Wednesday, January 7th

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Wednesday, January 7th

• AGENDA
• Continue my lecture on modeling cost behavior and
  answer questions
• Comment on Go and Igo assignments
• Lecture, discussion, and illustration of flexible
  budgeting
• Lecture, discussion, and illustrations of
  budgeted cost rates time permitting

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Cost Behavior

• Monday we said one of the key issues in
  managerial accounting is to determine the factors
  that drive the cost of an activity. We are
  continuing that discussion today.

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Discontinuous Costs

• Thus far we have assumed that costs are
  continuous (i.e., cost functions contain no jumps
  or gaps). As a starting point, this is a useful
  assumption. Even when this assumption is not
  satisfied we can be as accurate as necessary.

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Segmented Linear Costs

• A common variation on strictly variable costs is
  a cost function that contains multiple linear
  segments. At a specific level of volume, the
  variable cost per unit (the slope) changes.
  There could be several such changes over the
  range of possible volumes.

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Example - Segmented Cost

• Think about labor costs. At some level of
  volume, a company would have to begin to pay
  overtime. At an even higher level of volume, the
  company would have to start a second work shift
  and pay what is called a shift premium, etc.

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Total Segmented Var. Cost
Q2
Q3
0
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Total Segmented Var. Cost
Total cost
Q2
Q3
0
Activity Volume
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Segmented Variable Cost

• Total variable cost function
• TC v1 Q for 0 Q Q2 (4)

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Segmented Variable Cost

• Total variable cost function
• TC v1 Q for 0 Q Q2 (4)
• TC v1 Q v2 (Q Q2)
• for 0 Q2 Q Q3 (5)

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Segmented Variable Cost

• Total cost function
• TC v1 Q for 0 Q Q2 (4)
• TC v1 Q v2 (Q Q2)
• for Q2 Q Q3 (5)
• TC v1 Q v2 (Q Q2)
• v3 (Q Q3) for
• 0 Q2 Q3 Q (6)

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Total Segmented Var. Cost

• Notice that v3 is an increment to v2 and v2 is
  an increment to v1

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Total Segmented Var. Cost

• In per-unit terms, the unit variable cost is
  increasing in jumps at specified levels of volume
  as follows
• vT is v1 for 0 Q Q2
• vT is v1 v2 for Q2 Q Q3
• vT is v1 v2 v3 for Q3 Q

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Total Segmented Var. Cost

• To develop an Excel version of the above formula
  for segmented variable costs that will work for
  any volume level, you will need
• The IF-function, and
• and the GESTEP function.

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If-Statement

• An if-statement is required to determine if the
  activity volume level is above the base volume
  level. The base volume is likely to be the
  smallest value of the relevant volume
  interval--zero or a positive number.

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Relevant Volume Interval
Relevant Interval
Total cost
Q2
Q3
Q1
Activity Volume
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Total Cost Functions

• Format of an if-statement
• IF(logical test, value if true, value if false)

Test of a condition
Value or formula if condition is true
Value or formula if condition is false
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GESTEP Function

• When there are multiple linear segments within
  the relevant interval, or multiple relevant
  intervals, we need multiple, nested
  if-statements, or some other function. For our
  purposes, the simplest approach involves the
  GESTEP function.

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GESTEP Function

• The GESTEP function tests whether a number is
  greater than a threshold value.
• Format
• GESTEP(number, step value)

Number or formula
Threshold value number or formula
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GESTEP Function

• GESTEP(Q, Q1) returns the value of 0 if Q lt Q1,
  and 1 if Q Q1
• For purposes of developing cost forecasting
  formulas, one can use the GESTEP function to
  determine if Q is greater than either Q2 or Q3
  (slide 7).

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Excel Formulas

• Use the above information to develop the formulas
  you need to complete the assigned homework.

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Semi-Fixed (Lumpy) Cost

• Next let us move to what may be the most common
  situation, costs that increase in fixed amounts
  with respect to increments in volume that may
  range from small amounts of cost per whole unit
  to very large amounts per millions of units.

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Total Semi-Fixed Cost
Total cost
Total cost curve
Activity Volume
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Semi-Fixed (stair-step) Cost

• The total amount of a semi-fixed cost increases
  in stair-step fashion. To the extent that the
  stair-steps take place at regular intervals of
  volume, as in the following example, they can be
  modeled easily.

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Example

• Suppose we employ an additional supervisor for
  every 10 employees. If we must hire a minimum of
  1 supervisor, and each earns 50,000 per year,
  then the cost of super-vision varies with
  employment volume as follows

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Total Cost for Example

• TC 50,000 ? of groups of up to 10
  employees to be super- vised where 50,000 is
  the size of each step increase in total
  cost.

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Semi-fixed Cost Example

• Employment Supervisors Total Cost
• Case 1 1 1 50,000
• Case 2 10 1 50,000
• Case 3 11 2 100,000
• Case 4 19 2 100,000
• Case 5 20 2 100,000
• Case 6 21 3 150,000

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Computing the No. of Steps

• The problem is to compute the number of cost
  steps involved for a given activity volume
  level. Igo trailer Co., Yougo Trailer Co.,
  Exercise 2-21, Wego Trailer Co., and Letsgo
  Trailer Co. all involve the estimation of
  step-fixed costs.

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Computing the No. of Steps

• While there are several approaches one might
  take, the ROUNDUP function is a relatively
  straight-forward approach. A description of the
  ROUNDUP function follows.

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Semi-Fixed Costs

• General format of the ROUNDUP function
• ROUNDUP(number, num_digits)

No. to be rounded
No. of decimals
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ROUNDUP Function Format

• ROUNDUP(number, num_digits)
• ROUNDUP(expression, num_digits)
• ROUNDUP(Q/m, n), where
• Q the total number of units of the cost
  driver and
• m the number of cost driver units per step

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ROUNDUP Function Format

• Q/m is used to compute the number of step
  increases, and
• n tells Excel to round to n digits to the right
  of the decimal point.

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Changing values of n
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ROUNDUP Function

• Since we want integers, we are going to be using
  n 0 in our cost estimation equations

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Base Volumes

• Sometimes we want to start at the origin, and
  other times we want to start with a different
  base volume level. Is there an estimation
  equation formulation that serves both purposes?

YES!
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Base Volumes

• For a step-fixed cost for which the total cost
  increases in steps of FS dollars every m units
  above a base volume of Q1 units, we have the
  following partial formula
• TC ROUNDUP((Q Q1)/m, 0)FS

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ROUNDUP Function Values
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Semi-fixed Cost Formula

• TC FS ? ROUNDUP(Q/m, 0)
• for Q gt 0 and m gt 0. (7)

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Approximating Semi-Fixed Cost

• Sometimes it may be convenient to use a linear
  approximation of a semi-fixed cost for ease of
  computations, or because of the preferences of a
  user.
• Intercept is where approximation line crosses the
  y-axis
• Slope is the rate of change

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Conservative
Expected
Optimistic
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Approximating Semi-Fixed Cost

• Conservative (high) estimate
• Intercept Fs
• Slope ?y / ?x
• Slope (Fs / m)
• Estimation equation
• TC Fs (Fs / m)Q

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Approximating Semi-Fixed Cost

• Expected value (unbiased) estimate
• Intercept Fs / 2
• Slope ?y / ?x
• Slope (Fs / m)
• Estimation equation TC Fs / 2 (Fs / m)Q

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Approximating Semi-Fixed Cost

• Optimistic estimate
• Intercept 0
• Slope ?y / ?x
• Slope (Fs / m)
• Estimation equation
• TC (Fs / m)Q

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Remember Economics?

• How does what we are learning relate to what we
  learned in microeconomics?
• Are these cost formulas the theoretically correct
  versions or are they approximations?

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Total Cost (Micro)
Total cost
Total cost curve
Relevant range
Activity Volume
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Average Cost (Micro)
Average Unit Cost
Relevant range
Unit cost curve
Volume
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Cost Forecasting Formulas

• Fixed TC F (1)
• Variable TC vQ (2)
• Semi-variable (mixed)
• TC F vQ (3)
• Segmented variable
• TC v1 Q v2(Q Q2)
• v3 (Q Q3) for Q3 ? Q2 (4)

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Cost Estimation Equations

• Semi-fixed
• TC FS ? ROUNDUP(Q / m, 0) (7)
• where m represents the number of units of
  activity volume associated with each increment in
  cost, FS, and Q gt 0.

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Cost Estimation Equations

• For a single driver Q, the total of the five cost
  behaviors can be summarized by the formula
• TC FT vT Q v2 (Q Q2)
• v3 (Q Q3)
• FS ? ROUNDUP(Q/m, 0) (8)

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Multiple Measures of Activity

• Next consider two measures of activity volume, QA
  and QB for a cost center. In this case, the
  total cost function for both activities combined
  could be of the form
• TC FAT FBT vATQA vBTQB
• vA2 (Q QA2) vA3 (Q QA3)
• vB2 (Q QB2) vB3 (Q QB3)
• FAS ? ROUNDUP(QA/mA, 0)
• FBS ? ROUNDUP(QB/mB, 0) (9)

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Explanation of Terms (2)

• The amounts of the two semi-fixed cost steps are
  FAS and FBS
• For each semi-fixed cost, the total of that cost
  equals the number of semi-fixed cost steps
  involved in Qi units ? the size of each step

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Combining Terms

• If there is more than one cost driver, then the
  variable cost terms cannot be combined (vT ? v1
  v2).
• Normally the individual fixed costs can be
  combined into one amount (FAT FA1 FA2 )

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Concluding Comments

• The level of analysis will influence how a cost
  is modeled. To the extent that a decision is
  more focused and short-term, one can forecast
  costs accurately by modeling the behavior of
  total cost in the specific situation.

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Concluding Comments

• For strategic analyses, most costs would be
  considered variable. The focus would be on the
  opportunity for learning and cost management in
  broad terms, not on the specific behavior of
  costs during one operating period.

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Assignments Testing

• In the absence of additional information, assume
  costs are mixed, or may be approximated as though
  they are mixed.
• Read problems carefully for information or hints
  about the cost behavior assumed in a problem.

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Using Knowledge of Cost

• One of the primary ways we use cost projection
  equations is to develop budgets, particularly
  flexible budgets. A flexible budget is based on
  budgeted cost equation parameters, not simply a
  point estimate of cost, and the volume levels
  either budgeted or achieved.

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Questions Related to Go

• Comments about Go Trailer Company
• Questions about Go Trailer Co.?

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Using Knowledge of Cost

• One of the primary ways we use cost projection
  equations is to develop budgets, particularly
  flexible budgets. A flexible budget is based on
  budgeted cost equation parameters, not simply a
  point estimate of cost, and the volume levels
  either budgeted or achieved.

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Flexible Budgeting - Purpose

• The purpose of a flexible budget is to
  incorporate budgeted cost behavior information to
  forecast the cost to achieve a specified activity
  volume. Based on the budgeted cost parameters,
  we can forecast total cost for any specified
  level of activity within the relevant interval.

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Flexible Budget Uses - 1

• To forecast total activity costs for budgeting
  purposes.

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Flexible Budget Uses - 1

• To forecast total activity costs for budgeting
  purposes.
• To forecast total activity costs that, in turn,
  can be used to project earnings.

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Flexible Budget Uses - 2

• To forecast activity costs to compute budgeted
  activity cost rates (BACRs) to charge users

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Flexible Budget Uses - 2

• To forecast activity costs to compute budgeted
  activity cost rates (BACRs) to charge users
• To forecast total activity costs to compute
  budgeted and standard indirect cost rates (BACRs
  and SACRs) to charge products

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Flexible Budget Uses - 3

• To forecast costs to support the analysis of
  proposed changes in business activities
• Modifications to current activities
• Proposed new activities
• Hypothetical activities

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Flexible Budget Uses - 4

• To estimate, for performance evaluation purposes,
  the amount of cost that should have been incurred
  at the activity levels actually experienced.

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Flexible Budget Uses - 4

• In the context of performance measurement, a
  flexible budget becomes an ex-post standard
  (benchmark) of the cost that should have been
  incurred for the level of activity achieved.

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Finding Cost Drivers

• Causality between the activity measure used and
  the resulting cost

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Finding Cost Drivers

• Causality between the activity measure used and
  the resulting cost
• Independence of the activity measure from other
  influences

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Finding Cost Drivers

• Causality between the activity measure used and
  the resulting cost
• Independence of the activity measure from other
  influences
• Ease of understanding

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Finding Cost Drivers

• Causality between the activity measure used and
  the resulting cost
• Independence of the activity measure from other
  influences
• Ease of understanding
• Functionality of use

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Finding Cost Drivers

• Causality between a measure of activity and the
  resulting cost
• Functionally related as an inherent part of the
  production process (engineering)
• Statistical evidence of a theoretical
  relationship (regression analysis)

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Finding Cost Drivers

• Causality between a measure of activity and the
  resulting cost
• Experienced people, with direct knowledge of the
  process, believe the relationship holds.

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Finding Cost Drivers

• Independence of the activity measure from other
  influences
• This concerns clarity of the relationship
• Focus on the correct target measure
• Good (unspoiled) units produced, not total units
• Hours of labor, not dollars of labor cost
• Measures unaffected by other activities

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Finding Cost Drivers

• Ease of understanding
• Managers can articulate the relationship
• No more complex than required
• May need to start simple and revise

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Finding Cost Drivers

• Functionality of use
• Use of the measure leads to believable
  information
• Use of the measure leads to use of the
  information by managers
• Use of the information leads to actions in the
  best interests of the organization

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Final Thoughts on Topic

• A flexible budget is specific type of budget,
  based on budgeted cost equation parameters, for
  specified levels of activity volume.

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Final Thoughts on Topic

• In some situations, flexible budgets may be
  relatively simple. In other situations, flexible
  budgets may be based on many different cost
  drivers involving complex patterns of behavior.
  But the principal of flexing a budget is the
  same.

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Assumptions

• When an organization, case, or problem refers to
  a static budget, assume it does not change unless
  you are told otherwise.

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Assumptions

• When an organization, case, or problem refers to
  a flexible budget, assume it does change with
  respect to activity level. The situation,
  particularly in standard costing, determines
  which level of activity volume to use to flex
  the budget.