CHAPTER 6

Activity Analysis, Cost Behavior, and Cost

Estimation

ANSWERS TO REVIEW QUESTIONS

6-1 Cost behavior patterns are important in the process of
making cost predictions. Cost predictions are used in
planning, control, and decision making. For example, cost
budgets are based on predictions of costs at various
levels of activity. Cost control is accomplished by
comparing actual costs against budgeted costs, which are
based on cost predictions. Cost predictions are also
important in decision making, since the desirability of
various alternatives often depends on the costs that will
be incurred under those alternatives.
6-2 a. Cost estimation is the process of determining how a
particular cost behaves.
b. Cost behavior is the relationship between cost and
activity.
c. Cost prediction is the forecast of cost at a particular
level of activity.
Cost estimation determines the cost behavior pattern,
which is used to make a cost prediction about the cost at
a particular level of activity contemplated in the future.
6-3 a. Hotel: Percentage of rooms occupied or the number of
occupancy-days, where an occupancy-day is defined as
one room occupied for one day.
b. Hospital: Patient-days, where a patient-day is defined
as a one-day stay by one patient.
c. Computer manufacturer: Number of computers
manufactured, throughput, engineering specifications,
engineering change orders, or number of parts in the
finished product.
d. Computer sales store: Sales revenue.
e. Computer repair service: Repair calls or hours of repair
service.
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Managerial Accounting, 8/e 6-1
 f. Public accounting firm: Hours of auditing service
provided by each classification of personnel (partner,
manager, supervisor, senior accountant, and staff
accountant).

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6-2 Solutions Manual
 6.4 Graphs of the cost behavior patterns are as
follows:

Cos Cos
t t

Activ Activ
a. ity b. Step- ity
Variable variable
Cos Cos
t t

Activ Activ
Cos c. Fixed ity Cos d. Step-fixed ity
t t

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e. Semivariable
Managerial Accounting, 8/e
Curviline 6-3
ar
6-5 As the level of activity (or cost driver) increases, total
fixed cost remains constant. However, the fixed cost per
unit of activity declines as activity increases.
6-6 A manufacturer's cost of supervising production might be
a step-fixed cost, because one supervisor is needed for
each shift. Each shift can accommodate a certain range of
production activity; when activity exceeds that range, a
new shift must be added. When the new shift is added, a
new production supervisor must be employed. This new
position results in a jump in the step-fixed cost to a
higher level.
6-7 As the level of activity (or cost driver) increases, total
variable cost increases proportionately and the variable
cost per unit remains constant.
6-8 a. A semivariable cost behavior pattern can be used to
approximate a step-variable cost as shown in the
following graph:
Cos
t

Semivariabl
e
approximati
on

Step-
variable
cost
Activit
A semivariable cost behavior
y pattern can be used
b. to approximate a curvilinear cost as shown in the
following graph:
Cos
t

Curvilinear
cost

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6-4 le Solutions Manual
approxima Activ
tion
ity
6-9 (a) Annual cost of maintaining an interstate highway:
committed cost. (Once the highway has been built, it must
be maintained. The transportation authorities are largely
committed to spending the necessary funds to maintain
the highway adequately.)
(b) Ingredients in a breakfast cereal: engineered cost.
(c) Advertising for a credit card company: discretionary
cost.
(d) Depreciation on an insurance company's computer:
committed cost.
(e) Charitable donations: discretionary cost.
(f)Research and development: discretionary cost.
6-10 The cost analyst should respond by pointing out that in
most cases a cost behavior pattern should be limited to
the relevant range of activity. When the firm's utility cost
was shown as a semivariable cost, it is likely that only
some portion in the middle of the graph would fall within
the relevant range. Within the relevant range, the firm's
utility cost can be approximated reasonably closely by a
semivariable cost behavior pattern. However, outside that
range (including an activity level of zero), the
semivariable cost behavior pattern should not be used as
an approximation of the utility cost.
6-11 A learning curve shows how average labor time per unit of
production changes as cumulative output changes. In
many production processes, as production activity
increases and learning takes place, there is a significant
reduction in the amount of labor time required per unit.
The learning phenomenon is important in cost estimation,
since estimates must often be made for the level of cost
to be incurred after additional production experience is
gained.
6-12 Appropriate independent variables for several tasks are
as follows:
a. Handling materials at a loading dock: Weight of
materials handled.

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Managerial Accounting, 8/e 6-5
 b. Registering vehicles at a county motor vehicle office:
Number of registrations processed.
c. Picking oranges: Volume or weight of oranges picked.
d. Inspecting computer components in an electronics firm:
Number of components inspected.

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6-6 Solutions Manual
6-13 An outlier is a data point that falls far away from the
other points in the scatter diagram and is not
representative of the data. One possible cause of an
outlier is simply a mistake in recording the data. Another
cause of an outlier is a random event that occurred, which
caused the cost during a particular period to be unusually
high or low. For example, a power outage may have
resulted in unusually high costs of idle time for a
particular time period. Outliers should be eliminated from
a data set upon which cost estimates are based.
6-14 Fixed costs are often allocated on a per unit-of-activity
basis. For example, fixed manufacturing-overhead costs,
such as depreciation, may be allocated to units of
production. As a result, such costs may appear to be
variable in the cost records. Discretionary costs often are
budgeted in a manner that makes them appear variable. A
cost such as charitable donations, for example, may be
fixed once management decides on the level of donations
to be made. If management's policy is to budget
charitable donations on the basis of sales dollars,
however, the cost will appear to be variable to the cost
analyst. An experienced analyst should be wary of
allocated and discretionary costs and take steps to learn
how the amounts are determined.
6-15 In the first step of the visual-fit method of cost
estimation, data points are plotted on graph paper to
form a scatter diagram. Then a line is drawn through the
scatter diagram in an attempt to minimize the distance
between the line and the plotted points. The scatter
diagram and the visually-fitted cost line provide a
valuable first approximation in the analysis of any cost
suspected to be semivariable or curvilinear. The method
is easy to use and to explain to others and provides a
useful view of the overall cost behavior pattern. The
visual-fit method also enables an experienced cost
analyst to spot outliers in the data. The primary drawback
of the visual-fit method is its lack of objectivity. Two cost
analysts may draw two different visually-fitted cost lines.
6-16 The chief drawback of the high-low method of cost
estimation is that it uses only two data points. The rest of
the data are ignored by the method. An outlier can cause
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Managerial Accounting, 8/e 6-7
 a significant problem when the high-low method is used if
one of the two data points happens to be an outlier. In
other words, if the high activity level happens to be
associated with a cost that is not representative of the
data, the resulting cost line may not be representative of
the cost behavior pattern.
6-17 The term least squares in the least-squares regression
method of cost estimation refers to the process of
minimizing the sum of the squares of the vertical
distances between the data and the regression line.

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6-8 Solutions Manual
6-18 A least-squares regression line may be expressed in
equation form as follows:
Y = a + bX
In this equation, X is referred to as the independent
variable, since it is the variable upon which the estimate
is based. Y is called the dependent variable, since its
estimate depends on the independent variable. The
intercept of the line on the vertical axis is denoted by a,
and the slope of the line is denoted by b. Within the
relevant range, a is interpreted as an estimate of the
fixed-cost component, and b is interpreted as an estimate
of the variable cost per unit of activity.
6-19 In simple regression there is a single independent
variable. In multiple regression there are two or more
independent variables.
6-20 Potential cost drivers in the cruise industry include the
following: number of passengers, number of passenger
miles traveled, number of port calls, cruise ship tonnage
(i.e., ship size), and number of crew members, among
others.
6-21 A particular least-squares regression line may be
evaluated on the basis of economic plausibility or
goodness of fit.

The cost analyst should always evaluate a regression

line from the perspective of economic plausibility. Does
the regression line make economic sense? Is it intuitively
plausible? An experienced cost analyst should have a
good feel for whether the regression line looks
reasonable.

Statistical methods can also be used to determine how

well a regression line fits the data upon which it is based.
This method is referred to as assessing the goodness of
fit of the regression. A commonly used measure of
goodness of fit is the coefficient of determination, which
is described in the appendix at the end of the chapter.
The coefficient of determination is also denoted by R2.

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Managerial Accounting, 8/e 6-9
McGraw-Hill/Irwin  2009 The McGraw-Hill Companies,
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6-10 Solutions Manual
SOLUTIONS TO EXERCISES
EXERCISE 6-22 (15 MINUTES)

1.
Cost per Broadcast Hour
Cost Item August October
Production crew:
$5,330/410 hr.................... $13.00 per
hr.
$8,840/680 hr.................... $13.00 per
hr.
Supervisory employees:
$6,000/410 hr.................... $14.63 per
hr.*
$6,000/680 hr.................... $ 8.82 per
hr.*

*Rounded.

2. December cost predictions:

Production crew (440 × $13.00 per hr.)........ $5,720

Supervisory employees................................ 6,000

3.
Cost per
Cost Item Broadcast Hour
in December
Production crew........................... $13.00 per
hr.   
Supervisory employees 13.64 per
($6,000/440 hr.)........................... hr.*

*Rounded.

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Managerial Accounting, 8/e 6-11
EXERCISE 6-23 (40 MINUTES)

1. Cost of food:

Cost
$25,000 Total cost

$20,000

$15,000

$10,000

$5,000

Patient days
1,000 2,000 3,000

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6-12 Solutions Manual
EXERCISE 6-23 (CONTINUED)

2. Cost of salaries and fringe benefits for administrative

staff:

Cost per month

$13,000 Total cost

$10,000

$5,000

Patient days
1,000 2,000 3,000

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Managerial Accounting, 8/e 6-13
EXERCISE 6-23 (CONTINUED)

3. Laboratory costs:

Cost per
month
$80,000
Total
cost

$70,000

$60,000

$50,000

$40,000

$30,000

$20,000

$10,000

Patient days
1,000 2,000 3,000

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6-14 Solutions Manual
EXERCISE 6-23 (CONTINUED)

4. Cost of utilities:

Cost per month

$15,000
Total cost

$10,000

$5,000

Patient days
1,000 2,000 3,000

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Managerial Accounting, 8/e 6-15
EXERCISE 6-23 (CONTINUED)

5. Nursing costs:

Cost per
month
$17,
500
$15,
000
$12,
Total cost
500
$10,
000
$7,5
00
$5,0
00
$2,5
00
Patient
200 400 600 800 1,000days

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6-16 Solutions Manual
EXERCISE 6-24 (15 MINUTES)

1. a. Fixed

b. Variable

c. Variable

d. Fixed

e. Semivariable (or mixed)

2. Production cost per month = $37,000* + $2.30X †

*37,000 = $21,000 + $11,000 + $5,000

†
$2.30 = $1.20 + $.85 + $.25

EXERCISE 6-25 (15 MINUTES)

1. Variable
maintenance = (18,750r-16,500r) / (30,000 miles –
cost per tour 12,000 miles)
mile
= .125r

r denotes the real, Brazil’s national currency.

Total maintenance cost at 12,000 miles.............. 16,500r

Variable maintenance cost at 12,000 miles (.125r 1,500r
× 12,000)..........................................................
Fixed maintenance cost per month..................... 15,000r

2. Cost formula:

Total maintenance cost per month = 15,000r + .125rX ,

where X denotes tour miles traveled during the month.

3. Cost prediction at the 34,000-mile activity level:

Maintenance = 15,000r + (.125r)(34,000)

cost
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Managerial Accounting, 8/e 6-17
 = 19,250r

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6-18 Solutions Manual
EXERCISE 6-25 (CONTINUED)

2. IN THE ELECTRONIC VERSION OF THE SOLUTIONS MANUAL,

PRESS THE CTRL KEY AND CLICK ON THE FOLLOWING LINK:
BUILD A SPREADSHEET

EXERCISE 6-26 (15 MINUTES)

1.
Actual Estimat
ed
a. 20,000 miles.................................. $1,950 $2,200
b. 40,000 miles.................................. 2,600 2,600
c. 60,000 miles.................................. 3,000 3,000
d. 90,000 miles.................................. 4,250 3,600

2. (a The approximation is very accurate in the range 40,000

) to 60,000 miles per month.

(b The approximation is less accurate in the extremes of

) the longer range, 20,000 to 90,000 miles.

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Managerial Accounting, 8/e 6-19
EXERCISE 6-27 (30 MINUTES)

1 Scatter diagram and visually-fitted line:

.

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6-20 Solutions Manual
 Cost of diagnostic
testing
$50,00
•
0
•
•
••
•
$40,00
0 •• •
••

$30,00 •
0

$20,00
0

$10,00
0

Tests
500 1,000 1,500 2,000 2,500 3,000 3,500

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Managerial Accounting, 8/e 6-21
EXERCISE 6-27 (CONTINUED)

2 The requirement asks for an estimate based on the

. visually-fit cost line. Therefore, answers will vary on this
requirement because of variation in the visually-fitted lines.

Based on the preceding plot:

Monthly fixed cost................................................ $14,000

Variable cost per diagnostic test.......................... $ 10.56*

*Calculation of variable cost:

Total cost 3,600 tests........................ $52,000

at
Total cost     0 tests........................   
at 14,000
Differenc 3,600 tests........................ $38,000
e:

$38,000
Variable cost per = 3,600
diagnostic test
= $10.56†

†
Rounded.

EXERCISE 6-28 (30 MINUTES)

Answers will vary widely, depending on the company and costs

selected. Some examples of typical manufacturing costs
follow.

Direct material: variable

Electricity: variable

Depreciation on plant and equipment: fixed

Plant manager’s salary: fixed

Property taxes: fixed

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6-22 Solutions Manual
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Managerial Accounting, 8/e 6-23
EXERCISE 6-29 (15 MINUTES)

Variable cost per pint of applesauce produced =

1. −$66,300
$72,300
= $.10
123,000−63,000

Total cost at 123,000 pints............................... $72,300

Variable cost at 123,000 pints
(123,000 × $.10 per pint)............................  12,300
Fixed cost........................................................ $60,000

Cost equation:

Total energy cost = $60,000 + $.10X, where X denotes

pints of applesauce produced

2. Cost prediction when 78,000 pints of applesauce are

produced

Energy cost = $60,000 + ($.10)(78,000) = $67,800

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6-24 Solutions Manual
EXERCISE 6-30 (30 MINUTES)

1. Scatter diagram and visually-fitted line:

Monthly energy
cost
$90,00
0
•

$75,00 ••
0 •
•• • • ••• •

$60,00
0

$45,00
0

$30,00
0

$15,00
0

Pints of
apple-
120,00 150,00 sauce
30,000 60,000 90,000 produced
0 0

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Managerial Accounting, 8/e 6-25
EXERCISE 6-30 (CONTINUED)

2. Answers will vary on this requirement because of variation

in the visually-fitted lines.

Based on the preceding plot, the cost prediction at 78,000

pounds is:

Energy cost = $67,800

3. The July cost observation at the 120,000-pint activity level

appears to be an outlier. The cost analyst should check
the observation data for accuracy. If the data are accurate,
the outlier should be ignored in making cost predictions.

EXERCISE 6-31 (10 MINUTES)

1. (a Average time for 4 satellites........................ 195

) hours
(b Average time for 8 satellites........................ 150
) hours

2. (a Total time for 4 satellites (195 hr. X 4)........ 780

) hours
(b Total time for 8 satellites (150 hr. X 8)........ 1,200
) hours

3. Learning curves indicate how labor costs will change as the

company gains experience with the production process.
Since labor time and costs must be predicted both for
budgeting and for setting cost standards, the learning
curve is a valuable tool.

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6-26 Solutions Manual
EXERCISE 6-32 (15 MINUTES)

Monthly audit
cost
$100,00
0
Total cost when 100 audits are
performed
in a month: $78,200 = $10,000 +
$80,000
• ($682) (100) •

$60,000

$40,000

$20,000
Fixed cost per month:
•
$10,000
Tax
returns
20 40 60 80 100 audited

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Managerial Accounting, 8/e 6-27
EXERCISE 6-33 (45 MINUTES)

−$2,600
$3,800
1. Variable utility cost = = $4.00
700−400
per hour

Total utility cost at 700 hours............................ $ 3,800

Variable utility cost at 700 hours ($4.00 × 700   2,800
hours)...............................................................
Fixed cost per month......................................... $ 1,000

Cost formula:

Monthly utility cost = $1,000 + $4.00 X , where X denotes

hours of operation.

2 Variable-cost estimate based on the scatter diagram on the

. next page:

Cost at 600 ........................................... $3,400

hours
Cost at   0 ...........................................    900
hours
Differen 600 ........................................... $2,500
ce hours

Variable cost per hour = $2,500/600 hr. = $4.17 (rounded)

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6-28 Solutions Manual
EXERCISE 6-33 (CONTINUED)

Scatter diagram and visually-fit line:

Utility
cost
per month

5000

Hours of
operation

4000

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Managerial Accounting, 8/e 6-29
EXERCISE 6-33 (CONTINUED)

3. Estimation of variable- and fixed-cost components of

cost behavior using least-squares regression:

In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

4. Cost predictions at 300 hours of operation:

(a High-low
) method:

Utility cost = $1,000 + ($4.00)(300) = $2,200

(b Visually-
) fitted line:

Utility cost = $2,190

This cost prediction was simply read directly from the

visually-fitted cost line. This prediction will vary
because of variations in the visually-fitted lines.

(c Regression:
)

Utility cost = $1,002 + ($4.04)(300) = $2,214

5. Calculation of R2:

In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

The R2 is .9518.

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6-30 Solutions Manual
 EXERCISE 6-33 (CONTINUED)

The following alternative approach to calculating the

regression parameters is not a requirement in the problem.

Least-square regression using manual calculations:

(a Tabulation of data:
)
Dependen Indepen
t Variable dent
(cost) Variable
Month Y (hours) X2 XY
X
January.......... 3,240 550 302,500 1,782,0
00
February........ 3,400 600 360,000 2,040,0
00
March............ 3,800 700 490,000 2,660,0
00
April.............. 3,200 500 250,000 1,600,0
00
May............... 2,700 450 202,500 1,215,0
00
June............... 2,600   400   160,000 1,040,
000
Total.............. 18,940 3,20 1,765,000 10,337,
0 000

(b Calculation of parameters:
)
(∑Y)(∑X2 )−(∑X)(∑XY)
a =
n(∑X2 )−(∑X)(∑X)
= (18,940)(1,765,000)−(3,200)(10,337,000) = 1,002
0,00)−(3,200)(3
(6)(1,765 2,00)

b = n(∑XY)− (∑X)(∑Y)
n(∑X2) − (∑X)(∑X)
700)−(3,200)(1,9
(6)(10,33,0 840)
= =4.04
(6)(1,7650,00)−(3,200)(3
2,00)

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Managerial Accounting, 8/e 6-31
 (c Cost formula:
)

Monthly = $1,002 + $4.04X, where X denotes

utility cost hours of operation.

Variable = $4.04 per hour of operation

utility cost

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6-32 Solutions Manual
EXERCISE 6-34 (45 MINUTES)

1. In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

2. In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

The following alternative approach to calculating the

regression parameters and R2 is not a requirement in the
problem.

Least-square regression using manual calculations:

(a Tabulation of data:
)

Indepen
Dependen dent
t Variable Variable
(cost in (thousan
thousand ds
Month s) of X2 XY
Y passeng
ers)
X
July................. 54 16 256 864
August............ 54 17 289 918
September...... 57 16 256 912
October.......... 60 18 324 1,080
November....... 54 15 225 810
December....... 57 17   289 969
Total............... 336 99 1,639 5,553

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Managerial Accounting, 8/e 6-33
EXERCISE 6-34 (CONTINUED)

(b Calculation of parameters:
)
(∑Y)(∑X2)−(∑X)(∑XY)
a =
n(∑X2)−(∑X)(∑X)
3)−(99)(5,55)3
(336)(1,69
= = 29(rounded)
(6)(1,639−
) (99)(99)

n(∑ XY)− (∑ X)(∑Y)

b =
n(∑ X2 ) − (∑ X)(∑ X)
(6)(5,553−
) (99)(336)
= (6)(1,639− = 1.636(rounded)
) (99)(99)

(c Cost formula:
)

Monthly cost of flight service = $29,000 + $1,636X,

where X denotes thousands of passengers.

Calculation and interpretation of R2 using manual

calculations:

(a Formula for calculation:

)
∑(Y −Y')2
R2 = 1−
∑(Y−Y)2

whe Y denotes the observed value of the dependent

re variable (cost) at a particular activity level.

Y' denotes the predicted value of the

dependent variable (cost) based on the
regression line, at a particular activity level.

Y denotes the mean (average) observation of

the dependent variable (cost).

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6-34 Solutions Manual
EXERCISE 6-34 (CONTINUED)

(b Tabulation of data:*
)

Predicted
Cost (in
thousands)
Based on
Month Y X Regression [( Y – [(Y – Y )2]†
Line Y' Y')2]†
July......... 54 1 55.176 1.383 4.000
6
August.... 54 1 56.812 7.907 4.000
7
Septembe 57 1 55.176 3.327 1.000
r............. 6
October. . 60 1 58.448 2.409 16.000
8
November 54 1 53.540 .212 4.000
5
December 57 1 56.812 .035 1.000
7
Total....... 15.273 30.000

*Y = ($29,000 + $1,636X)/$1,000
'
Y =
∑
Y/6 = 56
†
Round
ed.

(c Calculation of R2:
)

15.273
R2 = 1 – = .49 (rounded)
30.000

(d Interpretation of R2:
)

The coefficient of determination, R2, is a measure of

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Managerial Accounting, 8/e 6-35
 the goodness of fit of the least-squares regression line.
An R2 of .49 means that 49% of the variability of the
dependent variable about its mean is explained by the
variability of the independent variable about its mean.
The higher the R2, the better the regression line fits
the data. The interpretation of a high R2 is that the
independent variable is a good predictor of the
behavior of the dependent variable. In cost estimation,
a high R2 means that the cost analyst can be relatively
confident in the cost predictions based on the
estimated-cost behavior pattern.

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6-36 Solutions Manual
SOLUTIONS TO PROBLEMS
PROBLEM 6-35 (20 MINUTES)

1 h 5 a 9. d
. .

2 i 6 g 1 k
. . 0.

3 f 7 c 1 l
. . 1.

4 e 8 b
. .

Note that j was not used.

PROBLEM 6-36 (15 MINUTES)

An appropriate activity measure for the school would be hours

of instruction. The costs are classified as follows:

1. Variable 6 Variable
.

2. Semivariable (or mixed)* 7 Fixed

.

3. Fixed 8 Fixed
.

4. Fixed 9 Semivariable (or mixed)

.

5. Fixed

*The fixed-cost component is the salary of the school's repair

technician. As activity increases, one would expect more
repairs beyond the technician's capability. This increase in
repairs would result in a variable-cost component equal to the
dealer's repair charges.

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Managerial Accounting, 8/e 6-37
PROBLEM 6-37 (25 MINUTES)
$4,710− $2,990
1. Variable maintenance cost per =
525− 310
hour of service

= $8.00

Total maintenance cost at 310 hours of service. . $2,990

Variable maintenance cost at 310 hours of  2,480
service (310 hr. × $8.00)...................................
Fixed maintenance cost per month..................... $  510

Cost formula:

Monthly maintenance cost = $510 + $8.00X,

where X denotes hours of maintenance service.

2. The variable component of the maintenance cost

is $8.00 per hour of service.

3. Cost prediction at 600 hours of activity:

Maintenance cost = $510 + ($8.00)(600) =

$5,310

4. Variable cost per hour [from requirement (2)].... $8.00

Fixed cost per hour at 610 hours of activity $ .84*
($510/610)........................................................
*Rounded.

The fixed cost per hour is a misleading amount,

because it will change as the number of hours
changes. For example, at 500 hours of
maintenance service, the fixed cost per hour is
$1.02 ($510/500 hours).

McGraw-Hill/Irwin  2009 The McGraw-Hill Companies,

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6-38 Solutions Manual
PROBLEM 6-38 (25 MINUTES)

1. Straight-line depreciation—committed fixed

Charitable contributions—discretionary fixed
Mining labor/fringe benefits—variable
Royalties—semivariable
Trucking and hauling—step-fixed

The per-ton mining labor/fringe benefit cost is constant at

both volume levels presented, which is characteristic of a
variable cost.

$315,000 ÷ 1,400 tons = $225 per ton

$607,500 ÷ 2,700 tons = $225 per ton

Royalties have both a variable and a fixed component,

making it a semivariable (mixed) cost.

Variable royalty cost = difference in cost ÷

difference in tons
= ($224,500 – $140,000) ÷ (2,700 –
1,400)
= $84,500 ÷ 1,300 tons
= $65 per ton

Fixed royalty cost:

June Decemb
(2,700 er
tons) (1,400
tons)

Total royalty $224,50 $140,00

cost………………………. 0 0
Less: Variable cost at 175,50 91,00
$65 per ton….. 0 0
Fixed royalty $ $
cost……………………… 49,000 49,000

2. Total cost for 1,700 tons:

Depreciation…………………………… $
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Managerial Accounting, 8/e 6-39
 ……………... 30,000
Charitable ----
contributions……………………………
.
Mining labor/fringe benefits at 382,5
$225 per ton……. 00
Royalties:
Variable at $65 per 110,5
ton………………………….. 00
Fixed…………………………………… 49,0
………….. 00
Trucking and 280,0
hauling……………………………….. 00
Total…………………………………… $852,0
………….. 00

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6-40 Solutions Manual
PROBLEM 6-38 (CONTINUED)

3. Hauling 1,400 tons is not particularly cost effective. Lone

Mountain Extraction will incur a cost of $280,000 if it
needs 1,400 tons hauled or, for that matter, 1,899 tons.
The company would be better off if it had 1,399 tons
hauled, saving outlays of $40,000. In general, with this
type of cost function, effectiveness is maximized if a firm
operates on the right-most portion of a step, just prior to
a jump in cost.

4. A committed fixed cost results from an entity’s ownership

or use of facilities and its basic organizational structure.
Examples of such costs include property taxes, depreciation,
rent, and management salaries. Discretionary fixed costs, on
the other hand, arise from a decision to spend a particular
amount of money for a specific purpose. Outlays for
research and development, advertising, and charitable
contributions fall in this category.

In times of severe economic difficulties, a company’s

management will often try to cut discretionary fixed
costs. Such costs are more easily altered in the short run
and do not have as significant long-term ramifications for
a firm as do more long-lasting actions. While it’s true that
cutting expenditures on advertising or R & D can often
have adverse long-term consequences, other cuts could
have even more significant negative consequences in the
future. The decision to close a manufacturing facility, for
example, could reduce property taxes, rent, and/or
depreciation. However, that decision may result in a
significant long-run change in operations that may be
difficult to overturn when economic conditions rebound.

5. Lone Mountain Extraction uses a calendar year for tax-

reporting purposes. At year-end, it may have ample funds
available and decide to make donations to charitable
causes. Such contributions are deductible in computing
the company’s tax obligation to the government. Tax
deductions reduce taxable income and, therefore,
produce a tax savings for the firm.

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Managerial Accounting, 8/e 6-41
PROBLEM 6-39 (25 MINUTES)

1. Machine supplies: $153,000 ÷ 34,000 direct-labor hours =

$4.50 per hour

So for April we have: 23,000 direct-labor hours x

$4.50 = $103,500

Depreciation: Fixed at $22,500

2. Plant maintenance cost:

April June

(23,000 (34,000
hours) hours)

Total $ $
cost*……………………. 681,00 879,00
. 0 0
Less: Machine (103, (153,
supplies……. 500) 000)
Depreciation… (22, (22,
……….. 500) 500)
Plant $ $
maintenance……… 555,00 703,50
…... 0 0

* Excludes supervisory labor

cost

Variable maintenance cost = difference in cost ÷

difference in direct-labor hours
= ($703,500 – $555,000) ÷ (34,000 –
23,000)
= $148,500 ÷ 11,000 hours
= $13.50 per hour

Fixed maintenance cost:

April June
(23,00 (34,00
0 0
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6-42 Solutions Manual
 hours) hours)

Total maintenance cost...... $555,0 $703,5

00 00
Less: Variable cost at 310,5 459,0
$13.50 per hour................. 00 00
Fixed maintenance cost...... $244,5 $244,5
00 00

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Managerial Accounting, 8/e 6-43
PROBLEM 6-39 (CONTINUED)

3. Manufacturing overhead at 29,500 labor hours:

Machine supplies at $4.50 per $132,75

hour...................................... 0
Depreciation.......................... 22,500
Plant maintenance cost:
Variable at $13.50 per hour 398,250
Fixed.................................. 244,500
Supervisory labor................... 135,00
0
Total............................ $933,00
0

4. A fixed cost remains constant when a change occurs in

the cost driver (or activity base). A step-fixed cost, on
the other hand, remains constant within a range but will
change (rise or fall) when activity falls outside that range.
In other words, a fixed cost is constant over a wider range
of activity than a step-fixed cost.

5. Ideally, the company should operate on the right-most

portion of a step, just prior to the jump in cost. In this
manner, a firm receives maximum benefit (i.e., the
maximum amount of activity) for the dollars invested.

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6-44 Solutions Manual
PROBLEM 6-40 (40 MINUTES)

1.

Material-handling costs

$12,500

$12,000

$11,500

$11,000
2.
$10,500 Visually-fitted
cost line
$10,000

$9,500

Hundreds of
pounds of
500 1,000 1,500 2,000 2,500
equipment
Thelower part of the
vertical axis has
beenshortened.

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Managerial Accounting, 8/e 6-45
PROBLEM 6-40 (CONTINUED)

2. See graph for requirement (1).

3. The estimate of the fixed cost is the intercept on the

vertical axis.

Fixed-cost component = $9,700

To estimate the variable-cost component, choose any two

points on the visually-fitted cost line. For example, choose
the following points:

Activity Cost
0......................................................... $
9,70
0
2,000.................................................. 11,7
00

Then proceed as follows to estimate the variable-

cost component:

$11,700−$9,700
Variable cost per unit of activity* = 2,000−0

= $1.00

*Pounds (in hundreds) of equipment

loaded or unloaded

4. Cost equation:

Total material-handling cost = $9,700 + $1.00X, where X

denotes the number pounds (in hundreds) of equipment
loaded or unloaded during the month.

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6-46 Solutions Manual
PROBLEM 6-40 (CONTINUED)

5. High-low method:

−$10,200
Variable cost unit of activity* = $12,120
2,600−1,000
= $1.20

*Pounds (in hundreds) of equipment loaded or

unloaded

Total cost at 2,600 units of activity..................... $12,120

Deduct: Variable cost at 2,600 units of activity   3,120
(2,600 × $1.20)..................................................
Fixed cost.......................................................... $ 9,000

Cost equation based on high-low

method:

Material-handling cost per month = $9,000 + $1.20X,

where X denotes the number of units of activity during the
month.

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Managerial Accounting, 8/e 6-47
PROBLEM 6-40 (CONTINUED)

6. Memorandum

Date: Today

To: President, Nantucket Marine Supply

From I.M. Student

:

Subje Material-handling cost estimates

ct:

On the basis of a scatter diagram and visually-fitted cost

line, the Material-Handling Department's monthly cost
behavior was estimated as follows:

Material-handling cost per month = $9,700 + $1.00 unit of

activity

A unit of activity is defined in this department as 100

pounds of equipment loaded or unloaded at the loading
dock.

Using the high-low method, the following cost estimate

was obtained:

Material-handling cost per month = $9,000 + $1.20 unit of

activity

The two methods yield different estimates because the

high-low method uses only two data points, ignoring the
rest of the information. The method of visually fitting a
cost line, while subjective, uses all of the data available.

In this case, the two data points used by the high-low

method do not appear to be representative of the entire
set of data.

7. Predicted Material-Handling Costs

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6-48 Solutions Manual
 Using Visually-Fit Using
Cost Line* High-Low Method
$11,950 = $9,700 + $11,700 = $9,000 +
($1.00)(2,250) ($1.20)(2,250)

*This method is preferable, because it

uses all of the data in developing the
cost equation.

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Managerial Accounting, 8/e 6-49
PROBLEM 6-41 (45 MINUTES)

1. Estimation of variable and fixed components of cost

behavior using least-squares regression:

In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

2. Least-squares regression equation:

In the electronic version of the solutions manual, press the

CTRL key and click on the following link: BUILD A
SPREADSHEET

Total monthly cost = $9,943 + $.89 per unit of activity

3. Cost prediction:

In the electronic version of the solutions manual, press the

CTRL key and click on the following link: BUILD A
SPREADSHEET

4. The cost predictions differ because the cost formulas differ

under the three cost-estimation methods. The high-low
method, while objective, uses only two data points.
Ten observations are excluded.

The visual-fit method, while it uses all of the data, is

somewhat subjective. Different analysts may draw
different cost lines.

Least-squares regression is objective, uses all of the

data, and is a statistically sound method of estimation.

Therefore, least-squares regression is the preferred

method of cost estimation.

5. Calculation of R2:

In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

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6-50 Solutions Manual
The following alternative approach to calculating the
regression parameters is not a requirement in the problem.

Least-squares regression using manual calculations:

(a Tabulation of data:
)
Indepen
Dependen dent
t Variable Variable
(cost in (units of
thousand activity
Month s) in X2 XY
Y thousan
ds)
X
January...........     1.8  3.24  21.060
11.70
February......... 11.30 1.6 2.56 18.080
March............. 11.25 1.3 1.69 14.625
April............... 10.20 1.0 1.00 10.200
May................ 11.10 2.2 4.84 24.420
June................ 12.55 2.4 5.76 30.120
July................. 12.00 2.0 4.00 24.000
August............ 11.40 1.8 3.24 20.520
September...... 12.12 2.6 6.76 31.512
October.......... 11.05 1.1 1.21 12.155
November....... 11.35 1.2 1.44 13.620
December....... 11.3 1.4 1.96 15.890
5
Total............... 137.3 20.4 37.70 236.202
7

(b Calculation of parameters:
)

(∑Y)(∑X2)−(∑X)(∑XY)
a =
n(∑X2)−(∑X)(∑X)
7.7)−(20.4)(23.2
(137.37)(3 602)
= =9.943(rounded)
(12)(37.7−) (20.4)(20
4.)

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Managerial Accounting, 8/e 6-51
 n(∑ XY)− (∑ X)(∑Y)
b =
n(∑ X2 ) − (∑ X)(∑ X)
02)−(20.4)(13.3
(12)(236.2 77)
= =.885(rounded)
(12)(37.7−
) (20.4)(20
4.)

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6-52 Solutions Manual
PROBLEM 6-41 (CONTINUED)

(c Fixed- and variable-cost components:

)

Monthly fixed cost = $9,943*

Variable cost = $.89 per unit of activity (rounded)†

*The intercept parameter (a) computed above is the

cost per month in thousands.
†
The slope parameter (b) calculated above is the cost in
thousands of dollars per thousand units of activity.
Equivalently, it is the cost per unit of activity.

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Managerial Accounting, 8/e 6-53
PROBLEM 6-42 (40 MINUTES)

Total coursemaintenancecost 1.
Step-variable
$13,250
component
of maintenance
$13,200
cost
2.
$13,150 Semivariable
cost approximation
$13,100

$13,050

$13,000
1.
Fixedcomponent
of maintenance
cost

0 50 100 150 200 250 300

Thelower part of the Number of golfers
vertical axis has
been shortened.

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6-54 Solutions Manual
PROBLEM 6-42 (CONTINUED)

3. Fixed-cost component = $13,005

Variable-cost component:

Variable cost − $13,005

$13,205
=
per golfer 200− 0
= $1
Cost equation:

Maintenance cost per month = $13,005 + $1X, where X

denotes the number of golfers during the month.

4. Predicted Course Maintenance Costs

Using
Fixed Cost
Coupled
with Step- Using
Variable Semivariabl
Cost e Cost
Behavior Approximati
Pattern on
150 people tee off.......... $13,150 $13,155
158 people tee off.......... 13,160 13,163

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Managerial Accounting, 8/e 6-55
PROBLEM 6-43 (35 MINUTES)

1. The regression equation's intercept on the vertical axis is

$190. It represents the portion of indirect material cost
that does not vary with machine hours when operating
within the relevant range. The slope of the regression line
is $5 per machine hour. For every machine hour, $5 of
indirect material costs are expected to be incurred.

2. Estimated cost of indirect material at 850 machine hours of

activity:
S = $190 + ($5 × 850)
= $4,440

3. Several questions should be asked:

(a Do the observations contain any outliers, or are they

) all representative of normal operations?

(b Are there any mismatched time periods in the data?

) Are all of the indirect material cost observations
matched properly with the machine hour observations?

(c Are there any allocated costs included in the indirect

) material cost data?

(d Are the cost data affected by inflation?

)

4. April August
Beginning inventory............................ $1,300 $1,000
+ Purchases....................................... 5,900 6,200
– Ending inventory..............................    (3,000)
(1,350
)
Indirect material used......................... $5,850 $4,200

5. High-low method:

Variable cost per machine hour

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6-56 Solutions Manual
 difference
incostlevels
= difference
inactivity
levels
− $4,200 $1,650
$5,850
= = = $5.50
permachine
hour
1,000− 700 300
PROBLEM 6-43 (CONTINUED)

Fixed cost per month:

Total cost at 1,000 hours.................................... $5,850

Variable cost at 1,000 hours
($5.50 × 1,000)..............................................  5,500
Fixed cost.......................................................... $  350

Equation form:

Indirect material cost = $350 + ($5.50 × machine hours)

6. The regression estimate should be recommended because it

uses all of the data, not just two pairs of observations when
developing the cost equation.

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Managerial Accounting, 8/e 6-57
PROBLEM 6-44 (25 MINUTES)

1. Scatter diagrams:

• Present, in graphic form, the relationship between costs and

cost drivers via a plot of data points
• Require that a straight line be fit through the data points,
with approximately the same number of data points above
and below the line
• Easy to use
• Provide a means to easily recognize outliers

Least-squares regression:

• Uses statistical formulas to fit a cost line through the data

points
• Is a very objective method of cost estimation that uses all
the data points
• Requires more computation than other cost-estimation
methods; however, software programs are readily available

High-low method:

• Relies on only two data points (for the highest and lowest
activity levels) in drawing conclusions about cost behavior
• Is considered more objective than the scatter diagram;
however, is weaker than the scatter diagram because it
relies on only two data points

The least-squares regression method will typically

produce the most accurate results.

2. Yes. The three methods produce equations by different

means. Scatter diagrams and least-squares regression
rely on an examination of all data points. The scatter
diagram, however, requires an analyst to fit a line
through the points by visual approximation, or
“eyeballing.” In contrast, least-squares regression
involves the use of statistical formulas to derive the best
possible fit of the line through the points. Finally, the

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6-58 Solutions Manual
 high-low method is based on an analysis of only two data
points: the highest and the lowest activity levels.

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Managerial Accounting, 8/e 6-59
PROBLEM 6-44 (CONTINUED)

3. These amounts represent the fixed and variable costs

associated with the ticketing operation. Fixed cost totals
$300,000 within the relevant range, and Florida
International incurs $2.25 of variable cost for each ticket
issued.

4. C = $295,000 + $2.20PT
C = $295,000 + ($2.20 x 570,000)
C = $1,549,000

5. Yes, she did err by including November data. November

is not representative because of the effects of the
Southeastern Airlines strike. The month is an outlier and
should be eliminated from the data set.

6. Currently, most of the airline’s tickets are written through

reservations personnel, whose wages are likely variable in
nature. Heavier reliance on the Internet means a greater
investment in software, Web-site maintenance and
development, and other similar expenditures. Outlays
that fall in these latter categories are typically fixed
costs, assuming that the cost driver is the number of
tickets. The outcome would parallel the experiences of a
manufacturing firm that automates its processes and
reduces its reliance on direct-labor personnel.

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6-60 Solutions Manual
PROBLEM 6-45 (40 MINUTES)

1. The original method was simply the average overhead per

hour for the last 12 months and did not distinguish
between fixed and variable costs. Dana divided total
overhead by total labor hours, which effectively treated
all overhead as variable. Regression analysis measures
the behavior of the overhead costs in relation to labor
hours and is a model that distinguishes between fixed and
variable costs within the relevant range of 2,500 to 7,500
labor hours.

2. a. Based on the regression analysis, the variable cost per

person for a cocktail party is $23, calculated as follows:

Food and beverages....................................... $14.00

Labor (.6 hr. @ $11/hr.).................................. 6.60
Variable overhead (.6 hr. @ $4/hr.)................. 2.40
Total.......................................................... $23.00

b. Based on the regression analysis, the full absorption

cost per person for a cocktail party is $29, calculated as
follows:

Food and beverages....................................... $14.00

Labor (.6 hr. @ $11/hr.).................................. 6.60
Variable overhead (.6 hr. @ $4/hr.)................. 2.40
Fixed overhead (.6 hr. @ $10/hr.)*.................. 6.00
Total.......................................................... $29.00

*$48,000 x 12 months = $576,000

$576,000/57,600 hr. = $10/hr.

3. The minimum bid for a 250-person cocktail party would be

$5,750. The amount is calculated by multiplying the
variable cost per person of $23 by 250 people. At any
price above the variable cost, Dana will be earning a
contribution toward his fixed costs.

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Managerial Accounting, 8/e 6-61
PROBLEM 6-45 (CONTINUED)

4. Other factors that Dana should consider in developing a

bid include the following:

 The assessment of the current capacity of Dana’s

business. If the business is at capacity, other work would
have to be sacrificed at some opportunity cost.
 Analyses of the competition. If competition is rigorous,
Dana may not have much bargaining power.
 A determination of whether or not Dana’s bid will set a
precedent for lower prices.
 The realization that regression analysis is based on
historical data, and that any anticipated changes in the
cost structure should be considered.

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6-62 Solutions Manual
PROBLEM 6-46 (45 MINUTES)
1. Scatter diagram:

Airport
costs
$30,000

$25,000
•

• •
$20,000 • •
• •
• •
• •
$15,000

$10,000

$5,000

250 500 750 1,000 1,250 1,500 1,750

Flights

Note: Only 11 data points appear, because two monthly

observations were identical (February and October).

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Managerial Accounting, 8/e 6-63
PROBLEM 6-46 (CONTINUED)

2. Estimation of variable- and fixed-cost components of

cost behavior using least-squares regression:

In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

3. Cost equation:

In the electronic version of the solutions manual, press the

CTRL key and click on the following link: BUILD A
SPREADSHEET

Total monthly airport cost = $11,796 + $677X, where X

denotes the number of flights

4. Cost prediction for 1,500 flights:

In the electronic version of the solutions manual, press the

CTRL key and click on the following link: BUILD A
SPREADSHEET

5. Calculation of R2;

In the electronic version of the solutions manual, press

the CTRL key and click on the following link: BUILD A
SPREADSHEET

Interpretation of R2:

The coefficient of determination, R2, is a measure of

the goodness of fit of the least-squares regression line.
An R2 of .58 means that 58% of the variability of the
dependent variable about its mean is explained by the
variability of the independent variable about its mean.
The higher the R2, the better the regression line fits
the data. The interpretation of a high R2 is that the
independent variable is a good predictor of the
behavior of the dependent variable. In the county’s

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6-64 Solutions Manual
 cost estimation, a high R2 would mean that the county
budget officer can be relatively confident in the cost
predictions based on the estimated-cost behavior
pattern. An R2 of .58 is not particularly high.

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Managerial Accounting, 8/e 6-65
PROBLEM 6-46 (CONTINUED)

The following alternative approach to calculating the

regression parameters and R2 is not a requirement in the
problem.

Least-squares regression using manual calculations:

(a Tabulation of data:
)
Dependen Indepen
t Variable dent
(cost in Variable
thousand (flights
Month s) in X2 XY
Y hundred
s)
X
January........... 20 12 144 240
February......... 19 10 100 190
March............. 18 9 81 162
April............... 19 14 196 266
May................ 17 8 64 136
June................ 20 11 121 220
July.................  21  15   225   315
August............ 17 9 81 153
September...... 21 12 144 252
October.......... 19 10 100 190
November....... 24 14 196 336
December....... 18 11 121 198
Total............... 233 135 1,573 2,658

(b Calculation of parameters:
)
(∑Y)(∑X2)−(∑X)(∑XY)
a =
n(∑X2)−(∑X)(∑X)
7)−(135)(2,68
(233)(1,53 5)
= = 11.796(rounded)
−(135)(135)
(12)(1,57)3

n(∑ XY)− (∑ X)(∑Y)

b =
n(∑ X2 ) − (∑ X)(∑ X)

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 )−(135)(233)
(12)(2,658
= (12)(1,573 =.677(rounded)
)−(135)(135)

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Managerial Accounting, 8/e 6-67
PROBLEM 6-46 (CONTINUED)

(c Fixed- and variable-cost components:

)

Monthly fixed cost = $11,796

Variable cost = $677 per hundred flights

Calculation and interpretation of R 2 using manual

calculations

(a Formula for calculation:

)
∑(Y −Y')2
R2 =1−
∑(Y−Y)2

whe Y denotes the observed value of the dependent

re variable (cost) at a particular activity level.

Y ' denotes the predicted value of the

dependent variable (cost) based on the
regression line, at a particular activity level.

Y denotes the mean (average) observation of

the dependent variable (cost).

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PROBLEM 6-46 (CONTINUED)

(b Tabulation of data:*
)
Predicted
Cost (in
thousands)
Based on
Month Y X Regression [( Y– [(Y – Y
Line Y' Y')2]† )2]†
January... 20 1 19.920 .006 .340
2
February. 19 1 18.566 .188 .174
0
March..... 18 9 17.889 .012 2.008
April....... 19 1 21.274 5.171 .174
4
May........ 17 8 17.212 .045 5.842
June........ 20 1 19.243 .573 .340
1
July......... 21 1 21.951   .904  2.506
5
August.... 17 9 17.889 .790 5.842
Septembe 21 1 19.920 1.166 2.506
r............. 2
October. . 19 1 18.566 .188 .174
0
November 24 1 21.274 7.431 21.004
4
December 18 1 19.243 1.545 2.008
1
Total....... 18.019 42.918

*Y = ($11,796 + $677X)/$1,000
'
Y =
∑
Y/12 = 233/12 = 19.417 (rounded)
†
Round
ed.

(c Calculation of R2:
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 )

18.019
R2 = 1 – = .58 (rounded)
42.918

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SOLUTIONS TO CASES
CASE 6-47 (45 MINUTES)

1. Cairns' preliminary estimate for overhead of $18.00 per

direct-labor hour does not distinguish between fixed and
variable overhead. This preliminary rate is applicable only
to the activity level at which it was computed (72,000
direct-labor hours per year) and may not be used to predict
total overhead at other activity levels.

The overhead rate developed from the least-squares

regression recognizes the relationship between cost and
volume in the data. The regression suggests that there is a
component of the cost ($52,400 per month) that is
unrelated to total direct-labor hours. This cost component
is the intercept on the vertical axis and is often considered
to be the fixed cost as long as the activity level is within
the relevant range. Thus, the least-squares regression
results in a cost function with two components: fixed cost
per month and variable cost per direct-labor hour. This
cost formula can be used to predict total overhead at any
activity level within the relevant range.

2. Direct material.................................................. $390.00

Direct labor (5 DLH* × $11.00 per DLH).............. 55.00
Variable overhead (5 DLH × $9.25 per DLH)........   46.25
Total variable cost per 1,000 square feet............ $491.25

*DLH denotes direct-labor hours.

3. The minimum bid should include the following incremental

costs of the project.:

Direct material ($390.00 × 50)........................... $19,500

.00
Direct labor ($55.00 × 50).................................. 2,750.0
0
Variable overhead ($9.25 per DLH × 5 DLH × 50) 2,312.5
0
Overtime premium ($5.50 per DLH × 5 DLH × 50 412
× .3).................................................................. .50

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 Minimum bid...................................................... $24,975
.00

4. Yes, Cairns can rely on the formula as long as she

recognizes that there are some shortcomings. The fact that
least-squares regression estimates cost behavior increases
the usefulness of rates computed from cost data. However,
the regression is based on historical costs that may change
in the future, and Cairns must assess whether the cost
equation would need to be revised for future cost
increases or decreases.

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CASE 6-47 (CONTINUED)

5. a. Variable OH1 (50 × 5 × $4.15)........................ $1,037.

50
Variable OH2 (50 × $13.60)............................ 680.00
Variable OH3 (70 × $5.90).............................. 413.
00
Total incremental variable overhead.............. $2,130.
50

b. Variable OH1 (50 × 5 × $4.15)........................ $1,037.

50
Variable OH2 (25 × $13.60)............................ 340.00
Variable OH3 (230 × $5.90)............................ 1,357.
00
Total incremental variable overhead.............. $2,734.
50

c. The two scenarios in (a) and (b) differ in terms of the

activities to be undertaken. Scenario (a) involves a
large amount of seeding activity and relatively little
planting activity. Scenario (b) involves considerably
less seeding activity, but a great deal more planting
activity. An activity-based costing system accounts for
the different costs in projects involving different mixes
of activity.

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CASE 6-48 (45 MINUTES)
1. Scatter diagram:

Administrative
cost

$25,0
00

$20,0
00
2
• .
Visually-
$15,0 fitted
• curviline
00 ar cost
line
•
•• 4
$10,0 •
• • .
Visually-
00 • fitted
• semivaria
• ble cost
line
$5,00
•
0

500 1,000 1,500 2,000 Patient

3 Relevant load
. range

2. See scatter diagram for requirement (1).

through

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4.

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CASE 6-48 (CONTINUED)

5. Fixed cost = $7,000

− $7,000
$10,600
Variable =
costperpatient = $3.00
−0
1,200

6. Administrative cost = $7,000 + $3.00X, where X denotes

the number of patients.

7. Cost predictions using visually-fit cost lines:

Patient Cost
Load Predicti
on

750. $9,30
0
350 5,50
……. 0

It makes no difference which visually-fit cost line is used to

make the cost prediction for 750 patients. The
semivariable approximation is very accurate at this patient
load, which is near the middle of the relevant range.
However, for a patient load of 350 patients, the visually-fit
curvilinear cost line yields a much more accurate
prediction.

CASE 6-49 (50 MINUTES)

1. High-low method:

Variable administrative cost per patient =

− $4,100
$16,100
= $10
− 300
1,500

Total cost at 1,500 patients................................ $16,100

Variable cost at 1,500 patients...........................  15,000
Fixed cost per month.......................................... $ 1,100

Cost formula:

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6-76 Solutions Manual
 Total monthly administrative cost = $1,100 + $10X, where
X denotes the number of patients for the month.

The variable cost per patient is $10.

2. In the electronic version of the solutions manual, press

the CTRL key and click on the following link: Build a
Spreadsheet

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CASE 6-49 (CONTINUED)

3. Memorandum
Date: Today

To: Jeffrey Mahoney, Administrator

From I.M. Student

:

Subje Comparison of cost estimates for clinic

ct: administrative costs

Three alternative cost-estimation methods were used to

estimate the pediatric clinic's administrative cost behavior.
The results of these three approaches (in formula form)
are shown below. In each formula, X denotes the number
of patients in a month.

(a Least-squares regression method:

)

Total monthly administrative cost = $2,671 + $7.81X

(b High-low method:
)

Total monthly administrative cost = $1,100 + $10X

(c Visual-fit method:
)

Total monthly administrative cost = $7,000 + $3.00X

These cost estimates differ very significantly. The

activity level in the clinic during its first year of operation
fluctuated greatly. This fluctuation is not expected in the
future; patient loads in the range of 600 to 1,200 patients
per month are anticipated.

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 The cost estimates differ so greatly because two of
the methods (least-squares and high-low) used data from
outside the relevant range of activity. The clinic's
administrative cost behavior appears from the scatter
diagram to be curvilinear over the entire range. The cost
behavior pattern exhibits very low costs in the range of
activity below the relevant range and very high costs in
the activity range above the relevant range. Since the
regression and high-low estimates are so heavily
influenced by observations outside the relevant range,
they do not provide the best estimate in this case of how
administrative costs are likely to behave within the
relevant range. In this instance, the visually-fitted cost line
probably provides the best estimate.

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 CASE 6-49 (CONTINUED)

Another possible approach would be to use least-

squares regression, but restrict the data to those
observations within the relevant range. However, only a
handful of observations would remain to include in the
analysis.

My overall recommendation is to use the visually-

fitted cost line as the best estimate until the clinic has
operated for its second year. Then I would recommend a
new cost analysis using least-squares regression on all of
the data from the relevant range of activity.

4. It is very inappropriate for the hospital administrator to

manipulate the cost information supplied by the director of
cost management in order to push his own agenda before
the board of trustees. It is the board's legitimate role to
decide whether or not to establish and continue operations
in the clinic. In making decisions about the clinic, the
board should have the best information possible, including
the controller's best estimate as to how administrative
costs will behave.

Megan McDonough, the hospital’s director of cost

management, has a professional obligation to provide her
best professional judgment to the board of trustees. The
standards of ethical conduct for management accountants
include the following requirements concerning objectivity:

(a Communicate information fairly and objectively.

)

(b Disclose fully all relevant information that could

) reasonably be expected to influence an intended user's
understanding of the reports, comments, and
recommendations presented.

McDonough should insist that the best and most

appropriate estimate of the clinic's administrative cost
behavior be presented to the board.

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CASE 6-49 (CONTINUED)

The following alternative approach to calculating the

regression parameters is not a requirement in the problem.

Least-squares regression using manual calculations

(a Tabulation of data:
)
Dependen Indepen
t Variable dent
(cost in Variable
hundreds (patient
Month ) s in X2 XY
Y hundred
s)
X
January........... 60 4 16 240
February......... 70 5 25 350
March............. 139 14 196 1,946
April............... 92 9 81 828
May................ 119 13 169 1,547
June................ 100 10 100 1,000
July................. 94 7 49 658
August............ 41 3 9 123
September...... 102 11 121 1,122
October..........    15   225   2,415
161
November....... 83 6 36 498
December....... 11 12 144 1,332
1
Total............... 1,17 109 1,171 12,059
2

(b Calculation of parameters:
)
(∑Y)(∑X2)−(∑X)(∑XY)
a =
n(∑X2)−(∑X)(∑X)
1,71)−(109)(12,0
(1,172)(1 59)
= = 26.707(rounded)
(12)(1,17 −(109)(109)
)1

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 n(∑ XY)− (∑ X)(∑Y)
b =
n(∑ X2 ) − (∑ X)(∑ X)
(12)(12,0
95)−(109)(1,1
27)
= =7.812(rounded)
(12)(1,17 −(109)(109)
)1

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CASE 6-49 (CONTINUED)

(c Cost behavior in formula form (with rounded

) parameters):*

Total monthly administrative cost = $2,671 + $7.81X,

where X denotes the number of patients for the month.

*When interpreting the regression parameters,

remember that both the cost and patient data were
transformed to hundreds. Thus, the 26.707 intercept
parameter (a) is in terms of hundreds of dollars of
cost, or $2,671 (rounded). The 7.812 slope parameter
(b) is in terms of hundreds of dollars of cost per
hundred patients, or $781 (rounded) per hundred
patients. This amount is equivalent to $7.81 per
patient.

(d The variable cost per patient is $7.81, as explained

) above.

FOCUS ON ETHICS (See page 253 in the text.)

Is direct labor a variable cost? Is it ethical to “tap and

zap” employees?

Direct labor is a variable cost if management is both able

and willing to continually adjust the workforce to meet
short-term needs. Many observers would argue that it is
ethical to “tap and zap” employees provided that those
employees are appropriately notified about and
compensated for the added risks and uncertainties
surrounding their employment. For example, hourly rates
for temporary employees may be set somewhat higher than
for permanent employees to account for temps not having
paid vacation, health benefits, and other standard
compensation features of the modern workforce. For many
cyclical industries (e.g., recreational resorts) such labor
flexibility is essential. For industries with more stable labor
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 levels, there are legal limitations, which seek to prevent
classifying labor incorrectly as “temporary.” The deliberate
misclassification of employees to avoid appropriate
compensation is unethical, and in certain circumstances may
be illegal.

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