Cost Behavior: Analysis and Use

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Cost BehaviorAnalysis and Use
Chapter 5
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Types of Cost Behavior Patterns
Recall the summary of our cost behavior
discussion from Chapter 2.
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The Activity Base
A measure of the event that causes the incurrence
of a variable cost a cost driver
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True Variable Cost Example

• Your total long distance telephone bill is
  based on how many minutes you talk.

Total Long DistanceTelephone Bill
Minutes Talked
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Variable Cost Per Unit Example

• The cost per minute talked is constant. For
  example, 10 cents per minute.

Per MinuteTelephone Charge
Minutes Talked
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Step-Variable Costs
Total cost remainsconstant within anarrow range
ofactivity.
Cost
Activity
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Step-Variable Costs
Total cost increases to a new higher cost for
the next higher range of activity.
Cost
Activity
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The Linearity Assumption and the Relevant Range
Exh. 5-4
EconomistsCurvilinear Cost Function
Total Cost
Activity
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Total Fixed Cost Example
Exh. 5-5

• Your monthly basic telephone bill is probably
  fixed and does not change when you make more
  local calls.

Monthly Basic Telephone Bill
Number of Local Calls
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Fixed Cost Per Unit Example
Exh. 5-5

• The fixed cost per local call decreases as more
  local calls are made.

Monthly Basic Telephone Bill per Local Call
Number of Local Calls
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Cost Behavior
Examples of normally variable costs
Service Organizations Supplies and travel
Merchandisers Cost of Goods Sold
Merchandisers and Manufacturers Sales commissions
and shipping costs
Manufacturers Direct Material, Direct Labor, and
Variable Manufacturing Overhead
Examples of normally fixed costs
Merchandisers, manufacturers, and service
organizations Real estate taxes, Insurance, Sales
salariesDepreciation, Advertising
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Types of Fixed Costs
Discretionary May be altered in the short-term by
current managerial decisions
Committed Long-term, cannot be reduced in the
short term.
Examples Advertising and Research and Development
Examples Depreciation on Buildings and Equipment
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Fixed Costs and Relevant Range

• Example Office space is available at a
  rental rate of 30,000 per year in increments of
  1,000 square feet. As the business grows more
  space is rented, increasing the total cost.

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Fixed Costs and Relevant Range
Exh. 5-6
90
Total cost doesnt change for a wide range of
activity, and then jumps to a new higher cost for
the next higher range of activity.
Relevant Range
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Rent Cost in Thousands of Dollars
30
0
0 1,000 2,000
3,000 Rented Area (Square Feet)
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Fixed Costs and Relevant Range
Step-variable costs can be adjusted more quickly
and . . . The width of the activity steps is much
wider for the fixed cost.
How does this type of fixed cost differ from a
step-variable cost?
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Quick Check ?

• Which of the following statements about cost
  behavior are true?
• Fixed costs per unit vary with the level of
  activity.
• Variable costs per unit are constant within the
  relevant range.
• Total fixed costs are constant within the
  relevant range.
• Total variable costs are constant within the
  relevant range.

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Mixed Costs
A mixed cost has both fixed and
variablecomponents. Consider the example of
utility cost.
Total mixed cost
Total Utility Cost
Variable Cost per KW
Fixed MonthlyUtility Charge
Activity (Kilowatt Hours)
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Mixed Costs
Total mixed cost Y a bX
Total Utility Cost
Variable Cost per KW
Fixed MonthlyUtility Charge
Activity (Kilowatt Hours)
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The Analysis of Mixed Costs
Account Analysis
Engineering Approach
Scattergraph Plot
High-Low Method
Least-Square Regression Method
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Account Analysis Engineering Estimates
Each account is classified as eithervariable or
fixed based on the analysts knowledge of how
the account behaves.
Cost estimates are based on an evaluation of
production methods, and material, labor and
overhead requirements.
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The Scattergraph Method
Plot the data points on a graph (total cost vs.
activity).
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Quick-and-Dirty Method
Draw a line through the data points with about
anequal numbers of points above and below the
line.
Y
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Total Cost in1,000s of Dollars


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Intercept is the estimated fixed cost 10,000
0
X
0 1 2 3 4
Activity, 1,000s of Units Produced
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Quick-and-Dirty Method
The slope is the estimated variable cost per
unit. Slope Change in cost Change in units
Y
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Total Cost in1,000s of Dollars


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Horizontal distance is the change in activity.
Vertical distance is the change in cost.
0
X
0 1 2 3 4
Activity, 1,000s of Units Produced
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The High-Low Method

• WiseCo recorded the following production activity
  and maintenance costs for two months
• Using these two levels of activity, compute
• the variable cost per unit
• the fixed cost and then
• express the costs in equation form Y a bX.

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The High-Low Method
Change?in costChange in units

• Variable cost per unit Change in cost
  change in units

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The High-Low Method

• Variable cost per unit 2,400 3,000 units
• 
  0.80 per unit

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The High-Low Method

• Variable cost 2,400 3,000 units 0.80
  per unit
• Fixed cost Total cost Total variable cost
• Fixed cost 9,800 (0.80 per unit
  8,000 units)
• Fixed cost 9,800 6,400 3,400

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The High-Low Method

• Variable cost 2,400 3,000 units 0.80
  per unit
• Fixed cost Total cost Total variable cost
• Fixed cost 9,800 (0.80 per unit
  8,000 units)
• Fixed cost 9,800 6,400 3,400
• Total cost Fixed cost Variable cost (Y a
  bX) Y 3,400 0.80X

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Quick Check ?

• Sales salaries and commissions are 10,000
  when 80,000 units are sold, and 14,000 when
  120,000 units are sold. Using the high-low
  method, what is the variable portion of sales
  salaries and commission?
• a. 0.08 per unit
• b. 0.10 per unit
• c. 0.12 per unit
• d. 0.125 per unit

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Quick Check ?

• Sales salaries and commissions are 10,000
  when 80,000 units are sold, and 14,000 when
  120,000 units are sold. Using the high-low
  method, what is the fixed portion of sales
  salaries and commissions?
• a. 2,000
• b. 4,000
• c. 10,000
• d. 12,000

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Least-Squares Regression Method

• Software can be used to fit a regression line
  through the data points.
• The cost analysis objective is the same Y a
  bx

Least-squares regression also provides a
statistic, called the R2, that is a measure of
the goodnessof fit of the regression line to the
data points.
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Least-Squares Regression Method
R2 is the percentage of the variation in total
cost explained by the activity.

Y
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Total Cost
10
R2 for this relationship is near100 since the
data points arevery close to the regression line.
0
X
0 1 2 3 4
Activity
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Cost Estimation MethodsRegression Analysis
A statistical method used to create an equation
relating independent (or X) variables to
dependent (or Y) variables. Past data is used to
estimate relationships between costs and
activities.
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Cost Estimation MethodsRegression Analysis
The simple cost model is actually a regression
model TC F VX
Caution Before doing the analysis, take time to
determine if a logical relationship between the
variables exists.
This model will only be useful within a relevant
range of activity.
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Cost Estimation MethodsRegression Analysis

• A set of data can be regressed using several
  techniques
• Manual computations
• SPSS or SAS Statistical Software
• Excel or other spreadsheet

Each regression model has an R-square (R2)
measure of how good the model is. Range of R2 0
to 1.0
The result of the regression process is a
regression model TC F VX
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Simple Regression AnalysisExample
Fasco wants to know its average fixed cost and
variable cost per unit. Using the data to the
right, lets see how to do a regression using
Excel.
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Simple Regression AnalysisExample

• You will need three pieces of information
  from your regression analysis
• Estimated Variable Cost per Unit (line slope)
• Estimated Fixed Costs (line intercept)
• Goodness of fit, or R2

To get these three pieces of information we
will need to use THREE different excel
functions. LINEST, INTERCEPT, RSQ
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Simple Regression Using Excel 2000
First, open the excel file with your data and
click on Insert and Function
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Simple Regression Using Excel 2000
When the function box opens, click on
Statistical, then on LINEST
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Simple Regression Using Excel 2000
By clicking on the buttons to the left, you can
highlight the desired cells directly from the
spreadsheet.
1. Enter the cell range for the cost amounts in
the Known_ys box. 2. Enter the cell range for
the quantity amounts in the Known_xs box.
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Simple Regression Using Excel 2000
The Slope, or estimated variable cost per unit,
is identified here. Click OK to put this value
on your spreadsheet.
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Simple Regression Using Excel 2000
Repeat the procedure using Intercept, to
estimate fixed cost.
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Simple Regression Using Excel 2000
As previously, enter the appropriate cell ranges
in their appropriate places.
The estimated fixed cost is identified here.
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Simple Regression Using Excel 2000
Finally, determine the goodness of fit, or R2,
by using the RSQ function.
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Simple Regression Using Excel 2000
As previously, enter the appropriate cell ranges
in their appropriate places.
The estimated R2 for your estimated cost function
is identified here.
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The Contribution Format
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The Contribution Format
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End of Chapter 5