Chapter 3 Special Addendum

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Chapter 3 Special Addendum
2
Separating Mixed Costs into their Fixed and
Variable Components
An account analysis method can be used when you
know which components are variable and fixed
within the relevant range. Often, however the
fixed and variable components must be estimated
based on recent past experience. For example how
much electricity cost is variable, and how much
is fixed.
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Product Costs (Manufacturing Firm)

• There are three basic categories of Product Costs
  -
• Direct materials - ex. raw materials
• Direct labor - ex. wages, fringe benefits related
  to completion of final inventory product (by
  assemblers)
• All other costs associated with the manufacture
  of the product
• also called indirect manufacturing costs,
  manufacturing overhead, factory overhead, factory
  burden).
• These costs are also known as Inventoriable Costs
• Under full absorption costing, these costs are
  inventoried (treated as an asset) until the
  product is sold.
• Prime Costs Direct Materials Direct Labor.
• Conversion Costs Direct Labor Factory
  Overhead.

4
Period Costs

• Costs that are not directly related to the
  manufacture of a product or the acquisition of
  inventory are called Period Costs
• Are expensed in the period they are incurred
• They are also called Non-manufacturing Costs.
• These costs consist of
• General and administrative costs,
• Research and development costs, and/or
• Marketing and selling costs.
• These costs are not inventoriable costs.
• Manufacturing Costs Product (or Inventoriable)
  Costs.
• Non-manufacturing Costs Period Costs.

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Cost Behavior/Level of Activity

• Cost Behavior - is defined as how costs react
  when the level of activity (or volume) changes .
• Identifying how different costs react as the
  level of activity changes allows management to
  determine how total costs will be affected by
  planned levels of activity
• Example Renting a car
• 100 a day with no mileage
• 50 a day plus .60 a mile
• The level of activity will determine the
  appropriate choice

6
Cost Drivers

• Cost driver (a.k.a. Level of Activity) -
• any factor whose change causes a change in the
  total cost of a related cost object
• more simply, any factor that causes costs.
• There is assumed to be a causal relation between
  the use of the cost driver and the incurrence of
  the cost.
• A Cost driver is the activity that causes a
  particular type of cost to change
• Cost drivers can be financial (e.g., direct
  materials costs) or non-financial (e.g., number
  of equipment setups).
• Costs are often categorized based on their
  behavior relative to a cost driver (see next
  slide).

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Cost Behavior Variable Versus Fixed Costs

• A fixed cost is a cost that does not change in
  total given changes in the level of the cost
  driver (overhead, depreciation, etc.).
• A variable cost is a cost that changes in total
  in direct proportion to changes in the level of
  the cost driver (direct labor, direct materials,
  etc.).
• We also have semi-variable (or mixed) costs which
  are costs that have both fixed and variable
  components (example renting a car for 50 a day
  plus .60 a mile).

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Cost Behavior Variable Versus Fixed Costs
(Continued)

• Step (or step-variable) costs are costs which
  change in steps as the cost driver changes.
• Remains constant over a given range of activity
  and increases in fixed incremental amounts within
  the relevant range
• Ex. machine operator gets paid 3000 per month
  for making 5,000 textbooks. For more than 5,000,
  company would have to hire another operator at
  another 5,000
• Each of these behaviors may be valid only over a
  relevant range.
• The relevant range is the operating range or
  activity level over which a firm finds it
  practical to operate in the short run.
• Over the relevant range, total fixed costs and
  unit variable costs remain constant. This
  implies a linear relation between cost and the
  cost driver.

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Other Cost Terms

• Full cost - the sum of all costs of manufacturing
  and selling a unit of product (including fixed
  and variable costs).
• Full absorption cost -
• all variable and fixed manufacturing costs are
  inventoried
• used to compute the value of inventory under
  GAAP.
• Variable costing -
• only variable manufacturing costs are
  inventoried.
• Gross margin Revenue - COGS.
• Contribution margin Revenue - Variable costs.

10
Summary of Cost Concepts

• For purposes of assigning costs to cost objects,
  costs are classified as either direct or
  indirect.
• For purposes of valuing inventories and measuring
  income, costs are classified as either product
  costs or period costs. For a manufacturing firm,
  costs can be classified as manufacturing or
  non-manufacturing costs.
• For purposes of predicting cost behavior, costs
  are classified as either variable or fixed.

11
Cost Behavior

• Why worry about cost behavior?
• If managers know how costs behave, they can then
  estimate future costs.
• Decision making involves choosing between
  alternatives.
• Management needs to know the costs that are
  likely to be incurred for each alternative.
• For example
• How much will costs increase if sales increase by
  10 percent?
• What will costs be if the firm introduces a new
  product?
• The link to firm value?
• More accurate costs gt Better decisions gt
  Increased firm value

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Cost Behavior

• Cost category In Total Per Unit
• Variable Total variable cost
  Variable cost per unit
• changes as the activity remains the
  same over wide
• level changes ranges of the
  activity
• Fixed Total fixed cost
  remains Fixed cost per unit
• constant even when the
  decreases when the
• activity level changes activity
  level increases
• Total costs Fixed costs Variable costs
• F VX
• where V is the variable cost per unit of the
  activity, and X is the volume of the activity in
  appropriate units. Managers often estimate the
  above linear cost function in order to forecast
  costs.

13
Types of Fixed Costs

• Committed fixed costs -
• relate to the investment in facilities,
  equipment, and the basic organizational structure
  of the firm.
• Examples include depreciation of buildings and
  equipment, taxes on real estate, insurance, etc.
  
• Costs are incurred on a long-term basis and
  cannot be reduced in the short-run without
  impairing the organization's ability to operate
  at current levels
• Discretionary fixed costs -
• usually arise from annual decisions by management
  to spend in certain fixed cost areas.
• Examples include advertising, research, public
  relations, etc.
• Discretionary fixed costs may be modified in the
  short-term without impairing the organization's
  ability to operate at current levels.

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The Relevant Range

• The relevant range can also be defined as the
  activity range within which a cost projection may
  be valid (see slide 12).
• Within the relevant range, both unit variable
  costs (V) and total fixed costs (F) remain
  essentially unchanged.
• The relevant range includes the upper and lower
  limits of past activity for which (historical)
  data is available.
• However, outside the relevant range, the general
  cost equation we estimate may not be valid.

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Methods of Estimating Costs

• There are several popular methods for estimating
  costs
• Regression Analysis and the High-Low Methods are
  the most commonly used methods to estimate fixed
  and variable cost elements.
• Each approach focuses on estimating cost
  functions that model mixed costs (a cost that has
  both fixed and variable components)
• Total costs Fixed costs Variable costs
• F VX

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Separating Mixed Costs into their Fixed and
Variable Components
Regression Analysis A statistical technique used
to estimate the fixed and variable components of
a mixed cost is called least squares regression.
Regression analysis uses statistical methods to
fit a cost line (regression line) through a set
of points which minimizes the sum of the squared
distance from each data point to the line (hence
the name least squares regression).
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Regression Analysis -Least Squares Regression
Method

• More specifically
• Regression analysis is a statistical procedure
  that is used
• (1) to assess the association(s) between
  variables and
• (2) to estimate the slope and intercept of a
  model that can be used for forecasting purposes.
• The coefficients of the following general cost
  equation are estimated
• Total costs F VX
• where
• F the estimate of total fixed costs (the
  intercept coefficient).
• V the estimate of variable cost per unit of
  the activity (the
• slope coefficient).
• X the volume of the activity.

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Advantages of Regression Analysis

• Unlike the high-low method, all data are used in
  computing parameter estimates
• The approach yields a model that represents the
  best possible fit (I.e., it is the best
  method)
• Statistical information generated can be used to
  assess the association between costs and activity
  levels and to forecast future costs given some
  anticipated level of the activity
• The approach can be generalized to incorporate
  more than one cost driver in explaining total
  costs
• Note There will not be any Least Squares Method
  calculations on the exam

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Regression Analysis
Regression Line Total Overhead Cost
Costs
Slope of Regression Line Variable Cost per unit
Fixed Cost
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Using a Spreadsheet Program to Perform Regression
Analysis
Using the actual values of the mixed costs
(dependent variable) and the volume of production
(independent variable) and a spread sheet program
such as Excel, you can compute the regression
line using least squares regression.
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Regression Statistics
Other uses for Regression Analysis Marketing
Managers can predict changes in sales based on
changes in advertising expenditures. Production
Managers interested in quality control might
collect data on overtime worked in a factory vs.
the number of defective items produced.
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Estimating Variable and Fixed Cost Using the
High-Low Method

• The high-low method is a computationally simple
  method of estimating the cost formula. The
  procedure is as follows
• 1. Use only two data points, the high and low
  level of activity and their related total
  overhead costs.
• 2. Subtract the smallest from the largest for
  each.
• The estimated variable cost per activity unit is
  estimated as high low cost
  high - low activity

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Estimating Variable and Fixed Cost Using the
High-Low Method
4. Substitute the total cost of one of the
points for y in the equation y a bx 5.
Substitute the variable cost found previously
for b 6. Substitute the number of activity
units for x and the corresponding cost for y
(either the high pair or the low pair can be
used) 7. Solve for fixed costs a 8. Use the
values derived for a and b for estimating
mixed costs at various levels of x
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Two-Point (or High-Low) Method

• Total Costs Fixed Costs (F) Variable Costs
  (VX)
• Slope of line
• V (Costhigh - Costlow) / (Unitshigh -
  Unitslow)
• V Variable Cost per Unit of Activity
• Intercept of line
• F Costhigh - V (Unitshigh) Costlow - V
  (Unitslow)

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Estimating Variable and Fixed Cost Using the
High-Low Method
EXAMPLE If the high point of activity was 2,500
units with 12,450 of overhead costs and the low
point of activity was 1,950 units with 10,300 of
overhead costs, what would be the estimated total
costs at 2,435 units of activity?
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Estimating Variable and Fixed Cost Using the
High-Low Method
1. High Point 2,500 units at 12,450 Low
Point 1,950 units at 10,525 2. high-low 2,500
- 1,950 550 units 12,450 - 10,525
1,925 3. 1,925 / 550 unit 3.50 variableb
cost/unit
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Estimating Variable and Fixed Cost Using the
High-Low Method
Steps 4,5,6,7.
Y 12,450 12,450 3,700 COST FORMULA Y
a bx a 3.50 (2,500) a 8,750 a 3,700
3.50X
8. Y 3,700 3.50 (2,435) Y 12,222.50
total overhead cost estimated for 2435 units
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Regression Analysis and High Low Method may yield
different results
Line Total Overhead Cost
Slope of regression line
Costs
Slope of high-low Line
Fixed Cost estimates for regression and high low
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Which method is better?

• An advantage of regression analysis is that it
  makes use of all information points, not just the
  high and low activity levels.
• Regression analysis also gives you more
  information because it tells you something about
  the strength of the relationship by means of R2
• High-low must be used with caution because the
  high and low points of activity may be atypical
  or outside the normal range of activity.
• The only advantage of the high-low method is its
  simplicity

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Alternate Methods of Estimating Costs

• There are three alternate methods for estimating
  costs that are also popular, especially when the
  use of Regression Analysis is not feasible
• Graphical method.
• Semi-averages method.
• Semi-averages less outliers method.
• As with the Regression Analysis and High-Low
  Methods, each of these approaches focuses on
  estimating cost functions that model mixed costs
  (a cost that has both fixed and variable
  components)
• Total costs Fixed costs Variable costs
• F VX

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Graphical Method

• Regardless of which method of estimation is used
  to estimate the cost formula, the graphical
  method approach is useful in analyzing costs.
• Steps
• - Plot the (historical) data points on a graph
  (total cost versus
• activity) that includes the origin (zero total
  costs, zero
• activity).
• - Draw a line through the plotted data points
  so that about equal
• numbers of points fall above and below the
  line.
• - Extend the line to Total Cost axis. The
  point at which the line
• intersects the Total Cost axis is F.
• - The slope of the drawn line is V. The
  vertical distance in the
• line is the change in cost, the horizontal
  distance the change
• in the activity. The slope is computed as
  (Change in
• cost/Change in units of activity).

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Semi-Averages Method

• Similar to Two-Point Method, except that more
  than one observation is used to assess a "high"
  and a "low" level of activity.
• The main benefit of using the Semi-Averages
  Method is that it uses more data to estimate the
  cost function, which can reduce the influence of
  abnormally high or low levels of cost and
  activity.

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Semi-Averages Method Example

• Using the Semi-Averages Method, determine the
  fixed and variable components of the following
  indirect labor costs
• Month Indirect Labor Labor Hours
• Cost
• January 15,000 3,500
• February 30,000 9,500
• March 28,000 7,500
• April 21,000 5,500
• May 24,000 6,000
• June 32,000 10,000

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Semi-Averages Method Example Contd

• Indirect Labor Cost Labor Hours
• Highest three months
• February 30,000 9,500
• March 28,000 7,500
• June 32,000 10,000
• Total 90,000 / 3 27,000 / 3
• Average 30,000 9,000
• Lowest three months
• January 15,000 3,500
• April 21,000 5,500
• May 24,000 6,000
• Total 60,000 / 3 15,000 / 3
• Average 20,000 5,000

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Semi-Averages Method (Contd)

• Variable Cost per Hour V
• (Costhigh - Costlow) / (Unitshigh - Unitslow)
• (30,000-20,000)/(9,000 hrs - 5,000 hrs)
• 2.50 per hour
• Total Costs Fixed costs Variable Costs
• 30,000 Fixed Costs (9,000 hours)(2.50
  per hour)
• 30,000 Fixed Costs 22,500
• Fixed Costs 30,000 - 22,500 7,500

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Semi-Averages less Outliers Method

• Similar to the Semi-Averages Method, except that
  more than one observation is used to assess a
  "high" and a "low" level of activity and the two
  extreme observations (outliers) are eliminated.
• The main benefit of using the Semi-Averages less
  Outliers Method is that, like the Semi-Averages
  Method uses more data to estimate the cost
  function, which can reduce the influence of
  abnormally high or low levels of cost and
  activity, but it also considers potential effects
  of outliers (note if these observations are not
  outliers, there is a negligible effect on the
  outcome).

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Semi-Averages less Outliers Method Example

• Using the Semi-Averages Method, determine the
  fixed and variable components of the following
  indirect labor costs
• Period Indirect Labor Labor Hours Cost/LH
• Cost
• January 15,000 3,500 4.29
• February 30,000 9,500 3.16
• March 28,000 7,500 3.73
• April 21,000 5,500 3.82
• May 24,000 6,000 4,00
• June 32,000 10,000 3.20

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Semi-Averages less Outliers Method Example
Contd

• Indirect Labor Cost Labor Hours
• Highest three months
• February
• March 28,000 7,500
• June 32,000 10,000
• Total 60,000 / 2 17,500 / 2
• Average 30,000 8,750
• Lowest three months
• January
• April 21,000 5,500
• May 24,000 6,000
• Total 45,000 / 2 11,500 / 2
• Average 22,500 5,750

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Semi-Averages less Outliers Method (Contd)

• Variable Cost per Hour V
• (Costhigh - Costlow) / (Unitshigh - Unitslow)
• (30,000-22,500)/(8,750 hrs - 5,750 hrs)
• 2.50 per hour
• Total Costs Fixed costs Variable Costs
• 30,000 Fixed Costs (8,750 hours)(2.50
  per hour)
• 30,000 Fixed Costs 21,875
• Fixed Costs 30,000 - 21,875 8,125
• Total Costs Fixed costs Variable Costs
• Total Costs 8,125 ( hours)(2.50 per
  hour)

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Advantages/Disadvantages of Graphical,Two-Point,
and Semi-Averages Methods

• Advantages
• - Plotting cost/activity data is useful in
  assessing
• associations and possible structural changes
• - Involve relatively simple calculations
• - Easy methods to apply
• Disadvantages
• - Inherently subjective in application
• - Model estimates do not use all of the data
• - No statistical means of assessing model fit