Activity Analysis, Cost Behavior and Cost Estimation Solution

CHAPTER 6

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

Cost Cost behavi behavior or patte patterns rns are are impo importa rtant nt in the the proce process ss of maki making ng cost cost predi predicti ctions ons.. Cost 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.

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a. Cost Cost est estim imat atio ion n is the the proc proces esss of dete determ rmin inin ing g how how a par parti ticu cular lar cost cost beh behav aves es.. b. Cost behavio behaviorr is the relati relationshi onship p between between cost and activi activity ty.. c. Cost predict prediction ion is the forecast forecast of cost cost at a particula particularr level of activity 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.

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a. "ote "otel# l# $erc $ercen enta tage ge of roo rooms ms occu occupi pied ed or the the numb number er of of occup occupan ancy cy-d -day ays, s, wher wheree an occupancy-day is defined as one room occupied for one day. b. "ospit "ospital# al# $atient $atient-day -days, s, where where a patient-d patient-day ay is define defined d as a one-da one-dayy stay by one patient. c. Comp Comput uter er manu manufa fact ctur urer er## %umb %umber er of comp comput uter erss manu manufa fact ctur ured ed,, thro throug ughp hput ut,, engineering specifications, engineering change orders, or number of parts in the finished product. d. Comput Computer er sales sales stor store# e# &ales &ales reve revenue nue.. e. Computer Computer repair repair servic service# e# 'epair 'epair calls calls or hours hours of repair repair service service.. f. $ublic $ublic accountin accounting g firm# "ours "ours of auditin auditing g service service provided provided by by each classi classificat fication ion of person personnel nel (partn (partner er,, manage managerr, super supervis visor or,, senior senior accoun accountan tant, t, and staff staff accountant).

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6.*

+raphs of the cost behavior patterns are as follows#

Cost

Cost

ctivity

ctivity

a. ariable

b. &tep-variable

Cost

Cost

ctivity Cost

c. Fixed

Cost

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ctivity d. &tep-fixed

ctivity f. Cu� r 2009 ilineThe ar McGraw-Hill Companies, v 2009 Solutions Manual

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s the the level level of acti activit vityy (or cost cost driv driver) er) incr increas eases, es, tota totall fixed fixed cost cost remain remainss consta constant. nt. "owever, "owever, the fixed cost per unit of activity declines as activity increases.

6-6

 manu manufac factur turer er/s /s cost cost of supe supervi rvisin sing g produc productio tion n might might be a step step-fix -fixed ed cost, cost, beca because use 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.

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s the level level of acti activi vity ty (or cost cost driv driver er)) incr increa ease ses, s, tota totall vari variab able le cost cost incr increa ease sess proportionately and the variable cost per unit remains constant.

6-

a.  semiva semivaria riable ble cost cost behav behavior ior patter pattern n can can be used used to approx approxima imate te a step-v step-var ariab iable le 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, Accounting, 8/e

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6-7 6-7

(a) (a) nnu nnual al cost cost of main mainta tain inin ing g an inte inters rsta tate te highw highway ay## comm commit itte ted d cost cost.. (8nc (8ncee the the highway highway has been built, it must be maintained maintained.. 3he transporta transportation tion authorities authorities are larg largel elyy comm commit itte ted d to spen spendi ding ng the the nece necess ssar aryy fund fundss to main mainta tain in the the high highwa wayy ade9uately.) (b) :ngredients in a breakfast breakfast cereal# cereal# engineered cost. (c) dvertising for a credit card card company# discretionary cost. (d) ;epreciation on an insurance company/s computer# computer# committed cost. (e) Charitabl Charitablee donations# donations# discretionar discretionaryy cost. (f) 'esearch 'esearch and and developm development# ent# discre discretiona tionary ry cost. cost.

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3he cost cost analy analyst st should should respo respond nd by point pointing ing out out that in most most cases cases a cost cost behav behavior ior 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 patter pattern. n. "oweve "oweverr, outsid outsidee that that range range (inclu (includin ding g an activi activity ty level level of =ero) =ero),, the semivariable cost behavior pattern should not be used as an approximation of the utility cost.

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 learn learning ing curv curvee shows shows how avera average ge labor labor time time per unit unit of produc productio tion n changes changes 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 labo laborr time time re9u re9uir ired ed per per unit unit.. 3he 3he lear learni ning ng phen phenom omen enon on is impo import rtan antt in cost cost estimation, since estimates must often be made for the level of cost to be incurred after additional production experience is gained.

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pprop ppropria riate te indepe independe ndent nt variab variables les for for sever several al tasks tasks are are as follows follows## a. "andling "andling materia materials ls at a loading loading dock# dock# 2eight 2eight of mater materials ials handled. handled. b. 'egist 'egisteri ering ng vehicl vehicles es at a county county motor vehicle vehicle office# office# %umber %umber of registra registratio tions ns processed. c. $icking $icking oranges oranges## olume olume or weight weight of orang oranges es picked. picked. d. :nspecting :nspecting compute computerr components components in an electroni electronics cs firm# %umber %umber of componen components ts inspected.

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n outli outlier er is a data data point point that that falls falls far away away from the the other other points points in the scatt scatter er 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.

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Fixe Fixed d cost costss are are ofte often n allo alloca cate ted d on a per per unit unit-o -of-a f-act ctiv ivit ityy basi basis. s. For exam exampl ple, e, fixed fixed 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, 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.

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:n the first first step step of the visua visual-f l-fit it method method of cost cost estima estimatio tion, n, data data points points are plott plotted ed 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. points. 3he scatter diagram and the visually-fitte visually-fitted d cost line provide provide a valuable valuable first appr approx oxim imat atio ion n in the the anal analys ysis is of any any cost cost susp suspec ecte ted d to be semi semiva vari riab able le 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 chief drawba drawback ck of the high-low high-low method method of cost cost estimat estimation ion is that itit uses uses only two data points. 3he rest of the data are ignored by the method. n outlier can cause a significan significantt problem problem when the high-low method method 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.

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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.


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 least least-s9uar -s9uares es regres regression sion line line may may be expresse expressed d in e9uati e9uation on form form as follows follows## Y = a + bX

:n this e9uation, X is is referred to as the independent variable, since it is the variable upon upon which which the estima estimate te is based. 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. activity. 6-17 6-17

:n simple simple regres regressio sion n there is a single single indepen independen dentt variable variable.. :n multip multiple le regres regressio sion n there are two or more independent variables.

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$ote $otent ntia iall cost cost driver driverss in the crui cruise se indu indust stry ry incl includ udee the foll follow owin ing# g# numb number er 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.

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 part partic icul ular ar leas leastt-s9 s9ua uare ress regr regres essi sion on line line may may be eval evalua uate ted d on the the basi basiss of economic plausibility or goodness of fit. 3he cost analyst should always evaluate a regression line from the perspective of econ econom omic ic plau plausi sibi bili lity ty.. ;oes ;oes the the regr regres essi sion on line line make make econ econom omic ic sens sense> e> :s it intuit intuitive ively ly plausi plausible ble> > n experi experienc enced ed cost cost analys analystt should should have have a good good feel feel for whether the regression line looks 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. chapter. 3he coefficient of determination is also denoted by R 2.

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3he re9uir re9uireme ement nt asks asks for an estima estimate te base based d 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# @onthl @onthlyy fixed fixed cost.. cost..... ....... ....... ...... ...... ...... ...... ...... ...... ...... ....... ....... ...... ...... ...... ...... ...... ...... ...... ...... ....... ....... ...... ...... ...... ...... ...... ...... ...... ..... aria ariabl blee cost cost per diagn diagnos osti ticc test. test... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... ..... ...... ...... ...... ...... ...... ...... .....

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nswer nswerss will will vary vary on this this re9u re9uire iremen mentt becaus becausee of varia variatio tion n in the the visual visuallyly-fit fitted ted line lines. s. Based on the preceding plot, the cost prediction at 5,<<< pounds is# 0nergy cost G 65,<<

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3he Luly Luly cost cost obse observa rvatio tion n at the the 1<,<< 1<,<<<-pi <-pint nt activ activity ity leve levell appear appearss to be an an outlie outlierr. 3he cost analyst should check the observation data for accuracy. accuracy. :f the data are accurate, the outlier should be ignored in making cost predictions.

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vera verage ge time time for for * sate satell llit ites es.. .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .. vera verage ge time time for for  satelli satellite tes. s... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... ..... ...... ...... ...... ...... ...... ...... ...... ...

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5< 5< hour hourss 1,< 1,<<< hour hourss

!.

ear earni ning ng cur curves indi indiccate ate how how labo laborr cost costss wil will cha change nge as the the compa ompan ny gain gainss 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.


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3otal otal util utilit ityy cost cost at 5<< 5<< hour hours. s... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... ..... ...... ...... ...... ...... ..... .. ariable ariable utility cost at 5<< hours (*.<< 5<< hours)............................... hours)......................... ...... Fixe Fixed d cost cost per per mont month.. h.... .... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... ..... ...... ...... ...... ...... ...

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

ariabl ariable-c e-cost ost estim estimate ate based based on the the scatte scatterr diagram diagram on the the next next page# page# Cost at at Cost at ;ifference

6<< ho hours ....................................................................... < hours ............ .................. ............. ............. ............ ............ ............. ........................... ...................... 6<< hours .......................................................................

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ariable ariable cost per hour G ,<

� 2009 2009


6- "

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

"ours of operation

McGraw-Hill/Irwin Inc. 6!""

� 2009 2009


Solutions Manual

0?0'C:&0 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:;  &$'0;&"003 &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.. www.mhhe.comDhiltone

*.

Cost Cost pre predi dict ctio ions ns at at !<< !<< hour hourss of oper operat atio ion# n# (a)

"igh-low me method# Atilit Atilityy cost cost

(b) (b)

G

1,<<< 1,<<< H (*.<< (*.<<)(! )(!<<) <<) G ,<< ,<<

isua isuall llyy-fi fitt tted ed line line## Atili tility ty cost ost

G ,1 ,177<

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# Atil Atilit ityy cos costt G 1,< 1,<< < H (* (*.< .<*) *)(! (!<< <<)) G , ,1* 1*

.

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


� 2009 2009


6- "#

0?0'C:&0 6-!! (C8%3:%A0;) 3he follow following ing altern alternati ative ve approa approach ch to calcul calculati ating ng the regres regressio sion n parame parameter terss is not a re9uirement in the problem. east-s9uare regression using manual calculations# (a) (a)

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

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

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

X  !<,<< !6<,<<< *7<,<<< <,<<< <,<< 16<,<<< 1,56,<<<

XY 1,5,<<< ,<*<,<<< ,66<,<<< 1,6<<,<<< 1,1,<<< 1,<*<,<<< 1<,!!5,<<<

(b) (b) Calc Calcul ulat atio ion n of para parame mete ters rs## a G

(

Y )( n(

X





)

X

)

(

X )(

(

X )(

G (1,7*<)(1,56,<<<) (6)(1,56,<<<)

b G

G (c)

XY ) X )

( !,<<)(1<,!!5,<<<) (!,<<)(!,<<)

n( XY)

( X)( Y)

n( X  )

( X)( X)

(6)(1<,!!5,<<<) (6)(1,56,<<<)

(!,<<)(1,7*<) (!,<<)(!,<<)

1,<<

*.<*

Cost fo formula# @onthl @onthlyy utilit utilityy cost cost

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

ariable ariable utility utility cost

G *.<* per hour of operation operation

McGraw-Hill/Irwin Inc. 6!"$

� 2009 2009


Solutions Manual

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.. 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) (a)

3abul abulaation tion of data 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

� 2009 2009

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) (b) Calc Calcul ulat atio ion n of para parame mete ters rs## a G

(

Y )( n(

X





)

X

) (

(!!6)(1,6!7) G (6)(1,6!7)

b G

G (c)

(

X )( X )(

XY ) X )

(77)(,!) (77)(77)

7 (rounded)

n( ∑ XY) − ( ∑ X)( ∑ Y) n( ∑ X 2 ) − ( ∑ X)( ∑ X) (6)(,!) (6)(1,6!7)

(77)(!!6)

1.6!6 (rounded)

(77)(77)

Cost fo formula# @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) (a)

For Formula mula for for ca calcul lculaation tion## R



= 1−

∑(Y − Y /) ∑(Y −Y )

where

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

McGraw-Hill/Irwin Inc. 6!"&

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

� 2009 2009


Solutions Manual

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

3abulation of of d daata#E

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

Y * * 5 6< * 5

X 16 15 16 1 1 15

$redicted Cost (in thousands) Based on 'egression ine Y' O( Y J J Y' )PI .156 1.!! 6.1 5.7<5 .156 !.!5 .** .*<7 !.*< .1 6.1 .
O(Y J J Y )PI *.<<< *.<<< 1.<<< 16.<<< *.<<< 1.<<< !<.<<<

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

'ounded.

(c)

Calculation of R# R G 1 J

(d)

1.5! G .*7 (rounded) !<.<<<

:nterpretation of of R# 3he coefficient coefficient of determinat determination, ion, R, is a measure of the goodness of fit of the least-s9uar least-s9uares es regressio regression n line. n R 2 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 high high R means that the cost analyst can be relatively confident in the cost predictions based on the estimated-cost behavior pattern.


� 2009 2009


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.

ariable

.

&emivariable (or mixed)E

5.

Fixed

!.

Fixed

.

Fixed

*.

Fixed

7.

&emivariable (or mixed)

.

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. capability. 3his increase in repairs would result in a variable-cost component e9ual to the dealer/s repair charges.

McGraw-Hill/Irwin Inc. 6!"*

� 2009 2009


Solutions Manual

$'8B0@ 6-!5 ( @:%A30&) 1.

ariable ma maintenance co cost pe per ho hour of of se service

G

C*,51<



C,77<

!1<

G .<< 3otal otal main mainte tena nanc ncee cost cost at !1< !1< hour hourss of serv servic ice. e... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ariable ariable maintenance cost at !1< hours of service (!1< hr. hr. .<<)....... Fixe Fixed d main mainte tena nanc ncee cost cost per per mont month. h... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ....

,7 ,77< 7< ,*<  1< 1<

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

3he 3he varia variabl blee compo compone nent nt of the the maint mainten enan ance ce cost cost is .< .<<< per hour hour of service.

!.

Cost Cost pred predic icti tion on at 6<< 6<< hou hours rs of acti activi vity ty## @aintenance cost G 1< H (.<<)(6<<) G ,!1<

*.

aria ariabl blee cost cost per per hour hour Ofro Ofrom m re9u re9uir irem emen entt ()P. ()P... .... .... .... .... .... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ... Fixed Fixed cost cost per hour hour at at 61< 61< hour hourss of activi activity ty (1 (1
.< .<<<  .*E .*E

E'ounded. 3he fixed cost per hour is a misleading amount, because it will change as the the numb number er of hour hourss chan change ges. s. For For exam exampl ple, e, at << << hour hourss of maintenance service, the fixed cost per hour is 1.< (1

� 2009 2009


6- "+

$'8B0@ 6-! ( @:%A30&) 1.

&trai traigh ghtt-li line ne dep depre reci ciaation tionSc Scom ommi mitt tted ed fix fixed ed Charitable contributionsSdiscretionary fixed @ining laborDfringe benefitsSvariable 'oyaltiesSsemivariable 3rucking 3rucking and haulingSstep-fixed 3he per-to per-ton n mining mining laborD laborDfri fringe nge benefi benefitt cost cost is consta constant nt at both both volume volume levels levels presented, which is characteristic of a variable cost. !1,<<< 1,*<< tons G  per ton 6<5,<< ,5<< tons G  per ton 'oyalties have both a variable and a fixed component, making it a semivariable (mixed) cost. ariable 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 * 7,<<<

1*<,<<< 71,<<<  *7 * 7,<<<

3otal cost for 1,5<< tons# ;eprec ;epreciat iation ionTTT TTTTTT TTTTTT TTTTTT TTTTTT TTTT.. T.... Charit Charitabl ablee contri contribut bution ionsTT sTTTTT TTTTTT TTTTTT TTT.. @ining @ining laborD laborDfri fringe nge benefi benefits ts at   per per tonTT. tonTT. 'oyalties# ariabl ariablee at 6 per tonTTT tonTTTTTT TTTTTT TTTT.. T.. Fixe FixedT dTTT TTTT TTTT TTTT TTTT TTTT TTTT TTTT TTT. T... 3ruck ruckin ing g and and haul haulin ingT gTTT TTTT TTTT TTTT TTTT TTT. T... 3otal otalTT TTTT TTTT TTTT TTTT TTTT TTTT TTTT TTTT TT.. ..

McGraw-Hill/Irwin Inc. 6!#

� 2009 2009

 !<,<<< !<,<<< ------!,< !,<<< 11<,<< 1<,<< *7,< *7,<<< << <, <,<< <<<<  ,< ,<<< << The McGraw-Hill Companies,

Solutions Manual

$'8B0@ 6-! (C8%3:%A0;) !.

"aul "aulin ing g 1,* 1,*<< << tons tons is is not not par parti ticu cula larl rlyy cost cost effe effect ctiv ive. e. one one @oun @ounta tain in 0xt 0xtra ract ctio ion n will 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, general, with this type of cost function, function, effectiveness effectiveness is maximi=ed maximi=ed if a firm operates on the right-most portion of a step, 4ust prior to a 4ump in cost.

*.

 com commi mitt tted ed fix fixed ed cos costt resu result ltss from from an ent entit ityK yKss owner ownersh ship ip or or use use of fac facil ilit itie iess and and its its basic organi= organi=ationa ationall structure. structure. 0xamples 0xamples of such costs costs include include property property taxes, taxes, depreciation, rent, and management management salaries. ;iscretionary fixed costs, costs, on the other hand, arise from a decision to spend a particular amount of money for a specific purpos purpose. e. 8utlay 8utlayss for resear research ch and develo developme pment, nt, adverti advertisin sing, g, and charit charitabl ablee contributions fall in this category. :n times of severe economic difficulties, a companyKs management will often try to cut discretionary fixed fixed costs. &uch costs are more easily altered in the short 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 adverse adverse long-term long-term conse9uences conse9uences,, other cuts could have even more sign signif ific ican antt nega negati tive ve cons conse9 e9ue uenc nces es in the the futu future re.. 3he 3he deci decisi sion on to clos closee a manufa manufactu cturin ring g facili facility ty,, for exampl example, e, could could reduce reduce proper property ty taxes, taxes, rent, rent, andDor andDor depreciation. "owever, "owever, that decision may result result in a significant long-run change in operations that may be difficult to overturn when economic conditions rebound.

.

one one @ou @ount ntai ain n 0xtr 0xtrac acti tion on use usess a cal calen enda darr year year for for tax tax-re -repo port rtin ing g purp purpos oses es.. t year year-end, it may have ample funds available and decide to make donations to charitable causes causes.. &uch &uch contri contributi butions ons are deductib deductible le in comput computing ing the compan companyK yKss tax obligation to the government. 3ax deductions reduce taxable taxable income and, therefore, therefore, produce a tax savings for the firm.


� 2009 2009


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.. es ess# @ach @achin inee suppl upplie iesT sTT. T. ;epreciationTTTT.. $lant ma maintenanceTTTT...

pril

Lune

(!,<<< hours)

(!*,<<< hours)

 61,<<< (1
 57,<<< (1! (1!,< ,<<<<) (,<<)  5< 5
E 0xcludes supervisory labor cost ariable ariable maintenance maintenance cost G difference difference in cost

difference in direct-labor hours

G (5
3otal otal main mainte tena nanc ncee cost. cost... .... .... .... .... .... .... .... .... .... .... .... .... .... .. es ess# aria ariabl blee cost ost at 1!. 1!.< per per hour hour.... .... Fixe Fixed d main mainte tena nanc ncee cost cost.. .... .... .... .... .... .... .... .... .... .... .... .... .... ..

McGraw-Hill/Irwin Inc. 6!#"

pril (!,<<< hours)

Lune (!*,<<< hours)

 ,< ,<<< << !1<, !1<,<< ** **, ,<< <<

5
� 2009 2009


Solutions Manual

$'8B0@ 6-!7 (C8%3:%A0;) !.

@anu @anufa fact ctur urin ing g ov overhe erheaad at at 7 7,< ,<< la labor bor hou hourrs# @achine su supplies at *.< pe per ho hour... ....... ...... .... .... .... .. ;epreciation.. n............................... ..................... ...... .... $lant maintenance cost# ariable at at 1 1!.< pe per ho hour.................... ........ Fixe Fixed. d... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .. &upe &uperrvisor isoryy la labor. bor... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... 3otal otal.. .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ....

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

*.

 fixe fixed d cost cost rema remain inss cons consta tant nt when when a chan change ge occu occurs rs in in the cos costt drive driverr (or (or acti activi vity ty base).  step-fixed cost, cost, on the other hand, remains constant within a range range but will change change (rise or fall) when activity activity falls outside that range. range. :n other words, a fixed cost is constant over a wider range of activity than a step-fixed cost.

.

:dea :deall llyy, the the comp compan anyy shou should ld ope opera rate te on the the righ right-m t-mos ostt port portio ion n of a ste step, p, 4ust 4ust pri prior or to to the 4ump in cost. :n this manner, manner, a firm receives maximum benefit (i.e., the maximum amount of activity) for the dollars invested.


� 2009 2009


6- ##

$'8B0@ 6-*< (*< @:%A30&) 1.

McGraw-Hill/Irwin Inc. 6!#$

� 2009 2009


Solutions Manual

$'8B0@ 6-*< (C8%3:%A0;) .

&ee grap graph h for for re9u e9uire irement ment (1). 1).

!.

3he estima estimate te of of the the fixed fixed cost cost is the interc intercept ept on the the vertic vertical al axis 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< 7,5<<< 11,5< 1,5<<<

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

G

C11,5<< − C7,5<< ,<<< − <

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 denotes the number pounds (in hundreds) of e9uipment loaded or unloaded during the month.


� 2009 2009


6- #%

$'8B0@ 6-*< (C8%3:%A0;) .

"igh-low method# aria ariabl blee cost cost uni unitt of act activ ivit ityE yE G

C1,1< − C1<,<< ,6<< − 1,<<<

G 1.< E$ounds (in hundreds) of e9uipment loaded or unloaded 3otal otal cos costt at ,6< ,6<<< unit unitss of acti activi vity. ty... .... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... ..... ...... ...... ..... .. ;educt# ariable ariable cost at ,6<< units of activity (,6<< 1.<).................. Fixe Fixed d cost cost.. ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ...... ...... ...... ..... ..

1, 1,1 1<< !,1<  7,<< 7,<<<<

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

McGraw-Hill/Irwin Inc. 6!#&

� 2009 2009


Solutions Manual

$'8B0@ 6-*< (C8%3:%A0;) 6.

@emorandum ;ate#

3oday

3o#

$resident, %antucket @arine &upply

From#

:.@. &tudent

&ub4ec &ub4ect# t# @ateri @aterial-h al-hand andlin ling g cost cost esti estimat mates es 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 different estimates because the high-low method uses only two data points, ignoring the rest of the information. 3he method of visually fitting 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-"andling Costs 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.


� 2009 2009


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$'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:;  &$'0;&"003 &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.. www.mhhe.comDhiltone

.

eas eastt-s9 s9ua uare ress regr regres essi sion on e9ua e9uati tion on## 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.. 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:;  &$'0;&"003 &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.. www.mhhe.comDhiltone

*.

3he 3he cost pred predic icti tion onss differ differ becau because se the cost cost formu formula lass differ differ under under the the three three costcostestimation methods. 3he high-low method, while ob4ective, uses only two data points. 3en observations are excluded. 3he visual visual-fi -fitt method method,, while while it uses uses all all of the data, data, is somewh somewhat at sub4ec sub4ectiv tive. e. ;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 3he elec electr tron onic ic vers versio ion n of the the &olu &oluti tion onss @anu @anual al MBA: MBA:; ;  &$'0 &$'0; ;&" &"00 003 3 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.. www.mhhe.comDhiltone

McGraw-Hill/Irwin Inc. 6!#*

� 2009 2009


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) (a)

3abul abulaation tion of data data## :ndependent ariable (units of activity in thousands) X 1. 1.6 1.! 1.< . .* .< 1. .6 1.1 1. 1.* <.*

;ependent ariable (cost in thousands) Y 11.5< 11.!< 11. 1<.< 11.1< 1. 1.<< 11.*< 1.1 11.< 11.! 11.! 1!5.!5

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

X  !.* .6 1.67 1.<< *.* .56 *.<< !.* 6.56 1.1 1.** 1.76 !5.5<

XY 1.<6< 1.<< 1*.6 1<.<< *.*< !<.1< *.<<< <.< !1.1 1.1 1!.6< 1.7< !6.<

(b) (b) Calc Calcul ulat atio ion n of para parame mete ters rs## 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) (<.*)(<.*)

� 2009 2009

. (rounded)


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Fixe Fixedd- and and varia variabl blee-co cost st comp compon onen ents ts## @onthly fixed cost G 7,7*!E ariable 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 activity. 09uivalently, 09uivalently, it is the cost per unit of activity. thousand units of activity.

McGraw-Hill/Irwin Inc. 6!$

� 2009 2009


Solutions Manual

$'8B0@ 6-* (*< @:%A30&)


� 2009 2009


6- $

$'8B0@ 6-* (C8%3:%A0;) !.

Fix Fixed-c ed-cos ostt com compo pone nent nt G 1!, 1!,<<< ariable-cost 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 denotes the number of golfers during the month. *.

$redicted Course @aintenance Costs

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!

� 2009 2009


Solutions Manual

$'8B0@ 6-*! (! @:%A30&) 1.

3he 3he regre regress ssio ion n e9uati e9uation on/s /s inter interce cept pt on the verti vertica call axis axis is 17<. 17<. :t repre represe sent ntss the the port portio ion n of indi indire rect ct mate materi rial al cost cost that that does does not not vary vary with with mach machin inee hour hourss when when operating within the relevant range. 3he slope of the regression line is  per machine hour hour. For every machin machinee hour hour,  of indire indirect ct mater material ial costs costs are expected expected to be incurred.

.

0stima 0stimated ted cost cost of indire indirect ct mate materia riall at < machin machinee hours hours of activi activity# ty#  G 17< H (

<)

G *,**<

!.

&eve &evera rall 9ues 9uesti tion onss shou should ld be aske asked# d# (a)

;o the the observ observation ationss contain contain any outliers, outliers, or are are they all represent representative ative of norma normall operations>

(b) (b)

re re ther theree any any mism mismat atch ched ed time time peri period odss in the data> data> re re all all of the indi indire rect ct mate materi rial al cost cost obse observ rvat atio ions ns matc matche hed d prop proper erly ly with with the the mach machin inee hour hour observations>

(c)

re ther theree any allo allocat cated ed costs costs inclu included ded in the the indire indirect ct materi material al cost cost data> data>

(d) (d)

re re the the cos costt data data aff affec ecte ted d by infl inflat atio ion> n>

*. Beginning inventory.............. ................................. .................... H $urc $urcha hase ses. s... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... ..... ...... ...... ...... ..... J 0nding inventory............................................................... :ndirect material used.......................................................... .

pril 1,!<< ,7< ,7<<< (1,!<) ,<

ugust 1,<<< 6,< 6,<<< (!,<<<) *,<<

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


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

C1,6< !<<

C.< per machine hour

� 2009 2009


6- $#

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

, ,< < ,<<  !< !<

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

machine hours)

3he regr regress ession ion esti estimat matee shoul should d be reco recomme mmende nded d becaus becausee it uses uses all all of the data data,, not not 4ust two pairs of observations when developing developing the cost e9uation.

McGraw-Hill/Irwin Inc. 6!$$

� 2009 2009


Solutions Manual

$'8B0@ 6-** ( @:%A30&) 1. •

•

• •

&catter di diagrams# $resent, in graphic form, the relationship between costs and cost drivers via a plot of data points 'e9uire 'e9uire that a straight line be fit through the data points, with approximately approximately 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 'e9uires more computation computation than other cost-estimation cost-estimation methods methods however however,, software 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 leastleast-s9u s9uare aress regres regressio sion n method method will will typica typically lly produc producee the most most accura accurate te results.

.

Qes. es. 3he 3he thre threee meth method odss pro produ duce ce e9ua e9uati tion onss by diff differ eren entt mea means ns.. &cat &catte terr diag diagra rams ms and least-s9uares regression regression rely on an examination 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, Finally, the high-low method is based on an analysis of only two data points# the highest and the lowest activity levels.


� 2009 2009


6-

%$ $'8B0@ 6-** (C8%3:%A0;) !.

3hes 3hesee amou amount ntss repr repres esent ent the the fix fixed ed and and var varia iabl blee cost costss asso associ ciat ated ed with with the the tic ticke keti ting ng operat operation ion.. Fixed Fixed cost totals totals !<<,< !<<,<<< << within within the relevan relevantt range, range, and Florid Florida a :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, es, she did did err err by by inc includi luding ng %ov %ovembe emberr data data.. %ov %ovembe emberr is not not repr repres eseentat ntativ ivee because because of the effects of the &outheastern &outheastern irlines irlines strike. strike. 3he month is an outlier and should be eliminated from the data set.

6.

Curr Curren entl tlyy, most most of the airl airlin ineK eKss ticke tickets ts are are writt written en thro throug ugh h reser reserva vati tion onss perso personn nnel el,, 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 similar expenditures. expenditures. 8utlays 8utlays that fall in these latter categories categories are typically fixed fixed costs, costs, assuming that the cost driver driver is the number of tickets. tickets. 3he outcome outcome 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!$&

� 2009 2009


Solutions Manual

$'8B0@ 6-* (*< @:%A30&) 1.

3he 3he orig origin inal al meth method od was was simpl implyy the ave average age ove overhe rhead per per hour our for the the last last 1 months and did not distinguish distinguish between fixed and variable 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 ased on on the the reg regres ression sion ana analy lyssis, is, the the var variabl iablee cos cost per per per person son for for a coc cockta ktail party is !, calculated as follows# Food Food and bever beverag ages es.. .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... ..... ...... ...... ...... ...... ... abo aborr (.6 hr hr. V 11D 11Dhr hr.) .).. .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... aria ariabl blee over overhe head ad (.6 (.6 hr. hr. V *Dh *Dhrr.)... .)..... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ...... ..... 3otal.. otal..... ...... ...... ...... ...... ...... ...... ....... ....... ...... ...... ...... ...... ...... ...... ...... ....... ....... ...... ...... ...... ...... ...... ....... ........ ......... .......... ......... ........ ....

1*. 1*.<< << 6.6< 6.6< .*< .*< !.<<

b. Base Based d on the the regr regres essi sion on anal analys ysis is,, the the full full abso absorp rpti tion on cost cost per per pers person on for for a cocktail party is 7, calculated as follows# Food Food and bever beverag ages es.. .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... ..... ...... ...... ...... ...... ... abo aborr (.6 hr hr. V 11D 11Dhr hr.) .).. .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... aria ariabl blee over overhe head ad (.6 (.6 hr. hr. V *Dh *Dhrr.)... .)..... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ...... ..... Fixe Fixed d over overhe head ad (.6 (.6 hr. hr. V 1
1*. 1*.<< << 6.6< 6.6< .*< .*< 6.<< .<< 7.<<

E*,<<< x 1 months G 56,<<< 56,<<
3he 3he mini minimu mum m bid bid for for a <<-pe pers rson on coc cockt ktai aill part partyy woul would d be , ,5 5<. <. 3he 3he amou amount nt is is calculated by multiplying the variable variable cost per person of ! by < < people. t any price above the variable cost, ;ana will be earning a contribution toward his fixed costs.


� 2009 2009


6- $)

$'8B0@ 6-* (C8%3:%A0;) *. 







8the 8therr fact factor orss that that ;an ;anaa shou should ld con consi side derr in dev devel elop opin ing g a bid bid incl includ udee the the foll follow owin ing# g# 3he assessm assessment ent of the curren currentt capaci capacity ty of ;anaK ;anaKss busine business. ss. :f the busine business ss is at capacity, capacity, other work would have to be sacrificed at some opportunity cost. nalys nalyses es of the competi competitio tion. n. :f competit competition ion is rigoro rigorous, us, ;ana may not have have much much bargaining power. power.  determination of whether or not ;anaKs bid will set a precedent for lower prices. 3he reali reali=a =atio tion n that that regres regressio sion n analys analysis is is based based on histor historica icall data, data, and that that any anticipated changes in the cost structure should be considered.

McGraw-Hill/Irwin Inc. 6!$*

� 2009 2009


Solutions Manual

$'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, Accounting, 8/e

� 2009 2009


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:;  &$'0;&"003 &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.. www.mhhe.comDhiltone

!.

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

*.

Cos Cost pre predi dict ctio ion n for for 1, 1,<< << flig flight htss# 3he electronic version of the &olutions @anual MBA:;  &$'0;&"003 &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# www.mhhe.comDhiltone.. www.mhhe.comDhiltone . Calc Calcul ulat atio ion n of ' 3he electronic version of the &olutions @anual MBA:; M BA:;  &$'0;&"003 &$'0;&"003 &8A3:8%&N is available on your :nstructors C; and on the "ilton, e website# w ebsite# www.mhhe.comDhiltone.. www.mhhe.comDhiltone :nterpretation of R# 3he coefficient coefficient of determinati determination, on, R, is a measure of the goodness of fit of the least-s9uar least-s9uares es regression 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 cost estima estimatio tion, n, a high 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.

McGraw-Hill/Irwin Inc. 6!%

� 2009 2009


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) (a)

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


(b) (b) Calc Calcul ulat atio ion n of para parame mete ters rs## ( a G G b G

Y )( n(

X





)

X

(!!)(1,5!) (1)(1,5!)

)

( (

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

X )( X )(

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)

� 2009 2009


6- %

$'8B0@ 6-*6 (C8%3:%A0;) (c) (c)

Fixe Fixedd- and and varia variabl blee-co cost st comp compon onen ents ts## @onthly fixed cost G 11,576 ariable ariable cost G 655 per hundred flights

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

For Formula mula for for ca calcul lculaation tion## 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 /

denote denotess the predi predicte cted d value value of the the depende dependent nt variab variable le (cost (cost)) based on the regression line, at a particular activity level.

Y

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

� 2009 2009


Solutions Manual

$'8B0@ 6-*6 (C8%3:%A0;) (b)

3abulation of of d daata#E

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

Y < 17 1 17 15 < 1 15 1 17 * 1

X 1 1< 7 1*  11 1 7 1 1< 1* 11

$redicted Cost (in thousands) Based on 'egression ine Y' O( Y! Y' )PI 17.7< .<<6 1.66 .1 15.7 .<1 1.5* .151 15.1 .<* 17.*! .5! 1.71 .7<* 15.7 .57< 17.7< 1.166 1.66 .1 1.5* 5.*!1 17.*! 1.* 1.<17

O(Y J J Y )PI .!*< .15* .<< .15* .* .!*< .<6 .* .<6 .15* 1.<<* .<< *.71

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

'ounded.

(c)

Calculation of R# R G 1 J


1.<17 G . (rounded) *.71

� 2009 2009


6- %#

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

Cair Cairns ns// prel prelim imin inar aryy estima estimate te for overh overhea ead d of 1.< 1.<<< per per direct direct-la -labo borr hour does does 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 component of the cost (,*<< (,*<< per month) that is unrelated unrelated to total direct-labo direct-laborr hour hours. s. 3his 3his cost cost comp compon onen entt is the the inte interc rcep eptt on the the vert vertic ical al axis axis and and is ofte often n considered to be the fixed cost as long as the activity level is within the relevant rang range. e. 3hus 3hus,, the the leas least-s t-s9u 9uar ares es regr regres essi sion on resu result ltss in a cost cost func functi tion on with with two two components components## fixed fixed cost per month and variable variable cost per direct-labor direct-labor hour. hour. 3his cost formula can be used to predict total overhead at any activity level within the relevant range.

.

;ire ;irect ct mate materi rial al.. .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... .... ;irect labor ( ;"E 11.<< 11.<< per ;")...................................................... ;")........................................................ ariable ariable overhead ( ;" 7. per ;")......................................... ;")................................. .............. ...... 3otal otal vari variab able le cost cost per per 1,<< 1,<<<< s9ua s9uare re feet. feet... .... .... .... ..... ..... .... .... .... .... .... .... .... ..... ...... ...... ...... ...... ...... ...... ...... ...

!7< !7<.< .<<< .<< *6. *71 *71. .

E;" denotes direct-labor hours. !.

3he mini minimum mum bid shou should ld inclu include de the the follo followin wing g increm increment ental al cost costss of the the pro4e pro4ect. ct.## ;irect material (!7<.<< <).......................................................... <).................................................................. ............ .... ;irect labor (.<< <).................................................................. <).......................................................................... ........... ... ariable ariable overhead (7. per ;"  ;" <)....................................... 8vertime premium (.< per ;"  ;" < .!)......................... .!)................. ............. ..... @inimu @inimum m bid... bid...... ....... ....... ...... ...... ...... ...... ...... ...... ...... ...... ....... ....... ...... ...... ...... ...... ...... ...... ...... ....... ....... ...... ...... ...... ...... ...... ...... ...... ........ .....

*.

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

Qes, es, Cairn Cairnss can rel relyy on the form formul ulaa as long long as she rec recog ogni ni=e =ess that that there there are are some some shortc shortcomi omings ngs.. 3he fact fact that that leastleast-s9u s9uare aress regres regressio sion n estima estimates tes cost cost behavi behavior or 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).......................................................... *.1).................................................................. ............. ..... 1,
b.

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

3he two two scena scenario rioss in (a) (a) and and (b) (b) diffe differr in term termss of the the acti activit vities ies to to be unde underta rtaken ken.. &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.


� 2009 2009


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

. thro through ugh *. *.

McGraw-Hill/Irwin Inc. 6!%&

&ee scatte scatterr diagra diagram m for re9ui re9uirem rement ent (1). (1).

� 2009 2009


Solutions Manual

C&0 6-* (C8%3:%A0;) .

Fixed co cost G 5,<<< -ariable cost per patient

C1<,6<< C5,<<< 1,<< < −

=

=

C!.<<

−

6.

dmi dmini nist stra rati tive ve cost cost G 5,< 5,<<< << H !.< !.<<< X , where X denotes denotes the number of patients.

5.

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

Cost $rediction

5<..................... 7,!<< !
:t makes no difference which visually-fit #ost line is used to make the cost prediction for 5< patients. 3he semivariable approximation is very accurate at this patient load, which is near the middle of the relevant relevant range. "owever, "owever, for a patient load of !< patients, the visually-fit #urvilinear #ost line yields a much more accurate prediction. C&0 6-*7 (< @:%A30&) 1.

"igh-low method# ariable ariable administrative cost per patient G

C16,1<< 1,<<

−

−

C*,1<< !<<

=

C1<

3otal otal cost cost at 1,< 1,<<< patie patients nts.. .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... ..... ...... ...... ...... ...... ...... ...... ..... .. ariable cost at 1,<< patients...................................................................... Fixe Fixed d cost cost per per mont month.. h.... .... .... .... .... .... .... .... .... .... .... .... .... .... ..... ..... .... .... .... .... .... .... .... .... .... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... .....

16, 16,1< 1<<< 1,<<<  1,1< 1,1<<<

Cost formula# 3otal monthly administrative cost G 1,1<< H 1< X , where X denotes denotes the number of patients for the month. 3he variable cost per patient is 1<.


� 2009 2009


6- %)

.


C&0 6-*7 (C8%3:%A0;) !.

@emorandum ;ate#

3oday

3o#

Leffrey @a @ahoney, d dministrator

From#

:.@. &tudent

&ub4ect# &ub4ect# Comparison Comparison of cost cost estimate estimatess for clinic clinic administ administrativ rativee costs 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 denotes the number of patients in a month. (a) (a)

eas east-s t-s9u 9uar ares es reg regre ress ssio ion n meth method od## 3otal monthly administrative cost G ,651 H 5.1 X

(b) (b) "igh "igh-l -low ow meth method od## 3otal monthly administrative cost G 1,1<< H 1< X (c) (c)

isua isuall-ffit met method# hod# 3otal monthly administrative cost G 5,<<< H !.<< X

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 the futur future e pati patien entt load loadss in the the rang rangee of 6<< 6<< to 1,< 1,<<< pati patien ents ts per per mont month h are are anticipated.

McGraw-Hill/Irwin Inc. 6!%*

� 2009 2009


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 observations observations outside the relevant relevant range, they do not provide the best estimate estimate 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.


� 2009 2009


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 ery inapp napprropr opriat iate for the hos hospita pitall admin dminis istr trat ator or to mani manipu pula late te the the cos 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 the clin clinic ic,, the the boar board d shou should ld have have the the best best info inform rmat atio ion n poss possib ible le,, incl includ udin ing g the the controller/s best estimate as to how administrative costs will behave. @ega @egan n @c;o @c;ono noug ugh, h, the the hosp hospit ital alKKs dire direct ctor or of cost cost mana manage geme ment nt,, has has a professional obligation to provide her best professional 4udgment to the board of trustees. trustees. 3he standards standards of ethical ethical conduct conduct for managemen managementt accountant accountantss include include the following re9uirements concerning ob4ectivity# (a) Commun Communica icate te infor informat mation ion fair fairly ly and and ob4ect ob4ective ively ly.. (b) ;isclose ;isclose fully fully all releva relevant nt informat information ion that that could could reasonab reasonably ly be expected expected to 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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� 2009 2009


Solutions Manual

C&0 6-*7 (C8%3:%A0;) 3he follow following ing altern alternati ative ve approa approach ch to calcul calculati ating ng the regres regressio sion n parame parameter terss is not a re9uirement in the problem. east-s9uares regression using manual calculations (a) (a)

3abul abulaation tion of data data## ;ependent ariable (cost in hundreds) Y 6< 5< 1!7 7 117 1<< 7* *1 1< 161 ! 111 1,15


(b) (b) Calc Calcul ulat atio ion n of para parame mete ters rs## ( a G G b G

G


Y )( n(

:ndependent ariable (patients in hundreds) X *  1* 7 1! 1< 5 ! 11 1 6 1 1<7

X





)

X

)

(1,15)(1,151) (1)(1,151)

( (

X  16  176 1 167 1<< *7 7 11  !6 1** 1,151

X )( X )(

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

(1<7)(1,15) (1<7)(1<7)

� 2009 2009

5.1 (rounded)


6- &

C&0 6-*7 (C8%3:%A0;) (c)

Cost Cost behav behavior ior in form formula ula form form (with (with rounde rounded d param paramete eters) rs)#E #E 3otal otal monthl monthlyy admini administr strati ative ve cost cost G ,651 ,651 H 5.1 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 var variab iable le cost cost per per pati patient ent is is 5.1 5.1,, as expl explain ained ed abov above. e.

/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 ad4ust the workforce workforce to meet short-term short-term needs. @any observer observerss 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 rates for temporary employees may 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 Mtemporary.N .N 3he deliberate misclassification misclassification of empl employ oyee eess to avoi avoid d appr approp opri riat atee comp compen ensa sati tion on is unet unethi hica cal, l, and and in cert certai ain n circumstances may be illegal.

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� 2009 2009


Solutions Manual

Activity Analysis, Cost Behavior and Cost Estimation Solution

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