Transcript Behavior of Costs - Villanova University

Chapter 16
The Behavior of Costs
McGraw-Hill
© 2004 The McGraw-Hill Companies, Inc. All rights reserved.
Behavior of Costs
 Cost-volume


relationships.
Fixed and variable costs.
Step-function costs.
16-2
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.
16-3
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.
16-4
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.
16-5
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.
16-6
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.
16-7
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.
16-8
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.
16-9
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.
16-10
“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.
16-11
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.
16-12
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.
16-13
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.

16-14
Estimating C-V Relationship
 First
method: Judgment or account-byaccount 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.
16-15
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.
16-16
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).
16-17
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.
16-18
Questions to Consider in
Selecting a Volume Measure

Input (resources used) or output (goods or
services produced)?

Money or non-monetary quantities?
16-19
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.
16-20
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.
16-21
Profit-graph
 Add



revenue line to C-V diagram.
Assumes constant selling price.
UR = unit revenue
TR = total revenue
16-22
Breakeven Volume
 TR



= UR*X
TC = TFC + (UVC*X)
Breakeven: TR = TC
Substituting: UR*X = TFC + (UVC*X)  X
= TFC/(UR - UVC)
16-23
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.
16-24
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
16-25
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)
16-26
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)
16-27
Profit-graph Shows to Improve
Profit Performance:
 Increase
selling price.
 Decrease variable cost.
 Decrease fixed cost.
 Increase volume.
16-28
Margin of Safety
 The
amount or ratio by which the current
volume exceeds breakeven volume.
16-29
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.
16-30
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.
16-31
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.
16-32
Quality 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
16-33
Prevention 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
16-34
Internal and External Failure
Costs
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
16-35
Examples of Quality Costs
Prevention Costs
• Quality training
• Quality circles
• Statistical process
control activities
Internal Failure Costs
• Scrap
• Spoilage
• Rework
Appraisal Costs
• Testing & inspecting
incoming materials
• Final product testing
• Depreciation of testing
equipment
External Failure Costs
• Cost of field servicing &
handling complaints
• Warranty repairs
• Lost sales
16-36
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.
16-37
Ventura Company
Quality Cost Report
For Years 1 and 2
Year 2
Amount
Percent*
Prevention costs:
Systems development
Quality training
Supervision of prevention activities
Quality improvement
Total prevention cost
$
400,000
210,000
70,000
320,000
1,000,000
Year 1
Amount Percent*
0.80% $ 270,000
0.42%
130,000
0.14%
40,000
0.64%
210,000
2.00%
650,000
0.54%
0.26%
0.08%
0.42%
1.30%
Appraisal costs:
Inspection
Reliability testing
Supervision of testing and inspection
Depreciation of test equipment
Total appraisal cost
600,000
580,000
120,000
200,000
1,500,000
1.20%
1.16%
0.24%
0.40%
3.00%
560,000
420,000
80,000
140,000
1,200,000
1.12%
0.84%
0.16%
0.28%
2.40%
Internal failure costs:
Net cost of scrap
Rework labor and overhead
Downtime due to defects in quality
Disposal of defective products
Total internal failure cost
900,000
1,430,000
170,000
500,000
3,000,000
1.80%
2.86%
0.34%
1.00%
6.00%
750,000
810,000
100,000
340,000
2,000,000
1.50%
1.62%
0.20%
0.68%
4.00%
External failure costs:
Warranty repairs
Warranty replacements
Allowances
Cost of field servicing
Total external failure cost
Total quality cost
400,000
870,000
130,000
600,000
2,000,000
7,500,000
0.80%
900,000
1.74% 2,300,000
0.26%
630,000
1.20% 1,320,000
4.00% 5,150,000
15.00% $ 9,000,000
1.80%
4.60%
1.26%
2.64%
10.30%
18.00%
$
* As a percentage of total sales. In each year sales totaled $50,000,000.
Quality cost
reports provide
an estimate of
the financial
consequences
of the
company’s
current defect
rate. Often
shown as a %
of Sales.
16-38
Quality Cost Reports: Graphic
Form
$10
20
Quality Cost (in millions)
8
7
6
External
Failure
External
Failure
5
Internal
Failure
4
3
Internal
Failure
2
1
0
Appraisal
Appraisal
Quality
reports
can also
be
prepared
in
graphic
form.
18
Quality Cost as a Percentage of Sales
9
16
14
12
Prevention
1
2
Year
External
Failure
10
Internal
Failure
8
6
Internal
Failure
4
2
Prevention
External
Failure
0
Appraisal
Appraisal
Prevention
Prevention
1
2
Year
16-39
Uses of Quality Cost
Information
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.
16-40
Limitations of Quality Cost
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.
16-41