EXERCISE 6-33 (45 MINUTES)
1.
Variable utility cost per hour
=
$3,800  $2,600
700  400
= $4.00
Total utility cost at 700 hours .....................................................................
Variable utility cost at 700 hours ($4.00  700 hours) ..............................
Fixed cost per month ..................................................................................
$ 3,800
2,800
$ 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
Cost at
Difference
600 hours .......................................................................
0 hours .......................................................................
600 hours .......................................................................
Variable cost per hour = $2,500/600 hr. = $4.17 (rounded)
$3,400
900
$2,500
EXERCISE 6-33 (CONTINUED)
Scatter diagram and visually-fit line:
Utility cost
per month
5000
4000
3000
2000
1000
0
0
100
200
300
400
500
600
700
Hours of
operation
EXERCISE 6-33 (CONTINUED)
3.
Estimation of variable- and fixed-cost components of cost behavior using leastsquares regression:
The electronic version of the Solutions Manual “BUILD A SPREADSHEET
SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website:
www.mhhe.com/hilton8e.
4.
Cost predictions at 300 hours of operation:
(a)
High-low method:
Utility cost =
(b)
$1,000 + ($4.00)(300) = $2,200
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:
The electronic version of the Solutions Manual “BUILD A SPREADSHEET
SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website:
www.mhhe.com/hilton8e.
The R2 is .9518.
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:
Dependent
Variable
(cost)
Y
3,240
3,400
3,800
3,200
2,700
2,600
18,940
Month
January .......................
February .....................
March ..........................
April.............................
May ..............................
June ............................
Total ............................
Independent
Variable
(hours)
X
550
600
700
500
450
400
3,200
X2
302,500
360,000
490,000
250,000
202,500
160,000
1,765,000
XY
1,782,000
2,040,000
2,660,000
1,600,000
1,215,000
1,040,000
10,337,000
(b) Calculation of parameters:
a =
( Y )( X 2 )  (  X )( XY )
n(  X 2 )  (  X )( X )
= (18,940)(1,765,000)  (3,200)(10,337,000)
 1,002
(6)(1,765,000)  (3,200)(3,200)
b = n(  XY)  (  X)( Y)
n(  X 2 )  (  X)(  X)
=
(c)
(6)(10,337,000)  (3,200)(18,940)
 4.04
(6)(1,765,000)  (3,200)(3,200)
Cost formula:
Monthly utility cost
= $1,002 + $4.04X, where X denotes hours of operation.
Variable utility cost
= $4.04 per hour of operation
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.
PROBLEM 6-37 (25 MINUTES)
1.
Variable maintenance cost per hour of service
=
$4,710  $2,990
525  310
= $8.00
Total maintenance cost at 310 hours of service .......................................
Variable maintenance cost at 310 hours of service (310 hr.  $8.00) ......
Fixed maintenance cost per month ............................................................
$2,990
2,480
$ 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)] ...........................................
Fixed cost per hour at 610 hours of activity ($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).
$8.00
$ .84*
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:
Total royalty cost……………………….
Less: Variable cost at $65 per ton…..
Fixed royalty cost………………………
2.
June
(2,700 tons)
December
(1,400 tons)
$224,500
175,500
$ 49,000
$140,000
91,000
$ 49,000
Total cost for 1,700 tons:
Depreciation…………………………………………... $ 30,000
Charitable contributions…………………………….
---Mining labor/fringe benefits at $225 per ton…….
382,500
Royalties:
Variable at $65 per ton………………………….. 110,500
Fixed………………………………………………..
49,000
Trucking and hauling………………………………..
280,000
Total……………………………………………….. $852,000
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.
its
A committed fixed cost results from an entity’s ownership or use of facilities and
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.
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.
Beginning inventory ............................................................
+ Purchases .........................................................................
– Ending inventory ..............................................................
Indirect material used ..........................................................
5.
April
$1,300
5,900
(1,350)
$5,850
High-low method:
Variable cost per machine hour
=
differencein cost levels
differencein activity levels
=
$5,850  $4,200 $1,650

 $5.50 per machine hour
1,000  700
300
PROBLEM 6-43 (CONTINUED)
Fixed cost per month:
August
$1,000
6,200
(3,000)
$4,200
Total cost at 1,000 hours ...............................................................................
Variable cost at 1,000 hours
($5.50  1,000) .........................................................................................
Fixed cost .......................................................................................................
$5,850
5,500
$ 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.
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 ..............................................................................
Labor (.6 hr. @ $11/hr.) ..........................................................................
Variable overhead (.6 hr. @ $4/hr.)........................................................
Total ..................................................................................................
$14.00
6.60
2.40
$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 ..............................................................................
Labor (.6 hr. @ $11/hr.) ..........................................................................
Variable overhead (.6 hr. @ $4/hr.)........................................................
Fixed overhead (.6 hr. @ $10/hr.)* .........................................................
Total ..................................................................................................
$14.00
6.60
2.40
6.00
$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.
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.
CASE 6-48 (45 MINUTES)
1.
Scatter diagram:
Administrative cost
$25,000
$20,000

$15,000

$10,000
$5,000








4.
Visually-fitted
semivariable
cost line

500
1,000
1,500
3. Relevant range
2. through 4.
2.
Visually-fitted
curvilinear
cost line
See scatter diagram for requirement (1).
2,000
Patient load
CASE 6-48 (CONTINUED)
5.
Fixed cost = $7,000
Variable cost per patient 
$10,600  $7,000
 $3.00
1,200  0
6.
Administrative cost = $7,000 + $3.00X, where X denotes the number of patients.
7.
Cost predictions using visually-fit cost lines:
Patient
Load
Cost
Prediction
750 ....................
$9,300
350…….
5,500
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 =
$16,100  $4,100
 $10
1,500  300
Total cost at 1,500 patients ...........................................................................
Variable cost at 1,500 patients ......................................................................
Fixed cost per month ....................................................................................
$16,100
15,000
$ 1,100
Cost formula:
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.
The electronic version of the Solutions Manual “BUILD A SPREADSHEET
SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website:
www.mhhe.com/hilton8e.
CASE 6-49 (CONTINUED)
3.
Memorandum
Date:
Today
To:
Jeffrey Mahoney, Administrator
From:
I.M. Student
Subject: Comparison of cost estimates for clinic 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.
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.
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.
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:
Dependent
Variable
(cost in
hundreds)
Y
60
70
139
92
119
100
94
41
102
161
83
111
1,172
Month
January .......................
February .....................
March ..........................
April.............................
May ..............................
June ............................
July .............................
August ........................
September ..................
October .......................
November ...................
December ...................
Total ............................
Independent
Variable
(patients in
hundreds)
X
4
5
14
9
13
10
7
3
11
15
6
12
109
X2
16
25
196
81
169
100
49
9
121
225
36
144
1,171
XY
240
350
1,946
828
1,547
1,000
658
123
1,122
2,415
498
1,332
12,059
(b) Calculation of parameters:
( Y )( X 2 )  (  X )( XY )
a =
n(  X 2 )  (  X )( X )
=
b =
=
(1,172)(1,171)  (109)(12,059)
 26.707 (rounded)
(12)(1,171)  (109)(109)
n(  XY)  (  X)( Y)
n(  X 2 )  (  X)(  X)
(12)(12,059)  (109)(1,172)
 7.812 (rounded)
(12)(1,171)  (109)(109)
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 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.