same information for the WLJ Boat Company as in Problem 10-40 with one exception. This exception is that WLJ Boat uses a 90% incremental unit-time learning model as a basis for predicting direct manufacturing labor-hours in its assembling operations. (A 90% learning curve means $b = -0.152004$.) 
   1. Required
   2. 1. Prepare a prediction of the total costs for producing the six PT109s for the Navy. 
   3. 2. If you solved requirement 1 of Problem 10-40, compare your cost prediction there with the one you made here. Why are the predictions different? How should WLJ Boat decide which model it should use?

1. 10-42. REGRESSION; CHOOSING AMONG MODELS. Apollo Hospital specializes in outpatient surgeries for relatively minor procedures. Apollo is a nonprofit institution and places great emphasis on controlling costs in order to provide services to the community in an efficient manner.  
2. Apollo’s CFO, Julie Chen, has been concerned of late about the hospital’s consumption of medical supplies. To better understand the behavior of this cost, Julie consults with Rhett Bratt, the person responsible for Apollo’s cost system. After some discussion, Julie and Rhett conclude that there are two potential cost drivers for the hospital’s medical supplies costs. The first driver is the total number of procedures performed. The second is the number of patient-hours generated by Apollo. Julie and Rhett view the latter as a potentially better cost driver because the hospital does perform a variety of procedures, some more complex than others. 
3. Rhett provides the following data relating to the past year to Julie.

1. Required

1. Estimate the regression equation for (a) medical supplies costs and number of procedures and (b) medical supplies costs and number of patient-hours. You should obtain the following results:

Regression 1 : $\text{Medical supplies costs}=a+(b\times \text{Number of procedures})$

Regression 2 : $\text{Medical supplies costs}=a+(b\times \mathrm{Number} \mathrm{of} \mathrm{patient}-\mathrm{hours})$

2. On different graphs plot the data and the regression lines for each of the following cost functions:

a. $\text{Medical supplies costs}=a+(b\times \text{Number of procedures})$

b. $\text{Medical supplies costs}=a+(b\times \mathrm{Number} \mathrm{of} \mathrm{patient}‐\mathrm{hours})$

3. Evaluate the regression models for “Number of procedures” and “Number of patient-hours” as the cost driver according to the format of Exhibit 10-19.

4. Based on your analysis, which cost driver should Julie Chen adopt for Apollo Hospital? Explain.

1. 10-43. MULTIPLE REGRESSION (CONTINUATION OF 10-42). After further discussion, Julie and Rhett wonder if they should view both the number of procedures and number of patient-hours as cost drivers in a multiple regression estimation in order to best understand Apollo’s medical supplies costs. 
   1. Required
   2. 1. Conduct a multiple regression to estimate the regression equation for medical supplies costs using both number of procedures and number of patient-hours as independent variables. You should obtain the following result: 
   3. Regression 3 : $\text{Medical supplies costs}=a+(b_1\times \mathrm{No}.\mathrm{of} \mathrm{procedures})+(b_2\times \mathrm{No}.\mathrm{of} \mathrm{patient}‐\mathrm{hours})$

2. Evaluate the multiple regression output using the criteria of economic plausibility goodness of fit, significance of independent variables, and specification of estimation assumptions.

3. What potential issues could arise in multiple regression analysis that are not present in simple regression models? Is there evidence of such difficulties in the multiple regression in this problem? Explain.

4. Which regression models from Problems 10-42 and 10-43 would you recommend Julie use? Explain.

1. 10-44. COST ESTIMATION. Hankuk Electronics started production on a sophisticated new smartphone running the Android operating system in January 2020. Given the razor-thin margins in the consumer electronics industry, Hankuk’s success depends heavily on being able to produce the phone as economically as possible. 
2. At the end of the first year of production, Hankuk’s controller, Inbee Kim, gathered data on its monthly levels of output, as well as monthly consumption of direct labor-hours (DLH). Inbee views labor-hours as the key driver of Hankuk’s direct and overhead costs. The information collected by Inbee is provided below:

1. Required

1. Inbee is keen to examine the relationship between direct labor consumption and output levels. She decides to estimate this relationship using a simple linear regression based on the monthly data. Verify that the following is the result obtained by Inbee:

Regression 1: $\mathrm{Direct} \mathrm{labor}-\mathrm{hours}=a+(b\times \text{Output units})$

2. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of economic plausibility, goodness of fit, and slope of the regression line.

3. Inbee estimates that Hankuk has a variable cost of $17.50 per direct labor-hour. She expects that Hankuk will produce 650 units in the next month, January 2021. What should she budget as the expected variable cost? How confident is she of her estimate?

1. 10-45. COST ESTIMATION, LEARNING CURVES (CONTINUATION OF 10-44). Inbee is concerned that she still does not understand the relationship between output and labor consumption. She consults with Jim Park, the head of engineering, and shares the results of her regression estimation. Jim indicates that the production of new smartphone models exhibits significant learning effects—as Hankuk gains experience with production, it can produce additional units using less time. He suggests that it is more appropriate to specify the following relationship:

1. where x is cumulative production in units, y is the cumulative average direct labor-hours per unit (i.e., cumulative DLH divided by cumulative production), and a and b are parameters of the learning effect. 
2. To estimate this, Inbee and Jim use the original data to calculate the cumulative output and cumulative average labor-hours per unit for each month. They then take natural logarithms of these variables in order to be able to estimate a regression equation. Here is the transformed data:

1. Required

1. Estimate the relationship between the cumulative average direct labor-hours per unit and cumulative output (both in logarithms). Verify that the following is the result obtained by Inbee and Jim:

Regression 1: $\mathrm{Ln}\hspace{0.17em}(\mathrm{Cumulative} \mathrm{avg} \mathrm{DLH} \mathrm{per} \mathrm{unit})=a+[b\times \mathrm{Ln}\hspace{0.17em}(\text{Cumulative Output}\left)\right]$ 

2. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of economic plausibility, goodness of fit, and slope of the regression line.

3. Verify that the estimated slope coefficient corresponds to an 86.6% cumulative average-time learning curve.

4. Based on this new estimation, how will Inbee revise her budget for Hankuk’s variable cost for the expected output of 650 units in January 2021? How confident is she of this new cost estimate?

1. 10-46. INTERPRETING REGRESSION RESULTS, MATCHING TIME PERIODS. Nandita Summers works at Modus, a store that caters to fashion for young adults. Nandita is responsible for the store’s online advertising and promotion budget. For the past year, she has studied search engine optimization and has been purchasing keywords and display advertising on Google, Facebook, and Twitter. In order to analyze the effectiveness of her efforts and to decide whether to continue online advertising or move her advertising dollars back to traditional print media, Nandita collects the following data:

1. Required

1. Nandita performs a regression analysis, comparing each month’s online advertising expense with that month’s revenue. Verify that she obtains the following result:

2. Plot the preceding data on a graph and draw the regression line. What does the cost formula indicate about the relationship between monthly online advertising expense and monthly sales revenue? Is the relationship economically plausible?

3. After further thought, Nandita realizes there may have been a flaw in her approach. In particular, there may be a lag between the time customers click through to the Modus website and peruse its social media content (which is when the online ad expense is incurred) and the time they actually shop in the physical store. Nandita modifies her analysis by comparing each month’s sales revenue to the advertising expense in the prior month. After discarding September sales revenue and August advertising expense, show that the modified regression yields the following:

4. What does the revised formula indicate? Plot the revised data on a graph. Is this relationship economically plausible?

5. Can Nandita conclude that there is a cause-and-effect relationship between online advertising expense and sales revenue? Why or why not?

1. 10-47.  PURCHASING DEPARTMENT COST DRIVERS, ACTIVITY-BASED COSTING, SIMPLE REGRESSION ANALYSIS. Perfect Fit operates a chain of 10 retail department stores. Each department store makes its own purchasing decisions. Carl Hart, assistant to the president of Perfect Fit, is interested in better understanding the drivers of purchasing department costs. For many years, Perfect Fit has allocated purchasing department costs to products on the basis of the dollar value of merchandise purchased. A $100 item is allocated 10 times as many overhead costs associated with the purchasing department as a $10 item. 
2. Hart recently attended a seminar titled “Cost Drivers in the Retail Industry.” In a presentation at the seminar, Kaliko Fabrics, a leading competitor that has implemented activity-based costing, reported number of purchase orders and number of suppliers to be the two most important cost drivers of purchasing department costs. The dollar value of merchandise purchased in each purchase order was not found to be a significant cost driver. Hart interviewed several members of the purchasing department at the Perfect Fit store in Miami. They believed that Kaliko Fabrics’ conclusions also applied to their purchasing department. 
3. Hart collects the following data for the most recent year for Perfect Fit’s 10 retail department stores:

1. Hart decides to use simple regression analysis to examine whether one or more of three variables (the last three columns in the table) are cost drivers of purchasing department costs. Summary results for these regressions are as follows: 
2. Regression 1 : $\text{PDC}=a+(b\times \text{MP\$})$

1. Regression 2 : $\mathrm{PDC}=a+(b\times \text{No. of\hspace{0.17em}} \mathrm{POs})$ 

1. Regression 3 : $\mathrm{PDC}=a+(b\times \text{No. of }\mathrm{Ss})$

1. Required

1. Compare and evaluate the three simple regression models estimated by Hart. Graph each one. Also, use the format employed in Exhibit 10-19 to evaluate the information.

2. Do the regression results support the Kaliko Fabrics’ presentation about the purchasing department’s cost drivers? Which of these cost drivers would you recommend in designing an ABC system?

3. How might Hart gain additional evidence on drivers of purchasing department costs at each of Perfect Fit’s stores?

1. 10-48. PURCHASING DEPARTMENT COST DRIVERS, MULTIPLE REGRESSION ANALYSIS (CONTINUATION OF 10-47). Carl Hart decides that the simple regression analysis used in Problem 10-47 could be extended to a multiple regression analysis. He finds the following results for two multiple regression analyses: 
2. Regression 4: $\mathrm{PDC}=a+(b_1\times \text{No. of}\hspace{0.17em}\mathrm{POs})+(b_2\times \text{No. of}\hspace{0.17em}\mathrm{Ss})$

1. Regression 5: $\mathrm{PDC}=a+(b_1\times \mathrm{No}.\mathrm{of} \mathrm{POs})+(b_2\times \mathrm{No}.\mathrm{of} \mathrm{Ss})+(b_3\times \mathrm{MP}\$)$

1. The coefficients of correlation between combinations of pairs of the variables are as follows:

1. Required

1. Evaluate regression 4 using the criteria of economic plausibility, goodness of fit, significance of independent variables, and specification analysis. Compare regression 4 with regressions 2 and 3 in Problem 10-47. Which one of these models would you recommend that Hart use? Why?

2. Compare regression 5 with regression 4. Which model would you recommend that Hart use? Why?

3. Hart estimates the following data for the Baltimore store for next year: dollar value of merchandise purchased, $78,500,000; number of purchase orders, 4,100; number of suppliers, 110. How much should Hart budget for purchasing department costs for the Baltimore store for next year?

4. What difficulties do not arise in simple regression analysis that may arise in multiple regression analysis? Is there evidence of such difficulties in either of the multiple regressions presented in this problem? Explain.

5. Give two examples of decisions in which the regression results reported here (and in Problem 10-47) could be informative.