ch02

Cost ManagementMeasuring, Monitoring, and Motivating Performance

Prepared byGail KaciubaMidwestern State UniversityChapter 2The Cost Function

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?

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.

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.

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

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

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.

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.

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.

Q1: Total Versus Per-unit (Average) Cost BehaviorIf total variable costs look like this . . . . . . then variable costs per unit look like this.

Q1: Total Versus Per-Unit (Average) Cost BehaviorIf total fixed costs look like this . . . . . . then fixed costs per unit look like this.

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

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.

Q1: Nonlinear Cost BehaviorSometimes nonlinear costs exhibit linear cost behavior over a range of the cost driver. This is the relevant range of activity.

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.

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

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.

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.

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.

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. . . .

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

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

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

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

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

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.

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.

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.

Q5: What is the Underlying Cost Behavior?This cost is probably linear and fixed.This cost is probably linear and variable.

Q5: What is the Underlying Cost Behavior?This cost is probably linear and mixed.This is likely a stepwise linear cost.

Q5: What is the Underlying Cost Behavior?This cost may be piecewise linear.This cost appears to have a nonlinear relationship with units sold.

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)

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

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.

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



Bolts of fabric

Dyes for yard goods



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 #


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


Machine Hours Line Fit Plot

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


0.75-0.28768207250.6931471806-0.415037499355155551textbook p 44


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


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


HrsperDesk


garment example

Cost Object



Bolts of fabric

Dyes for yard goods



Buttons

Zippers


1 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

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 #


Regress OH on MH

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

Values of Y by X Value


$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



R Square0.9305210918



Observations16

ANOVA


Regression1765000000765000000187.50.0000000017

Residual14571200004080000

Total15822120000


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


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


00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00



Machine Hours



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?

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.

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.

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


0.75-0.28768207250.6931471806-0.415037499355155551textbook p 44


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


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


HrsperDesk


garment example

Cost Object



Bolts of fabric

Dyes for yard goods



Buttons

Zippers


1 Jacket


Leather

Rent

Total

Regress OH on MH


$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



R Square0.7830568817



Observations16

ANOVA


Regression1924828.106617647924828.10661764750.53304493070.000005265

Residual14256220.33088235318301.4522058824

Total151181048.4375


Intercept2936.654411764764.588346835445.46724843802798.12606206253075.18276146692798.12606206253075.1827614669

Machine Hours5.21544117650.73367431887.10865985480.0000052653.64186486466.78901748833.64186486466.7890174883

RESIDUAL OUTPUT


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



Lrng Curve Example

Y


0.75-0.28768207250.6931471806-0.415037499355155551textbook p 44


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


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


HrsperDesk


garment example

Cost Object



Bolts of fabric

Dyes for yard goods



Buttons

Zippers


1 Jacket


Leather

Rent

Total

Regress OH on MH


$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



R Square0.7830568817



Observations16

ANOVA


Regression1924828.106617647924828.10661764750.53304493070.000005265

Residual14256220.33088235318301.4522058824

Total151181048.4375


Intercept2936.654411764764.588346835445.46724843802798.12606206253075.18276146692798.12606206253075.1827614669

Machine Hours5.21544117650.73367431887.10865985480.0000052653.64186486466.78901748833.64186486466.7890174883

RESIDUAL OUTPUT


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



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.

Documents

ch02