capitol 10 corect

8/13/2019 Capitol 10 Corect

1/50

CHAPTER 10

DETERMINING HOW COSTS BEHAVE

10-1 The two assumptions are:1. Variations in total costs are explained by variations in the level of a single activity related

to those costs (the cost driver).2. ost behavior is approximated by a linear cost function within the relevant range. ! linear

cost function is a cost function where" within the relevant range" the graph of total costsversus the level of a single activity forms a straight line.

10-2 Three alternative linear cost functions are:1. Variable cost function##a cost function in which total costs change in proportion to the

changes in the level of activity in the relevant range.2. $ixed cost function##a cost function in which total costs do not change with changes in the

level of activity in the relevant range.%. &ixed cost function##a cost function that has both variable and fixed elements. Total costs

change but not in proportion to the changes in the level of activity in the relevant range.

10-3 ! linear cost function is a cost function where" within the relevant range" the graph oftotal costs versus the level of a single activity related to that cost is a straight line. !n exampleof a linear cost function is a cost function for use of a telephone line where the terms are a fixedcharge of '1" per year plus a '2 per minute charge for phone use. ! nonlinear cost functionis a cost function where" within the relevant range" the graph of total costs versus the level of asingle activity related to that cost is not a straight line. xamples include economies of scale inadvertising where an agency can double the number of advertisements for less than twice thecosts" step*function costs" and learning*curve*based costs.

10-4 +o. ,igh correlation merely indicates that the two variables move together in the dataexamined. -t is essential to also consider economic plausibility before maing inferences aboutcause and effect. /ithout any economic plausibility for a relationship" it is less liely that a highlevel of correlation observed in one set of data will be similarly found in other sets of data.

10-5 $our approaches to estimating a cost function are:1. -ndustrial engineering method.2. onference method.%. !ccount analysis method.0. uantitative analysis of current or past cost relationships.

10-6 The conference method estimates cost functions on the basis of analysis and opinionsabout costs and their drivers gathered from various departments of a company (purchasing"process engineering" manufacturing" employee relations" etc.). !dvantages of the conferencemethod include:1. The speed with which cost estimates can be developed.2. The pooling of nowledge from experts across functional areas.%. The improved credibility of the cost function to all personnel.

1*1


2/50

10-7 The account analysis method estimates cost functions by classifying cost accounts inthe subsidiary ledger as variable" fixed" or mixed with respect to the identified level of activity.Typically" managers use ualitative" rather than uantitative" analysis when maing these cost*classification decisions.

10-8 The six steps are:

1. hoose the dependent variable (the variable to be predicted" which is some type of cost).2. -dentify the independent variable or cost driver.%. ollect data on the dependent variable and the cost driver.0. 3lot the data.4. stimate the cost function.5. valuate the cost driver of the estimated cost function.

6tep % typically is the most difficult for a cost analyst.

10-9 ausality in a cost function runs from the cost driver to the dependent variable. Thus"choosing the highest observation and the lowest observation of the cost driver is appropriate in

the high*low method.

10-10 riteria important when choosing among alternative cost functions are:1. conomic plausibility.2. 7oodness of fit.%. 6lope of the regression line.

10-11 ! learning curve is a function that measures how labor*hours per unit decline as unitsof production increase because worers are learning and becoming better at their 8obs. Twomodels used to capture different forms of learning are:

1. umulative average*time learning model. The cumulative average time per unit declinesby a constant percentage each time the cumulative uantity of units produced doubles.

2. -ncremental unit*time learning model. The incremental time needed to produce the lastunit declines by a constant percentage each time the cumulative uantity of units produceddoubles.

10-12 $reuently encountered problems when collecting cost data on variables included in acost function are:

1. The time period used to measure the dependent variable is not properly matched with thetime period used to measure the cost driver(s).

2. $ixed costs are allocated as if they are variable.%. 9ata are either not available for all observations or are not uniformly reliable.0. xtreme values of observations occur.4. ! homogeneous relationship between the individual cost items in the dependent variable

cost pool and the cost driver(s) does not exist.5. The relationship between the cost and the cost driver is not stationary.. -nflation has occurred in a dependent variable" a cost driver" or both.

1*2


3/50

10-13 $our ey assumptions examined in specification analysis are:

1. ;inearity between the dependent variable and the independent variable within the relevantrange.

2. onstant variance of residuals for all values of the independent variable.%.


4/50

10-17 (14 min.) I*+#t',#$ "."/+- '+*- "#* !+*-%&st '(#%ts

1. 6ee 6olution xhibit 1*1.

2. ontract 1: y > '4ontract 2: y > '% A '.2X

ontract %: y> '1XwhereXis the number of miles traveled in the day.

%. Ct."%t C&st (#%t%

$ixed&ixedVariable

SOTION EHIBIT 10-17

3lots of ar


5/50

10-18 (2 min.) V".&(s %&st-/+"&. "tt+.#s

1. C2. D%. 70. E +ote that ! is incorrect because" although the cost per pound eventually euals a

constant at '?.2" the total dollars of cost increases linearly from that pointonward.

4. - The total costs will be the same regardless of the volume level.5. ;. $ This is a classic step*cost function.@. C?.

10-19 (% min.) M"t%#$ $."s :t *+s%.ts &' %&st "#* .++#(+/+"&.

a. (1)b. (5) ! step*cost function.c. (?)d. (2)e. (@)f. (1) -t is data plottedon a scatter diagram" showing a linear variable cost function with

constant variance of residuals. The constant variance of residuals implies that there is auniform dispersion of the data points about the regression line.

g. (%)h. (@)

1*4


6/50

10-20 (14 min.) A%%&(#t "#",ss !+t&*

1 Variable costs:ar wash labor '20"6oap" cloth" and supplies %2"/ater 2@"

lectric power to move conveyor belt 2"Total variable costs '%2"

$ixed costs:9epreciation ' 50"6alaries 05"

Total fixed costs '11"

osts are classified as variable because the totalcosts in these categories change in proportion tothe number of cars washed in ;oren=oFs operation. osts are classified as fixed because the totalcosts in these categories do not vary with the number of cars washed. -f the conveyor belt moves

regardless of the number of cars on it" the electricity costs to power the conveyor belt would be afixed cost.

2 Variable costs per car >@"

'%:2"> '0.54 per car

Total costs estimated for ?" cars > '11" A ('0.54 G ?") > '42@"4

10-21 (% min.) A%%&(#t "#",ss !+t&*

1. &anufacturing cost classification for 20:

A%%&(#t

T&t"

C&sts

;1@"

'1"02":4> '1%.%

%. ost classification into variable and fixed costs is based on ualitative" rather than

uantitative" analysis. ,ow good the classifications are depends on the nowledge of individualmanagers who classify the costs. 7ower may want to undertae uantitative analysis of costs"using regression analysis on time*series or cross*sectional data to better estimate the fixed andvariable components of costs. Detter nowledge of fixed and variable costs will help 7ower tobetter price his products" now when he is getting a positive contribution margin" and to bettermanage costs.

1*


8/50

10-22 (2 min.) Est!"t#$ " %&st '(#%t $-&: !+t&*

1. 6ee 6olution xhibit 1*22. There is a positive relationship between the number of servicereports (a cost driver) and the customer*service department costs. This relationship iseconomically plausible.

2. N(!/+. &' C(st&!+.-S+.%+S+.%+ R+&.ts D+".t!+#t C&sts

,ighest observation of cost driver 0%5 '21"@?;owest observation of cost driver 122 12"?019ifference %10 ' @"?0?

ustomer*service department costs > a A b(number of service reports)

6lope coefficient (b) >%10

'@"?0?) '[email protected] per service report

onstant (a) > '21"@? # '[email protected] (0%5) > '?"050

> '12"?01 # '[email protected] (122) > '?"050ustomer*servicedepartment costs > '?"050 A '[email protected] (number of service reports)

%. Bther possible cost drivers of customer*service department costs are:a. +umber of products replaced with a new product (and the dollar value of the new

products charged to the customer*service department).b. +umber of products repaired and the time and cost of repairs.

SOTION EHIBIT 10-22

3lot of +umber of 6ervice


9/50

10-23 (%#0 min.) #+". %&st ".&!"t

1. 6lope coefficient (b) >

)0":"

0"'42?"

-

-

) '0%.

onstant (a) > '42?" # ('0%. G ")> '22@"

ost function > '22@" A '0%. (professional labor*hours)

The linear cost function is plotted in 6olution xhibit 1*2%.

+o" the constant component of the cost function does not represent the fixed overhead costof the &emphis 7roup. The relevant range of professional labor*hours is from %" to @".The constant component provides the best available starting point for a straight line that

approximates how a cost behaves within the %" to @" relevant range.

2. ! comparison at various levels of professional labor*hours follows. The linear costfunction is based on the formula of '22@" per month plus '0%. per professional labor*hour.

Total overhead cost behavior:

Mt 1 Mt 2 Mt 3 Mt 4 Mt 5 Mt 6

!ctual total overhead costs;inear approximation

!ctual minus linear approximation

'%0" %4"

'(1" )

'0" 0"

'

'0%4" 00%"

' (@" )

'0" 0@5"

' (?" )

'42?" 42?"

'

'4@" 42"

' 14"3rofessional labor*hours %" 0" 4" 5" " @"

The data are shown in 6olution xhibit 1*2%. The linear cost function overstates costs by'@" at the 4"*hour level and understates costs by '14" at the @"*hour level.

%. B"s+* B"s+* #+". A%t(" C&st (#%t

ontribution before deducting incremental overhead '%@" '%@"-ncremental overhead %4" 0%"

ontribution after incremental overhead ' %" ' (4")

The total contribution margin actually forgone is '%".

1*?


10/50

10-23 (ontFd.)

SOTION EHIBIT 10-23

;inear ost $unction 3lot of 3rofessional ;abor*,ourson Total Bverhead osts for &emphis onsulting 7roup

10-24 (2 min.) C&st-&(!+-.&'t "#* .+$.+ss "#",ss.

1a. !verage cost of manufacturing > framesbicycleof+umber

costsingmanufacturTotal

>%"

'?"> '% per frame

This cost is greater than the '[email protected] per frame that


11/50

10-24(ontFd.)

6ome students could argue that another reason for not being able to determine the cost ofmanufacturing %5" bicycle frames is that not all costs are output unit*level costs. -f somecosts are" for example" batch*level costs" more information would be needed on the number ofbatches in which the %5" bicycle frames would be produced" in order to determine the cost of

manufacturing %5" bicycle frames.

2. framesbicycle%5"(((ma.ecost to)xpected

> '0%2" A '14 %5"

> '0%2" A '40" > '?2"

3urchasing bicycle frames from


12/50

10-25 (24 min.) R+$.+ss "#",ss s+.%+ %&!"#,

1. 6olution xhibit 1*24 plots the relationship between labor*hours and overhead costs andshows the regression line.

y> '0@"21 A '%.?%X

Economic plausibility. ;abor*hours appears to be an economically plausible driver ofoverhead costs for a catering company. Bverhead costs such as scheduling" hiring and trainingof worers" and managing the worforce are largely incurred to support labor.

Goodness of fit. The vertical differences between actual and predicted costs are extremelysmall" indicating a very good fit. The good fit indicates a strong relationship between the labor*hour cost driver and overhead costs.

Slope of regression line. The regression line has a reasonably steep slope from left to right.7iven the small scatter of the observations around the line" the positive slope indicates that" onaverage" overhead costs increase as labor*hours increase.

2. The regression analysis indicates that" within the relevant range of 2"4 to "4 labor*hours" the variable cost per person for a coctail party euals:

$ood and beverages '14.

;abor (.4 hrs. '1 per hour) 4.

Variable overhead (.4 hrs '%.?% per labor*hour) 1 .?

Total variable cost per person '21 .?

%. To earn a positive contribution margin" the minimum bid for a 2*person coctail partywould be any amount greater than '0"%?0. This amount is calculated by multiplying the variable

cost per person of '21.? by the 2 people. !t a price above the variable costs of '0"%?0" DobEones will be earning a contribution margin toward coverage of his fixed costs.

Bf course" Dob Eones will consider other factors in developing his bid including (a) ananalysis of the competition##vigorous competition will limit EonesJs ability to obtain a higherprice (b) a determination of whether or not his bid will set a precedent for lower prices##overall"the prices Dob Eones charges should generate enough contribution to cover fixed costs and earn areasonable profit" and (c) a 8udgment of how representative past historical data (used in theregression analysis) is about future costs.

1*12


13/50

10-25 (ontFd.)

SOTION EHIBIT 10-25


14/50

10-25 (ontFd.)

1*10

Relationship Between Overhead Costs and Labor-

Hours

$0

$10,000

$20,000

$30,000

$40,000

$50,000

$60,000

$70,000

$0,000

$90,000

0 1000 2000 3000 4000 5000 6000 7000 000

Labor-Hours

Overhead

Costs


15/50

10-25 (ontFd.)Regression Output

)MMA*+ ")()(

Regression Statistics

Multiple * 0-90995276* .uare 0-962351731

A/uste/ * .uare 0-9556904tan/ar/ rr#r 1447-99647

"bser&ati#ns 12

A%"A

df SS MS F SignificanceF

*egressi#n 1 53594971 53594971 255-616459 1-91260*esi/ual 10 2096694-69 2096694-

(#tal 11 556916666-7

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95!% Upper 95!%

ntercept 4270-6112 124-7161 3-65619 3-2035612 454-30459 51052-93166 454-30459 51052-9316 ariable 1 3-9261317 0-245567266 15-900 1-91260 3-3797309 4-47329931 3-3797309 4-4732993

1*14


16/50

10-26 (% min.) R+$.+ss "#",ss "%tt,-/"s+* %&st#$ %&&s#$ %&st

*.+.s

1a. 6olution xhibit 1*25! presents the plots and regression line of number of pacaged unitsmoved on distribution costs.

SOTION EHIBIT 10-26A3lots and


17/50

10-26 (ontFd.)

+umber of pacaged units moved appears to be a better cost driver of distribution costs for thefollowing reasons:

(i) Economic plausibility. Doth number of pacaged units moved and number of shipments

are economically plausible cost drivers. Decause the product is heavy" however" costs offreight are liely to be a si=able component of distribution costs. Thus" number ofpacaged units moved will affect distribution costs significantly because freight costs arelargely a function of the number of units transported.

(ii) Goodness of fit. ompare 6olution xhibits 1*25! and 1*25D. +umber of pacagedunits moved has a better goodness of fit with distribution costs than do number ofshipments made. That is" the vertical differences between actual and predicted distributioncosts are smaller for the number of pacaged units moved regression than for the number ofshipments made regression.

(iii) Slope of regression line. !gain" compare 6olution xhibits 1*25! and 1*25D. Thenumber of pacaged units moved regression line has a relatively steep slope and a smallscatter of observations around the regression lines indicating a strong relationship betweennumber of pacaged units moved and distribution costs. Bn average" distribution costsincrease with the number of pacaged units moved. The number of shipments maderegression line is flatter and has more scatter of observations about the line indicating awea relationship between the number of shipments made and distribution costs. Bnaverage" the number of shipments made has a smaller effect on distribution costs.

2. Ksing the preferred cost function"

9istribution costs > '1"%0? A ('.0?5 +umber of pacaged units moved)"

$laherty would budget distribution costs of'1"%0? A ('.0?5 0") > '1"%0? A '1?"@0 > '21"1@?

10-27 (2 min.) +".##$ %(.+ %(!("t+ "+."$+-t!+ +".##$ !&*+

The direct manufacturing labor*hours (9&;,) reuired to produce the first 2" 0" and @units given the assumption of a cumulative average*time learning curve of ?H" is as follows:

C(!("t+

N(!/+. &' #ts

;1 %""X> 2" 0" or @" and b > # .142" which gives

whenX> 2" y> %" 2# .142> 2"

whenX> 0" y> %" 0# .142> 2"0%

whenX> @" y> %" @# .142> 2"1@

V"."/+ C&sts &' P.&*(%#$

2 #ts 4 #ts 8 #ts

9irect materials '@" 2L 0L @

9irect manufacturing labor

'24 4"0L ?"2L 1"0?5

Variable manufacturing overhead

'14 4"0L ?"2L 1"0?5

Total variable costs

'15"

1%4"

@1"

'%5"

'%2"

20%"

104"@

'@"@

' 50"

0%"0

252"00

'1"%%?"@0

10-28 (2 min.) +".##$ %(.+ #%.+!+#t" (#t-t!+ +".##$ !&*+

1. The direct manufacturing labor*hours (9&;,) reuired to produce the first 2" %" and 0units" given the assumption of an incremental unit*time learning curve of ?H" is as follows:

C(!("t+

N(!/+.

&' #ts

;1 # .142" which gives

whenX> 2" y> %" 2# .142> 2"

whenX> %" y> %" %# .142> 2"4%?

whenX> 0" y> %" 0# .142> 2"0%

1*1@


19/50

10-28 (ontFd.)V"."/+ C&sts &' P.&*(%#$

2 #ts 3 #ts 4 #ts

9irect materials '@" 2L %L 0

9irect manufacturing labor

'24 4"L @"2%?L 1"55?

Variable manufacturing overhead '14 4"L @"2%?L 1"55?

Total variable costs

'15"

102"4

@4"4'%@@"

'20"

24"?4

12%"4@4'45?"45

' %2"

255"24

15"%4'05"5

2. V"."/+ C&sts &'P.&*(%#$

2 #ts 4 #ts

-ncremental unit*time learning model (from reuirement 1)umulative average*time learning model (from xercise 1*2)

9ifference

'%@@"

%5"

' 12"

'05"5

@"@

' %"?5

Total variable costs for manufacturing 2 and 0 units are lower under the cumulativeaverage*time learning curve relative to the incremental unit*time learning curve. 9irectmanufacturing labor*hours reuired to mae additional units decline more slowly in theincremental unit*time learning curve relative to the cumulative average*time learning curve whenthe same ?H factor is used for both curves. The reason is that" in the incremental unit*timelearning curve" as the number of units double" only the last unit produced has a cost of ?H ofthe initial cost. -n the cumulative average*time learning model" doubling the number of unitscauses the average cost of allthe additional units produced (not 8ust the last unit) to be ?H ofthe initial cost.

10-29 (24 min.) H$-&: !+t&*

1. M"%#+-H&(.s M"#t+#"#%+ C&sts

,ighest observation of cost driver 124" '24";owest observation of cost driver @4" 1"9ifference 0" ' @"

&aintenance costs > aA b(&achine*hours)

6lope coefficient (b) > 0"

'@"

> '2onstant (a) > '24" # ('2 G 124")

> '24" # '24" > 'or onstant (a) > '1" # ('2 G @4")

> '1" # '1" > '&aintenance costs > '2 G &achine*hours

1*1?


20/50

10-29 (ontFd.)

2.SOTION EHIBIT 10-293lot and ,igh*;ow ;ine of &achine*,ours on &aintenance osts

6olution xhibit 1*2? presents the high*low line.

Economic plausibility. The cost function shows a positive economically plausible relationshipbetween machine*hours and maintenance costs. There is a clear*cut engineering relationship ofhigher machine*hours and maintenance costs.

Goodness of fit. The high*low line appears to MfitN the data well. The vertical differencesbetween the actual and predicted costs appear to be uite small.

Slope of high-low line.The slope of the line appears to be reasonably steep indicating that" onaverage" maintenance costs in a uarter varies with machine*hours used.

%. Ksing the cost function estimated in 1" predicted maintenance costs would be '2 G ?"> '1@".

,oward should budget '1@" in uarter 1% because the relationship between machine*hours and maintenance costs in 6olution xhibit 1*2? is economically plausible" has anexcellent goodness of fit" and indicates that an increase in machine*hours in a uarter causesmaintenance costs to increase in the uarter.

1*2

1(("(((

12("(((

10("(((

15("(((

1@("(((

2(("(((

22("(((

20("(((

'25("(((

@("((( ?("((( 1(("((( 11("((( 12("((( 1%("(((

M"%8#+-H&(.s

M"#t+#"#%+C&sts


21/50

10-30 (%0 min.) H$-&: !+t&* +.s(s .+$.+ss "#",ss

1. 6olution xhibit 1*% presents the plots of advertising costs on revenues.

SOTION EHIBIT 10-30

3lot and


22/50

10-30(ontFd.)

%. The high*low method would estimate the cost function as follows:

A*+.ts#$ C&sts R++#(+s

,ighest observation of cost driver '0" '@"

;owest observation of cost driver 1" 44"9ifference '%" '24"

aA (badvertising costs)

6lope coefficient (b) ='%"

'24"> @.%%%

onstant (a) > '@" ('0" @.%%%)

> '@" %%"%%2 > '05"55@

or onstant (a) > '44" ('1" @.%%%)

> '44" @"%%% > '05"55

'05"55 A (@.%%% !dvertising costs)

0. The increase in revenues for each '1" spent on advertising within the relevant range is

a. Ksing the regression euation" @.2% '1" > '@"2%

b. Ksing the high*low euation" @.%%% '1" > '@"%%%

The high*low euation does fairly well in estimating the relationship between advertisingcosts and revenues. ,owever" &artine= and Drown should use the regression euation. Thereason is that the regression euation uses information from all observations whereas the high*low method relies only on the observations that have the highest and lowest values of the costdriver. These observations are generally not representative of all the data.

10-31 (%#%4 min.) R+$.+ss "#",ss "%tt,-/"s+* %&st#$ %&&s#$ %&st*.+.s

1. 6olution xhibit 1*%1! presents the plots and regression line of machine#hours onsupport overhead. 6olution xhibit 1*%1D presents the plots and regression line of number ofbatches on support overhead. !s described below" using the three criteria of economicplausibility" goodness of fit" and slope of regression line" hu should choose number of batchesas the cost driver of support overhead costs.

Economic plausibility. +umber of batches appears to be a more plausible cost driver of supportoverhead costs than machine*hours. 6upport staff indicate that they spend a good portion of their

time at the start of each batch ensuring that the euipment is set up correctly and checing thatthe first units of production in each batch are of good uality. Bnce the machine is woringproperly" support staff are not needed to supervise the actual running of the machines.onseuently" support staff resources are more liely to vary with the number of batches ratherthan the total number of machine*hours wored.

1*22


23/50

10-31(ontFd.)

Goodness of fit. ompare 6olution xhibits 1*%1! and 1*%1D. The vertical differencesbetween actual and predicted costs are much smaller for number of batches than for machine*hours. This indicates that number of batches has a better fit and a stronger relationship withsupport overhead costs.

Slope of regression line. !gain" compare 6olution xhibits 1*%1! and 1*%1D. The slope ofthe regression line of number of batches on support overhead is relatively steep with less scatterof observations about the regression line while the regression line of machine*hours on supportoverhead is relatively flat (small slope) with more scatter of observations about the regressionline. ! relatively steep regression line with less scatter for number of batches indicates that" onaverage" support overhead costs increase as number of batches increase. Bn the other hand" therelatively flat regression line for machine*hours with more scatter indicates a wea or norelationship between support overhead costs and machine hours##on average" changes inmachine*hours appear to have a minimal effect on support overhead costs.

2. !s described in reuirement 1" number of batches is the preferred cost driver. Ksing thiscost driver and the regression euation y > '15"%1 A '1?.% number of batches" hu should

budget the following support overhead costs for the % batches that will be run next month:

y > '15"%1 A '1?.% % > '15"%1 A '4?"1? > '4"221.

%a. Ksing machine*hours as the cost driver and the regression euationy> '2@"@? A '1.2%

machine*hours" hu would budget support overhead costs for the 2"5 machine*hours that willbe wored next month as:

y> '2@"@? A '1.2% 2"5 > '2@"@? A '25"4?@ > '40"5@

B(*$+t+* R++#(+s "#* C&sts '&.

N+t Mt s#$

N(!/+. &' B"t%+s

"s t+ C&st D.+.

M"%#+-H&(.s "s

t+ C&st D.+.

osts other than support overhead6upport overhead costsTotal costs!dd margin of 2H of total costsTarget revenues

'124" 4"2212"221

0"00'20"254

'124" 40"5@

1?"5@ %4"?%'214"520

3icing machine*hours rather than the number of batches as the cost driver will cause huto underestimate costs and choose lower target revenues and prices. 6upport overhead costs"however" will vary with number of batches rather than machine*hours. Ksing information fromthe preceding table" actual costs will be closer to '2"221 against target revenues of '214"520.Target profitability is unliely to be met. /ith better cost driver information hu wouldprobably have priced products higher and earned greater revenues" assuming" of course" thatcustomers are willing to pay the higher prices.

1*2%


24/50

10-31(ontFd.)

hoosing the OwrongO cost driver and estimating the incorrect cost function will alsohave repercussions for cost management and cost control. 6uppose


25/50

10-31(ontFd.)

SOTION EHIBIT 10-31B


26/50

10-33 (%#0 min.) C&st +st!"t %(!("t+ "+."$+-t!+ +".##$

%(.+

1. ost to 3roduce the 6econd through the ighth Troop 9eployment Doats:

9irect materials" '1" ' "9irect manufacturing labor" %?"1%P '% 1"1%"?

Variable manufacturing overhead" %?"1% '2 @2"5

Bther manufacturing overhead" 24H of '1"1%"? 2?%"04Total costs '2"?0?"?4

PThe direct manufacturing labor*hours to produce the second to eighth boats can be calculated in several ways"given the assumption of a cumulative average*time learning curve of @4H:

a. Kse of Table $ormat:

C(!("t+N(!/+. &'

#ts

C(!("t+A+."$+-T!+

+. #t

C(!("t+T&t"

T!+

120@

1".

@"4. (1" .@4)

"224. (@"4 .@4)

5"101.24 ("224 .@4)

1"1"2@"?0?"1%

The direct labor*hours reuired to produce the second through the eighth boats is 0?"1% #1" > %?"1% hours.

b. Kse of $ormula:

y> aXb

where a> 1"" X> @" and b> # .2%04

y > 1" @# .2%04> 5"101 hours (rounded)

The total direct labor*hours for @ units is 5"101 @ > 0?"12@ hours

The direct labor*hours reuired to produce the second through the eighth boats is 0?"12@ #

1" > %?"12@ hours. (Dy taing the bfactor to 5 decimal digits" an estimate of 0?"1%hours would result.)

Note: 6ome students will debate the exclusion of the tooling cost. The uestion specifies thatthe tooling Ocost was assigned to the first boat.O !lthough +autilus may well see to ensure itstotal revenue covers the '24" cost of the first boat" the concern in this uestion is only withthe cost of producing seven more 3T1?s.

1*25


27/50

10-33 (ontFd.)

2. ost to 3roduce the 6econd through the ighth Doats !ssuming ;inear $unction for 9irect;abor*,ours and Knits 3roduced:

9irect materials" '1" ' "

9irect manufacturing labor" 1" hours '% 2"1"

Variable manufacturing overhead" 1" hours '2 1"0"Bther manufacturing overhead" 24H of '2"1" 424"Total costs '0"24"

The difference in predicted costs is:

3redicted cost in reuirement 2 (based on linear cost function) '0"24"3redicted cost in reuirement 1 (based on an @4H learning curve) 2"?0?"?49ifference '1"4"24

10-34 (2#% min.) C&st +st!"t #%.+!+#t" (#t-t!+ +".##$ !&*+

1. ost to 3roduce the 6econd through the ighth Doats:

9irect materials" '1" ' "

9irect manufacturing labor" 0?"%45P '% 1"0@"5@

Variable overhead" 0?"%45 '2 ?@"12

Bther overhead" 24H of '1"0@"5@ %"1Total costs '%"4%"?

PThe direct labor hours to produce the second through the eighth boats can be calculated via atable format" given the assumption of an incremental unit*time learning curve of @4H:

C(!("t+

N(!/+.

&' #ts

I#**("

#t T!+

'&.Xt #t ;mpXq

wherep> 1"" q> # .2%04" and X> 1" 2" %". . ." @.

1*2


28/50

10-34 (ontFd.)

The direct manufacturing labor*hours to produce the second through the eighth boat is 4?"%45 #1" > 0?"%45 hours.

2. 9ifference in total costs to manufacture the second through the eighth boat under the

incremental unit*time learning model and the cumulative average*time learning model is'%"4%"? (calculated in reuirement 1 of this problem) # '2"?0?"?4 (from reuirement 1 of3roblem 1*%%) > '4@"??4.

The incremental unit*time learning curve has a slower decline in the reduction in timereuired to produce successive units than does the cumulative average*time learning curve (see3roblem 1*%%" reuirement 1). !ssuming the same @4H factor is used for both curves:

Est!"t+* C(!("t+ D.+%t M"#('"%t(.#$ "/&.-H&(.s

C(!("t+

N(!/+. &' #ts

C(!("t+ A+."$+-

T!+ +".##$ M&*+

I#%.+!+#t" #t-T!+

+".##$ M&*+

120@

1"1"2@"?0?"1%

1"1@"4%%"0404?"%45

The reason is that" in the incremental unit*time learning model" as the number of unitsdouble" only the last unit produced has a cost of @4H of the initial cost. -n the cumulativeaverage*time learning model" doubling the number of units causes the average cost of all theadditional units produced (not 8ust the last unit) to be @4H of the initial cost.

+autilus should examine its own internal records on past 8obs and see information fromengineers" plant managers" and worers when deciding which learning curve better describes thebehavior of direct manufacturing labor*hours on the production of the 3T1? boats.

1*2@


29/50

10-35 (%#0 min.) E"("t#$ "t+.#"t+ .+$.+ss !&*+s #.&'t

1a. 6olution xhibit 1*%4! plots the relationship between number of academic programs andoverhead costs.

1b. 6olution xhibit 1*%4D plots the relationship between number of enrolled students and

overhead costs.

2. 6olution xhibit 1*%4 compares the two simple regression models estimated by ,ans.Doth regression models appear to perform well when estimating overhead costs. ost function 1using number of academic programs as the independent variable appears to perform slightlybetter than cost function 2 which uses number of enrolled students as the independent variable.

ost function 1 has a high r and goodness of fit" a high t*value indicating a significantrelationship between number of academic programs and overhead costs" and meets all the

specification assumptions for ordinary least suares regression. ost function 2 has a lower r

than cost function 1 and exhibits positive autocorrelation among the residuals" as indicated by alow 9urbin*/atson statistic.

%. The analysis indicates that overhead costs are related to the number of academic programsand the number of enrolled students. -f 6outhwestern has pressures to reduce and controloverhead costs" it may need to loo hard at closing down some of its academic programs andreducing its intae of students.


30/50

10-35(ontFd.)


3lot of +umber of nrolled 6tudents versus Bverhead osts (in thousands)

1*%

(

( 1"((( 2"((( %"((( 0"((( 4"((( 5"((( :"(((

N(!/+. &' E#.&00+* St(*+#ts

@"(((

O+.8+"*C&sts

%4"(((

'0("(((

%("(((

24"(((

2("(((

14"(((

1("(((

4"(((


31/50

10-35 (ontFd.)

SOTION EHIBIT 10-35C

omparison of !lternative ost $unctions for Bverhead osts stimated with 6imple . indicates thatindependence of residualsdoes not hold.

10-36 (% min.) E"("t#$ !(t+ .+$.+ss !&*+s #.&'t;%t#("t &' P.&/+! 10-35


32/50

10-36 (ontFd.)

2. 6olution xhibit 1*%5! evaluates the multiple regression model using the format ofxhibit 1*1?. ,ans should use the multiple regression model over the two simple regressionmodels of 3roblem 1*%4. The multiple regression model appears economically plausible" andthe regression model performs very well when estimating overhead costs. -t has an excellent

goodness of fit" significant t-values on both independent variables" and meets all the specificationassumptions for ordinary least*suares regression.There is some correlation between the two independent variables but multicollinearity does

not appear to be a problem here. The significance of both independent variables (despite somecorrelation between them) suggests that each variable is a driver of overhead cost. Bf course" asthe chapter describes" even if the independent variables exhibited multicollinearity" ,ans shouldstill prefer to use the multiple regression model over the simple regression models of 3roblem1*%4. Bmitting any one of the variables will cause the estimated coefficient of the independentvariable" included in the model" to be biased away from its true value.

%. 3ossible uses for the multiple regression results include:

a. 3lanning and budgeting at 6outhwestern Kniversity. The regression analysisindicates the variables (number of academic programs and number of enrolledstudents) that help predict changes in overhead costs.

b. ost control and performance evaluation. ,ans could compare actual performancewith budgeted or expected numbers and see ways to improve the efficiency of theKniversity operations" and evaluate the performance of managers responsible forcontrolling overhead costs.

c. ost management. -f cost pressures increase" the Kniversity might save costs byclosing down academic programs that have few students enrolled.

1*%2


33/50

10-36(ontFd.)

SOTION EHIBIT 10-36A

valuation of ost $unction for Bverhead osts stimated with &ultiple 1.@0 indicates thatindependence of residuals holds.

1*%%


34/50

10-37 (0#4 min.) P(.%"s#$ D+".t!+#t %&st *.+.s "%tt,-/"s+*

%&st#$ s!+ .+$.+ss "#",ss

The problem reports the exact t*values from the computer runs of the data. Decause thecoefficients and standard errors given in the problem are rounded to three decimal places"

dividing the coefficient by the standard error may yield slightly different t*values.

1. 3lots of the data used in


35/50

10-37(ontFd.)

SOTION EHIBIT 10-37A


36/50

10-37(ontJd.)


omparison of !lternative ost $unctions for 3urchasing 9epartmentosts stimated with 6imple 2.01!ssumption ofindependence is notre8ected.

9urbin*/atson6tatistic > 1.?@!ssumption ofindependence is notre8ected.

9urbin*/atson6tatistic > 1.?!ssumption ofindependence is notre8ected.

9. +ormality ofresiduals

9ata base too small tomae reliableinferences.

9ata base too small tomae reliable inferences.

9ata base too small tomae reliableinferences.

1*%5


37/50

10-38 (%#0 min.) P(.%"s#$ D+".t!+#t %&st *.+.s !(t+

.+$.+ss "#",ss ;Ct#("t &' 10-37


38/50

10-38(ontFd.)

V"."/+s

t-"(+ #

M(t+ R+$.+ss

t-"(+ '.&!

S!+ R+$.+sss

# P.&/+! 10-37

#egression $:

Q of 3BsQ of 6s

2.102.

2.0%2.2@

#egression %:

Q of 3BsQ of 6s&3'

1.?41.@0

#.

2.0%2.2@.@0

The decline in the t*values in the multiple regressions is consistent with some (but not very high)collinearity among the independent variables. 3airwise correlations between the independentvariables are:

C&..+"t

Q of 3Bs R Q of 6s .2?Q of 3Bs R &3' .2Q of 6s R &3' .%0

There is no evidence of difficulties due to multicollinearity in


39/50

10-39 (%4 min.) R+$.+ss %&!(t"ts +t%s

1. Ksing the formulas given in the appendix"

a =)S)(S()S(n

)ST)(S()ST)((

2

2

and b>

)S)(S()S(n

))(S()S(n

2

where n > 0

S > sum of the given S values (units produced) > ?" A 1" A ?" A 12"> 0"

S2 > sum of suares of 6 values > (?")2A (1")2A (?")2 (12")2> 05""

> sum of the given values (manuf. labor costs) > '15" A '10" A '154"

'24" > '2"

S > (?" 15") A (1" 10") A (?" 154") A (12" 24")

> "25?""

a >)"0"0()""05(0

)""25?":"0()""05":2(

> 54"

b >)"0)("0()""05(0

)":2)("0()""25?":(0

> 11.4

The regression euation isy> '54" A ('11.4 units produced)

2. !llison ,artJs benchmar for uarter 4 is

'54" A ('11.4 12") > '2%"

%. 3eter 6mithJs benchmar differs from !llison ,artJs benchmar because 6mith considers

all manufacturing labor costs as variable at '1@ per motor ('2" 0"). ,art recogni=es

that some manufacturing labor costs are fixed and other manufacturing labor costs are variable.The cost function that ,art estimates separates out '54" as the fixed component of costswithin the relevant range and '11.4 as the variable cost per motor. leveland ngineeringproduces a large uantity of motors in uarter 4 (12"). 6mithJs benchmar is high because itassumes a proportionate increase in manufacturing labor costs at '1@ per motor. ,artJsbenchmar is lower because fixed manufacturing labor costs will not change even though thevolume of production is high. Bnly the variable component of manufacturing labor costs (eualto '11.4 per motor) will increase.

,artJs benchmar is preferred because it recogni=es the appropriate cost*behavior patternsof manufacturing labor costs.

0. ,art should explain to 6mith why the benchmar is lower than what 6mith had calculated.6he should also indicate to 6mith her concern about ad8usting the numbers. 6uch behavior

would violate the M6tandards of thical conduct for &anagement !ccountsN described inhapter 1. !d8usting the numbers would violate the standards of competence" integrity" andob8ectivity reuired of management accountants and would be unethical. -f 6mith still insists onreporting a higher benchmar" ,art should raise the matter with 6mithJs superior. -f" after taingall these steps" there is continued pressure to overstate the benchmar" ,art should considerresigning from the company rather than engaging in unethical behavior.

1*%?


40/50

10-40 (0 min.) H$-&: !+t&* "t+.#"t+ .+$.+ss '(#%ts "%%.("

"%%&(#t#$ "*F(st!+#ts

1. 6olution xhibit 1*0! presents the two data plots. The plot of engineering supportreported costs and machine*hours shows two separate groups of data" each of which may beapproximated by a separate cost function. The problem arises because the plant records

materials and parts costs on an Oas purchased"O rather than an Oas used"O basis. The plot ofengineering support restated costs and machine*hours shows a high positive correlation betweenthe two variables (the coefficient of determination is .?0)L a single linear cost function providesa good fit to the data. Detter estimates of the cost relation result because Cennedy ad8usts thematerials and parts costs to an accrual accounting basis.

2.C&st D.+.

M"%#+-H&(.s

R+&.t+* E#$#++.#$

S(&.t C&sts

,ighest observation of cost driver (!ugust);owest observation of cost driver (6eptember)

9ifference

%1?

40

' 51 1"55

' (00?)

6lope coefficient" b >

> > #'@.%1 per machine*hour

onstant (at highest observation of cost driver) > ' 51 # (#'@.%1 %) > '1"220

onstant (at lowest observation of cost driver) > '1"55 # (#'@.%1 1?) > '1"220

The estimated cost function isy> '1"220 # '@.%1X

C&st D.+.M"%#+-H&(.s

R+st"t+* E#$#++.#$S(&.t C&sts

,ighest observation of cost driver (!ugust);owest observation of cost driver (6eptember)9ifference

%1?40

'?55 %'4?5

6lope coefficient" b >

> > '11.0 per machine*hour

1*0


41/50

10-40(ontFd.)

onstant (at highest observation of cost driver) > ' ?55 # ('11.0 %) > '15

onstant (at lowest observation of cost driver) > ' % # ('11.0 1?) > '15

The estimated cost function isy > '15 A '11.0X

%. The cost function estimated with engineering support restated costs better approximates theregression analysis assumptions. 6ee 6olution xhibit 1*0D for a comparison of the tworegressions.

0. Bf all the cost functions estimated in reuirements 2 and %" Cennedy should choose .?0) and appears to be well specified.

4. 3roblems Cennedy might encounter include:a. ! perpetual inventory system may not be used in this caseL the amounts reuisitioned

liely will not permit an accurate matching of costs with the independent variable ona month*by*month basis.

b. uality of the source records for usage by engineers may be relatively lowL e.g."

engineers may reuisition materials and parts in batches" but not use themimmediately.c.


42/50

10-40(ontFd.)

Bn the other hand" if machine*hours wored in a month were low" say 24 hours" '1"%.04. -f

actual costs are '" management would conclude that its performance has been very good. -n

fact" compared to the costs predicted by the preferred '052.%@" the actual performance is rather poor. Ksing


43/50

10-40(ontFd.)


omparison of !lternative ost $unctions for ngineering 6upport osts at Knited 3acaging

CRITERION

R+$.+ss 1

D++#*+#t V"."/+

E#$#++.#$ S(&.t

R+&.t+* C&sts

R+$.+ss 2

D++#*+#t V"."/+

E#$#++.#$ S(&.t

R+st"t+* C&sts

1. conomic 3lausibility +egative slope relationship iseconomically implausible overthe long run.

3ositive slope relationship iseconomically plausible.

2. 7oodness of $it r2> .0%. &oderate goodness

of fit.

r2> .?0. xcellent goodness

of fit.

%. 6ignificance of-ndependent Variables

t*statistic on machine*hours isstatistically significant(t> #2.%1)" albeit economicallyimplausible.

t*statistic on machine*hours ishighly statistically significant(t>1.4?).

0. 6pecification !nalysis:!. ;inearity ;inearity does not describe

data very well.;inearity describes data verywell.

D. onstant variance ofresiduals !ppears uestionable" although12 observations do notfacilitate the drawing ofreliable inferences.

!ppears reasonable" although12 observations do notfacilitate the drawing ofreliable inferences.

. -ndependence ofresiduals

9urbin*/atson > 2.25. 1.%1. 6omeevidence of serial correlationin the residuals.

9. +ormality ofresiduals

9atabase too small to maereliable inferences.

9atabase too small to maereliable inferences.

1*0%


44/50

C"t+. 10 I#t+.#+t E+.%s+

)he *nternet e+ercise is a"ailable to students only on the 'rentice ,all &ompanion ebsitewww.prenhall.comhorngren. Students can clic/ on &ost (ccounting0 !!thed.0 and access the

*nternet E+ercise for the chapter0 which lin/s to the eb site of a company or organi1ation. )he

*nternet E+ercise on the eb will be updated periodically so that it is current with the latest

information a"ailable on the sub2ect organi1ation3s eb site. ( printout copy of the *nternete+ercise for this chapter as of early 44 appears below.

)he solution to the *nternet e+ercise0 which will also be updated periodically0 is a"ailable

to instructors from the &ompanion ebsite3s faculty "iew. )o access the solution0 clic/ on &ost(ccounting0 !!thed.0 5aculty lin/0 and then register once to obtain your password through the

online form. (fter the initial registration0 you will ha"e a personal login *6 and password to use

to log in. ( printout of the solution to the *nternet e+ercise for this chapter as of early 44follows. )he e+ercise and solution pro"ide instructors with an idea of the content of the *nternet

e+ercise for this chapter.

I#t+.#+t E+.%s+

6outhwest !irlines is the nationJs fifth largest domestic carrier. -t serves 4 cities with a fleet of%42 Doeing %s. 6outhwest 8ust mared its 2@th consecutive year of profitability and en8oys thedistinction of having the lowest operating cost structure in the domestic airline industry. -n thisexercise you will investigate possible cost drivers for allocating salary" wages" and benefitsexpense.

7o to http:RRwww.iflyswa.comR" and clic on the O!bout 6/!O lin" followed by theO-nvestor


45/50

I#t+.#+t E+.%s+ (ontFd.)

S&(t t& I#t+.#+t E+.%s+

1a.


46/50

C"t+. 10 C"s+

S BREWING INDSTR COST ESTIMATION

1. (a) Ksing the high*low method:

,ighest Darrels 6old > 1.% ost of 6ales > '5?5.%?;owest Darrels 6old > 4.@00 ost of 6ales > '155.?0%9ifference 11.1?% '42?.?5slope coefficient (b) > '42?.?5 11.1?% > '0.2

constant (a) > '5?5.%? # ('0.2 1.%)

> #' 1?.%

t > #'1?.% A ('0.2 Vt)

! potential ambiguity in the high*low method is whether high*low is defined in terms ofthe dependent or independent variable. -n this case" the choice is important as the highest cost of

sales figure is 2" whereas the highest volume figure is 1??5. The independent variable isused when determining the high and low observations as the causality runs from barrels producesto costs incurred.

(b) The results are reported in .21?). The conseuence is that theestimated standard errors are underestimates of the underlying population values.

7oodness of $it # The ad8usted


47/50

C"s+ (ontFd.)

2. The results are reported in .510.

3roblems include:

(a) The /holesale 3rice -ndex of Deer (/3-D) is an output*based index for the whole industrythat need not be representative of the specific wholesale price changes for !ce. Bne could builda firm specific index to overcome this problem.

(b) The /3-D may not be a good proxy for changes in input prices to either the industry or !ce.The Most of 6alesN series is an aggregate of the costs of labor" raw materials (malt" corn" barley"hops" etc.)" depreciation" excise taxes" mareting" etc. 9eflating by the /3-D assumes thatchanges in the prices of the inputs can be well approximated by changes in the /3-D. !nalternative approach is to build a firm*specific index based on changes in prices of !ceFs inputs.(c) /ith any time*series index" issues of structural change arise. The /3-D may reflect anonconstant mix of beer products over time (malt" light" premium" super*premium" etc.).&oreover" even if the mix of the output was constant" the mix of the inputs may have changed inthe 1?@2*2 period" e.g." an increase in the capitalRlabor ratio through the construction ofmechani=ed" high*volume breweries.(d) 9ata availability problems may arise due to the delay in publishing aggregate industry

indexes.

%. Dacground information: 6erial correlation in the residuals exists when there is asystematic pattern in the residuals such that nowledge of the residual at time t conveysinformation about the residuals at time tA1" tA2" etc. ! variety of reasons could cause serialcorrelation in the residuals of a linear model" e.g."

(i) Knderlying model is nonlinearUtwo possible rationales for a nonlinear model are:* costs are MsticyN downwardsUi.e." when volume decreases by 1H" costs do not

decrease as much as the linear model predicts. $ixed capacity costs couldpotentially be important for !ce in the 1??5 to 2 period when volume declined

from 1.% to 14.?1 million barrels.* Mexperience curveN phenomenon could result in costs increasing less than thelinear model predicts.

(ii) Knderlying model is linear but includes more than one variable and the omittedvariable results in the MresidualsN being serially correlated. Bmitted variables couldinclude the number of employees and the number of advertisements placed in variousmedia.

1*0


48/50

C"s+(ontFd.)

(iii) !ctivity levels over time have high percentage of commonality. -t is a commonfinding that models estimated in levels exhibit serial correlation * * see . /. E.7ranger and 3. +ewbold" M6purious


49/50

V*+& C"s+ (ontFd.)

Case Ehibit !

Regression a t-value bt-value

R"Durbin-#atson

1 8t :;t< =267-10 =3-91 59-52 10-749 0-64 0-219

2t

t

'

& :;t< =30-517 =2-20 55-360 50-910 0-993 0-614

3 =

1

1

t

t

t

t

'

&

'

& :;t = t

1

capitol 10 corect

Documents