ASSIGNMENT MATERIAL 429

When multicollinearity exists, try to obtain new data that do not suffer from multicol-
linearity problems. Do not drop an independent variable (cost driver) that should be included
in a model because it is correlated with another independent variable. Omitting such a variable
will cause the estimated coefficient of the independent variable included in the model to be
biased away from its true value.

TERMS TO LEARN
This chapter and the Glossary at the end of this book contain definitions of the following important terms:

account analysis method (p. 398) incremental unit-time learning residual term (p. 404)
coefficient of determination (r2) (p. 420) model (p. 412) semivariable cost (p. 394)
conference method (p. 398) independent variable (p. 400) simple regression (p. 404)
constant (p. 394) industrial engineering method (p. 398) slope coefficient (p. 393)
cost estimation (p. 396) intercept (p. 394) specification analysis (p. 423)
cost function (p. 393) learning curve (p. 410) standard error of the estimated
cost predictions (p. 396) linear cost function (p. 393) coefficient (p. 421)
cumulative average-time learning mixed cost (p. 394) standard error of the regression
model (p. 411) multicollinearity (p. 428) (p. 421)
dependent variable (p. 400) multiple regression (p. 404) step cost function (p. 409)
experience curve (p. 411) nonlinear cost function (p. 409) work-measurement method (p. 398)
high-low method (p. 402) regression analysis (p. 404)

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

Pearson MyLab Accounting Multiple-Choice Questions

In partnership with:

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:
a. $8,000 b. $12,000
c. $23,000 d. $29,000
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?
a. 21,400 b. 47,000
c. 60,000 d. 107,000
10-18 In regression analysis, the coefficient of determination:
a. Is used to determine the proportion of the total variation in the dependent variable (y) explained by the
independent variable (X).
b. Ranges between negative one and positive one.
c. Is used to determine the expected value of the net income based on the regression line.
d. Becomes smaller as the fit of the regression line improves.
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:
a. The coefficient of determination is negative.
b. The level of production explains 49% of the variation in total costs
c. There is a slightly inverse relationship between production and total costs.
d. A correlation coefficient of 1.30 would produce a regression line with better fit to the data.
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?
a. 1.0 b. 0
c. - 1.0 d. -100

©2016 DeVry/Becker Educational Development Corp. All Rights Reserved.

Pearson MyLab Accounting Exercises

10-21 Estimating a cost function. The controller of the Ijiri Company wants you to estimate a cost func-
tion from the following two observations in a general ledger account called Maintenance:

Month Machine-Hours Maintenance Costs Incurred

January 6,000 $4,000
February 10,000 $5,400

Required 1. Estimate the cost function for maintenance.

2. Can the constant in the cost function be used as an estimate of fixed maintenance cost per month?
Explain.
10-22 Identifying variable-, fixed-, and mixed-cost functions. The Bengal Corporation operates car
rental agencies at more than 20 airports across India. Customers can choose from one of three contracts
for car rentals of one day or less:
■ Contract 1: $50 for the day
■ Contract 2: $30 for the day plus $0.20 per mile traveled
■ Contract 3: $1 per mile traveled

Required 1. Plot separate graphs for each of the three contracts, with costs on the vertical axis and miles traveled
on the horizontal axis.
2. Express each contract as a linear cost function of the form y = a + bX .
3. Identify each contract as a variable-, fixed-, or mixed-cost function.
 ASSIGNMENT MATERIAL 431

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.

A B C D

E F G H

I J K L

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.
1. Annual depreciation of equipment, where the amount of depreciation charged is computed by the Required
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:

First 1,000,000 gallons or less $1,000 flat fee

Next 10,000 gallons $0.003 per gallon used
Next 10,000 gallons $0.006 per gallon used
Next 10,000 gallons $0.009 per gallon used
and so on and so on

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.
432 CHAPTER 10 DETERMINING HOW COSTS BEHAVE

10-24 Matching graphs with descriptions of cost and revenue behavior. (D. Green, adapted) Given here
are a number of graphs.

1 2 3 4

5 6 7 8

Some other
pattern

9 10 11 12

The horizontal axis of each graph represents the units produced over the year, and the vertical axis repre-
sents total cost or revenues.
Required 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.
a. Direct material costs
b. Supervisors’ salaries for one shift and two shifts
c. A cost–volume–profit graph
d. Mixed costs—for example, car rental fixed charge plus a rate per mile driven
e. Depreciation of plant, computed on a straight-line basis
f. Data supporting the use of a variable-cost rate, such as manufacturing labor cost of $14 per unit produced
g. Incentive bonus plan that pays managers $0.10 for every unit produced above some level of production
h. Interest expense on $2 million borrowed at a fixed rate of interest

10-25 Account analysis, high-low. Stein Corporation wants to find an equation to estimate some of their
monthly operating costs for the operating budget for 2018. The following cost and other data were gathered
for 2017:

Maintenance Machine Health Number of Shipping Units

Month Costs Hours Insurance Employees Costs Shipped
January $4,500 165 $8,600 68 $25,776 7,160
February $4,452 120 $8,600 75 $29,664 8,240
March $4,600 230 $8,600 92 $28,674 7,965
April $4,850 318 $8,600 105 $23,058 6,405
May $5,166 460 $8,600 89 $21,294 5,915
June $4,760 280 $8,600 87 $33,282 9,245
July $4,910 340 $8,600 93 $31,428 8,730
August $4,960 360 $8,600 88 $30,294 8,415
September $5,070 420 $8,600 95 $25,110 6,975
October $5,250 495 $8,600 102 $25,866 7,185
November $5,271 510 $8,600 97 $20,124 5,590
December $4,760 275 $8,600 94 $34,596 9,610

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 Stein Corporation.
4. Next month, Stein expects to use 400 machine hours, have 80 employees, and ship 9,000 units. Estimate
the total operating cost for the month.
 ASSIGNMENT MATERIAL 433

10-26 Account analysis method. Gower, Inc., a manufacturer of plastic products, reports the following
manufacturing costs and account analysis classification for the year ended December 31, 2017.

Account Classification Amount

Direct materials All variable $300,000
Direct manufacturing labor All variable 225,000
Power All variable 37,500
Supervision labor 20% variable 56,250
Materials-handling labor 50% variable 60,000
Maintenance labor 40% variable 75,000
Depreciation 0% variable 95,000
Rent, property taxes, and administration 0% variable 100,000

Gower, Inc., produced 75,000 units of product in 2017. Gower’s management is estimating costs for 2018 on
the basis of 2017 numbers. The following additional information is available for 2018.
a. Direct materials prices in 2018 are expected to increase by 5% compared with 2017.
b. Under the terms of the labor contract, direct manufacturing labor wage rates are expected to increase
by 10% in 2018 compared with 2017.
c. Power rates and wage rates for supervision, materials handling, and maintenance are not expected to
change from 2017 to 2018.
d. Depreciation costs are expected to increase by 5%, and rent, property taxes, and administration costs
are expected to increase by 7%.
e. Gower expects to manufacture and sell 80,000 units in 2018.
1. Prepare a schedule of variable, fixed, and total manufacturing costs for each account category in 2018. Required
Estimate total manufacturing costs for 2018.
2. Calculate Gower’s total manufacturing cost per unit in 2017, and estimate total manufacturing cost per
unit in 2018.
3. How can you obtain better estimates of fixed and variable costs? Why would these better estimates be
useful to Gower?
10-27 Estimating a cost function, high-low method. FlyHigh Vacations offers helicopter service from
suburban towns to Heathrow Airport in the United Kingdom. Each of its 10 helicopters makes between 1,000
and 2,000 round-trips per year. The records indicate that a helicopter that has made 1,000 round-trips in the
year incurs an average operating cost of $350 per round-trip, and one that has made 2,000 round-trips in the
year incurs an average operating cost of $300 per round-trip.
1. Using the high-low method, estimate the linear relationship y = a + bX, where y is the total annual oper- Required
ating cost of a helicopter and X is the number of round-trips it makes to Heathrow Airport during the year.
2. Give examples of costs that would be included in a and in b.
3. If FlyHigh Vacations expects each helicopter to make, on average, 1,200 round-trips in the coming year,
what should its estimated operating budget for the helicopter fleet be?
10-28 Estimating a cost function, high-low method. Lacy Dallas is examining customer-service costs in
the southern region of Camilla Products. Camilla 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:

Week Customer-Service Department Costs Number of Service Reports

1 $13,300 185
2 20,500 285
3 12,000 120
4 18,500 360
5 14,900 275
6 21,600 440
7 16,500 350
8 21,300 315

1. Plot the relationship between customer-service costs and number of service reports. Is the relationship Required
economically plausible?
434 CHAPTER 10 DETERMINING HOW COSTS BEHAVE

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 Camilla Products?
10-29 Linear cost approximation. Terry Lawler, managing director of the Little Rock Reviewers Company,
is examining how overhead costs behave with changes in monthly professional labor-hours billed to clients.
Assume the following historical data:

Total Overhead Costs Professional Labor-Hours Billed to Clients

$330,000 3,000
395,000 4,000
425,000 5,000
467,000 6,000
521,000 7,500
577,000 8,500

Required 1. Compute the linear cost function, relating total overhead costs to professional labor-hours, using the
representative observations of 4,000 and 7,500 hours. Plot the linear cost function. Does the constant
component of the cost function represent the fixed overhead costs of the Little Rock Reviewers Com-
pany? Why?
2. What would be the predicted total overhead costs for (a) 5,000 hours and (b) 8,500 hours using the cost
function estimated in requirement 1? Plot the predicted costs and actual costs for 5,000 and 8,500 hours.
3. Lawler had a chance to accept a special job that would have boosted professional labor-hours from
4,000 to 5,000 hours. Suppose Lawler, guided by the linear cost function, rejected this job because it
would have brought a total increase in contribution margin of $31,000, before deducting the predicted
increase in total overhead cost, $36,000. What is the total contribution margin actually forgone?
10-30 Cost-volume-profit and regression analysis. Goldstein Corporation manufactures a children’s bi-
cycle, model CT8. Goldstein currently manufactures the bicycle frame. During 2017, Goldstein made 32,000
frames at a total cost of $1,056,000. Ryan Corporation has offered to supply as many frames as Goldstein wants
at a cost of $32.50 per frame. Goldstein anticipates needing 35,000 frames each year for the next few years.
Required 1. a. What is the average cost of manufacturing a bicycle frame in 2017? How does it compare to Ryan’s
offer?
b. Can Goldstein use the answer in requirement 1a to determine the cost of manufacturing 35,000
bicycle frames? Explain.
2. Goldstein’s cost analyst uses annual data from past years to estimate the following regression equa-
tion with total manufacturing costs of the bicycle frame as the dependent variable and bicycle frames
produced as the independent variable:

y = $435,000 + $19X
During the years used to estimate the regression equation, the production of bicycle frames varied from
31,000 to 35,000. Using this equation, estimate how much it would cost Goldstein to manufacture 35,000 bicycle
frames. How much more or less costly is it to manufacture the frames rather than to acquire them from Ryan?
3. What other information would you need to be confident that the equation in requirement 2 accurately
predicts the cost of manufacturing bicycle frames?
10-31 Regression analysis, service company. (CMA, adapted) Linda Olson owns a professional char-
acter 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:

Balloons, cupcakes, and punch $ 7

Labor (0.25 hour * $20 per hour) 5
Overhead (0.25 hour * $40 per hour) 10
Total cost per person $22

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
 ASSIGNMENT MATERIAL 435

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.

Month Labor-Hours Overhead Costs

April 1,400 $ 65,000
May 1,800 71,000
June 2,100 73,000
July 2,200 76,000
August 1,650 67,000
September 1,725 68,000
October 1,500 66,500
November 1,200 60,000
December 1,900 72,500
Total 15,475 $619,000

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:
y = $43,563 + $14.66X
1. Plot the relationship between overhead costs and labor-hours. Draw the regression line and evaluate it Required
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. Deter-
mine the minimum bid price that Linda would be willing to submit to recoup variable costs.
10-32 High-low, regression. Mandy Knox is the new manager of the materials storeroom for Timken
Manufacturing. Mandy has been asked to estimate future monthly purchase costs for part #696, used in two
of Timken’s products. Mandy has purchase cost and quantity data for the past 9 months as follows:

Month Cost of Purchase Quantity Purchased

January $12,468 2,700 parts
February 12,660 2,820
March 17,280 4,068
April 15,816 3,744
May 13,164 2,988
June 13,896 3,216
July 15,228 3,636
August 10,272 2,316
September 14,940 3,552

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

Month Purchase Quantity Expected

October 3,360 parts
November 3,720
December 3,000

1. The computer in Mandy’s office is down, and Mandy has been asked to immediately provide an equa- Required
tion to estimate the future purchase cost for part #696. Mandy 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 Mandy’s computer is fixed. Mandy 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 Mandy obtains is as follows:
y = $2,135.5 + 3.67X
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?
436 CHAPTER 10 DETERMINING HOW COSTS BEHAVE

4. Use the regression results to calculate the expected purchase costs for October, November, and De-
cember. Compare the expected purchase costs to the expected purchase costs calculated using the
high-low method in requirement 2. Comment on your results.
10-33 Learning curve, cumulative average-time learning model. Northern Defense manufactures radar
systems. It has just completed the manufacture of its first newly designed system, RS-32. Manufacturing
data for the RS-32 follow:

$ % &
 Direct material cost $ 84,000 per unit of RS-32
 Direct manufacturing labor time for first unit 4,400 direct manufacturing labor-hours
 Learning curve for manufacturing labor time per radar system 85% cumulative average timea
 Direct manufacturing labor cost $ 27 per direct manufacturing labor-hour
 Variable manufacturing overhead cost $ 13 per direct manufacturing labor-hour

a ln 0.85 –0.162519
 Using the formula (page 411), for an 85% learning curve, b =
ln 2 = 0.693147 = –0.234465

Required Calculate the total variable costs of producing 2, 4, and 8 units.

10-34 Learning curve, incremental unit-time learning model. Assume the same information for Northern
Defense as in Exercise 10-33, except that Northern Defense uses an 85% incremental unit-time learning model
as a basis for predicting direct manufacturing labor-hours. (An 85% learning curve means b = - 0.234465.)
Required 1. Calculate the total variable costs of producing 2, 3, and 4 units.
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 Northern Defense decide which model it should use?
10-35 High-low method. Ken Howard, financial analyst at KMW Corporation, is examining the behavior
of quarterly maintenance costs for budgeting purposes. Howard collects the following data on machine-
hours worked and maintenance costs for the past 12 quarters:

Quarter Machine-Hours Maintenance Costs

1 100,000 $205,000
2 120,000 240,000
3 110,000 220,000
4 130,000 260,000
5 95,000 190,000
6 115,000 235,000
7 105,000 215,000
8 125,000 255,000
9 105,000 210,000
10 125,000 245,000
11 115,000 200,000
12 140,000 280,000

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. Howard anticipates that KMW will operate machines for 100,000 hours in quarter 13. Calculate the
predicted maintenance costs in quarter 13 using the cost function estimated in requirement 1.

Pearson MyLab Accounting Problems

10-36 High-low method and regression analysis. Farm Fresh, a cooperative of organic family-owned
farms outside of New South Wales, Australia, 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 to the
nearby suburban community. Families pay a seasonal membership fee of $75 and place their orders a week
in advance for a price of $35 per order. In turn, Farm Fresh delivers fresh-picked seasonal local produce to
 ASSIGNMENT MATERIAL 437

several neighborhood distribution points. Seven hundred families joined the club for the first season, but the
number of orders varied from week to week.
Sam Baker has run the produce club for the first 10-week season. Before becoming a farmer, Sam had been
a business major in college, and he remembers a few things about cost analysis. 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 10 weeks of operation:
Week Number of Orders per Week Weekly Total Costs
1 353 $19,005
2 390 22,605
3 414 22,850
4 450 22,500
5 422 21,950
6 491 24,750
7 449 23,650
8 472 23,005
9 529 25,275
10 508 24,350

1. Plot the relationship between number of orders per week and weekly total costs. Required
2. Estimate the cost equation using the high-low method, and draw this line on your graph.
3. Harvey uses his computer to calculate the following regression formula:
Total weekly costs = $10,048 + ($28.91 * Number of weekly orders)
Draw the regression line on your graph. Use your graph to evaluate the regression line using the cri-
teria 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 Farm Fresh break even this season? Remember that each of the families paid a seasonal member-
ship fee of $75.
5. Assume that 850 families join the club next year and that prices and costs do not change. How many
orders, on average, must Farm Fresh receive each week to break even?
10-37 High-low method; regression analysis. (CIMA, adapted) Anna Schaub, the financial manager at
the Mangiamo restaurant, is checking to see if there is any relationship between newspaper advertising
and sales revenues at the restaurant. She obtains the following data for the past 10 months:
Month Revenues Advertising Costs
March $51,000 $1,500
April 72,000 3,500
May 56,000 1,000
June 64,000 4,000
July 56,000 500
August 64,000 1,500
September 43,000 1,000
October 83,000 4,500
November 56,000 2,000
December 61,000 2,000

She estimates the following regression equation:

Monthly revenues = $46,443 + ($6.584 * Advertising costs)
1. Plot the relationship between advertising costs and revenues. Also draw the regression line and evalu- Required
ate 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 advertising costs and revenues.
3. Using (a) the regression equation and (b) the high-low equation, what is the increase in revenues
for each $1,000 spent on advertising within the relevant range? Which method should Schaub use to
predict the effect of advertising costs on revenues? Explain briefly.
10-38 Regression, activity-based costing, choosing cost drivers. Parker Manufacturing has been using
activity-based costing to determine the cost of product X-678. One of the activities, “Inspection”, occurs just
before the product is finished. Fitzgerald inspects every 10th unit and has been using “number of units inspected”
as the cost driver for inspection costs. A significant component of inspection costs is the cost of the test kit used
438 CHAPTER 10 DETERMINING HOW COSTS BEHAVE

in each inspection. Sharon MacPhen, the line manager, is wondering if inspection labor-hours might be a better
cost driver for inspection costs. Sharon gathers information for weekly inspection costs, units inspected, and
inspection labor-hours as follows:

Week Units Inspected Inspection Labor-Hours Inspection Costs

1 1,800 210 $3,600
2 800 90 1,700
3 2,100 250 4,400
4 2,800 260 5,700
5 2,500 230 5,200
6 1,100 110 2,300
7 1,300 130 2,800

Sharon runs regressions on each of the possible cost drivers and estimates these cost functions:
Inspection Costs = $98.79 + ($ 2.02 * Number of units inspected)
Inspection Costs = $ 3.89 + ($20.06 * Inspection labor@hours)
Required 1. Explain why number of units inspected and inspection labor-hours are plausible cost drivers of inspection
costs.
2. Plot the data and regression line for units 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. Sharon expects inspectors to work 160 hours next period and to inspect 1,500 units. Using the cost
driver you chose in requirement 2, what amount of inspection costs should Sharon budget? Explain any
implications of Sharon choosing the cost driver you did not choose in requirement 2 to budget.
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 behav-
ior of transportation costs for budgeting purposes. Transportation costs at Spirit are of two types: (a) operating
costs (such as labor and fuel) and (b) maintenance costs (primarily overhaul of vehicles).
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):

Month Operating Costs Maintenance Costs Freight Miles

January $ 942 $ 974 1,710
February 1,008 776 2,655
March 1,218 686 2,705
April 1,380 694 4,220
May 1,484 588 4,660
June 1,548 422 4,455
July 1,568 352 4,435
August 1,972 420 4,990
September 1,190 564 2,990
October 1,302 788 2,610
November 962 762 2,240
December 772 1,028 1,490

Required 1. Conduct a regression using the monthly data of operating costs on freight miles. You should obtain the
following result:
Regression: Operating costs = a + (b * Number of freight miles)

Variable Coefficient Standard Error t-Value

Constant $445.76 $112.97 3.95
Independent variable: No. of freight miles $ 0.26 $ 0.03 7.83
r 2 = 0.86; Durbin@Watson statistic = 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?
 ASSIGNMENT MATERIAL 439

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: Maintenance costs = a + (b * Number of freight miles)

Variable Coefficient Standard Error t-Value

Constant $1,170.57 $91.07 12.85
Independent variable: No. of freight miles $ -0.15 $ 0.03 -5.83
r 2 = 0.77; Durbin@Watson statistic = 1.94

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?
10-40 Cost estimation, cumulative average-time learning curve. The Blue Seas Company, which is un-
der contract to the 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 Blue Seas submit a proposal on the cost of producing another six PT109s. Blue Seas
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 b = -0.152004.)

$ % &
 Direct material $ 201,000
 Direct manufacturing labor time for first boat 15,700 labor-hours
 Direct manufacturing labor rate $ 43 per direct manufacturing labor-hour
 Variable manufacturing overhead cost $ 24 per direct manufacturing labor-hour
 Other manufacturing overhead 15% of direct manufacturing labor costs
 Tooling costsa $ 281,000
b
 Learning curve for manufacturing labor time per boat 90% cumulative average time

a
 Tooling can be reused at no extra cost because all of its cost has been assigned to the first deployment boat.

b ln 0.9 ]0.105361
 Using the formula (page 411) for a 90% learning curve, b 5 ln 2 5 0.693147 5 ]0.152004

1. Calculate predicted total costs of producing the six PT109s for the Navy. (Blue Seas will keep the first Required
deployment boat assembled, cost at $1,533,900, 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.
10-41 Cost estimation, incremental unit-time learning model. Assume the same information for the Blue
Seas Company as in Problem 10-40 with one exception. This exception is that the Blue Seas Company 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. Prepare a prediction of the total costs for producing the six PT109s for the Navy. Required
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 the Blue Seas Company decide which
model it should use?
440 CHAPTER 10 DETERMINING HOW COSTS BEHAVE

10-42 Regression; choosing among models. Apollo Hospital specializes in outpatient surgeries for rela-
tively 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.
Apollo’s CFO, Julie Chen, has been concerned of late about the hospital’s consumption of medical sup-
plies. 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 poten-
tially better cost driver because the hospital does perform a variety of procedures, some more complex than
others.
Rhett provides the following data relating to the past year to Julie.

$ % & '
 Month Medical supplies costs Number of procedures Number of patient-hours
 1 $106,000 320 2,000
 2 230,000 500 3,900
 3 84,000 240 1,900
 4 238,000 520 4,100
 5 193,000 240 3,400
 6 180,000 340 3,700
 7 210,000 420 3,100
 8 92,000 360 1,200
 9 222,000 320 3,000
 10 78,000 180 1,300
 11 127,000 440 2,800
 12 225,000 380 3,800

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: Medical supplies costs = a + (b * Number of procedures)

Variable Coefficient Standard Error t-Value

Constant $36,939.77 $56,404.86 0.65
Independent variable: No. of procedures $ 361.91 $ 152.93 2.37
r 2 = 0.36; Durbin@Watson statistic = 2.48

Regression 2: Medical supplies costs = a + (b * Number of patient@hours)

Variable Coefficient Standard Error t-Value

Constant $3,654.86 $23,569.51 0.16
Independent variable: No. of patient-hours $ 56.76 $ 7.82 7.25
r 2 = 0.84; Durbin@Watson statistic = 1.91

2. On different graphs plot the data and the regression lines for each of the following cost functions:
a. Medical supplies costs = a + (b * Number of procedures)
b. Medical supplies costs = a + (b * Number of patient@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 10-18 (page 426).
4. Based on your analysis, which cost driver should Julie Chen adopt for Apollo Hospital? Explain your
answer.
 ASSIGNMENT MATERIAL 441

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. Conduct a multiple regression to estimate the regression equation for medical supplies costs using Required
both number of procedures and number of patient-hours as independent variables. You should obtain
the following result:
Regression 3: Medical supplies costs = a + (b1 * No. of procedures) + (b2 * No. of patient@hours)

Variable Coefficient Standard Error t-Value

Constant -$3,103.76 $30,406.54 -0.10
Independent variable 1: No. of procedures $ 38.24 $ 100.76 0.38
Independent variable 2: No. of patient-hours $ 54.37 $ 10.33 5.26
r 2 = 0.84; Durbin@Watson statistic = 1.96

2. Evaluate the multiple regression output using the criteria of economic plausibility goodness of fit, sig-
nificance of independent variables, and specification of estimation assumptions.
3. What potential issues could arise in multiple regression analysis that are not present in simple regres-
sion models? Is there evidence of such difficulties in the multiple regression presented in this problem?
Explain.
4. Which of the regression models from Problems 10-42 and 10-43 would you recommend Julie Chen use?
Explain.
10-44 Cost estimation. Hankuk Electronics started production on a sophisticated new smartphone running
the Android operating system in January 2017. Given the razor-thin margins in the consumer electronics indus-
try, Hankuk’s success depends heavily on being able to produce the phone as economically as possible.
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:

$ % &
 Month Output (Units) Direct Labor-Hours
 January 684 1,400
 February 492 820
 March 660 875
 April 504 670
 May 612 760
 June 636 765
 July 648 735
 August 600 660
 September 648 695
 October 696 710
 November 672 690
 December 675 700

1. Inbee is keen to examine the relationship between direct labor consumption and output levels. She Required
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: Direct labor@hours = a + (b * Output units)

Variable Coefficient Standard Error t-Value

Constant 345.24 589.07 0.59
Independent variable: Output units 0.71 0.93 0.76
r 2 = 0.054; Durbin@Watson statistic = 0.50
442 CHAPTER 10 DETERMINING HOW COSTS BEHAVE

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 Han-
kuk will produce 650 units in the next month, January 2018. What should she budget as the expected
variable cost? How confident is she of her estimate?
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 produc-
tion, it can produce additional units using less time. He suggests that it is more appropriate to specify the
following relationship:

y = ax b

where x is cumulative production in units, y is the cumulative average direct labor-hours per unit (i.e., cumu-
lative DLH divided by cumulative production), and a and b are parameters of the learning effect.
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:

$ % & ' ( )
 Cumulative Cumulative
Output Cumulative Avg DLH
Month (x) DLH (y) LN (y) LN (x)
 January 684 1,400 2.047 0.716 6.528
 February 1,176 2,220 1.888 0.635 7.070
 March 1,836 3,095 1.686 0.522 7.515
 April 2,340 3,765 1.609 0.476 7.758
 May 2,952 4,525 1.533 0.427 7.990
 June 3,588 5,290 1.474 0.388 8.185
 July 4,236 6,025 1.422 0.352 8.351
 August 4,836 6,685 1.382 0.324 8.484
 September 5,484 7,380 1.346 0.297 8.610
 October 6,180 8,090 1.309 0.269 8.729
 November 6,852 8,780 1.281 0.248 8.832
 December 7,527 9,480 1.259 0.231 8.926

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: Ln (Cumulative avg DLH per unit) = a + [b * Ln (Cumulative Output)]

Variable Coefficient Standard Error t-Value

Constant 2.087 0.024 85.44
Independent variable: Ln (Cum Output) -0.208 0.003 -69.046
r 2 = 0.998; Durbin@Watson statistic = 2.66

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 ex-
pected output of 650 units in January 2018? How confident is she of this new cost estimate?
 ASSIGNMENT MATERIAL 443

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:

$ % &
Online
Advertising Sales
 Month Expense Revenue
 September $5,125 $44,875
 October 5,472 42,480
 November 3,942 53,106
 December 1,440 64,560
 January 4,919 34,517
 February 4,142 59,438
 March 1,290 51,840
 April 5,722 36,720
 May 5,730 62,564
 June 2,214 59,568
 July 1,716 35,450
 August 1,875 36,211

1. Nandita performs a regression analysis, comparing each month’s online advertising expense with that Required
month’s revenue. Verify that she obtains the following result:
Revenue = $51,999.64 - (0.98 * Online advertising expense)

Variable Coefficient Standard Error t-Value

Constant $51,999.64 7,988.68 6.51
Independent variable: Online advertising expense -0.98 1.99 -0.49
r 2 = 0.02; Durbin@Watson statistic = 2.14

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 revenues? Is the rela-
tionship 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 advertis-
ing expense in the prior month. After discarding September revenue and August advertising expense,
show that the modified regression yields the following:
Revenue = $28,361.37 + (5.38 * Online advertising expense)

Variable Coefficient Standard Error t-Value

Constant $28,361.37 5,428.69 5.22
Independent variable: Previous month’s online advertising 5.38 1.31 4.12
expense r 2 = 0.65; Durbin@Watson statistic = 1.71

4. What does the revised formula indicate? Plot the revised data on a graph. Is this relationship economi-
cally plausible?
5. Can Nandita conclude that there is a cause-and-effect relationship between online advertising ex-
pense and sales revenue? Why or why not?
444 CHAPTER 10 DETERMINING HOW COSTS BEHAVE

10-47 Purchasing department cost drivers, activity-based costing, simple regression analysis. Designer
Wear operates a chain of 10 retail department stores. Each department store makes its own purchasing
decisions. Barry Lee, assistant to the president of Designer Wear, is interested in better understanding the
drivers of purchasing department costs. For many years, Designer Wear has allocated purchasing depart-
ment 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. Lee recently
attended a seminar titled “Cost Drivers in the Retail Industry.” In a presentation at the seminar, Couture
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. Lee interviewed several members of the purchasing department at the Designer Wear store in
Miami. They believed that Couture Fabrics’ conclusions also applied to their purchasing department. Lee
collects the following data for the most recent year for Designer Wear’s 10 retail department stores:

$ % & ' (
Purchasing Dollar Value of Number of
Department Merchandise Purchase Number of
Costs Purchased Orders Suppliers
 Department Store (PDC) (MP$) (No. of POs) (No. of Ss)
 Baltimore $1,525,000 $ 68,325,000 4,350 130
 Chicago 1,120,000 33,450,000 2,555 225
 Los Angeles 535,000 121,100,000 1,438 12
 Miami 2,042,000 119,550,000 5,940 193
 New York 1,050,000 33,520,000 2,795 20
 Phoenix 522,000 29,847,000 1,315 39
 Seattle 1,533,000 102,886,000 7,592 112
 St. Louis 1,748,000 38,665,000 3,610 124
 Toronto 1,618,000 139,315,000 1,710 215
 Vancouver 1,251,000 130,940,000 4,725 208

Lee 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:

Regression 1: PDC = a + (b * MP$)

Variable Coefficient Standard Error t-Value

Constant $1,040,594 $344,830 3.02
Independent variable 1: MP$ 0.0031 0.0037 0.83
r 2 = 0.08; Durbin9Watson statistic = 2.42

Regression 2: PDC = a (b * No. of POs)

Variable Coefficient Standard Error t-Value

Constant $731,687 $267,395 2.74
Independent variable 1: No. of POs $ 156.18 $ 65.19 2.40
r 2 = 0.42; Durbin9Watson statistic = 1.99

Regression 3: PDC = a + (b * No. of Ss)

Variable Coefficient Standard Error t-Value

Constant $802,629 $248,566 3.23
Independent variable 1: No. of Ss $ 3,848 $ 1,660 2.32
r 2 = 0.40; Durbin9Watson statistic = 2.00
 ASSIGNMENT MATERIAL 445

1. Compare and evaluate the three simple regression models estimated by Lee. Graph each one. Also, use
the format employed in Exhibit 10-18 (page 426) to evaluate the information.
2. Do the regression results support the Couture 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 Lee gain additional evidence on drivers of purchasing department costs at each of Designer
Wear’s stores?
10-48 Purchasing department cost drivers, multiple regression analysis (continuation of 10-47). Barry
Lee decides that the simple regression analysis used in Problem 10-47 could be extended to a multiple re-
gression analysis. He finds the following results for two multiple regression analyses:
Regression 4: PDC = a + (b1 * No. of POs) + (b2 * No. of Ss)

Variable Coefficient Standard Error t-Value

Constant $ 481,186 $ 259,020 1.86
Independent variable 1: No. of POs $ 121.37 $ 58.04 2.09
Independent variable 2: No. of Ss $ 2,941 $ 1,458 2.02
r2 = 0.63; Durbin-Watson statistic = 1.91

Regression 5: PDC = a + (b1 * No. of POs) + (b2 * No. of Ss) + (b3 * MP$)

Variable Coefficient Standard Error t-Value

Constant $ 496,544 $ 311,137 1.60
Independent variable 1: No. of POs $ 122.73 $ 63.79 1.92
Independent variable 2: No. of Ss $ 2,996 $ 1,646 1.82
Independent variable 3: MP$ −0.00033 −0.0030 −0.11
r2 = 0.63; Durbin-Watson statistic = 1.92

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

PDC MP$ No. of POs

MP$ 0.28
No. of POs 0.65 0.27
No. of Ss 0.63 0.35 0.30

1. Evaluate regression 4 using the criteria of economic plausibility, goodness of fit, significance of Required
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 Lee use? Why?
2. Compare regression 5 with regression 4. Which one of these models would you recommend that Lee
use? Why?
3. Lee estimates the following data for the Baltimore store for next year: dollar value of merchandise
purchased, $77,000,000; number of purchase orders, 4,200; number of suppliers, 120. How much should
Lee 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 analy-
sis? 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.