Managerial Judgment
2. High-Low and Least-Squares Methods
Kim Wilson, controller for Max Enterprises, has decided to estimate the fixed and variable components associated with the company’s shipping activity. She has collected the following data for the past six months:
Discretionary fixed costs, 79
Fixed activity rate, 81 Fixed cost, 72
Flexible resources, 78 Goodness of fit, 93
High-low method, 86 Independent
variable, 85
Intercept parameter, 85 Long run, 76
Method of least
squares, 90 Mixed cost, 74
Multiple regression, 95 Practical capacity, 78 Relevant range, 72 Scattergraph, 87
Scatterplot method, 87 Short run, 76
Slope parameter, 85 Step cost, 79
Variable activity rate, 81 Variable cost, 73
Packages Shipped Total Shipping Costs
10 $ 800
20 1,100
15 900
12 900
18 1,050
25 1,250
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Required
1. Estimate the fixed and variable components for the shipping costs using the high-low method. Using the cost formula, predict the total cost of shipping if 14 packages are shipped.
2. Estimate the fixed and variable components using the method of least squares.
Using the cost formula, predict the total cost of shipping if 14 packages are shipped.
3. For the method of least squares, explain what the coefficient of determination tells us. Compute the coefficient of correlation.
Solution
1. The estimate of fixed and variable costs using the high-low method is as follows:
Variable rate($1,250 $800)/(25 10) $450/15
$30 per package
Fixed amount $1,250 $30(25) $500 Total cost $500 $30X
$500 $30(14) $920
2. The output of a spreadsheet regression routine is as follows:
Regression Output:
Constant 509.911894273125
Std Err of Y Est 32.1965672507378
R Squared 0.96928536465981
4
No. of Observations 6
Degrees of Freedom 4
X Coefficient(s) 29.4052863436125
Std Err of Coef. 2.61723229918858
Y$509.91 $29.41(14) $921.65
3. The coefficient of determination (R2) tells us that about 96.9 percent of total shipping cost is explained by the number of packages shipped. The correlation coefficient (r) equals the square root of the coefficient of determination, or 0.984.
1. Why is knowledge of cost behavior important for managerial decision making? Give an example to illustrate your answer.
2. How does the length of the time horizon affect the classification of a cost as fixed or variable?
What is the meaning of short run? Long run?
3. Explain the difference between resource spending and resource usage.
4. What is the relationship between flexible resources and cost behavior?
5. What is the relationship between committed resources and cost behavior?
6. Explain the difference between committed and discretionary fixed costs. Give examples of each.
7. Describe the difference between a variable cost and a step cost with narrow steps. When is it rea- sonable to treat these step costs as if they were variable costs?
8. What is the difference between a step cost with narrow steps and a step cost with wide steps?
9. What is an activity rate?
10. Why do mixed costs pose a problem when it comes to classifying costs into fixed and variable categories?
Questions for Writing and Discussion
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11. Why is a scattergraph a good first step in decom- posing mixed costs into their fixed and variable components?
12. Describe how the scatterplot method breaks out the fixed and variable costs from a mixed cost.
Now describe how the high-low method works.
How do the two methods differ?
13. What are the advantages of the scatterplot method over the high-low method? The high-low method over the scatterplot method?
14. Describe the method of least squares. Why is this method better than either the high-low method or the scatterplot method?
15. What is meant by the “best-fitting line”?
16. Is the best-fitting line necessarily a good-fitting line? Explain.
17. Describe what is meant by “goodness of fit.”
Explain the meaning of the coefficient of determination.
18. What is the difference between the coefficient of determination and the coefficient of correlation?
Which of the two measures of goodness of fit do you prefer? Why?
19. When is multiple regression required to explain cost behavior?
20. Some firms assign mixed costs to either the fixed or variable cost categories without using any for- mal methodology to separate them. Explain how this practice can be defended.
Exercises
The salary for a plant supervisor for a manufacturing facility is $120,000 per year.
The plant’s capacity is 300,000 units per year.
Required
1. Prepare a table that shows how the cost of supervision behaves in total and on a per-unit basis as production increases from 0 to 250,000 units per year, using 50,000-unit increments.
2. How would you classify the behavior of the cost of supervision?
Rico Food Company sells and delivers various specialty foods to homes. Rico believes that the best driver for its delivery activity is “miles traveled.” Not surpris- ingly, it discovered that the cost of fuel for delivery trucks doubled as the miles trav- eled doubled. The fuel cost for 4,000 miles was $1,200 and for 10,000 miles was
$3,000.
Required
1. Prepare a table that shows the total cost of fuel and unit cost for miles traveled ranging from 0 to 10,000 miles, using increments of 2,000 miles.
2. How would you describe the behavior of the cost of fuel for delivery trucks?
Smith Concrete Company owns enough ready-mix trucks to deliver up to 100,000 cubic yards of concrete per year (considering each truck’s capacity, weather, and dis- tance to each job). Total truck depreciation is $200,000 per year. Raw materials (cement, gravel, and so on) cost about $25 per cubic yard of cement.
Required
1. Prepare a graph for truck depreciation. Use the vertical axis for cost and the hor- izontal axis for cubic yards of cement.
2. Prepare a graph for raw materials. Use the vertical axis for cost and the horizon- tal axis for cubic yards of cement.
3. Assume that the normal operating range for the company is 90,000 to 96,000 cubic yards per year. Classify truck depreciation and raw materials as variable or fixed costs.
3-1
Cost Behavior LO1
3-2
Cost Behavior LO1
3-3
Cost Behavior LO1
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Lorberg Company produces a variety of products, including some that require the use of a specialized forming machine. Lorberg can rent forming machines for
$10,000 per year. Each machine can produce as many as 20,000 units per year.
Required
1. Prepare a table that shows the total cost of forming equipment rental and unit cost for units ranging from 0 to 50,000, using increments of 10,000 units.
2. How would you describe the behavior of the forming equipment rental cost?
Mallory, Inc., produces large industrial machinery. Mallory has a machining depart- ment and a group of direct laborers called machinists. Each machinist is paid $50,000 and can machine up to 500 units per year. Mallory also hires supervisors to develop machine specification plans and to oversee production within the machining depart- ment. Given the planning and supervisory work, a supervisor can oversee at most three machinists. Mallory’s accounting and production history shows the following relationships between number of units produced and the costs of materials handling and supervision (measured on an annual basis):
Units Produced Direct Labor Supervision
0–500 $ 50,000 $ 40,000
501–1,000 72,000 40,000
1,001–1,500 108,000 40,000
1,501–2,000 144,000 80,000
2,001–2,500 180,000 80,000
2,501–3,000 216,000 80,000
3,001–3,500 252,000 120,000
3,501–4,000 288,000 120,000
Required
1. Prepare a graph that illustrates the relationship between direct labor cost and number of units produced in the machining department. (Let cost be the verti- cal axis and number of units produced the horizontal axis.) Would you classify this cost as a strictly variable cost, a fixed cost, or a step cost?
2. Prepare a graph that illustrates the relationship between the cost of supervision and the number of units produced. (Let cost be the vertical axis and number of units produced the horizontal axis.) Would you classify this cost as a strictly variable cost, a fixed cost, or a step cost?
3. Suppose that the normal range of activity is between 1,400 and 1,500 units and that the exact number of machinists is currently hired to support this level of activity. Further suppose that production for the next year is expected to increase by an additional 500 units. By how much will the cost of direct labor increase?
Cost of supervision?
Morrison Community Hospital has five laboratory technicians who are responsible for doing a series of standard blood tests. Each technician is paid a salary of $30,000.
The lab facility represents a recent addition to the hospital and cost $300,000. It is expected to last 20 years. Equipment used for the testing cost $10,000 and has a life expectancy of five years. In addition to the salaries, facility, and equipment, the hos- pital expects to spend $200,000 for chemicals, forms, power, and other supplies.
This $200,000 is enough for 200,000 blood tests.
3-4
Cost Behavior LO1
3-5
Step Costs, Relevant Range
LO1
3-6
Cost Behavior in a Service
Organization LO1, LO2
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Required
Assuming that the driver (measure of output) for each type of cost is the number of blood tests run, classify the costs by completing the following table. Put a check mark in the appropriate box for variable cost, discretionary fixed cost, or committed fixed cost.
Cost Variable Discretionary Committed
Category Cost Fixed Cost Fixed Cost
Technician salaries Laboratory facility Laboratory equipment Chemicals and other supplies
State University’s football team just received a bowl game invitation, and the stu- dents and alumni are excited. Holiday Travel Agency, located close to campus, decided to put together a bowl game package. For $50,000, a 737 jet could be char- tered to take up to 170 people to and from the bowl city. A block of 85 hotel rooms could be confirmed for $400 each (a three-night commitment); Holiday Travel must pay for all the rooms in advance and cannot cancel any of them. The day of the game, a pregame buffet will be catered at $20 per person, and each person will receive a game favor package (consisting of a sweatshirt, a T-shirt, a commemorative pin with the school and bowl logos, and two pom-poms in the school’s colors). All items in the favor package can be purchased by Holiday Travel on December 21 and will cost the agency $25 per set. Buses will be chartered in the bowl city to transport participants to and from the airport and the game. Each bus holds 50 people and can be chartered for $500. The bowl game is scheduled for December 28, and the trip will span three nights—December 26, 27, and 28. Purchasers must reserve their package and pay in full by December 20.
Required
List the resources that are mentioned in the above scenario. Then, for each resource, determine: (1) whether it is a flexible or committed resource and (2) the type of cost behavior displayed (variable, fixed, mixed, step cost).
Custom-Molding, Inc., is a manufacturer of molded plastic action figures that fast- food restaurants purchase to include in children’s meal packs. Each action figure takes about 0.90 ounces of plastic costing $0.03 per ounce and is molded in a mold.
Custom-Molding contracts with an outside supplier to develop new molds based on current movie and cartoon characters. Each set of molds costs $5,000 and could be used indefinitely but, practically speaking, lasts for three months and makes 100,000 action figures. (After that, the children are tired of those figures and want to move on to others.) Direct labor and variable overhead cost $0.02 per unit and other facil- ity costs total $10,000 per year. Custom-Molding, Inc., produces 400,000 action fig- ures over the course of the year.
3-7
Cost Behavior in a Service Organization LO1, LO2
3-8
Cost Behavior LO1, LO2
EEXCEL
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Required
1. What is the total cost of producing action figures for the year? The per unit cost?
2. Categorize each resource as flexible or committed. What is the cost behavior of each resource?
Colby Company manufactures digital thermometers. Based on past experience, Colby has found that its total maintenance costs can be represented by the following formula: Maintenance cost $24,000 $0.30X, where X Number of digital ther- mometers. Last year, Colby produced 200,000 thermometers. Actual maintenance costs for the year were as expected.
Required
1. What is the total maintenance cost incurred by Colby last year?
2. What is the total fixed maintenance cost incurred by Colby last year?
3. What is the total variable maintenance cost incurred by Colby last year?
4. What is the maintenance cost per unit produced?
5. What is the fixed maintenance cost per unit?
6. What is the variable maintenance cost per unit?
7. Recalculate Requirements 1 to 6 assuming that only 100,000 thermometers were produced.
Enid Communications provides cable television service to a number of communities in a midwestern state, including the town of Helena. In the Helena operation, there are 20 service technicians who install cable service and provide repairs. Each techni- cian is salaried at $24,000 per year and works one of two daily eight-hour shifts.
Each technician can perform an average of eight service calls per day. There are 250 working days per year.
Enid uses 12 trucks for the Helena operation, each fully equipped to perform installations and repairs on site. Each truck has a depreciation cost of $10,000 per year. (The 12 trucks allow each technician to have a truck for his or her shift, with two extra trucks in case of breakdown or scheduled maintenance.)
Last year, supplies, small tools, and fuel cost approximately $420,000; these seem to be highly correlated with the number of service calls. A total of 35,000 service calls were made last year.
Required
1. Classify the resources associated with the cable repair and installation activity into one of the following: (1) committed resources and (2) flexible resources.
2. Calculate the variable activity rate and the fixed activity rate for the repair and installation activity. What is the total cost of one service call?
3. Using the average data given above, what is the largest number of service calls that could be completed per year? This is the total activity availability. Break this total activity availability into activity usage (number of service calls actually made) and unused capacity (calls that could have been made but were not).
4. Calculate the total cost of committed resources used last year, and break this into the cost of service calls made and the cost of unused service call capacity.
Jana Morgan is about to sign up for cellular telephone service. She is primarily inter- ested in the safety aspect of the phone—that is, she wants to have one available for emergencies. She does not want to use it as her primary phone. Jana has narrowed her options down to two plans:
3-9
Cost Behavior LO1
3-10
Resource Supply and Usage; Activity Rates; Service Organization LO2
3-11
Flexible and Commit- ted Resources; Capa- city Usage for a Service Organization LO2
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Plan 1 Plan 2 Monthly fee . . . $ 20 $ 30 Free local minutes . . . 60 120 Additional charges per minute:
Airtime . . . $0.40 $0.30 Long distance . . . 0.15 — Regional roaming . . . 0.60 — National roaming . . . 0.60 0.60
Both plans are subject to a $25 activation fee and a $120 cancellation fee if the ser- vice is cancelled before one year. Jana’s brother will give her a cell phone that he no longer needs. It is not the latest version (and is not Internet capable), but will work well with both plans.
Required
1. Classify the charges associated with the cellular phone service as (1) committed resources or (2) flexible resources.
2. Assume that Jana will use, on average, 45 minutes per month in local calling.
For each plan, split her minute allotment into used and unused capacity. Which plan would be more cost effective? Why?
3. Assume that Jana loves her cell phone and ends up talking frequently with friends while traveling within her region. On average, she uses 60 local minutes a month and 30 regional minutes. For each plan, split her minute allotment into used and unused capacity. Which plan would be more cost effective? Why?
Ben Hanson owns an art gallery. He accepts paintings and sculpture on consignment and then receives 20 percent of the price of each piece as his fee. Space is limited, and there are costs involved, so Ben is careful about accepting artists. When he does accept one, he arranges for an opening show (usually for three hours on a weekend night) and sends out invitations to his customer list. At the opening, he serves soft drinks and casual munchies to create a comfortable environment for prospective customers to view the new works and chat with the artist. On average, each opening costs $500. Ben has given as many as 20 opening shows in a year. The total cost of running the gallery, including rent, furniture and fixtures, utilities, and a part-time assistant, amounts to $80,000 per year.
Required
1. Prepare a graph that illustrates the relationship between the cost of giving open- ing shows and the number of opening shows given. (Let opening show cost be the vertical axis and number of opening shows given the horizontal axis.) Would you classify this cost as a strictly variable cost, a fixed cost, or a mixed cost?
2. Prepare a graph that illustrates the relationship between the cost of running the gallery and the number of opening shows given. (Let gallery cost be the vertical axis and number of opening shows given the horizontal axis.) Would you clas- sify this cost as a strictly variable cost, a fixed cost, or a mixed cost?
3. Prepare a graph that illustrates the relationship between Ben’s total costs (the sum of the costs of giving opening shows and running the gallery) and the number of opening shows given. Let the cost be the vertical axis and number of opening shows given the horizontal axis. Would you classify this cost as a strictly variable cost, a fixed cost, or a mixed cost?
4. Assume that the cost driver is number of opening shows. Develop the cost for- mula for the gallery’s costs for a year.
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Mixed Costs, Scattergraph, Service Organization LO1, LO3
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5. Using the formula developed in Requirement 1, what is the total cost for Ben in a year with 12 opening shows? With 14 opening shows?
Kylie Hepworth has been operating a beauty shop in a college town for the past 10 years. Recently, Kylie rented space next to her shop and opened a tanning salon. She anticipated that the costs for the tanning service would be primarily fixed but found that tanning salon costs increased with the number of appointments. Costs for this service over the past eight months are as follows:
Month Tanning Appointments Total Cost
January 700 $1,758
February 2,000 2,140
March 3,100 2,790
April 2,500 2,400
May 1,500 1,800
June 2,300 2,275
July 2,150 2,200
August 3,000 2,640
Required
1. Which month represents the high point? The low point?
2. Using the high-low method, compute the variable rate for tanning. Compute the fixed cost per month.
3. Using your answers to Requirement 2, write the cost formula for tanning services.
4. Calculate the total predicted cost of tanning services for September for 2,500 appointments using the formula found in Requirement 3. Of that total cost, how much is the total fixed cost for September? How much is the total pre- dicted variable cost for September?
Refer to Exercise 3-13 for data on Kylie Hepworth’s tanning salon. Assume that Kylie’s accountant used an Excel spreadsheet program to run ordinary least squares on the data the following results were produced.
Intercept 1,290 X Variable 0.45 Required
1. Prepare a scattergraph based on Kylie’s data. Use cost for the vertical axis and number of tanning appointments for the horizontal. Based on an examination of the scattergraph, does there appear to be a linear relationship between the cost of tanning services and the number of appointments?
2. Identify the cost formula for tanning services using the results from the method of least squares.
3. Using the formula computed in Requirement 1, what is the predicted cost of tanning services for September for 2,500 appointments?
Jim Beaumont, the owner of Lube ‘n’ Go, is interested in determining the fixed and variable costs of performing a standard oil change. Since the oil changes are fairly standard, each one taking about the same amount of time and using about the same amount of grease, paper towels, etc., Jim thinks the number of oil changes would be a good independent variable. The total monthly cost includes the salaries of the two service persons, depreciation on the facility and equipment, utilities, and supplies such as grease and wipes. (The cost of oil is not included, as it differs from car to car and is charged to each customer based on the number of quarts actually used.) Data for the past eight months are as follows:
3-13
High-Low Method, Service Organization LO3
3-14
Scattergraph Method, Service Organization LO3, LO4
3-15
Separating Fixed and Variable Costs;
Service Setting LO3, LO4