Chapter 16Chapter 16

The Behavior of CostsThe Behavior of Costs

© 2004 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill

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Behavior of CostsBehavior of Costs

Cost-volume relationships.Cost-volume relationships. Fixed and variable costs.Fixed and variable costs. Step-function costs.Step-function costs.

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Relation of Costs to VolumeRelation of Costs to Volume

Higher volume causes higher costs.Higher volume causes higher costs. Variable costs = items of cost that vary, in Variable costs = items of cost that vary, in

total, directly and proportionately with volume.total, directly and proportionately with volume. Fixed costs = non-variable costs = items of Fixed costs = non-variable costs = items of

cost that, in total, do not vary at all with cost that, in total, do not vary at all with volumevolume

Semi-variable costs = semi-fixed costs = Semi-variable costs = semi-fixed costs = partly variable costs = mixed costs = costs partly variable costs = mixed costs = costs that include a combination of variable cost that include a combination of variable cost and fixed cost items.and fixed cost items.

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Variable CostsVariable Costs

Items of cost that vary, in total, directly and Items of cost that vary, in total, directly and proportionately with volume.proportionately with volume. Volume refers to activity level.Volume refers to activity level. Examples:Examples:

Material costs varies with units sold.Material costs varies with units sold. Electricity costs varies with production hours.Electricity costs varies with production hours. Stationery and postage costs varies with number Stationery and postage costs varies with number

of letters written.of letters written.

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Fixed costsFixed costs

Non-variable costs = items of cost that, in Non-variable costs = items of cost that, in total, do not vary at all with volume.total, do not vary at all with volume. Examples: Examples:

Building rent, property taxes, management salaries.Building rent, property taxes, management salaries. Fixed cost per unit of activity decreases as the Fixed cost per unit of activity decreases as the

level of activity increases.level of activity increases. For fixed costs, cost per unit is an average cost.For fixed costs, cost per unit is an average cost. Fixed costs are fixed for a range of activity and a Fixed costs are fixed for a range of activity and a

limited period of time.limited period of time. Fixed costs may change for reasons such as a Fixed costs may change for reasons such as a

deliberate management decision to change them.deliberate management decision to change them.

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Cost-volume (C-V) diagramCost-volume (C-V) diagram

Illustration 16-1.Illustration 16-1. Y or vertical axis reflects total cost.Y or vertical axis reflects total cost. X or horizontal axis reflects volume.X or horizontal axis reflects volume. y = mx + b.y = mx + b.

y is the cost at a volume of x; y is the cost at a volume of x; m is the rate of cost change per unit of volume m is the rate of cost change per unit of volume

change, or the slope (variable costs).change, or the slope (variable costs). b is the vertical intercept, which represents the b is the vertical intercept, which represents the

fixed cost component.fixed cost component.

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TC = TFC +(UVC*X)TC = TFC +(UVC*X)

TC = total cost; TC = total cost; TFC = total fixed cost (per time period),TFC = total fixed cost (per time period), UVC = Unit variable cost (per unit of volume),UVC = Unit variable cost (per unit of volume), X = volume.X = volume. Equations for:Equations for:

Variable cost line: TC = UVC*XVariable cost line: TC = UVC*X Fixed cost line: TC = TFCFixed cost line: TC = TFC Semivariable cost: TC = TFC + (UVC*X), same as Semivariable cost: TC = TFC + (UVC*X), same as

above.above.

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Cost RelationsCost Relations

Average costs = total cost/volume.Average costs = total cost/volume. Average cost behaves differently than Average cost behaves differently than

total cost.total cost. As volume goes up As volume goes up

Total fixed cost remains constant, total Total fixed cost remains constant, total variable costs goes up, per unit variable variable costs goes up, per unit variable costs stays the same, per unit fixed cost costs stays the same, per unit fixed cost goes down, per unit total cost goes down.goes down, per unit total cost goes down. As volume increases without limit, unit cost As volume increases without limit, unit cost

approaches variable unit cost and fixed cost approaches variable unit cost and fixed cost per unit approaches zero.per unit approaches zero.

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Limitations of C-V RelationsLimitations of C-V Relations

A straight line approximates cost behavior A straight line approximates cost behavior only within a certain range of volume, the only within a certain range of volume, the relevant range.relevant range. When volume approaches zero, management When volume approaches zero, management

takes steps to reduce fixed costs. takes steps to reduce fixed costs. When volume exceeds relevant range, fixed When volume exceeds relevant range, fixed

costs increase. costs increase.

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Limitations (continued)Limitations (continued) Amount of variable costs depends on Amount of variable costs depends on

the time period over which behavior is the time period over which behavior is estimated (the relevant time period).estimated (the relevant time period). If the time period is one day, few costs are If the time period is one day, few costs are

variable.variable. Over an extremely long time period, no Over an extremely long time period, no

costs are fixed.costs are fixed. Environmental assumptions must be Environmental assumptions must be

made.made. Wage rates, fringe benefits, material Wage rates, fringe benefits, material

prices, technology changes.prices, technology changes.

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““Sticky” CostsSticky” Costs

Generally considered variable but fall less Generally considered variable but fall less with decreases of activity than they rise with decreases of activity than they rise with increases.with increases.

Managers tend to increase resources Managers tend to increase resources more quickly than they decrease.more quickly than they decrease.

Examples:Examples: Sales commissions with minimum guarantees.Sales commissions with minimum guarantees. Managers slower to fire employees than to Managers slower to fire employees than to

hire.hire.

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Linear AssumptionLinear Assumption

C-V relationship is often not linear.C-V relationship is often not linear. Some cost functions are curved (curvilinear).Some cost functions are curved (curvilinear). Segments of the curve can be approximated Segments of the curve can be approximated

by a straight line, each with its own relevant by a straight line, each with its own relevant range.range.

Step function costs = items of cost vary in Step function costs = items of cost vary in steps.steps.

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Step-function costsStep-function costs

Incurred when costs are added in discrete Incurred when costs are added in discrete chunks, e.g., a supervisor for every 10. chunks, e.g., a supervisor for every 10.

Adding the “chunk” of costs increases Adding the “chunk” of costs increases capacity.capacity.

Height of a stair step (riser) indicates the cost Height of a stair step (riser) indicates the cost of adding incremental capacity.of adding incremental capacity.

Step width (tread) shows how much Step width (tread) shows how much additional volume of that activity can be additional volume of that activity can be serviced by this additional increment of serviced by this additional increment of capacity.capacity.

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Step function (continued)Step function (continued)

If treads” are narrow and “risers” are low (i.e., If treads” are narrow and “risers” are low (i.e., steps are small), then the steps can be steps are small), then the steps can be approximated by a variable cost line.approximated by a variable cost line.

If is believed within the relevant time period If is believed within the relevant time period that cost will remain within the relevant range that cost will remain within the relevant range for a single stair step (tread), then the cost is for a single stair step (tread), then the cost is appropriately treated as a fixed cost for the appropriately treated as a fixed cost for the time period. time period.

Step functions are often hidden in C-V Step functions are often hidden in C-V diagrams as either variable or fixed costs.diagrams as either variable or fixed costs.

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Estimating C-V RelationshipEstimating C-V Relationship

First method: Judgment or account-by-First method: Judgment or account-by-account method.account method. Each account in cost structure is estimated Each account in cost structure is estimated

and divided between fixed and variable costs.and divided between fixed and variable costs. Second: Scatter diagramSecond: Scatter diagram

Plot a number of observations (perhaps prior Plot a number of observations (perhaps prior period results) of costs and volumes on a period results) of costs and volumes on a graph and visually draw a line of best fit.graph and visually draw a line of best fit.

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Third method: High-Low MethodThird method: High-Low Method

Estimate total costs for two volume levels, Estimate total costs for two volume levels, preferably one high level and one low level.preferably one high level and one low level. To determine slope or variable cost per unit: To determine slope or variable cost per unit:

Change in total cost between the two points divided Change in total cost between the two points divided by change in units of output.by change in units of output.

To determine fixed costs: To determine fixed costs: Subtract from total costs at either one of the points Subtract from total costs at either one of the points

the unit volume times the unit variable costs.the unit volume times the unit variable costs.

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Fourth: Linear regressionFourth: Linear regression Use a statistical method of fitting a line to a Use a statistical method of fitting a line to a

number of observations of volume and cost number of observations of volume and cost (method of least squares or linear regression).(method of least squares or linear regression). Eliminate outliers, that is, unusual Eliminate outliers, that is, unusual

observations (e.g., period during which there observations (e.g., period during which there was a strike).was a strike).

Assumes the future will be the same as the Assumes the future will be the same as the past (rarely a completely accurate past (rarely a completely accurate assumption).assumption).

Scattergrams covering long periods of time Scattergrams covering long periods of time may reflect nothing more than price changes may reflect nothing more than price changes over the period (drift).over the period (drift).

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Measures of VolumeMeasures of Volume

Have assumed a single-product.Have assumed a single-product. If multiple products, with different cost If multiple products, with different cost

structures, unlikely that units would be a structures, unlikely that units would be a reliable measure of activity.reliable measure of activity. Possible common denominators include: labor Possible common denominators include: labor

hours, labor dollars, machine hours, hours, labor dollars, machine hours, homogeneous quantities such as tons or homogeneous quantities such as tons or barrels and sales value.barrels and sales value.

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Questions to Consider in Questions to Consider in Selecting a Volume MeasureSelecting a Volume Measure

Input (resources used) or output (goods or Input (resources used) or output (goods or services produced)?services produced)?

Money or non-monetary quantities?Money or non-monetary quantities?

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Input or Output?Input or Output?

Input measures: resources used: labor Input measures: resources used: labor hours worked, labor cost, machine hours, hours worked, labor cost, machine hours, kilowatt hours of electricity, pounds of kilowatt hours of electricity, pounds of material.material.

Output measures: units or dollars.Output measures: units or dollars. Manufacturing costs might use input Manufacturing costs might use input

measures such as labor or machine hours.measures such as labor or machine hours. Retail stores might use dollar sales.Retail stores might use dollar sales.

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Money or Non-monetary Money or Non-monetary Quantities?Quantities?

A non-monetary measure is not affected by A non-monetary measure is not affected by price changes and therefore may have some price changes and therefore may have some advantages.advantages.

If price changes affect all costs equally, the If price changes affect all costs equally, the use of labor costs as an activity measure use of labor costs as an activity measure implicitly allows for price changes.implicitly allows for price changes.

Best volume measure should be related to Best volume measure should be related to the activity that causes the cost.the activity that causes the cost.

The more items of cost that are combined in The more items of cost that are combined in the cost function the more difficult it is to the cost function the more difficult it is to relate the causality to a single measure.relate the causality to a single measure.

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Profit-graphProfit-graph

Add revenue line to C-V diagram.Add revenue line to C-V diagram. Assumes constant selling price.Assumes constant selling price. UR = unit revenue UR = unit revenue TR = total revenueTR = total revenue

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Breakeven VolumeBreakeven Volume

TR = UR*XTR = UR*X TC = TFC + (UVC*X)TC = TFC + (UVC*X) Breakeven: TR = TCBreakeven: TR = TC Substituting: UR*X = TFC + (UVC*X) Substituting: UR*X = TFC + (UVC*X) X X

= TFC/(UR - UVC)= TFC/(UR - UVC)

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ContributionContribution

Unit contribution = unit contribution margin Unit contribution = unit contribution margin = marginal income = unit selling price - = marginal income = unit selling price - variable cost per unit = UR - UVC.variable cost per unit = UR - UVC.

I = total income = (UR - UVC) * X - TFC.I = total income = (UR - UVC) * X - TFC. What is contribution:What is contribution:

First it is the contribution to cover fixed costs.First it is the contribution to cover fixed costs. Then it is the contribution toward profit.Then it is the contribution toward profit.

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Break-even VolumeBreak-even Volume

In units = Fixed costs/unit contributionIn units = Fixed costs/unit contribution In revenue dollars = Fixed costs / In revenue dollars = Fixed costs /

contribution percentcontribution percent Contribution percent = contribution margin Contribution percent = contribution margin

percentage = contribution as a percent of percentage = contribution as a percent of revenues = (UR - UVC)/ URrevenues = (UR - UVC)/ UR

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Target ProfitTarget Profit

Add to breakeven analysis to show units Add to breakeven analysis to show units or dollar of sales to achieve a target (T) or dollar of sales to achieve a target (T) level of profit:level of profit:

UR*X = TFC + (UVC*X) + TUR*X = TFC + (UVC*X) + T

X = (TFC+T)/(UR - UVC)X = (TFC+T)/(UR - UVC)

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Target Profit with TaxesTarget Profit with Taxes

Add to breakeven analysis to show units or Add to breakeven analysis to show units or dollar of sales to achieve a target level of dollar of sales to achieve a target level of profit after taxes (PAT): (assume tax rate = profit after taxes (PAT): (assume tax rate = TR)TR)

UR*X = TFC + (UVC*X) + TUR*X = TFC + (UVC*X) + T

Need to convert PAT to T =>Need to convert PAT to T =>

T – (T*TR) = T * (1 – TR) = PAT =>T – (T*TR) = T * (1 – TR) = PAT =>

T = PAT/(1 – TR); thusT = PAT/(1 – TR); thus

X = (TFC+[PAT/(1-TR)])/(UR - UVC)X = (TFC+[PAT/(1-TR)])/(UR - UVC)

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Profit-graph Shows to Improve Profit-graph Shows to Improve Profit Performance:Profit Performance:

Increase selling price.Increase selling price. Decrease variable cost.Decrease variable cost. Decrease fixed cost.Decrease fixed cost. Increase volume.Increase volume.

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Margin of SafetyMargin of Safety

The amount or ratio by which the current The amount or ratio by which the current volume exceeds breakeven volume.volume exceeds breakeven volume.

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C-V-P with Several ProductsC-V-P with Several Products

Relationships hold if each product has Relationships hold if each product has about the same contribution margin about the same contribution margin percentage.percentage.

Profit-graph can be constructed by using Profit-graph can be constructed by using sales revenue rather than units.sales revenue rather than units.

Complicates C-V-P relationships:Complicates C-V-P relationships: Particularly if different contribution margin Particularly if different contribution margin

percentages unless product mix remains percentages unless product mix remains constant.constant. If product mix is constant can use a weighted If product mix is constant can use a weighted

average unit contribution.average unit contribution.

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Influences on CostsInfluences on Costs

Changes in input prices.Changes in input prices. Rate at which volume changes. Rate at which volume changes.

Rapid changes in volume make it more Rapid changes in volume make it more difficult to change personnel costs, therefore, difficult to change personnel costs, therefore, the more likely costs depart from a straight the more likely costs depart from a straight line relationship.line relationship.

Direction of change in volume. Tends to Direction of change in volume. Tends to be a lag in cost changes.be a lag in cost changes.

Duration of change. Temporary changes Duration of change. Temporary changes affects costs less than a long term affects costs less than a long term change.change.

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Influences on Costs (cont.)Influences on Costs (cont.)

Prior knowledge of change allows planning Prior knowledge of change allows planning for change.for change.

As productivity changes costs change.As productivity changes costs change. Management discretion. Costs change Management discretion. Costs change

because of management decisions.because of management decisions. Learning curves. Productivity increases, i.e., Learning curves. Productivity increases, i.e.,

unit production costs decrease, as the unit production costs decrease, as the company gains experience producing the company gains experience producing the product.product.

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Quality of ConformanceQuality of Conformance

When the overwhelming majority of products produced conform to design

specifications and are free from defects.

Quality of Design (Performance)A measure of the quality of the design itself and the features offered by the product or service; how closely it meets the needs and wants of customers

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Prevention and Appraisal CostsPrevention and Appraisal Costs

Prevention Costs

Support activities whose purpose is to

reduce the number of defects

Appraisal Costs

Incurred to identify defective products

before the products are shipped

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Internal and External Failure Internal and External Failure CostsCosts

Internal Failure Costs

Incurred as a result of identifying defects

before they are shipped

External Failure Costs

Incurred as a result of defective products being delivered to

customers

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Examples of Quality CostsExamples of Quality Costs

Prevention Costs• Quality training• Quality circles• Statistical process control activities

Appraisal Costs• Testing & inspecting incoming materials• Final product testing• Depreciation of testing equipment

Internal Failure Costs• Scrap• Spoilage• Rework

External Failure Costs• Cost of field servicing & handling complaints• Warranty repairs• Lost sales

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Distribution of Quality CostsDistribution of Quality CostsWhen quality of conformance is low, total quality cost is high and consists mostly of internal and external failure.

Companies can reduce their total quality cost by

focusing on prevention and appraisal. The cost savings

from reduced defects usually swamps the costs

of the additional prevention and appraisal efforts.

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Quality cost reports provide an estimate of the financial

consequences of the

company’s current defect

rate. Often shown as a %

of Sales.

Amount Percent* Amount Percent*Prevention costs:

Systems development 400,000$ 0.80% 270,000$ 0.54%Quality training 210,000 0.42% 130,000 0.26%Supervision of prevention activities 70,000 0.14% 40,000 0.08%Quality improvement 320,000 0.64% 210,000 0.42%

Total prevention cost 1,000,000 2.00% 650,000 1.30%

Appraisal costs:Inspection 600,000 1.20% 560,000 1.12%Reliability testing 580,000 1.16% 420,000 0.84%Supervision of testing and inspection 120,000 0.24% 80,000 0.16%Depreciation of test equipment 200,000 0.40% 140,000 0.28%

Total appraisal cost 1,500,000 3.00% 1,200,000 2.40%

Internal failure costs:Net cost of scrap 900,000 1.80% 750,000 1.50%Rework labor and overhead 1,430,000 2.86% 810,000 1.62%Downtime due to defects in quality 170,000 0.34% 100,000 0.20%Disposal of defective products 500,000 1.00% 340,000 0.68%

Total internal failure cost 3,000,000 6.00% 2,000,000 4.00%

External failure costs:Warranty repairs 400,000 0.80% 900,000 1.80%Warranty replacements 870,000 1.74% 2,300,000 4.60%Allowances 130,000 0.26% 630,000 1.26%Cost of field servicing 600,000 1.20% 1,320,000 2.64%

Total external failure cost 2,000,000 4.00% 5,150,000 10.30%Total quality cost 7,500,000$ 15.00% 9,000,000$ 18.00%

* As a percentage of total sales. In each year sales totaled $50,000,000.

Year 2 Year 1

Ventura CompanyQuality Cost ReportFor Years 1 and 2

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Quality Cost Reports: Graphic Quality Cost Reports: Graphic FormForm

$10

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7

6

5

4

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Uses of Quality Cost Uses of Quality Cost InformationInformation

Help managers see the financial significance of

defects.

Help managers identify the relative importance of

the quality problems.

Help managers see whether their quality

costs are poorly distributed.

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Limitations of Quality Cost Limitations of Quality Cost Information Information

Simply measuring quality cost problems does not solve quality problems.

Results usually lag behind quality

improvement programs.

The most important quality cost, lost sales, is

often omitted from quality cost reports.