costacctg13_keyxl_ch10

8/12/2019 costacctg13_keyxl_ch10

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Week

Cost Driver:

Machine-Hours

Indirect

Manufacturing

Labor Costs XX Y-Y (X-X)2 (y-y)2(X) (Y)

1 68.00 1190.00 -3.83 148.25 14.69 21978.06252 88.00 1211.00 16.17 169.25 261.36 28645.5625

3 62.00 1004.00 -9.83 -37.75 96.69 1425.06254 72.00 917.00 0.17 -124.75 0.03 15562.56255 60.00 770.00 -11.83 -271.75 140.03 73848.06256 96.00 1456.00 24.17 414.25 584.03 171603.06257 78.00 1180.00 6.17 138.25 38.03 19113.06258 46.00 710.00 -25.83 -331.75 667.36 110058.06259 82.00 1316.00 10.17 274.25 103.36 75213.062510 94.00 1032.00 22.17 -9.75 491.36 95.0625

11 68.00 752.00 -3.83 -289.75 14.69 83955.062512 48.00 963.00 -23.83 -78.75 568.03 6201.5625

Total 862.00 12501.00 0.00 0.00 2979.67 607698.25

71.83 1041.75 1810738219

Intercept 300.9762837 b=((x-x)(y-y))/(X-X)2Slope 10.31239512Rsquare 0.521433328 b 10.31239512


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(X-X)(Y-Y)

-568.29166672736.208333

371.2083333-20.791666673215.70833310011.04167852.54166678570.2083332788.208333

-216.125

1110.7083331876.875

30727.50

1.69696E-05


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Week

Original

Cost Driver:

Machine-Hours

Alternate Cost Driver:

Direct Manufacturing

Labor-Hours

(X)

Indirect

Manufacturing

Labor Costs

(Y)

1 68 30 $ 1,1902 88 35 1,211

3 62 36 1,0044 72 20 9175 60 47 7706 96 45 1,4567 78 44 1,1808 46 38 7109 82 70 1,31610 94 30 1,032

11 68 29 75212 48 38 963

Total 862 462 $12,501


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Cumulative Average-Time Learning Model for Rayburn Corporation

80% Learning Curve

Cumulative Cumulative Cumulative Individual UnitsNumber Average Time Total Time: Time for Xth

of Units (X) per Unit (y )*: Labor Hours Labor-Hours Unit: Labor Hours

100.002 80.00 =(100 0.8) 160.00 60.003 70.21 210.63 50.634 64.00 =(80 0.8) 256.00 45.37

5 59.56 297.82 41.826 56.17 337.01 39.197 53.45 374.14 37.138 51.20 =(64 0.8) 409.60 35.46

9 49.29 443.65 34.0510 47.65 476.51 32.8611 46.21 508.32 31.8112 44.93 539.22 30.8913 43.79 569.29 30.0714 42.76 598.63 29.34

15 41.82 627.30 28.6716 40.96 =(51.2 0.8) 655.36 28.06

1 100.00 100.00

D = Col A x Col B

*The mathematical re

learning model is:

wherey= Cumulative

X= Cumulative

a= Time (labob= Factor used

produce u

The value of bis calc

For an 80% learning cwhenX= 3, a= 100,

Numbers in table may

ln (learning

y = 100 x 3-0.


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E13 = D13 D12

= 210.63 160.00

lationship underlying the cumulative average-time

average time (labor-hours) per unit

number of units producedr-hours) required to produce the first unit

to calculate cumulative average time to its

lated as

urve, b= ln 0.8/ln 2 = -0.2231/0.6931 = -0.3219

= -0.3219,

not be exact because of rounding.

-curve % in decimal form

y=aXb

.3219= 70.21 labor hours


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Learning curve 80% For an 80% learning curve, y = 100 X^-0.3219


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Incremental Unit-Time Learning Model for Rayburn Corporation

80% Learning Curve

Cumulative Individual Unit Time Cumulative CumulativeNumber for Xth Unit (y )* Total Time: Average Time

of Units (X) Labor Hours Labor-Hours per Unit:Labor-Hours

100.002 80.00 =(100 0.8) 180.00 90.003 70.21 250.21 83.40

4 64.00 =(80 0.8) 314.21 78.555 59.56 373.77 74.756 56.17 429.94 71.667 53.45 483.39 69.06

8 51.20 =(64 0.8) 534.59 66.829 49.29 583.89 64.8810 47.65 631.54 63.1511 46.21 677.75 61.6112 44.93 722.68 60.2213 43.79 766.47 58.96

14 42.76 809.23 57.8015 41.82 851.05 56.7416 40.96 =(51.2 0.8) 892.01 55.75

E = Col D Col A

1 100.00 100.00

*The mathematicallearning model is:

wherey= Time (lab

X= Cumulati

a= Time (lab b= Factor us

=For an 80% learningWhereX= 3, a= 10

The cumulative tota

Numbers in table m

ln (lear

y = 100 x 3-0.


8/36

D14 = D13 + B14= 180.00 + 70.21

elationship underlying the incremental unit-time

or-hours) taken to produce the last single unit e number of units produced

or-hours) required to produce the first unit ed to calculate incremental unit time to produce units

curve, b= ln 0.8 ln 2 = -0.2231 0.6931 = -0.32190, b= -0.3219,

l time whenX= 3 is 100+80+70.21=250.21 labor-hours.

y not be exact because of rounding.

ning-curve % in decimal form

y=aXb



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Learning curve 80% For an 80% learning curve, y = 100 X^-0.3219


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0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

CumulativeAverageTimepe

rUnit

(Labor-Hours)(Y)

Cumulative Number of Units(X)

Panel A: Cumulative Average Time per Unit (80%Learning Curve; First Unit Takes 100 Labor-Hours)

Incremental Unit-TimeLearning Model

Cumulative Average-TimeLearning Model

0100200300400500600700800

9001,000

1 2

CumulativeTotalLabor-Hours(Y)

Panel B:Lea

IncLe


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3 4 5 6 7 8 9 10 11 12 13 14 15 16

Cumulative Number of Units(X)

Cumulative Total Labor-Hours (80%rning Curve; First Unit Takes 100 Labor-Hours)

remental Unit-Timerning Model

Cumulative Average-TimeLearning Model


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Cumulative Average-Time Learning Model for Rayburn Corporation

80% Learning Curve

Cumulative Cumulative Cumulative Individual UnitsNumber Average Time Total Time: Time for Xth

of Units (X) per Unit (y )*: Labor Hours Labor-Hours Unit: Labor Hours

1 100.00 100.00 100.002 80.00 =(100 0.8) 160.00 60.003 70.21 210.63 50.634 64.00 =(80 0.8) 256.00 45.375 59.56 297.82 41.82

6 56.17 337.01 39.197 53.45 374.14 37.138 51.20 =(64 0.8) 409.60 35.469 49.29 443.65 34.05

10 47.65 476.51 32.8611 46.21 508.32 31.8112 44.93 539.22 30.8913 43.79 569.29 30.0714 42.76 598.63 29.3415 41.82 627.30 28.67

16 40.96 =(51.2 0.8) 655.36 28.06

D = Col A x Col B

The mathematical rela

learning model is:

wherey= CumulativeX= Cumulative numb

a= Time (labor-hours

b= Factor used to calcproduce units

The value of bis calcu

For an 80% learning cwhenX= 3, a= 100,,

Numbers in table ma.

ln (learning

y = 100 x 3-0.


13/36

E13 = D13 D12

= 256.00 210.63

* tionship underlying the cumulative average-time

average time (labor-hours) per unit

er of units produced

) required to produce the first unitulate cumulative average time to

lated as

urve, b= ln 0.8/ln 2 = -0.2231/0.6931 = -0.3219b= -0.3219

not be exact because of rounding

-curve % in decimal form

y=aXb



14/36

Incremental Unit-Time Learning Model for Rayburn Corporation

80% Learning Curve

Cumulative Individual Unit Time Cumulative CumulativeNumber for Xth Unit (y )* Total Time: Average Time

of Units (X) Labor Hours Labor-Hours per Unit:Labor-Hours

1 100.00 100.00 100.002 80.00 =(100 0.8) 180.00 90.003 70.21 250.21 83.404 64.00 =(80 0.8) 314.21 78.55

5 59.56 373.77 74.756 56.17 429.94 71.667 53.45 483.39 69.068 51.20 =(64 0.8) 534.59 66.82

9 49.29 583.89 64.8810 47.65 631.54 63.1511 46.21 677.75 61.6112 44.93 722.68 60.2213 43.79 766.47 58.9614 42.76 809.23 57.80

15 41.82 851.05 56.7416 40.96 =(51.2 0.8) 892.01 55.75

E = Col D Col A

The mathematical relearning model is:

wherey= Time (lab

X= Cumulative nua= Time (labor-hou

b= Factor used to c=

For an 80% learningWhereX= 3, a= 1,

The cumulative tot.

Numbers in table m.

ln (lear

y = 100 x 3-0.


15/36

D14 = D13 + B14= 180.00 + 70.21

* lationship underlying the incremental unit-time

or-hours) taken to produce the last single unit

ber of units produced

rs) required to produce the first unit

lculate incremental unit time to produce units

curve, b= ln 0.8 ln 2 = -0.2231 0.6931 = -0.3219

0, b= -0.3219

l time whenX= 3 is 100+80+70.21=250.21 labor-hours

ay not be exact because of rounding

ning-curve % in decimal form

y=aXb



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CumulativeCumulative Average Time Cumulative Cumulative Costs Additions toNumber of per Unit: Total Time: at $50 per Cumulative

Units Labor-Hoursa Labor-Hoursa Labor-Hour Costs

1 100.00 100.00 5,000$ (100.00 $50) $ 5,0002 80.00 160.00 8,000 (160.00 $50) 3,000

4 64.00 256.00 12,800 (256.00 $50) 4,8008 51.20 409.60 20,480 (409.60 $50) 7,680

16 40.96 655.36 32,768 (655.36 $50) 12,288

aBased on the cumulative average-time learning model. See Exhibit 10-10 for the computations

of these amounts.


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Cumulative costs (per labor hour) 50$


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Labor-Intensive Assembl MethodDirect material cost per helicopter $40,000Direct-assembly labor time for first helicopter 2,000 labor-hoursLearning curve for assembly labor time per helicopter 85% cumulative average time*Direct-assembly labor cost $ 30 per hourEquipment-related indirect manufacturing cost $ 12 per direct-assembly labor-hourMaterial-handling-related indirect manufacturing cost 50% of direct material cost

*Using the formula (p. 356), for an 85% learning curve, b =

**Using the formula (p. 357), for a 90% learning curve, b =

ln 0.85ln 2

-0.1625190.693147

= = -0.234465

ln 0.90ln 2

-0.1053610.693147

= = -0.152004


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Cumulative Cumulative IndividualNumber Total Time: time for of Units Labor-Hours Xth unit:

Labor-HoursCol J = Col G Col H

1 2,000 2,000 2,000

2 1,700 (2,000 0.85) 3,400 1,4003 1,546 4,637 1,2374 1,445 (1,700 0.85) 5,780 1,1435 1,371 6,857 1,0776 1,314 7,884 1,0277 1,267 8,871 9878 1,228.25 (1,445 0.85) 9,826 955

CumulativeAverage Timeper Unit (y):Labor Hours


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Direct-assembly labor time for first helicopter 2,000 labor-hoursLearning curve for assembly labor time per helicopter 85% cumulative average time


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For an 85% learning curve, y = 2,000 X -0.2345


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Cumulative Cumulative CumulativeNumber Total Time: Average Timeof Units Labor-Hours Per Unit:

Labor-HoursCol K = Col J Col G

1 800 800 800

2 720 (800 0.9) 1,520 7603 677 2,197 7324 648 (720 0.9) 2,845 7115 626 3,471 6946 609 4,081 6807 595 4,676 6688 583 (648 0.9) 5,259 657

IndividualUnit Time

for Xth Unit (y):Labor Hours


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Direct-assembly labor time for first helicopter 800 labor-hours For an 9Learning curve for assembly labor time per helicopter 90% cumulative average time


25/36

0% learning curve, y = 800 X^ -0.1520


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Labor-IntensiveAssembly Method

(using data from part 1a)Direct materials: 8 helicopters $40,000; $36,000 per helicopter $320,000Direct-assembly labor:

9,826 hrs.; 5,258 hrs. $30/hr. 294,780Indirect manufacturing costs Equipment related 9,826 hrs. $12/hr.; 5,258 hrs. $45/hr. 117,912

Materials-handling related 0.50 $320,000; $288,000 160,000Total assembly costs $892,692


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Machine-IntensiveAssembly Method

(using data from part 1b)

$288,000

157,740

236,610

144,000$826,350


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Labor-Intensive Assembly Method MachiDirect material cost per helicopter $40,000 $36,000Direct-assembly labor time for first helicopter 2,000 labor-hours 800

Learning curve for assembly labor time per helicopter 85% cumulative average time 90%Direct-assembly labor cost $ 30 per hour $ 30Equipment-related indirect manufacturing cost $ 12 per direct-assembly labor-hour $ 45

Material-handling-related indirect manufacturing cost 50% of direct material cost 50%Cumulative total time: labor-hours 9,826 hours 5,258Number of helicopters 8


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e-Intensive Assembly Method

labor-hours

incremental unit timeper hourper direct-assembly labor-hour

of direct material costhours


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Coefficients Standard Error t Stat

(1) (2) (3) = (1) (2)Intercept $300.98 $229.75 1.31Independent Variable:Machine-Hours (X) $ 10.31 $ 3.12 3.30

R Square 0.52Durbin-Watson Statistic 2.05

Regression Statistics


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= Coefficient/Standard Error= B3/C3= 300.98/229.75


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Coefficients Standard Error t Stat

(1) (2) (3) = (1) (2)Intercept $744.67 $217.61 3.42n epen ent ar a e:Direct ManufacturingLabor-Hours (X) $ 7.72 $ 5.40 1.43



= Coefficient= B4/C4= 7.72/5.40


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Standard Error


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Week

Machine-

Hours

(X1 )

um er o

Production

Batches

(X2 )

Direct

Manufacturing

Labor-Hours

n rec

Manufacturing

Labor Costs

(Y)

1 68 12 30 $ 1,1902 88 15 35 1,211

3 62 13 36 1,0044 72 11 20 917

5 60 10 47 7706 96 12 45 1,4567 78 17 44 1,1808 46 7 38 7109 82 14 70 1,316

10 94 12 30 1,03211 68 7 29 75212 48 14 38 963

Total 862 144 462 $12,501


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Coefficients Standard Error t Stat(1) (2) (3) = (1) (2)

Intercept $42.58 $213.91 0.20Independent variable 1: Machine-Hours (X1 ) $ 7.60 $ 2.77 2.74Independent variable 2: Number of

production batches (X2 ) $37.77 $ 15.25 2.48




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= Coefficient/Standard Error= B4/C4= 7.60/2.77

costacctg13_keyxl_ch10

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