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Cost ManagementMeasuring, Monitoring, and Motivating
Performance
Prepared byGail KaciubaMidwestern State UniversityChapter 2The
Cost Function
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Chapter 2: The Cost FunctionLearning objectivesQ1: What are the
different ways to describe cost behavior?Q2: What is a learning
curve?Q3: What process is used to estimate future costs?Q4: How are
engineered estimates, account analysis, and two-point methods used
to estimate cost functions?Q5: How does a scatter plot assist with
categorizing a cost?Q6: How is regression analysis used to estimate
a cost function?Q7: What are the uses and limitations of future
cost estimates?
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Q1: Different Ways to Describe CostsCosts can be defined by how
they relate to a cost object, which is defined as any thing or
activity for which we measure costs.Costs can also be categorized
as to how they are used in decision making.Costs can also be
distinguished by the way they change as activity or volume levels
change.
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Q1: Assigning Costs to a Cost ObjectDirect costs are easily
traced to the cost object.Determining the costs that should attach
to a cost object is called cost assignment.Indirect costs are not
easily traced to the cost object, and must be allocated.
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Q1: Direct and Indirect CostsIn manufacturing: all labor costs
that are easily traced to the product are called direct labor
costsall materials costs that are easily traced to the product are
called direct material costsall other production costs are called
overhead costsWhether or not a cost is a direct cost depends
upon:the technology available to capture cost informationthe
definition of the cost objectwhether the benefits of tracking the
cost as direct exceed the resources expended to track the costthe
precision of the bookkeeping system that tracks coststhe nature of
the operations that produce the product or service
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Q1: Direct and Indirect CostsListed below are some of the costs
incurred by a garment manufacturer. Determine whether the cost is
most likely to be considered a direct cost or an indirect cost if
the cost object is a single garment as opposed to a batch of 500
identical garments. If it depends, state what it depends
on.IndirectIndirectDirectIndirectIndirectIt dependsIndirectIt
dependsIndirectIt dependsIndirectIndirectIt dependsDirect
garment example
Cost Object
Single GarmentBatch of 500 Garments
Property taxes on factory
Bolts of fabric
Dyes for yard goods
Seamstresses hourly wage
Depreciation on sewing machines
Buttons
Zippers
Sheet2
Sheet3
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Q1: Linear Cost Behavior TerminologyTotal fixed costs are costs
that do not change (in total) as activity levels change.Total
variable costs are costs that increase (in total) in proportion to
the increase in activity levels.The relevant range is the span of
activity levels for which the cost behavior patterns hold.A cost
driver is a measure of activity or volume level; increases in a
cost driver cause total costs to increase.Total costs equal total
fixed costs plus total variable costs.
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Q1: Behavior of Total (Linear) CostsIf costs are linear, then
total costs graphically look like this. Total fixed costs do not
change as the cost driver increases. Higher total fixed costs are
higher above the x axis.
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Q1: Behavior of Total (Linear) CostsIf costs are linear, then
total costs graphically look like this. Total variable costs
increase as the cost driver increases.A steeper slope represents
higher variable costs per unit of the cost driver.
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Q1: Total Versus Per-unit (Average) Cost BehaviorIf total
variable costs look like this . . . . . . then variable costs per
unit look like this.
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Q1: Total Versus Per-Unit (Average) Cost BehaviorIf total fixed
costs look like this . . . . . . then fixed costs per unit look
like this.
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Q1: Total Versus Per-Unit (Average) Cost BehaviorLaris Leather
produces customized motorcycle jackets. The leather for one jacket
costs $50, and Lari rents a shop for $450/month. Compute the total
costs per month and the average cost per jacket if she made only
one jacket per month. What if she made 10 jackets per month?
$50$450$500 $50$450$500$500$450$950 $50$45$95
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Q1: The Cost FunctionWhen costs are linear, the cost function
is:TC = F + V x Q, whereF = total fixed cost, V = variable cost per
unit of the cost driver, and Q = the quantity of the cost
driver.Fslope = $V/unit of cost driverThe intercept is the total
fixed cost.The slope is the variable cost per unit of the cost
driver.A cost that includes a fixed cost element and a variable
cost element is known as a mixed cost.
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Q1: Nonlinear Cost BehaviorSometimes nonlinear costs exhibit
linear cost behavior over a range of the cost driver. This is the
relevant range of activity.
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Q1: Stepwise Linear Cost BehaviorSome costs are fixed at one
level for one range of activity and fixed at another level for
another range of activity. These are known as stepwise linear
costs.Example: A production supervisor makes $40,000 per year and
the factory can produce 100,000 units annually for each 8-hour
shift it operates.
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Q1: Piecewise Linear Cost BehaviorSome variable costs per unit
are constant at one level for one range of activity and constant at
another level for another range of activity. These are known as
piecewise linear costs.Example: A supplier sells us raw materials
at $9/gallon for the first 1000 gallons, $8/gallon for the second
1000 gallons, and at $7.50/gallon for all gallons purchased over
2000 gallons. slope=$9/gallonslope=$8/gallonslope=$7.50/gallon
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Q1: Cost Terms for Decision MakingIn Chapter 1 we learned the
distinction between relevant and irrelevant cash flows.Opportunity
costs are the benefits of an alternative one gives up when that
alternative is not chosen.Sunk costs are costs that were incurred
in the past.Opportunity costs are difficult to measure because they
are associated with something that did not occur.Opportunity costs
are always relevant in decision making.Sunk costs are never
relevant for decision making.
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Q1: Cost Terms for Decision MakingDiscretionary costs are
periodic costs incurred for activities that management may or may
not determine are worthwhile.These costs may be variable or fixed
costs.Discretionary costs are relevant for decision making only if
they vary across the alternatives under consideration.Marginal cost
is the incremental cost of producing the next unit.When costs are
linear and the level of activity is within the relevant range,
marginal cost is the same as variable cost per unit.Marginal costs
are often relevant in decision making.
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Q2: What is a Learning Curve?A learning curve is the rate at
which labor hours per unit decrease as the volume of activity
increasesthe relationship between cumulative average hours per unit
and the cumulative number of units produced. A learning curve can
be represented mathematically as:Y = Xr, whereX = cumulative number
of units produced,r = an index for learning = ln(% learning)/ln(2),
andY = cumulative average labor hours, = time required for the
first unit,ln is the natural logarithmic function.
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Q2: Learning Curve ExampleDeannas Designer Desks just designed a
new solid wood desk for executives. The first desk took her
workforce 55 labor hours to make, but she estimates that each desk
will require 75% of the time of the prior desk (i.e. % learning =
75%). Compute the cumulative average time to make 7 desks, and draw
a learning curve.First compute r:r = ln(75%)/ln(2) = -0.2877/0.693
= -0.4152Then compute the cumulative average time for 7 desks:Y =
55 x 7(-0.4152) = 25.42 hrsIn order to draw a learning curve, you
must compute the value of Y for all X values from 1 to 7. . . .
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Q3: What Process is Usedto Estimate Future Costs?Past costs are
often used to estimate future, non-discretionary, costs. In these
instances, one must also consider: whether the past costs are
relevant to the decision at handwhether the future cost behavior is
likely to mimic the past cost behaviorwhether the past fixed and
variable cost estimates are likely to hold in the future
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Q4: Engineered Estimates of Cost FunctionsUse accountants,
engineers, employees, and/or consultants to analyze the resources
used in the activities required to complete a product, service, or
process.For example, a company making inflatable rubber kayaks
would estimate some of the following:the amount and cost of the
rubber requiredthe amount and cost of labor required in the cutting
departmentthe amount and cost of labor required in the assembly
departmentthe distribution costs the selling costs, including
commissions and advertisingoverhead costs and the best cost
allocation base to use
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Q4: Account Analysis Method ofEstimating a Cost FunctionReview
past costs in the general ledger and past activity levels to
determine each costs past behavior.For example, a company producing
clay wine goblets might review its records and find: the cost of
clay is piecewise linear with respect to the number of pounds of
clay purchasedskilled production labor is variable with respect to
the number of goblets producedunskilled production labor is mixed,
and the variable portion varies with respect to the number of times
the kiln is operatedproduction supervisors salary costs are
stepwise lineardistribution costs are mixed, with the variable
portion dependent upon the number of retailers ordering goblets
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Q4: Two-Point Method ofEstimating a Cost FunctionUse the
information contained in two past observations of cost and activity
to separate mixed and variable costs.It is much easier and less
costly to use than the account analysis or engineered estimate of
cost methods, but:it estimates only mixed cost functions,it is not
very accurate, andit can grossly misrepresent costs if the data
points come from different relevant ranges of activity
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Q4: Two-Point Method ofEstimating a Cost FunctionWe first need
to determine V, using the equation for the slope of a line.In July
the Gibson Co. incurred total overhead costs of $58,000 and made
6,200 units. In December it produced 3,200 units and total overhead
costs were $40,000. What are the total fixed factory costs per
month and average variable factory costs?= $18,000/3,000 unitsThen,
using TC = F + V x Q, and one of the data points, determine F. =
$6/unit$58,000 = F + $6/unit x 6,200 units$58,000 = F +
$37,200$20,800 = F$20,800
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Q4: High-Low Method ofEstimating a Cost FunctionThe high-low
method is a two-point methodthe two data points used to estimate
costs are observations with the highest and the lowest activity
levelsThe extreme points for activity levels may not be
representative of costs in the relevant rangethis method may
underestimate total fixed costs and overestimate variable costs per
unit, or vice versa.
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Q5: How Does a ScatterplotAssist with Categorizing a Cost?A
scatterplot shows cost observations plotted against levels of a
possible cost driver.A scatterplot can assist in determining:which
cost driver might be the best for analyzing total costs, andthe
cost behavior of the cost against the potential cost driver.
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Q5: Which Cost Driver Has the BestCause & Effect
Relationship with Total Cost?8 observations of total selling
expenses plotted against 3 potential cost driversThe number of
salespersons appears to be the best cost driver of the 3.
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Q5: What is the Underlying Cost Behavior?This cost is probably
linear and fixed.This cost is probably linear and variable.
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Q5: What is the Underlying Cost Behavior?This cost is probably
linear and mixed.This is likely a stepwise linear cost.
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Q5: What is the Underlying Cost Behavior?This cost may be
piecewise linear.This cost appears to have a nonlinear relationship
with units sold.
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Q6: How is Regression Analysis Used toEstimate a Mixed Cost
Function?Regression analysis estimates the parameters for a linear
relationship between a dependent variable and one or more
independent (explanatory) variables.When there is only one
independent variable, it is called simple regression.When there is
more than one independent variable, it is called multiple
regression.Y = + X + and are the parameters; is the error term (or
residual)
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Q6: How is Regression Analysis Used toEstimate a Mixed Cost
Function?We can use regression to separate the fixed and variable
components of a mixed cost.Yi = + Xi + i
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Q6: Regression Output Terminology: Adjusted R-SquareGoodness of
fitHow well does the line from the regression output fit the actual
data points?The adjusted R-square statistic shows the percentage of
variation in the Y variable that is explained by the regression
equation.The next slide has an illustration of how a regression
equation can explain the variation in a Y variable.
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Q6: Regression Output Terminology: Adjusted R-SquareWe have 29
observations of a Y variable, and the average of the Y variables is
56,700. If we plot them in order of the observation number, there
is no discernable pattern. We have no explanation as to why the
observations vary about the average of 56,700.
Chart1
16057
11752
76619
73776
71638
81249
91545
51672
97895
71711
56048
22712
32551
91071
88583
49981
69375
41406
27830
60677
57483
37383
39926
12994
64565
24788
90918
38855
54362
Observation #
Values of Y by Observation #
Lrng Curve Example
Y
% learningln(% learning)ln(2)r = A/BalphaXavg timetotal
timeX^r-0.4151515152
0.75-0.28768207250.6931471806-0.415037499355155551textbook p
44
0.75-0.28768207250.6931471806-0.41503749935524182.50.75demonstration
problem0.4458166337
0.75-0.28768207250.6931471806-0.415037499355335104.58291240270.633835832724.5199148529
0.75-0.28768207250.6931471806-0.415037499355431123.750.5625
0.75-0.28768207250.6931471806-0.415037499355528141.00481112440.5127447677
0.75-0.28768207250.6931471806-0.415037499355626156.8743686040.4753768746
0.75-0.28768207250.6931471806-0.415037499355725171.677488910.4459155556
24.5205357822eighth table
5527.8642452077
41.2531.6639150086
34.860970800935.98172165
30.937540.888324
28.200962224946.4643
26.145728100752.82
24.5253555586601
320.1827375972
40.0228421997
XrX^r
1-0.35845397091.0000060.00
2-0.35845397090.7800046.80
3-0.35845397090.6744940.47
4-0.35845397090.6084036.50
5-0.35845397090.5616333.70
6-0.35845397090.5261031.57
7-0.35845397090.4978229.87
8-0.35845397090.4745528.47227.8
5695
Lrng Curve Example
0
0
0
0
0
0
0
Cumul Avg Time
Cumulative Number of Desks
HrsperDesk
Cumulative Average Hours Per Desk
garment example
Cost Object
Single GarmentBatch of 500 Garments
Property taxes on factory
Bolts of fabric
Dyes for yard goods
Seamstresses hourly wage
Depreciation on sewing machines
Buttons
Zippers
Leather shop example
1 Jacket
Total Costs/ MonthAverage Cost/ Jacket
Leather
Rent
Total
Explanatory power
YX
16,0571,965,309
11,7521,997,510
76,6194,344,886
73,7763,683,793
71,6383,620,390
81,2495,459,005
91,5455,611,818
51,6724,066,248
97,8955,543,481
71,7114,216,245
56,0483,727,308
22,7122,360,997
32,5512,595,601
91,0714,700,385
88,5834,905,372
49,9813,277,859
69,3753,652,816
41,4063,276,771
27,8303,436,420
60,6774,746,356
57,4834,706,040
37,3833,322,789
39,9262,814,353
12,9942,091,217
64,5653,347,669
24,7882,714,684
90,9184,766,838
38,8553,300,307
54,3623,674,820
Explanatory power
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Observation #
Values of Y by Observation #
Regress OH on MH
Total Overhead CostsMachine Hours
$1800
$28010
$58020
$1,08030
$1,78040
$2,68050
$3,78060
$5,08070
$6,58080
$8,28090
$10,180100
$12,280110
$14,580120
$17,080130
$19,780140
$22,680150
SUMMARY OUTPUT
Regression Statistics
Multiple R0.9646352118
R Square0.9305210918
Adjusted R Square0.9255583127
Standard Error2019.9009876724
Observations16
ANOVA
dfSSMSFSignificance F
Regression1765000000765000000187.50.0000000017
Residual14571200004080000
Total15822120000
CoefficientsStd Errort StatP-valueLower 95%Upper 95%Lower
95.0%Upper 95.0%
Intercept-3320964.3650760993-3.44267962650.0039618982-5388.3592172271-1251.6407827729-5388.3592172271-1251.6407827729
Machine
Hours15010.954451150113.69306393760.0000000017126.505018102173.494981898126.505018102173.494981898
RESIDUAL OUTPUT
ObservationPredicted Total Overhead CostsResiduals
1-33203500
2-18202100
3-320900
41180-100
52680-900
64180-1500
75680-1900
87180-2100
98680-2100
1010180-1900
1111680-1500
1213180-900
1314680-100
1416180900
15176802100
16191803500
Regress OH on MH
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Machine Hours
Residuals
Machine Hours Residual Plot
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Total Overhead Costs
Predicted Total Overhead Costs
Machine Hours
Total Overhead Costs
Machine Hours Line Fit Plot
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Q6: Regression Output Terminology: Adjusted R-SquareIf each Y
value had an associated X value, then we could reorder the Y
observations along the X axis according to the value of the
associated X.Now we can measure how the Y observations vary from
the line of best fit instead of from the average of the Y
observations. Adjusted R-Square measures the portion of Ys
variation about its mean that is explained by Ys relationship to
X.
Chart3
16057
11752
76619
73776
71638
81249
91545
51672
97895
71711
56048
22712
32551
91071
88583
49981
69375
41406
27830
60677
57483
37383
39926
12994
64565
24788
90918
38855
54362
Values of Y by X Value
Lrng Curve Example
Y
% learningln(% learning)ln(2)r = A/BalphaXavg timetotal
timeX^r-0.4151515152
0.75-0.28768207250.6931471806-0.415037499355155551textbook p
44
0.75-0.28768207250.6931471806-0.41503749935524182.50.75demonstration
problem0.4458166337
0.75-0.28768207250.6931471806-0.415037499355335104.58291240270.633835832724.5199148529
0.75-0.28768207250.6931471806-0.415037499355431123.750.5625
0.75-0.28768207250.6931471806-0.415037499355528141.00481112440.5127447677
0.75-0.28768207250.6931471806-0.415037499355626156.8743686040.4753768746
0.75-0.28768207250.6931471806-0.415037499355725171.677488910.4459155556
24.5205357822eighth table
5527.8642452077
41.2531.6639150086
34.860970800935.98172165
30.937540.888324
28.200962224946.4643
26.145728100752.82
24.5253555586601
320.1827375972
40.0228421997
XrX^r
1-0.35845397091.0000060.00
2-0.35845397090.7800046.80
3-0.35845397090.6744940.47
4-0.35845397090.6084036.50
5-0.35845397090.5616333.70
6-0.35845397090.5261031.57
7-0.35845397090.4978229.87
8-0.35845397090.4745528.47227.8
5695
Lrng Curve Example
0
0
0
0
0
0
0
Cumul Avg Time
Cumulative Number of Desks
HrsperDesk
Cumulative Average Hours Per Desk
garment example
Cost Object
Single GarmentBatch of 500 Garments
Property taxes on factory
Bolts of fabric
Dyes for yard goods
Seamstresses hourly wage
Depreciation on sewing machines
Buttons
Zippers
Leather shop example
1 Jacket
Total Costs/ MonthAverage Cost/ Jacket
Leather
Rent
Total
Explanatory power
YXX
16,0571,965,3091,965165
11,7521,997,5101,998198
76,6194,344,8864,3452,545
73,7763,683,7933,6841,884
71,6383,620,3903,6201,820
81,2495,459,0055,4593,659
91,5455,611,8185,6123,812
51,6724,066,2484,0662,266
97,8955,543,4815,5433,743
71,7114,216,2454,2162,416
56,0483,727,3083,7271,927
22,7122,360,9972,361561
32,5512,595,6012,596796
91,0714,700,3854,7002,900
88,5834,905,3724,9053,105
49,9813,277,8593,2781,478
69,3753,652,8163,6531,853
41,4063,276,7713,2771,477
27,8303,436,4203,4361,636
60,6774,746,3564,7462,946
57,4834,706,0404,7062,906
37,3833,322,7893,3231,523
39,9262,814,3532,8141,014
12,9942,091,2172,091291
64,5653,347,6693,3481,548
24,7882,714,6842,715915
90,9184,766,8384,7672,967
38,8553,300,3073,3001,500
54,3623,674,8203,6751,875
3,812
56,763
Explanatory power
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
Observation #
Values of Y by Observation #
Regress OH on MH
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
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0
0
0
0
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0
0
Values of Y by X Value
Total Overhead CostsMachine Hours
$1800
$28010
$58020
$1,08030
$1,78040
$2,68050
$3,78060
$5,08070
$6,58080
$8,28090
$10,180100
$12,280110
$14,580120
$17,080130
$19,780140
$22,680150
SUMMARY OUTPUT
Regression Statistics
Multiple R0.9646352118
R Square0.9305210918
Adjusted R Square0.9255583127
Standard Error2019.9009876724
Observations16
ANOVA
dfSSMSFSignificance F
Regression1765000000765000000187.50.0000000017
Residual14571200004080000
Total15822120000
CoefficientsStd Errort StatP-valueLower 95%Upper 95%Lower
95.0%Upper 95.0%
Intercept-3320964.3650760993-3.44267962650.0039618982-5388.3592172271-1251.6407827729-5388.3592172271-1251.6407827729
Machine
Hours15010.954451150113.69306393760.0000000017126.505018102173.494981898126.505018102173.494981898
RESIDUAL OUTPUT
ObservationPredicted Total Overhead CostsResiduals
1-33203500
2-18202100
3-320900
41180-100
52680-900
64180-1500
75680-1900
87180-2100
98680-2100
1010180-1900
1111680-1500
1213180-900
1314680-100
1416180900
15176802100
16191803500
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Machine Hours
Residuals
Machine Hours Residual Plot
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Total Overhead Costs
Predicted Total Overhead Costs
Machine Hours
Total Overhead Costs
Machine Hours Line Fit Plot
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Q6: Regression Output Terminology: p-value and
t-statistic.Statistical significance of regression coefficientsWhen
running a regression we are concerned about whether the true
(unknown) coefficients are non-zero.Did we get a non-zero intercept
(or slope coefficient) in the regression output only because of the
particular data set we used?
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Q6: Regression Output Terminology: p-value and t-statistic.In
general, if the t-statistic for the intercept (slope) term > 2,
we can be about 95% confident (at least) that the true intercept
(slope) term is not zero.The t-statistic and the p-value both
measure our confidence that the true coefficient is non-zero.The
p-value is more preciseit tells us the probability that the true
coefficient being estimated is zeroif the p-value is less than 5%,
we are more than 95% confident that the true coefficient is
non-zero.
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Q6: Interpreting Regression OutputThe coefficients give you the
parameters of the estimated cost function.Predicted total costs
=$2,937+ ($5.215/mach hr)x (# of mach hrs)Suppose we had 16
observations of total costs and activity levels (measured in
machine hours) for each total cost. If we regressed the total costs
against the machine hours, we would get . . . Total fixed costs are
estimated at $2,937.Variable costs per machine hour are estimated
at $5.215.
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Q6: Interpreting Regression OutputThe regression line explains
76.8% of the variation in the total cost observations.The high
t-statistics . . .. . . and the low p-values on both of the
regression parameters tell us that the intercept and the slope
coefficient are statistically significant.(5.26E-06 means 5.26 x
10-6, or 0.00000526)
Lrng Curve Example
Y
% learningln(% learning)ln(2)r = A/BalphaXavg timetotal
timeX^r-0.4151515152
0.75-0.28768207250.6931471806-0.415037499355155551textbook p
44
0.75-0.28768207250.6931471806-0.41503749935524182.50.75demonstration
problem0.4458166337
0.75-0.28768207250.6931471806-0.415037499355335104.58291240270.633835832724.5199148529
0.75-0.28768207250.6931471806-0.415037499355431123.750.5625
0.75-0.28768207250.6931471806-0.415037499355528141.00481112440.5127447677
0.75-0.28768207250.6931471806-0.415037499355626156.8743686040.4753768746
0.75-0.28768207250.6931471806-0.415037499355725171.677488910.4459155556
24.5205357822eighth table
5527.8642452077
41.2531.6639150086
34.860970800935.98172165
30.937540.888324
28.200962224946.4643
26.145728100752.82
24.5253555586601
320.1827375972
40.0228421997
XrX^r
1-0.35845397091.0000060.00
2-0.35845397090.7800046.80
3-0.35845397090.6744940.47
4-0.35845397090.6084036.50
5-0.35845397090.5616333.70
6-0.35845397090.5261031.57
7-0.35845397090.4978229.87
8-0.35845397090.4745528.47227.8
5695
Lrng Curve Example
0
0
0
0
0
0
0
Cumul Avg Time
Cumulative Number of Desks
HrsperDesk
Cumulative Average Hours Per Desk
garment example
Cost Object
Single GarmentBatch of 500 Garments
Property taxes on factory
Bolts of fabric
Dyes for yard goods
Seamstresses hourly wage
Depreciation on sewing machines
Buttons
Zippers
Leather shop example
1 Jacket
Total Costs/ MonthAverage Cost/ Jacket
Leather
Rent
Total
Regress OH on MH
Total Overhead CostsMachine Hours
$2,8200280028005.5
$2,920102855
$3,100202910
$2,990302965
$3,300403020
$3,350503075
$3,420603130
$3,200703185
$3,480803240
$3,300903295
$3,2051003350
$3,6101103405
$3,6201203460
$3,4801303515
$3,6201403570
$3,8301503625
SUMMARY OUTPUT
Regression Statistics
Multiple R0.8849050128
R Square0.7830568817
Adjusted R Square0.7675609447
Standard Error135.2828599856
Observations16
ANOVA
dfSSMSFSignificance F
Regression1924828.106617647924828.10661764750.53304493070.000005265
Residual14256220.33088235318301.4522058824
Total151181048.4375
CoefficientsStd Errort StatP-valueLower 95%Upper 95%Lower
95.0%Upper 95.0%
Intercept2936.654411764764.588346835445.46724843802798.12606206253075.18276146692798.12606206253075.1827614669
Machine
Hours5.21544117650.73367431887.10865985480.0000052653.64186486466.78901748833.64186486466.7890174883
RESIDUAL OUTPUT
ObservationPredicted Total Overhead CostsResiduals
12936.6544117647-116.6544117647
22988.8088235294-68.8088235294
33040.963235294159.0367647059
43093.1176470588-103.1176470588
53145.2720588235154.7279411765
63197.4264705882152.5735294118
73249.5808823529170.4191176471
83301.7352941176-101.7352941176
93353.8897058824126.1102941176
103406.0441176471-106.0441176471
113458.1985294118-253.1985294118
123510.352941176599.6470588235
133562.507352941257.4926470588
143614.6617647059-134.6617647059
153666.8161764706-46.8161764706
163718.9705882353111.0294117647
Regress OH on MH
Machine Hours
Residuals
Machine Hours Residual Plot
Total Overhead Costs
Predicted Total Overhead Costs
Machine Hours
Total Overhead Costs
Machine Hours Line Fit Plot
Lrng Curve Example
Y
% learningln(% learning)ln(2)r = A/BalphaXavg timetotal
timeX^r-0.4151515152
0.75-0.28768207250.6931471806-0.415037499355155551textbook p
44
0.75-0.28768207250.6931471806-0.41503749935524182.50.75demonstration
problem0.4458166337
0.75-0.28768207250.6931471806-0.415037499355335104.58291240270.633835832724.5199148529
0.75-0.28768207250.6931471806-0.415037499355431123.750.5625
0.75-0.28768207250.6931471806-0.415037499355528141.00481112440.5127447677
0.75-0.28768207250.6931471806-0.415037499355626156.8743686040.4753768746
0.75-0.28768207250.6931471806-0.415037499355725171.677488910.4459155556
24.5205357822eighth table
5527.8642452077
41.2531.6639150086
34.860970800935.98172165
30.937540.888324
28.200962224946.4643
26.145728100752.82
24.5253555586601
320.1827375972
40.0228421997
XrX^r
1-0.35845397091.0000060.00
2-0.35845397090.7800046.80
3-0.35845397090.6744940.47
4-0.35845397090.6084036.50
5-0.35845397090.5616333.70
6-0.35845397090.5261031.57
7-0.35845397090.4978229.87
8-0.35845397090.4745528.47227.8
5695
Lrng Curve Example
0
0
0
0
0
0
0
Cumul Avg Time
Cumulative Number of Desks
HrsperDesk
Cumulative Average Hours Per Desk
garment example
Cost Object
Single GarmentBatch of 500 Garments
Property taxes on factory
Bolts of fabric
Dyes for yard goods
Seamstresses hourly wage
Depreciation on sewing machines
Buttons
Zippers
Leather shop example
1 Jacket
Total Costs/ MonthAverage Cost/ Jacket
Leather
Rent
Total
Regress OH on MH
Total Overhead CostsMachine Hours
$2,8200280028005.5
$2,920102855
$3,100202910
$2,990302965
$3,300403020
$3,350503075
$3,420603130
$3,200703185
$3,480803240
$3,300903295
$3,2051003350
$3,6101103405
$3,6201203460
$3,4801303515
$3,6201403570
$3,8301503625
SUMMARY OUTPUT
Regression Statistics
Multiple R0.8849050128
R Square0.7830568817
Adjusted R Square0.7675609447
Standard Error135.2828599856
Observations16
ANOVA
dfSSMSFSignificance F
Regression1924828.106617647924828.10661764750.53304493070.000005265
Residual14256220.33088235318301.4522058824
Total151181048.4375
CoefficientsStd Errort StatP-valueLower 95%Upper 95%Lower
95.0%Upper 95.0%
Intercept2936.654411764764.588346835445.46724843802798.12606206253075.18276146692798.12606206253075.1827614669
Machine
Hours5.21544117650.73367431887.10865985480.0000052653.64186486466.78901748833.64186486466.7890174883
RESIDUAL OUTPUT
ObservationPredicted Total Overhead CostsResiduals
12936.6544117647-116.6544117647
22988.8088235294-68.8088235294
33040.963235294159.0367647059
43093.1176470588-103.1176470588
53145.2720588235154.7279411765
63197.4264705882152.5735294118
73249.5808823529170.4191176471
83301.7352941176-101.7352941176
93353.8897058824126.1102941176
103406.0441176471-106.0441176471
113458.1985294118-253.1985294118
123510.352941176599.6470588235
133562.507352941257.4926470588
143614.6617647059-134.6617647059
153666.8161764706-46.8161764706
163718.9705882353111.0294117647
Regress OH on MH
Machine Hours
Residuals
Machine Hours Residual Plot
Total Overhead Costs
Predicted Total Overhead Costs
Machine Hours
Total Overhead Costs
Machine Hours Line Fit Plot
-
Q6: Regression Interpretation ExampleCaroles Coffee asked you to
help determine its cost function for its chain of coffee shops.
Carole gave you 16 observations of total monthly costs and the
number of customers served in the month. The data is presented
below, and the a portion of the output from the regression you ran
is presented on the next slide. Help Carole interpret this
output.
-
Q6: Regression Interpretation ExampleWhat is Caroles estimated
cost function? In a store that serves 10,000 customers, what would
you predict for the stores total monthly costs?
-
Q6: Regression Interpretation ExampleWhat is the explanatory
power of this model? Are the coefficients statistically significant
or not? What does this mean about the cost function?*(Some would
say the intercept is significant as long as the p-value is less
than 10%, rather than 5%.)
-
Q7: Considerations When UsingEstimates of Future CostsThe future
is always unknown, so there are uncertainties when estimating
future costs.The estimated cost function may have mis-specified the
cost behavior.Future cost behavior may not mimic past cost
behavior.Future costs may be different from past costs.The cost
function may be using an incorrect cost driver.
-
Q7: Considerations When UsingEstimates of Future CostsThe data
used to estimate past costs may not be of high-quality.The
accounting system may aggregate costs in a way that mis-specifies
cost behavior.The true cost function may not be in agreement with
the cost function assumptions.For example, if variable costs per
unit of the cost driver are not constant over any reasonable range
of activity, the linearity of total cost assumption is
violated.Information from outside the accounting system may not be
accurate.
-
Appendix 2A: Multiple Regression ExampleWe have 10 observations
of total project cost, the number of machine hours used by the
projects, and the number of machine set-ups the projects used.
-
Appendix 2A: Multiple Regression ExampleRegress total costs on
the number of set-ups to get the following output and estimated
cost function:The explanatory power is 57.4%. The # of set-ups is
significant, but the intercept is not significant if we use a 5%
limit for the p-value.
-
Appendix 2A: Multiple Regression ExampleRegress total costs on
the number of machine hours to get the following output and
estimated cost function:The explanatory power is 62.1%. The
intercept shows up negative, which is impossible as total fixed
costs can not be negative. However, the p-value on the intercept
tells us that there is a 93% probability that the true intercept is
zero. The # of machine hours is significant.
-
Appendix 2A: Multiple Regression ExampleRegress total costs on
the # of set ups and the # of machine hours to get the
following:The explanatory power is now 89.6%. The p-values on both
slope coefficients show that both are significant. Since the
intercept is not significant, project costs can be estimated based
on the projects usage of set-ups and machine hours.
This slide is entirely automated, with each bullet on a 1.5
second delay.The first bullet is automated, then one click is
required for each bullet.The cost assignment text box is
automated.The first click begins the sequence to define direct
costs.The second click begins the sequence to define indirect
costs.
The first primary bullet is automated, and one click is required
for every remaining primary and secondary bullet on this slide.The
text box and the grid for the solution are automated.Then one click
is required to reveal each of the answers to the problem, with the
first click revealing the answer for property taxes/single garment,
the second click revealing the answer for property taxes/batch of
500 garments, and so on. Notice that many of the answers are it
depends. This slide is intended to generate a discussion about how
different methods of capturing costs (& different production
processes) can affect whether costs are direct or indirect.The
first bullet is automated and then one click is required for each
subsequent bullet.The first click completes the top graph and
brings in the first text box, which disappears on the next
click.The second click brings in all of the elements on the rest of
the slide in an automated sequence.The first click brings in all of
the elements on the rest of the slide in an automated sequence.The
top part of the slide is automated.The first click brings in the
rest of the elements on the slide in an automated sequence.The
first click brings in the rest of the elements on the slide in an
automated sequence.
The text box and the solution grid are automated.The first click
begins the sequence that displays the answers for the 1
jacket/total costs column.The second click begins the sequence that
displays the answers for the 1 jacket/average costs column.The
third click begins the sequence that displays the answers for the
10 jackets/total costs column.The fourth click begins the sequence
that displays the answers for the 10 jackets/average costs
column.The fifth click shows the total variable costs go up text
and arrow, which disappears on the next mouse click.The sixth click
shows the average variable costs are constant text and arrow, which
disappears on the next mouse click.The seventh click shows the
total fixed cost are constant text and arrow, which disappears on
the next mouse click.The eighth click shows the average fixed costs
go down text and arrow.
The cost function discussion text box and the graph are
automated.The first click brings in the definition of the
intercept, which is hidden on the next click.The second click
brings in the definition of the slope, which is hidden on the next
click.The third click brings in the definition of a mixed cost.This
slide is entirely automated.The first click starts the sequence to
draw the costs graph.The first click starts the sequence to draw
the costs graph.
The first primary bullet is automated.The first click brings in
the a sequence with the second primary bullet and its secondary
bullets.The second click brings in the a sequence with the third
primary bullet and its secondary bullet.The first primary bullet is
automated; the first click begins the sequence for its two
secondary bullets.The second click begins the sequence for the
second primary bullet and its two secondary bullets.The first
primary bullet with its secondary bullets is automated.The first
click begins a sequence to bring in the rest of the elements of the
slide.The text box is automated.The first click brings in first
compute r.The 2nd click computes r.The 3rd click brings in Then
compute the The 4th click computes Y.The 5th click brings in the
last text box and the graph.The top text box is automated. One
click is required for each bullet.The first primary bullet is
automated.The 2nd click brings in the second primary bullet.The 3rd
click brings in the sequence for the secondary bullets.The first
primary bullet is automated.The 2nd click brings in the second
primary bullet.The 3rd click brings in the sequence for the
secondary bullets.
The first primary bullet is automated.The 2nd click brings in
the second primary bullet.The 3rd click brings in the sequence for
the secondary bullets.The text box is automated.The 1st click
brings in the We first need to determine text box.The 2nd click
starts the sequence that draws the graph.The 3rd click begins the
rise/run computation.The 4th click brings in the Then, using TC=
text box.The 5th click begins the calculation to find total fixed
costs.The first primary bullet and its sub-bullet are automated.The
first click brings in the second primary bullet and its
sub-bullets.The first bullet is automated.The first click begins
the sequence for the remaining text.All elements of this slide are
automated, except the text box stating that # salespersons is the
best cost driver this requires one click.The top graph is
automated.The first click brings in the blue text for the top
graph.The second click brings in the second graph.The third click
brings in the orange text for the bottom graph.The top graph is
automated.The first click brings in the blue text for the top
graph.The second click brings in the second graph.The third click
brings in the orange text for the bottom graph.The top graph is
automated.The first click brings in the blue text for the top
graph.The second click brings in the second graph.The third click
brings in the orange text for the bottom graph.
The first bullet is automated.The first click brings in the
simple regression bullet.The second click brings in the multiple
regression bullet.The third click starts the sequence to show the
regression equation.The first text box and the regression equation
are automated.The 1st click brings in the Yi definition.The 2nd
click brings in the Xi definition.The 3rd click brings in the
epsilon definition.The 4th click brings in the slope text. The 5th
click brings in the intercept text.
One click is required for each of the three secondary
bullets.This slide is entirely automated.This slide is entirely
automated.This slide is entirely automated.This slide is entirely
automated.The top portion of the slide is automated.The first click
begins the sequence for the remaining elements on the slide.The
first click brings in the red text.The second click begins a
sequence to bring in the rest of the slide elements.This slide is
entirely automated.The first click brings in the predicted total
costs computation.The second click brings in the predicted total
costs at 10,000 customers computation.One click required for the
red text, one for the blue and one for the green. Note that the red
and blue text disappear on the next mouse click.This slide is
entirely automatedThe first primary bullet and its secondary
bullets are automated.The first click starts the sequence for the
rest of the slide.This slide is entirely automated.The top portion
of the slide is not animated.The first click brings in the
Predicted project cost = textThe second click brings in the bottom
text box.The top portion of the slide is not animated.The first
click brings in the Predicted project cost = textThe second click
brings in the bottom text box.
The top portion of the slide is not animated.The first click
brings in the Predicted project cost = textThe second click brings
in the bottom text box.