1. Chapter 16 The Behavior of Costs
McGraw-Hill
© 2004 The McGraw-Hill Companies, Inc. All rights reserved.

2. Behavior of Costs Cost-volume relationships. Fixed and variable costs.
Step-function costs.

3. Relation of Costs to Volume
Higher volume causes higher costs.
Variable costs = items of cost that vary, in total, directly and proportionately with volume.
Fixed costs = non-variable costs = items of cost that, in total, do not vary at all with volume
Semi-variable costs = semi-fixed costs = partly variable costs = mixed costs = costs that include a combination of variable cost and fixed cost items.

4. Variable Costs
Items of cost that vary, in total, directly and proportionately with volume.
Volume refers to activity level.
Examples:
Material costs varies with units sold.
Electricity costs varies with production hours.
Stationery and postage costs varies with number of letters written.

5. Fixed costs
Non-variable costs = items of cost that, in total, do not vary at all with volume.
Examples:
Building rent, property taxes, management salaries.
Fixed cost per unit of activity decreases as the level of activity increases.
For fixed costs, cost per unit is an average cost.
Fixed costs are fixed for a range of activity and a limited period of time.
Fixed costs may change for reasons such as a deliberate management decision to change them.

6. Cost-volume (C-V) diagram
Illustration 16-1.
Y or vertical axis reflects total cost.
X or horizontal axis reflects volume.
y = mx + b.
y is the cost at a volume of x;
m is the rate of cost change per unit of volume change, or the slope (variable costs).
b is the vertical intercept, which represents the fixed cost component.

7. TC = TFC +(UVC*X) TC = total cost;
TFC = total fixed cost (per time period),
UVC = Unit variable cost (per unit of volume),
X = volume.
Equations for:
Variable cost line: TC = UVC*X
Fixed cost line: TC = TFC
Semivariable cost: TC = TFC + (UVC*X), same as above.

8. Cost Relations Average costs = total cost/volume.
Average cost behaves differently than total cost.
As volume goes up 
Total fixed cost remains constant, total variable costs goes up, per unit variable costs stays the same, per unit fixed cost goes down, per unit total cost goes down.
As volume increases without limit, unit cost approaches variable unit cost and fixed cost per unit approaches zero.

9. Limitations of C-V Relations
A straight line approximates cost behavior only within a certain range of volume, the relevant range.
When volume approaches zero, management takes steps to reduce fixed costs.
When volume exceeds relevant range, fixed costs increase.

10. Limitations (continued)
Amount of variable costs depends on the time period over which behavior is estimated (the relevant time period).
If the time period is one day, few costs are variable.
Over an extremely long time period, no costs are fixed.
Environmental assumptions must be made.
Wage rates, fringe benefits, material prices, technology changes.

11. “Sticky” Costs
Generally considered variable but fall less with decreases of activity than they rise with increases.
Managers tend to increase resources more quickly than they decrease.
Examples:
Sales commissions with minimum guarantees.
Managers slower to fire employees than to hire.

12. Linear Assumption C-V relationship is often not linear.
Some cost functions are curved (curvilinear).
Segments of the curve can be approximated by a straight line, each with its own relevant range.
Step function costs = items of cost vary in steps.

13. Step-function costs
Incurred when costs are added in discrete chunks, e.g., a supervisor for every 10.
Adding the “chunk” of costs increases capacity.
Height of a stair step (riser) indicates the cost of adding incremental capacity.
Step width (tread) shows how much additional volume of that activity can be serviced by this additional increment of capacity.

14. Step function (continued)
If treads” are narrow and “risers” are low (i.e., steps are small), then the steps can be approximated by a variable cost line.
If is believed within the relevant time period that cost will remain within the relevant range for a single stair step (tread), then the cost is appropriately treated as a fixed cost for the time period.
Step functions are often hidden in C-V diagrams as either variable or fixed costs.

15. Estimating C-V Relationship
First method: Judgment or account-by-account method.
Each account in cost structure is estimated and divided between fixed and variable costs.
Second: Scatter diagram
Plot a number of observations (perhaps prior period results) of costs and volumes on a graph and visually draw a line of best fit.

16. Third method: High-Low Method
Estimate total costs for two volume levels, preferably one high level and one low level.
To determine slope or variable cost per unit:
Change in total cost between the two points divided by change in units of output.
To determine fixed costs:
Subtract from total costs at either one of the points the unit volume times the unit variable costs.

17. Fourth: Linear regression
Use a statistical method of fitting a line to a number of observations of volume and cost (method of least squares or linear regression).
Eliminate outliers, that is, unusual observations (e.g., period during which there was a strike).
Assumes the future will be the same as the past (rarely a completely accurate assumption).
Scattergrams covering long periods of time may reflect nothing more than price changes over the period (drift).

18. Measures of Volume Have assumed a single-product.
If multiple products, with different cost structures, unlikely that units would be a reliable measure of activity.
Possible common denominators include: labor hours, labor dollars, machine hours, homogeneous quantities such as tons or barrels and sales value.

19. Questions to Consider in Selecting a Volume Measure
Input (resources used) or output (goods or services produced)?
Money or non-monetary quantities?

20. Input or Output?
Input measures: resources used: labor hours worked, labor cost, machine hours, kilowatt hours of electricity, pounds of material.
Output measures: units or dollars.
Manufacturing costs might use input measures such as labor or machine hours.
Retail stores might use dollar sales.

21. Money or Non-monetary Quantities?
A non-monetary measure is not affected by price changes and therefore may have some advantages.
If price changes affect all costs equally, the use of labor costs as an activity measure implicitly allows for price changes.
Best volume measure should be related to the activity that causes the cost.
The more items of cost that are combined in the cost function the more difficult it is to relate the causality to a single measure.

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

23. Breakeven Volume TR = UR*X TC = TFC + (UVC*X) Breakeven: TR = TC
Substituting: UR*X = TFC + (UVC*X)  X = TFC/(UR - UVC)

24. Contribution
Unit contribution = unit contribution margin = marginal income = unit selling price - variable cost per unit = UR - UVC.
I = total income = (UR - UVC) * X - TFC.
What is contribution:
First it is the contribution to cover fixed costs.
Then it is the contribution toward profit.

25. Break-even Volume In units = Fixed costs/unit contribution
In revenue dollars = Fixed costs / contribution percent
Contribution percent = contribution margin percentage = contribution as a percent of revenues = (UR - UVC)/ UR

26. Target Profit
Add to breakeven analysis to show units or dollar of sales to achieve a target (T) level of profit:
UR*X = TFC + (UVC*X) + T
X = (TFC+T)/(UR - UVC)

27. Target Profit with Taxes
Add to breakeven analysis to show units or dollar of sales to achieve a target level of profit after taxes (PAT): (assume tax rate = TR)
UR*X = TFC + (UVC*X) + T
Need to convert PAT to T =>
T – (T*TR) = T * (1 – TR) = PAT =>
T = PAT/(1 – TR); thus
X = (TFC+[PAT/(1-TR)])/(UR - UVC)

28. Profit-graph Shows to Improve Profit Performance:
Increase selling price.
Decrease variable cost.
Decrease fixed cost.
Increase volume.

29. Margin of Safety
The amount or ratio by which the current volume exceeds breakeven volume.

30. C-V-P with Several Products
Relationships hold if each product has about the same contribution margin percentage.
Profit-graph can be constructed by using sales revenue rather than units.
Complicates C-V-P relationships:
Particularly if different contribution margin percentages unless product mix remains constant.
If product mix is constant can use a weighted average unit contribution.

31. Influences on Costs Changes in input prices.
Rate at which volume changes.
Rapid changes in volume make it more difficult to change personnel costs, therefore, the more likely costs depart from a straight line relationship.
Direction of change in volume. Tends to be a lag in cost changes.
Duration of change. Temporary changes affects costs less than a long term change.

32. Influences on Costs (cont.)
Prior knowledge of change allows planning for change.
As productivity changes costs change.
Management discretion. Costs change because of management decisions.
Learning curves. Productivity increases, i.e., unit production costs decrease, as the company gains experience producing the product.

33. Quality of Conformance
When the overwhelming majority of products produced conform to design specifications and are free from defects.
Quality of Design (Performance)
The term quality has many meanings. Quality can mean that a product has many features not found in other products; it can mean that it is well-designed; or it can mean that it is defect-free. In this appendix, the focus is on the presence or absence of defects. Quality of conformance is the degree to which the actual product or service meets its design specifications. Anything that does not meet design specifications is a defect and is indicative of low quality of conformance.
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

34. Prevention and Appraisal Costs
Prevention Costs
Support activities whose purpose is to reduce the number of defects
There are four broad categories of quality costs: prevention costs, appraisal costs, internal failure costs, and external failure costs. Prevention costs are incurred to support activities whose purpose is to reduce the number of defects. Appraisal costs are incurred to identify defective products before the products are shipped to customers.
Appraisal Costs
Incurred to identify defective products before the products are shipped

35. Internal and External Failure Costs
Internal Failure Costs
Incurred as a result of identifying defects before they are shipped
Internal failure costs are incurred as a result of identifying defects before they are shipped to customers. External failure costs are incurred as a result of defective products being delivered to customers.
External Failure Costs
Incurred as a result of defective products being delivered to customers

36. Examples 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
Here are some examples of each type of quality cost. 
Prevention costs include quality training, quality circles, and statistical process control activities.
Appraisal costs include testing and inspection of incoming materials, final product testing, and depreciation of testing equipment.
Internal failure costs include scrap, spoilage, and rework.
External failure costs include the cost of field servicing and handling customer complaints, warranty repairs, and lost sales arising from reputation of poor quality.

37. Distribution of Quality Costs
When 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.
Here are four key concepts about the relationship between the four types of quality costs.
When the quality of conformance is low, total quality cost is high and most of this cost consists of internal and external failure costs.
Total quality costs drop rapidly as the quality of conformance increases.
Companies reduce their total quality costs by focusing their efforts on prevention and appraisal because the cost savings from reduced defects usually overwhelm the costs of additional prevention and appraisal.
Total quality costs are minimized when the quality of conformance is slightly less than one hundred percent. This is a debatable point in the sense that some experts believe that total quality costs are not minimized until the quality of conformance is one hundred percent.

38. Quality cost reports provide an estimate of the financial consequences of the company’s current defect rate. Often shown as a % of Sales.
A quality cost report details the prevention, appraisal, internal failure, and external failure costs that arise from a company’s current quality control efforts. When interpreting a cost of quality report managers should look for two trends. First, increases in prevention and appraisal costs should be more than offset by decreases in internal and external failure costs. Second, the total quality costs as a percent of sales should decrease.

39. Quality Cost Reports: Graphic Form
Quality reports can also be prepared in graphic form.
Quality cost reports can also be prepared in graphic form. Managers should still look for the same two trends whether the data is presented in a graphic or table format.

40. Uses of Quality Cost Information
Help managers see the financial significance of defects.
Help managers identify the relative importance of the quality problems.
Uses of quality cost information include the following.
It helps managers see the financial significance of defects.
It helps managers identify the relative importance of the quality problems faced by the company.
It helps managers see whether their quality costs are poorly distributed. In general, costs should be distributed more toward prevention and to a lesser extent appraisal than toward failures.
Help managers see whether their quality costs are poorly distributed.

41. Limitations of Quality Cost Information
Simply measuring quality cost problems does not solve quality problems.
Results usually lag behind quality improvement programs.
Limitations of quality cost information include the following.
Simply measuring and reporting quality cost problems does not solve quality problems.
Results usually lag behind quality improvement programs. Initially, prevention and appraisal cost increases may not be offset by decreases in failure costs.
The most important quality cost, lost sales arising from customer ill-will, is often omitted from quality cost reports because it is difficult to estimate.
The most important quality cost, lost sales, is often omitted from quality cost reports.