Activity Analysis, Cost Behavior and Cost Estimation Solution

CHAPTER 6

Activity Analysis, Cost Behavior, and Cost Estimation ANSWERS TO REVIEW QUESTIONS 6-1

Cost behavior patterns are important in t he process of m aking 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-

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 for ecast of co st at a part icular level of ac tivity. 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-!

a. "otel# $e rcentage of r ooms oc cupied or t he nu mber o f occ upancy-days, wh ere an occupancy-day is defined as one room occupied for one day. b. "ospital# $ati ent-days, wher e a patie nt-day is defined as a one-day stay by one patient. c. Computer manufacturer# %umber of computers manufactured, throughput, engineering specifications, engineering change orders, or number of parts in the finished product. d. Computer sales store# &ales revenue. e. Computer repair service# 'epair calls or hours of repair service. f. $ublic accounting firm# "ours of auditing service provided by each classification of personnel (partner, manager, supervisor, senior accountant, and staff accountant).

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6- 

6.*

+raphs of the cost behavior patterns are as follows#

Cost

Cost

ctivity

ctivity

a. ariable

b&. tep-variable

Cost

Cost

ctivity Cost

cF.ixed

C os t

ctivity e.&emivariable McGraw-Hill/Irwin Inc. 6!"

ctivity d&.tep-fixed

ctivity f.Curvili2009 nearThe McGraw-Hill Companies, Solutions Manual

6-

s the level of a ctivity (or c ost driver) increases, total fixed cost remains constant. "owever, the fixed cost per unit of activity declines as activity increases.

6-6

 manufacturer/s cost of s upervising production might be a s tep-fixed cost, because one supervisor is needed for each shift. 0ach shift can accommodate a certain range of production activity when activity exceeds that range, a new shift must be added. 2hen the new shift is added, a new production supervisor must be employed. 3his new position results in a 4ump in the step-fixed cost to a higher level.

6-5

s the lev el of activity (or cos t driver) increases, total variable cos t increases

6-

proportionately and the variable cost per unit remains constant. a.  semivariable cost behavior pattern can be used to approximate a step-variable cost as shown in the following graph# Cost &emivariable approximation

&tep-variable cost ctivity b.  semivariable cost behavior pattern can be used to approximate a curvilinear cost as shown in the following graph# Cost

Curvilinear cost

&emivariable approximation ctivity McGraw-Hill/Irwin Inc. Managerial Accounting, 8/e


6- #

6-7

(a) nnual co st of maintaining an in terstate hig hway# committed cost. (8nce the highway has been built, it must be maintained. 3he transportation author ities are largely committed to spending the necessary funds to maintain the highway ade9uately.) (b) :ngredients in a breakfast cereal# engineered cost. (c) dvertising for a credit card company# discretionary cost. (d) ;epreciation on an insurance company/s computer# committed cost. (e) Charitable donation s# discretionary cost. (f) 'esearch and development# discretionary cost.

6-1<

3he co st analyst sho uld respond by po inting ou t that in m ost cases a co st behavior pattern should be limited to the relevant range of activity. 2hen 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. 2ithin the relevant range, the firm/s utility cost can be approximated reasonably closely by a semivariable cost behavior pattern. "owever, outside that range (including an activity level of =ero), the semivariable cost behavior pattern should not be used as an approximation of the utility cost.

6-11

 learning cu rve show s how ave rage lab or tim e per uni t of pro duction chan ges as cumulative output changes. :n many production processes, as production activity increases and learning takes place, there is a significant reduction in the amount of labor time re9uired per unit. 3he 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.

6-1

ppropriate ind ependent var iables for sev eral tas ks are as foll ows# a. "andling materials at a loading dock# 2eight of materials handled. b. 'egistering vehicles at a county motor vehi cle offi ce# %umbe r of regis trations processed. c. $icking oranges# olume or weight of oranges picked. d. :nspecting computer components in an elec tronics firm# %umber of com ponents inspected.

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6-1!

n out lier is a data poi nt tha t fall s far awa y from th e othe r poin ts in the sca tter diagram and is not representative of the data. 8ne possible cause of an outlier is simply a mistake in recording the data. nother 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. 8utliers should be eliminated from a data set upon which cost estimates are based.

6-1*

Fixed costs are often allocated on a per unit-of-activity basis. For example, fixe d manufacturing-overhead costs, such as depreciation, may be allocated to units of production. s a result, such costs may appear to be variable in the cost records. ;iscretionary costs often are budgeted in a manner that makes them appear variable.  cost such as charitable donations, for example, may be fixed once management decides on the level of donations to be made. :f 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. n experienced analyst should be wary of allocated and discretionary costs and take steps to learn how the amounts are determined.

6-1

:n the fi rst st ep of the vi sual-fit met hod of co st est imation, dat a poin ts are pl otted on graph paper to form a scatter diagram. 3hen a line is drawn through the scatter diagram in an attempt to minimi=e the distance between the line and the plotted points. 3he 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. 3he method is easy to use and to explain to others and provides a useful view of the overall cost behavior pattern. 3he visual-fit method also enables an experienced cost analyst to spot outliers in the data. 3he primary drawback of the visual-fit method is its lack of ob4ectivity. 3wo cost analysts may draw two different visually-fitted cost lines.

6-16

3he chief drawback of the high-low method of cost estimation is that it uses only two data points. 3he rest of the data are ignored by the method. n outlier can cause a significant problem when the high-low metho d is used if one of the two data points happens to be an outlier. :n 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.

6-15

3he term least squares in the least-s9uares regression method of cost estimation refers to the process of minimi=ing the sum of the s9uares of the vertical distances between the data and the regression line.



6- %

6-1

 least-s9uares regression line may be expressed in e9uation form as follows# Y = a + bX

:n this e9uation, 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. 3he intercept of the line on the vertical axis is denoted by a, and the slope of the line is denoted by b. 2ithin 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. 6-17

:n simp le reg ression there is a singl e inde pendent varia ble. :n multiple reg ression there are two or more independent variables.

6-<

$otential cos t driv ers in the cr uise in dustry in clude the fo llowing# number of passengers, number of passenger miles traveled, number of port calls, cruise ship tonnage (i.e., ship si=e), and number of crew members, among others.

6-1

 particular least-s9uares regression line may be evaluated on the basis of economic plausibility or goodness of fit. 3he cost analyst should always evaluate a regression line from the perspective of economic plausibility. ;oes the regression line make economic sense> :s it intuitively plausible> n experienced cost analyst should have a good feel for whether the regression line looks reasonable. &tatistical methods can also be used to determine how well a regression line fits the data upon which it is based. 3his method is referred to as assessing the goodness of fit of the regression.  commonly used measure of goodness of fit is the coefficient of determination, which is described in the appendix at the end of the chapter. 3he coefficient of determination is also denoted by R2.

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SO'UTIONS TO E(ERCISES 0?0'C:&0 6- (1 @:%A30&) 1. Co:stet m $roduction crew# ,!!
Cost per Broadcast "our ugust 8ctober 1!.<< pe r hr. 1!.<< per hr. 1*.6! per hr.E  . per hr.E

E'ounded. .

;ecember c ost p redictions#

$roduction crew (**< 1!.<< per hr.).............................................. &upervisory employees......................................................................

,5< 6,<<<

!. Cost per Broadcast "our Cost :tem $roduc tion crew..................................... ..... ......... ..... &upervisory employees (6,<<
in per ;ecember 1!.<< hr. 1!.6* per hr.E

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0?0'C:&0 6-! (*< @:%A30&) 1.

Cost of food#

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0?0'C:&0 6-! (C8%3:%A0;) .

Cost of salaries and fringe benefits for administrative staff#



6- +

0?0'C:&0 6-! (C8%3:%A0;) !.

aboratory costs#

Cost per month <,<<< 3otal cost 5<,<<<

6<,<<<

<,<<<

*<,<<<

!<,<<<

<,<<<

1<,<<<

$atient days 1,<<<

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0?0'C:&0 6-! (C8%3:%A0;) *.

Cost of utilities#



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0?0'C:&0 6-! (C8%3:%A0;) .

%ursing costs#

Cost per month 15,<< 1,<<< 3otal cost

1,<< 1<,<<< 5,<< ,<<< ,<<

$atient days <<

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0?0'C:&0 6-* (1 @:%A30&) 1.

.

a.

Fixed

b.

ariable

c.

ariable

d.

Fixed

e.

&emivariable (or mixed)

$roduction cost per month G  !5,<<
.!< G 1.< H . H .

0?0'C:&0 6- (1 @:%A30&) 1.

ariable maintenance cost per tour mile

G (1,5< r-16,<
r denotes the real, Bra=ilKs national currency.

3otal maintenance cost at 1,<<< miles...................................................... ariable maintenance cost at 1,<<< miles (.1 r 1,<<<)..................... Fixed maintenance cost per month.............................................. .............. .

16,<< r 1,<
Cost formula# 3otal maintenance cost per month G 1,<<
!.

Cost prediction at the !*,<<<-mile activity level# @aintenance cost


G

1,<<< r H (.1r)(!*,<<<)

G

17,

6- #

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T.E E'ECTRONIC VERSION O/ T.E SO'UTIONS 0ANU A' 1BUI'2 A S3REA2S.EET SO'UTIONS4 IS AVAI'AB'E ON 5OUR INSTRUCTORS C2 AN2 ON T.E .I'TON, *E WEBSITE6 WWW-0..E-CO07.I'TON*E-

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ctual 1,7< ,6<< !,<<< *,<

0stimated ,<< ,6<< !,<<< !,6<<

a. b. c. d.

<,<<< miles.................................................................. *<,<<< miles.................................................................. 6<,<<< miles.................................................................. 7<,<<< miles..................................................................

(a)

3he approximation is very accurate in the range *<,<<< to 6<,<<< miles per month.

(b)

3he approximation is less accurate in the extremes of the longer range, <,<<< to 7<,<<< miles.

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0?0'C:&0 6-5 (!< @:%A30&) 1.

&catter dia gram a nd vi sually-fitted lin e#

Cost of diagnostic testing •

<,<<<

• •

*<,<<< •

!<,<<<

• •

•• •

•

•

•

<,<<<

1<,<<<

3ests <<


1,<<<

1,<<

,<<<

,<<

!,<<<

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0?0'C:&0 6-5 (C8%3:%A0;) .

3he re9uirement asks for an estimate based on the visually-fit cost line. 3herefore, answers will vary on this re9uirement because of variation in the visually-fitted lines. Based on the preceding plot# @onthly fixed cost............................................................................................. ariable cost per dia gnostic test.................................................................... .

1*,<<<  1<.6E

ECalculation of variable cost# 3otal cost at 3otal cost at ;ifference#

!,6<< tests........................................... < tests........................................... !,6<< tests...........................................

ariable co st p er diagnostic t est

G

,<<< 1*,<<< !,<<<

C!,<<< !,6<<

G 1<.6I I

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0?0'C:&0 6- (!< @:%A30&) nswers will vary widely, depending on the company and costs selected. &ome examples of typical manufacturing costs follow. ;irect material# variable 0lectricity# variable ;epreciation on plant and e9uipment# fixed $lant managerKs salary# fixed $roperty taxes# fixed

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0?0'C:&0 6-7 (1 @:%A30&) 1.

ariable cost per pint of applesauce produced G C5,!<< 1!,<<<

C66,!<< 6!,<<<

C.1<

3otal cos t at 1! ,<<< pin ts......................................................................... ariable cost at 1!,<<< pints (1!,<<< .1< per pint)............................................................... ....

5,!<<

Fixed cost............................................................................................ ........

6<,<<<

1,!<<

Cost e9uation# 3otal energy cost G 6<,<<< H .1
Cost prediction whe n 5,<<< pints o f applesauce a re produced 0nergy cost G 6<,<<< H (.1<)(5,<<<) G 65,<<



6- )

0?0'C:&0 6-!< (!< @:%A30&) 1.

&catter di agram an d vi sually-fitted li ne#

@onthly energy cost

7<,<<< •

5,<<<

•

• • •

• •• •

•

•

•

6<,<<<

*,<<<

!<,<<<

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6<,<<<

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Solutions Manual

0?0'C:&0 6-!< (C8%3:%A0;) .

nswers will vary on th is re9uirement because of variation in th e visually-fitted lines. Based on the preceding plot, the cost prediction at 5,<<< pounds is# 0nergy cost G 65,<<

!.

3he Luly cost observation at th e 1<,<<<-pint activity level appears to be a n outlier. 3he cost analyst should check the observation data for accuracy. :f the data are accurate, the outlier should be ignored in making cost predictions.

0?0'C:&0 6-!1 (1< @:%A30&) 1.

(a) (b)

verage time for * satellites.............................................................. verage ti me fo r  sate llites........................................................... ...

17 hours 1< hou rs

.

(a) (b)

3otal time for * satellites (17 hr. ? *).............................................. 3otal time for  satellites (1< hr. ? )..............................................

5< hours 1,<< hours

!.

earning curves indicate how labor costs will change as the company gains experience with the production process. &ince labor time and costs must be predicted both for budgeting and for setting cost standards, the learning curve is a valuable tool.



6- +

0?0'C:&0 6-! (1 @:%A30&)

@onthly audit cost 1<<,<<< 3otal cost when 1<< audits are performed in a month# 5,<< G 1<,<<< H (6) (1<<) <,<<<

•

6<,<<<

*<,<<<

<,<<< Fixed cost per month# 1<,<<<

<

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0?0'C:&0 6-!! (* @:%A30&) 1.

ariable utility cost per hour

G

C!,<< 5<<

C,6<< *<<

G *.<<

3otal utility cost at 5<< hours........................................................... ........... ariable utility cost at 5<< hours (*.<< 5<< hours)......................... ...... Fixed cost per month...................................................................................

 !,<< ,<<  1,<<<

Cost formula# @onthly utility cost G 1,<<< H *.<< X , where X denotes hours of operation. .

ariable-cost es timate ba sed on t he sca tter diag ram on t he nex t page # Cost a t Cost at ;ifference

6<< h ours ....................................................................... < hours ...................................................................... . 6<< hours .......................................................................

!,*<< 7<< ,<<

ariable cost per hour G ,<


6- "

0?0'C:&0 6-!! (C8%3:%A0;) &catter diagram and visually-fit line# Atility cost per month

"ours of operation

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0?0'C:&0 6-!! (C8%3:%A0;)

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0stimation of variable- and fixed-cost components of cost behavior using leasts9uares regression# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.

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Cost predictions a t !<< ho urs of operation# (a)

"igh-low m ethod# Atility cost

(b)

G

1,<<< H (*.<<)(!<<) G ,<<

isually-fitted line# Atility cost

G ,17<

3his cost prediction was simply read directly from the visually-fitted cost line. 3his prediction will vary because of variations in the visually-fitted lines. (c)

'egression# Atility cost G 1,<< H (*.<*)(!<<) G ,1*

.

Calculation of ' # 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# 222.@""0.C8@D":38%0. 3he ' is .71.



6- "#

0?0'C:&0 6-!! (C8%3:%A0;) 3he following alternative approach to calculating the regression parameters is not a re9uirement in the problem. east-s9uare regression using manual calculations# (a)

3abulation of data# ;ependent ariable (cost) Y !,*< !,*<< !,<< !,<< ,5<< ,6<< 1,7*<

@onth Lanuary....................... February...................... @arch.......................... pril............................. @ay.............................. Lune............................ 3otal............................

:ndependent ariable (hours) X < 6<< 5<< << *< *<< !,<<

X XY !<,<< 1,5,<<< !6<,<<< ,<*<,<<< *7<,<<< ,66<,<<< <,<<< 1,6<<,<<< <,<< 1,1,<<< 16<,<<< 1,<*<,<<< 1,56,<<< 1<,!!5,<<<

(b) Calculation of parameters# a G

(

Y )(

X

n(

X 



)

)

(

X )( X )(

(

G (1,7*<)(1,56,<<<) (6)(1,56,<<<)

b G

G (c)

(!,<<)(!,<<)

XY)

(

X)(

Y)

n(



(

X)(

X)

(6)(1<,!!5,<<<) (6)(1,56,<<<)

X)

( !,<<)(1<,!!5,<<<)

n(

X )

XY )

(!,<<)(1,7*<) (!,<<)(!,<<)

1,<<

*.<*

Cost f ormula# @onthly utility cost

G 1,<< H *.<* X, where X denotes hours of operation.

ariable utility cost

G *.<* per hour of operation

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0?0'C:&0 6-!* (* @:%A30&) 1.

3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.

.


3he following alternative approach to calculating the regression parameters and '  is not a re9uirement in the problem. east-s9uare regression using manual calculations# (a)

3abulation of data#

@onth Luly.............................. ugust........................ &eptember.................. 8ctober....................... %ovember................... ;ecember.................... 3otal............................


;ependent ariable (cost in thousands) Y * * 5 6< * 5 !!6

:ndependent ariable (thousands of passengers) X 16 15 16 1 1 15 77

X 6 7 6 !*  7 1,6!7

XY 6* 71 71 1,<< 1< 767 ,!


6- "%

0?0'C:&0 6-!* (C8%3:%A0;) (b) Calculation of parameters# a G

G

(

Y )( n(

X X





)

)

( (

X )( X )(

XY ) X)

(!!6)(1,6!7) (77)(,!) (6)(1,6!7) (77)(77)

7 (rounded)

n( ∑ XY) − ( ∑ X)( ∑ Y) b G n( ∑ X 2 ) − ( ∑ X)( ∑ X) G (c)

(6)(,!) (6)(1,6!7)

(77)(!!6)

1.6!6 (rounded)

(77)(77)

Cost f ormula# @onthly cost of flight service G 7,<<< H 1,6!6?, where ? denotes thousands of passengers.

Calculation and interpretation of R using manual calculations# (a)

Formula for c alculation# R

where

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

= 1−

∑(Y − Y /)  ∑(Y −Y ) 

Y

denotes the observed value of the dependent 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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0?0'C:&0 6-!* (C8%3:%A0;) (b)

3abulation o f data#E

$redicted Cost (in thousands) Based on 'egression  I

L@onth uly................. ugust............ &eptember. . . . . 8ctober......... . %ovember. . . . . . ;ecember....... 3otal................ EY' Y

Y* * 5 6< * 5

1X6 15 16 1 1 15

ine .15Y' 6 6.1 .156 .** !.*< 6.1

O( Y1.J!Y'!) P 5.7<5 !.!5 .*<7 .1 .
Y

 I

O(Y*J.<<< ) P *.<<< 1.<<< 16.<<< *.<<< 1.<<< !<.<<<

G (7,<<< H 1,6!6 X)D1,<<< G QD6 G 6

I

'ounded.

(c)

Calculation of R# R G 1 J

(d)

1.5! G .*7 (rounded) !<.<<<

:nterpretation o f R# 3he coefficie nt of determination, R, is a measure of the goodness of fit of the least-s9uares regression line. n R2 of .*7 means that *7R of the variability of the dependent variable about its mean is explained by the variability of the independent variable about its mean. 3he higher the R, the better the regression line fits the data. 3he interpretation of a high R is that the independent variable is a good predictor of the behavior of the dependent variable. :n cost estimation, a hig h R means that the cost analyst can be relatively confident in the cost predictions based on the estimated-cost behavior pattern.



6- ")

SO'UTIONS TO 3ROB'E0S $'8B0@ 6-! (< @:%A30&) 1.

h

.

a

7.

d

.

i

6.

g

1<. k

!.

f

5.

c

11.

*.

e

.

b

l

%ote that 4 was not used. $'8B0@ 6-!6 (1 @:%A30&) n appropriate activity measure for the school would be hours of instruction. 3he costs are classified as follows# 1.

ariable

6.

.

&emivariable(ormixed)E

!.

Fixed

.

Fixed

*.

Fixed

7.

&emivariable(om r ixed)

.

Fixed

5.

ariable Fixed

E3he fixed-cost component is the salary of the school/s repair technician. s activity increases, one would expect more repairs beyond the technician/s capability. 3his increase in repairs would result in a variable-cost component e9ual to the dealer/s repair charges.

McGraw-Hill/Irwin Inc. 6!"*


Solutions Manual

$'8B0@ 6-!5 ( @:%A30&) 1.

ariable m aintenance c ost p er h our o f s ervice

G

C*,51<



C,77<

!1<

G .<< 3otal maintenance cost at !1< hours of service........................................ ariable maintenance cost at !1< hours of service (!1< hr. .<<).......

,77< ,*<

Fixed maintenance cost per month............................................................

 1<

Cost formula# @onthly maintenance cost G 1< H .<< X, where X denotes hours of maintenance service. .

3he var iable com ponent of th e mai ntenance co st is  .<< per ho ur of service.

!.

Cost prediction at 6<< hours of activity# @aintenance cost G 1< H (.<<)(6<<) G ,!1<

*.

 ared iablceost coper st pehou r hor ur Ofro
 .<
E'ounded. 3he fixed cost per hour is a misleading amount, because it will change as the number of hours changes. For example, at << hours of maintenance service, the fixed cost per hour is 1.< (1


6- "+

$'8B0@ 6-! ( @:%A30&) 1.

&traight-line d epreciationScommitted f ixed Charitable contributionsSdiscretionary fixed @ining laborDfringe benefitsSvariable 'oyaltiesSsemivariable 3rucking and haulingSstep-fixed 3he per-ton mining laborDfringe benefit cost is constant at both volume levels presented, which is characteristic of a variable cost. !1,<<< 6<5,<<

1,*<< tons G  per ton ,5<< tons G  per ton

'oyalties have both a variable and a fixed component, making it a semivariable (mixed) cost. ariable royalty cost G difference in cost difference in tons G (*,<< J 1*<,<<<) (,5<< J 1,*<<) G *,<< 1,!<< tons G 6 per ton Fixed royalty cost#

3otal royalty costTTTTTTTTT. ess# ariable cost at 6 per tonT.. Fixed royalty costTTTTTTTTT .

Lune (,5<< tons)

;ecember (1,*<< tons)

*,<< 15,<<  * 7,<<<

1*<,<<< 71,<<<  * 7,<<<

3otal cost for 1,5<< tons# ;epreciationTTTTTTTTTTTTTTTT... Charitable contributionsTTTTTTTTTTT. @ining laborDfringe benefits at  per tonTT. 'oyalties# ariable at 6 per tonTTTTTTTTTT.. FixedTTTTTTTTTTTTTTTTTT.. 3rucking and haulingTTTTTTTTTTTT.. 3otalTTTTTTTTTTTTTTTTTT..

McGraw-Hill/Irwin Inc. 6!#

 !<,<<< ---!,<< 11<,<< *7,<<< <,<<< ,<<<


Solutions Manual

$'8B0@ 6-! (C8%3:%A0;) !.

"auling 1,*<< tons is not particularly cost effective. one @ountain 0xtraction will incur a cost of <,<<< if it needs 1,*<< tons hauled or, for that matter, 1,77 tons. 3he company would be better off if it had 1,!77 tons hauled, saving outlays of *<,<<<. :n general , with this type of cost function , effective ness is maximi= ed if a firm operates on the right-most portion of a step, 4ust prior to a 4ump in cost.

*.

 committed f ixed cost results from an e ntityKs own ership o r use of f acilities and it s basic organi=ational structure. 0xamples of such cos ts include property taxes, depreciation, rent, and management salaries. ;iscretionary fixed costs, on the other hand, arise from a decision to spend a particular amount of money for a specific purpose. 8utlays for res earch and development, adve rtising, and charitable contributions fall in this category. :n times of severe economic difficulties, a companyKs management will often try to cut discretionary fixed costs. &uch 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. 2hile itKs true that cutting expenditures on advertising or ' U ; can often have advers e long-term conse9u ences, other cuts could have even more significant negative conse9uences in the future. 3he decision to close a manufacturing facility, for example, could reduce property taxes, rent, andDor depreciation. "owever, that decision may result in a significant long-run change in operations that may be difficult to overturn when economic conditions rebound.

.

one @ountain 0xtraction u ses a calendar year for tax-reporting purposes. t yearend, it may have ample funds available and decide to make donations to charitable causes. &uch contributions are deduc tible in computing the companyKs tax obligation to the government. 3ax deductions reduce taxable income and, therefore, produce a tax savings for the firm.



6- #

$'8B0@ 6-!7 ( @:%A30&) 1.

@achine supplies# 1!,<<<

!*,<<< direct-labor hours G *.< per hour

&o for pril we have# !,<<< direct-labor hours x *.< G 1
$lant maintenance cost#

3otal costETTTTTTTT.. ess# @achine suppliesTT. ;epreciationTTTT.. $lant m aintenanceTTTT...

pril

Lune

(!,<<< hours)

(!*,<<< hours)

 61,<<< (1
 57,<<< (1!,<<<) (,<<)  5
E 0xcludes supervisory labor cost ariable maintena nce cost G differenc e in cost G (5
difference in direct-labor hours (!*,<<< J !,<<<)

G 1*,<< 11,<<< hours G 1!.< per hour Fixed maintenance cost#

3otal ma intenance cos t............................. ess# ariable cost at 1!.< per hour.... Fixed ma intenance co st............................

McGraw-Hill/Irwin Inc. 6!#"

pril (!,<<< hours)

Lune (!*,<<< hours)

,<<< !1<,<< **,<<

5

Solutions Manual

$'8B0@ 6-!7 (C8%3:%A0;) !.

@anufacturing o verhead a t  7,<< l abor hours# @achine supplies at *.< per hour........... .. .. ;epreciation..................................................... $lant maintenance cost# ariable a t 1!.< p er hour.................. .. ... Fixed........................................................... &upervisory labor............................................ 3otal.....................................................

1!,5< ,<< !7,< **,<< 1!,<<< 7!!,<<<

*.

 fi xed co st re mains co nstant wh en a ch ange oc curs i n the c ost dri ver (o r ac tivity base).  step-fixed cost, on the other hand, remains constant within a range but will change (rise or fall) when activit y falls outside that rang e. :n other words, a fixed cost is constant over a wider range of activity than a step-fixed cost.

.

:deally, the company sh ould o perate on the right-most portion of a s tep, 4u st p rior to the 4ump in cost. :n this manner, a firm receives maximum benefit (i.e., the maximum amount of activity) for the dollars invested.



6- ##

$'8B0@ 6-*< (*< @:%A30&) 1.

McGraw-Hill/Irwin Inc. 6!#$


Solutions Manual

$'8B0@ 6-*< (C8%3:%A0;) .

&ee graph for re9uirement (1).

!.

3he estimate of the fixed cost is the intercept on the vertical axis. Fixed-cost component G 7,5<< 3o estimate the variable-cost component, choose any two points on the visually-fitted cost line. For example, choose the following points# ctivity <...................................................................................... ........ ,<<<........................................................................................

Cost  7,5<< 11,5<<

3hen proceed as follows to estimate the variable-cost component# ariable cost per unit of activityE

C11,5<< − C7,5<< ,<<< − <

G

G 1.<< E$ounds (in hundreds) of e9uipment loaded or unloaded *.

Cost e9uation# 3otal material-handling cost G 7,5<< H 1.<< X, where X denotes the number pounds (in hundreds) of e9uipment loaded or unloaded during the month.



6- #%

$'8B0@ 6-*< (C8%3:%A0;) .

"igh-low method# ariable cost u nit of a ctivityE G

C1,1< − C1<,<< ,6<< − 1,<<<

G 1.< E$ounds (in hundreds) of e9uipment loaded or unloaded 3otal c ost at , 6<< un its of ac tivity............................................................... ;educt# ariable cost at ,6<< units of activity (,6<< 1.<).................. Fixed cost.......................................................................................................

1,1< !,1<  7,<<<

Cost e9uation based on high-low method# @aterial-handling cost per month G 7,<<< H 1.< X, where X denotes the number of units of activity during the month.

McGraw-Hill/Irwin Inc. 6!#&


Solutions Manual

$'8B0@ 6-*< (C8%3:%A0;) 6.

@emorandum ;ate#

3oday

3o#

$resident, %antucket @arine &upply

From#

:.@. &tudent

&ub4ect# @aterial-handling cost estimates 8n the basis of a scatter diagram and visually-fitted cost line, the @aterial-"andling ;epartment/s monthly cost behavior was estimated as follows# @aterial-handling cost per month G 7,5<< H 1.<< unit of activity  unit of activity is defined in this department as 1<< pounds of e9uipment loaded or unloaded at the loading dock. Asing the high-low method, the following cost estimate was obtained# @aterial-handling cost per month G 7,<<< H 1.< unit of activity 3he two methods yield the different because themethod high-low method fitting uses only two data points, ignoring rest ofestimates the information. 3he of visually a cost line, while sub4ective, uses all of the data available. :n this case, the two data points used by the high-low method do not appear to be representative of the entire set of data. 5.

$redicted@aterial-"andlingCosts Asing isually-Fit Cost ineE 11,7< G 7,5<< H (1.<<)(,<)

Asing "igh-ow @ethod 11,5<< G 7,<<< H (1.<)(,<)

E3his method is preferable, because it uses all of the data in developing the cost e9uation.



6- #)

$'8B0@ 6-*1 (* @:%A30&) 1.

0stimation of variable and fixed components of cost behavior using least-s9uares regression# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.

.

east-s9uares regression e9uation# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone. 3otal monthly cost G 7,7*! H .7 per unit of activity

!.

Cost prediction# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.

*.

3he cost pr edictions diff er bec ause the co st for mulas diff er und er th e thr ee cos testimation methods. 3he high-low method, while ob4ective, uses only two data points. 3en observations are excluded. 3he visual-fit method, while it uses all of the data, is somewhat sub4ective. ;ifferent analysts may draw different cost lines. east-s9uares regression is ob4ective, uses all of the data, and is a statistically sound method of estimation. 3herefore, least-s9uares regression is the preferred method of cost estimation. .

Calculation of ' # 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.

McGraw-Hill/Irwin Inc. 6!#*


Solutions Manual

3he following alternative approach to calculating the regression parameters is not a re9uirement in the problem. east-s9uares regression using manual calculations# (a)

3abulation of data#

@onth Lanuary....................... February...................... @arch.......................... pril............................. @ay.............................. Lune............................ Luly.............................. ugust........................ &eptember.................. 8ctober....................... %ovember...................

;ependent ariable (cost in thousands) Y 11.5< 11.!< 11. 1<.< 11.1< 1. 1.<< 11.*< 1.1 11.< 11.!

;oetcael.m 3 ...b..e..r........................................

11!15.!.!5

:ndependent ariable (units of activity in thousands) X 1. 1.6 1.! 1.< . .* .< 1. .6 1.1 1. 1.<*.*

X !.* .6 1.67 1.<< *.* .56 *.<< !.* 6.56 1.1 1.**

XY 1.<6< 1.<< 1*.6 1<.<< *.*< !<.1< *.<<< <.< !1.1 1.1 1!.6<

1!.756.5<

1.!67.<<

(b) Calculation of parameters# a G

G b G

G

(

Y )( n(

X X





)

)

(1!5.!5)(!5.5) (1)(!5.5)

X )( X )(

XY ) X)

(<.*)(!6.<) (<.*)(<.*)

7.7*! (rounded)

n( ∑ XY) − ( ∑ X)( ∑ Y) n( ∑ X 2 ) − ( ∑ X)( ∑ X) (1)(!6.<) (1)(!5.5)


( (

(<.*)(1!5.!5)

. (rounded)

(<.*)(<.*)


6- #+

$'8B0@ 6-*1 (C8%3:%A0;) (c)

Fixed- an d var iable-cost co mponents# @onthly fixed cost G 7,7*!E ariable cost G .7 per unit of activity (rounded) I E3he intercept parameter (a) computed above is the cost per month in thousands. I 3he slope parameter (b) calculated above is the cost in thousands of dollars per thousand units of activity. 09uivalently, it is the cost per unit of activity.

McGraw-Hill/Irwin Inc. 6!$


Solutions Manual

$'8B0@ 6-* (*< @:%A30&)



6- $

$'8B0@ 6-* (C8%3:%A0;) !.

Fixed-cost component G 1!,<< ariable-cost component# ariable cost G per golfer

C1!,< C1!,<< << <

G 1 Cost e9uation# @aintenance cost per month G 1!,<< H 1 X, where X denotes the number of golfers during the month. *.

$redictedCourse @aintenanceCosts

1< people tee off................................ 1 people tee off................................

McGraw-Hill/Irwin Inc. 6!$"

Asing Fixed Cost Coupled with &tepariable Cost Behavior $attern 1!,1< 1!,16<

Asing &emivariable Cost pproximation 1!,1 1!,16!


Solutions Manual

$'8B0@ 6-*! (! @:%A30&) 1.

3he reg ression e9ua tion/s int ercept on the ver tical axis is 17 <. :t rep resents the portion of indirect material cost that does not vary with machine hours when operating within the relevant range. 3he slope of the regression line is  per machine hour. For every machine hour,  of indirect material costs are expec ted to be incurred.

.

0stimated cost of indirect material at < machine hours of activity#  G 17< H ( G *,**<

!.

<)

&everal 9uestions should be asked# (a)

;o the observations contain any outliers, or are they all representative of normal operations>

(b)

re there any mismatched tim e periods in the dat a> r e all of the indirect material cost observations matched properly with the machine hour observations>

(c)

re there any a llocated costs in cluded in t he ind irect material cost data>

(d)

re the cost data affected by inflation>

*. Beginning inventory............................................................. H $urchases.......................................................................... J 0nding inventory............................................................... :ndirect material used.......................................................... .

pril 1,!<< ,7<< (1,!<) ,<

ugust 1,<<< 6,<< (!,<<<) *,<<

"igh-low method# ariable cost per machine hour G G


difference in cost levels difference in activity levels C,< C*,<< 1,<<< 5<<

C1,6< !<<

C.< per machinehour


6- $#

$'8B0@ 6-*! (C8%3:%A0;) Fixed cost per month# 3otal co st at 1, <<< hou rs............................................................................... ariable cost at 1,<<< hours (.< 1,<<<)......................................................................................... Fixed cost.......................................................................................................

,< ,<<  !<

09uation form# :ndirect material cost G !< H (.< 6.

machine hours)

3he regression estimate should be recommended because it uses all of the data, not 4ust two pairs of observations when developing the cost e9uation.

McGraw-Hill/Irwin Inc. 6!$$


Solutions Manual

$'8B0@ 6-** ( @:%A30&) 1. •

•

• •

&catterd iagrams# $resent, in graphic form, the relationship between costs and cost drivers via a plot of data points 'e9uire that a straight line be fit through the data points, with approxim ately the same number of data points above and below the line 0asy to use $rovide a means to easily recogni=e outliers east-s9uares regression#

• • •

Ases statistical formulas to fit a cost line through the data points :s a very ob4ective method of cost estimation that uses all the data points 'e9uires more computatio n than other cost-estim ation methods however, software programs are readily available "igh-low method#

•

•

'elies on only two data points (for the highest and lowest activity levels) in drawing conclusions about cost behavior :s considered more ob4ective than the scatter diagram however, is weaker than the scatter diagram because it relies on only two data points 3he least-s9uares regression method will typically produce the most accurate results.

.

Qes. 3he three methods produce e9uations by different means. &catter diagrams and least-s9uares regression rely on an examination of all data points. 3he scatter diagram, however, re9uires an analyst to fit a line through the points by visual approximation, or Meyeballing.N :n contrast, least-s9uares regression involves the use of statistical formulas to derive the best possible fit of the line through the points. Finally, the high-low method is based on an analysis of only two data points# the highest and the lowest activity levels.



6-

%$ $'8B0@ 6-** (C8%3:%A0;) !.

3hese am ounts represent t he f ixed and v ariable co sts as sociated wi th t he t icketing operation. Fixed cost total s !<<,<<< withi n the rele vant range, and Florida :nternational incurs . of variable cost for each ticket issued.

*.

C G 7,<<< H .<$3 C G 7,<<< H (.< x 5<,<<<) C G 1,*7,<<<

.

Qes, she d id e rr b y in cluding %o vember da ta. %ovember is no t re presentative because of the effects of the &outheas tern irlines strike. 3he month is an outlier and should be eliminated from the data set.

6.

Currently, mos t of the ai rlineKs tic kets ar e wri tten th rough res ervations per sonnel, whose wages are likely variable in nature. "eavier reliance on the :nternet means a greater investment in software, 2eb-site maintenance and development, and other similar expendit ures. 8utlays that fall in these latter categor ies are typically fixe d costs, assuming that the cost driv er is the number of tickets . 3he outcom e would parallel the experiences of a manufacturing firm that automates its processes and reduces its reliance on direct-labor personnel.

McGraw-Hill/Irwin Inc. 6!$&


Solutions Manual

$'8B0@ 6-* (*< @:%A30&) 1.

3he original me thod wa s simply the av erage overhead pe r hour for th e last 1 months and did not distinguish between fixed and variable costs. ;ana divided total overhead by total labor hours, which effectively treated all overhead as variable. 'egression 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 ,<< to 5,<< labor hours.

.

a. Based o n th e re gression a nalysis, th e va riable co st pe r pe rson fo r a co cktail party is !, calculated as follows# Food and bev erages............................................................................... abor (.6 h r. V 1 1Dhr.)........................................................................... ariable overhead (.6 hr. V *Dhr.)..................................................... .... 3otal...................................................................................... ..... ........

1*.<< 6.6< .*< !.<<

b. Based on the regression analysis, the full absorption cost per person for a cocktail party is 7, calculated as follows# Food and bev erages............................................................................... abor (.6 h r. V 1 1Dhr.)........................................................................... ariable overhead (.6 hr. V *Dhr.)..................................................... .... Fixed overhead (.6 hr. V 1
1*.<< 6.6< .*< 6.<<

3otal...................................................................................... ..... ........

7.<<

E*,<<< x 1 months G 56,<<< 56,<<
3he mi nimum bi d fo r a  <-person c ocktail pa rty wo uld be  ,5<. 3he am ount i s calculated by multiplying the variable cost per person of ! by < people. t any price above the variable cost, ;ana will be earning a contribution toward his fixed costs.



6- $)

$'8B0@ 6-* (C8%3:%A0;) *. 







8ther fa ctors th at ;ana should consider in d eveloping a bi d include th e following# 3he asse ssment of the cur rent capacity of ;anaKs business. :f the business is at capacity, other work would have to be sacrificed at some opportunity cost. nalyses of the comp etition. :f compe tition is rigorous, ;ana may not have much bargaining power.  determination of whether or not ;anaKs bid will set a precedent for lower prices. 3he reali=ation that regression analysis is based on historical data, and that any anticipated changes in the cost structure should be considered.

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$'8B0@ 6-*6 (* @:%A30&) 1. &catter diagram#

irport costs !<,<<<

,<<< •

•

<,<<<

• • • •

•

• •

•

•

1,<<<

1<,<<<

,<<<

<

<<

5<

1,<<<

1,<

1,<<

1,5< Flights

%ote# 8nly 11 data points appear, because two monthly observations were identical (February and 8ctober). McGraw-Hill/Irwin Inc. Managerial Accounting, 8/e


6- $+

$'8B0@ 6-*6 (C8%3:%A0;) .

0stimation of variable- and fixed-cost components of cost behavior using leasts9uares regression# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.

!.

Cost e9uation# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone. 3otal monthly airport cost G 11,576 H 655 X, where X denotes the number of flights

*.

Cost p rediction fo r 1 ,<< flights# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.

. Calculation of '  3he electronic version of the &olutions @anual M BA:;  &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e w ebsite# www.mhhe.comDhiltone. :nterpretation of R# 3he coefficient of determination, R, is a measure of the goodness of fit of the least-s9uares regression line. n R of . means that R of the variability of the dependent variable about its mean is explained by the variability of the independent variable about its mean. 3he higher the R, the better the regression line fits the data. 3he interpretation of a high R is that the independent variable is a good predictor of the behavior of the dependent variable. :n the countyKs cost estimation, a high R would mean that the county budget officer can be relatively confident in the cost predictions based on the estimated-cost behavior pattern. n R of . is not particularly high.

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Solutions Manual

$'8B0@ 6-*6 (C8%3:%A0;) 3he following alternative approach to calculating the regression parameters and '  is not a re9uirement in the problem. east-s9uares regression using manual calculations# (a)

3abulation of data# ;ependent ariable (cost in thousands) Y < 17 1 17 15 < 1 15 1 17 * 1 !!

@onth Lanuary....................... February...................... @arch.......................... pril............................. @ay.............................. Lune............................ Luly.............................. ugust........................ &eptember.................. 8ctober....................... %ovember................... ;ecember.................... 3otal............................

(b) Calculation of parameters# ( a G G b G

Y )( n(

X X





)

(!!)(1,5!) (1)(1,5!)

)

( (

X )( X )(

X 1** 1<< 1 176 6* 11  1 1** 1<< 176 11 1,5!

XY *< 17< 16 66 1!6 <

!1 1!  17< !!6 17 ,6

XY ) X)

(1!)(,6) (1!)(1!)

11.576 (rounded)

n( ∑ XY) − ( ∑ X)( ∑ Y) n( ∑ X 2 ) − ( ∑ X)( ∑ X) (1)(,6)

G (1)(1,5!)


:ndependent ariable (flights in hundreds) X 1 1< 7 1*  11 1 7 1 1< 1* 11 1!

(1!)(!!) (1!)(1!)

.655 (rounded)


6- %

$'8B0@ 6-*6 (C8%3:%A0;) (c)

Fixed- an d var iable-cost co mponents# @onthly fixed cost G 11,576 ariable cost G 655 per hundred flights

Calculation and interpretation of R  using manual calculations (a)

Formula for c alculation# R



= 1−

∑(Y − Y /) ∑(Y −Y )

where

McGraw-Hill/Irwin Inc. 6!%"





Y

denotes the observed value of the dependent variable (cost) at a particular activity level.

Y/

denotes the pr edicted value of th e dependent var iable (cost) based on the regression line, at a particular activity level.

Y

denotes the mean (average) observation of the dependent variable (cost).


Solutions Manual

$'8B0@ 6-*6 (C8%3:%A0;) (b)

3abulation o f data#E

@onth

Y

X

Laenburuaaryry................... F @arch............. pril................ @ay................. Lune................ Luly................. ugust............ &eptember. . . . . 8ctober......... . %ovember. . . . . . ;ecember....... 3otal................

17< 1 17 15 < 1 15 1 17 * 1

11< 7 1*  11 1 7 1 1< 1* 11

EY' Y

$redicted Cost (in thousands) Based on 'egression ine Y' O( Y! Y')PI 117..766< 15.7 1.5* 15.1 17.*! 1.71 15.7 17.7< 1.66 1.5* 17.*!

..1<<6 .<1 .151 .<* .5! .7<* .57< 1.166 .1 5.*!1 1.* 1.<17

O(Y J

Y

)PI

..1!5**< .<< .15* .* .!*< .<6 .* .<6 .15* 1.<<* .<< *.71

G (11,576 H 655 X)D1,<<< G QD1 G !!D1 G 17.*15 (rounded)

I

'ounded.

(c)

Calculation of R# R G 1 J


1.<17 G . (rounded) *.71


6- %#

SO'UTIONS TO CASES C&0 6-*5 (* @:%A30&) 1.

Cairns/ preliminary esti mate for ove rhead of 1 .<< per dire ct-labor hour doe s not distinguish between fixed and variable overhead. 3his preliminary rate is applicable only to the activity level at which it was computed (5,<<< direct-labor hours per year) and may not be used to predict total overhead at other activity levels. 3he overhead rate developed from the least-s9uares regression recogni=es the relationship between cost and volume in the data. 3he regression suggests that there is a component of the cost (,*<< per month) that is unrelat ed to total direc t-labor hours. 3his 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. 3hus, the least-s9uares regression results in a cost function with two components# fixed cost per month and variable cost per direct-l abor hour. 3his cost formula can be used to predict total overhead at any activity level within the relevant range.

.

;irect ma terial............................................................................................... ;irect labor ( ;"E 11.<< per ;")...................................................... . ariable overhead ( ;" 7. per ;")................................. ........ ...... 3otal variable cost per 1,<<< s9uare feet....................................................

!7<.<< .<< *6. *71.

E;" denotes direct-labor hours. !.

3he minimum bid should include the following incremental costs of the pro4ect.# ;irect material (!7<.<< <).......................................................... ........ .... ;irect labor (.<< <).................................................................. ........ ... ariable overhead (7. per ;"  ;" <)....................................... 8vertime premium (.< per ;"  ;" < .!)................. ........ ..... @inimum bid..................................................................................................

*.

17,<<.<< ,5<.<< ,!1.< *1.< *,75.<<

Qes, Cai rns can r ely on the fo rmula as lon g as she r ecogni=es tha t the re ar e som e shortcomings. 3he fact that least-s9uares regression estimates cost behavior increases the usefulness of rates computed from cost data. "owever, the regression is based on historical costs that may change in the future, and Cairns must assess whether the cost e9uation would need to be revised for future cost increases or decreases.

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Solutions Manual

C&0 6-*5 (C8%3:%A0;) .

a.

ariable 8"(<  *.1).......................................................... ........ ..... 1,
b.

ariable 8"(<  *.1).......................................................... ........ ..... 1,
c.

3he two scenarios in (a) and (b) differ in terms of the activities to be undertaken. &cenario (a) involves a large amount of seeding activity and relatively little planting activity. &cenario (b) involves considerably less seeding activity, but a great deal more planting activity. n activity-based costing system accounts for the different costs in pro4ects involving different mixes of activity.



6- %%

CASE &!$* 8$% 0INUTES9 1.

&catter diagram#

dministrative cost

,<<<

<,<<< . isually-fitted curvilinear cost line

1,<<<

*. isually-fitted semivariable cost line

1<,<<<

,<<<

<<

1,<<<

1,<<

,<<<

$atient load

!. 'elevant range

. through *.

McGraw-Hill/Irwin Inc. 6!%&

&ee scatter diagram for re9uirement (1).


Solutions Manual

C&0 6-* (C8%3:%A0;) .

Fixed c ost G 5,<<< -ariable cost per patient

C1<,6<< C5,<<< 1,<< < −

=

=

C!.<<

−

6.

dministrative cost G 5,<<< H !.<< X, where X denotes the number of patients.

5.

Cost predictions usin" visually-fit #ost lines# $atient oad

Cost $rediction

5<..................... 7,!<< !
"igh-low method# ariable administrative cost per patient G

C16,1<< C*,1<< 1,<< !<< −

=

C1<

−

3otal co st at 1, << pat ients........................................................................... ariable cost at 1,<< patients...................................................................... Fixed cost per month............................................................................. .......

16,1<< 1,<<<  1,1<<

Cost formula# 3otal monthly administrative cost G 1,1<< H 1


6- %)

.


C&0 6-*7 (C8%3:%A0;) !.

@emorandum ;ate#

3oday

3o#

Leffrey @ ahoney,  dministrator

From#

:.@. &tudent

&ub4ect# Comparison of cost estimates for clinic administrative costs 3hree alternative cost-estimation methods were used to estimate the pediatric clinic/s administrative cost behavior. 3he results of these three approaches (in formula form) are shown below. :n each formula, X denotes the number of patients in a month. (a)

east-s9uares regression me thod# 3otal monthly administrative cost G ,651 H 5.1X

(b) "igh-low method# 3otal monthly administrative cost G 1,1<< H 1
isual-fit method# 3otal monthly administrative cost G 5,<<< H !.<
3hese cost estimates differ very significantly. 3he activity level in the clinic during its first year of operation fluctuated greatly. 3his fluctuation is not expected in the future patient loads in the range of 6<< to 1,<< patients per month are anticipated.

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Solutions Manual

3he cost estimates differ so greatly because two of the methods (least-s9uares and high-low) used data from outside the relevant range of activity. 3he clinic/s administrative cost behavior appears from the scatter diagram to be curvilinear over the entire range. 3he 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. &ince the regression and high-low estimates are so heavily influenced by observat ions outside the relevant range, they do not provide the best estima te in this case of how administrative costs are likely to behave within the relevant range. :n this instance, the visually-fitted cost line probably provides the best estimate.



6- %+

C&0 6-*7 (C8%3:%A0;) nother possible approach would be to use least-s9uares regression, but restrict the data to those observations within the relevant range. "owever, only a handful of observations would remain to include in the analysis. @y overall recommendation is to use the visually-fitted cost line as the best estimate until the clinic has operated for its second year. 3hen : would recommend a new cost analysis using least-s9uares regression on all of the data from the relevant range of activity. *.

:t 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. :t is the board/s legitimate role to decide whether or not to establish and continue operations in the clinic. :n 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. @egan @c;onough, the hospitalKs director of cost management, has a professional obligation to provide her best professional 4udgment to the board of trustees. 3he standards of ethical conduct for management accountants include the following re9uirements concerning ob4ectivity# (a)

Communicate information fairly and ob4ectively.

(b) ;isclose fully all relevant information that could reasonably be expected to influence an intended user/s understanding of the reports, comments, and recommendations presented. @c;onough 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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Solutions Manual

C&0 6-*7 (C8%3:%A0;) 3he following alternative approach to calculating the regression parameters is not a re9uirement in the problem. east-s9uares regression using manual calculations (a)

3abulation of data# ;ependent ariable (cost in hundreds) Y 6< 5< 1!7 7 117 1<< 7* *1 1< 161

@onth Lanuary....................... February...................... @arch.......................... pril............................. @ay.............................. Lune............................ Luly.............................. ugust........................ &eptember.................. 8ctober....................... %eocveem mbbeerr....................................... ; 3otal............................

:ndependent ariable (patients in hundreds) X *  1* 7 1! 1< 5 ! 11 1

111! 1,15

(b) Calculation of parameters# ( a G G b G

G

Y )( n(

1 6 1<7

X X





(1,15)(1,151) (1)(1,151)

( (

X )( X )(

XY *< !< 1,7*6  1,*5 1,<<< 6 1! 1,1 ,*1

1** !6 1,151

1,!! *7 1,<7

XY ) X)

(1<7)(1,<7) (1<7)(1<7)

6.5<5 (rounded)

n( ∑ XY) − ( ∑ X)( ∑ Y) n( ∑ X 2 ) − ( ∑ X)( ∑ X) (1)(1,<7) (1)(1,151)


)

)

X 16  176 1 167 1<< *7 7 11 

(1<7)(1,15)

5.1 (rounded)

(1<7)(1<7)


6- &

C&0 6-*7 (C8%3:%A0;) (c)

Cost behavior in formula form (with rounded parameters)#E 3otal monthly administrative cost G ,651 H 5.1 X, where X denotes the number of patients for the month. E2hen interpreting the regression parameters, remember that both the cost and patient data were transformed to hundreds. 3hus, the 6.5<5 intercept parameter (a) is in terms of hundreds of dollars of cost, or ,651 (rounded). 3he 5.1 slope parameter ( b) is in terms of hundreds of dollars of cost per hundred patients, or 51 (rounded) per hundred patients. 3his amount is e9uivalent to 5.1 per patient.

(d)

3he variable cost per patient is 5.1, as explained above.

/OCUS ON ET.ICS (&ee page ! in the text.) :s direct labor a variable cost> :s it ethical to Mtap and =apN employees> ;irect labor is a variable cost if management is both able and willing to continually ad4ust the workforce to meet short-te rm needs. @any observers would argue that it is ethical to Mtap and =apN 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 Mtemporary.N 3he deliberate misclassification of employees to avoid appropriate compensation is unethical, and in certain circumstances may be illegal.

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Activity Analysis, Cost Behavior and Cost Estimation Solution

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