Cost Behaviour: Analysis and Use

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Cost BehaviourAnalysis and Use
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LEARNING OBJECTIVES
After studying this chapter, you should be able
to

• 1. Understand how fixed and variable costs behave
  and how to use then to predict costs.
• 2. Use a scattergram plot to diagnose cost
  behaviour.
• 3. Analyze a mixed cost using the high-low
  method.
• 4. Prepare an income statement using the
  contribution format.
• 5. (Appendix 5A) Analyze a mixed cost using the
  least-squares regression method.

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Types of Cost Behaviour Patterns
Recall the summary of our cost behaviour
discussion from Chapter 2.
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Total 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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Total Fixed Cost Example

• 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

• 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 Behaviour
Examples of costs normally variable
Service Organizations Supplies and travel
Merchandisers Cost of Goods Sold
Merchandisers and Manufacturers Sales commissions
and shipping costs
Manufacturers Direct Material, Direct Labour, and
Variable Manufacturing Overhead
Examples of costs normally fixed
Merchandisers, manufacturers, and service
organizations Real estate taxes, Insurance, Sales
salariesAmortization, Advertising
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The Activity Base
Unitsproduced
Machinehours
A measure of the event causing the occurrence
of a variable cost a cost driver
Labourhours
Kilometresdriven
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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
EconomistsCurvilinear Cost Function
Total Cost
Activity
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The Linearity Assumption and the Relevant Range
EconomistsCurvilinear Cost Function
Total Cost
Accountants Straight-Line Approximation
(constant unit variable cost)
Activity
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The Linearity Assumption and the Relevant Range
A straight line closely approximates a
curvilinear variable cost line within the
relevant range.
EconomistsCurvilinear Cost Function
RelevantRange
Total Cost
Accountants Straight-Line Approximation
(constant unit variable cost)
Activity
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Types of Fixed Costs
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 Amortization on Buildings and Equipment
Examples Advertising and Research and Development
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Trend Toward Fixed Costs

• Increased automation.
• Increase in salaried knowledge workers who are
  difficult to train and replace.

Implications Managers are more locked-in with
fewer decision alternatives. Planning becomes
more crucial because fixed costs are difficult to
change with current operating decisions.
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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 metres. As the business grows more
  space is rented, increasing the total cost.

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Fixed Costs and Relevant Range
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
Metres)
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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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Mixed Costs

• A mixed costhas both fixed and
  variablecomponents.

Consider thefollowing electric utility example.
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Mixed Costs
Total mixed cost
Variable Utility Charge
Total Utility Cost
Fixed MonthlyUtility Charge
Activity (Kilowatt Hours)
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Mixed Costs
Total mixed cost Y a bX
Variable Utility Charge
Total Utility Cost
Fixed MonthlyUtility Charge
Activity (Kilowatt Hours)
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Mixed Costs
Total mixed cost Y a bX
Variable Utility Charge
Total Utility Cost
bX
Fixed MonthlyUtility Charge
a
Activity (Kilowatt Hours)
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The Analysis of Mixed Costs
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Account Analysis
Each account is classified as eithervariable or
fixed based on the analysts knowledge of how
the account behaves.
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Engineering Approach
Cost estimates are based on an evaluation of
production methods, and material, labourand
overhead requirements.
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The Scattergram Method
Plot the data points on a graph (total cost vs.
activity).
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The Scattergram Method
Draw a line through the data points with about
anequal numbers of points above and below the
line.
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The Scattergram Method
The slope of this line is the variable unit cost.
(Slope is the change in total cost for a one unit
change in activity.)
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The Scattergram Method
Vertical distance is the change in cost.
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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

• Unit variable cost

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The High-Low Method

• Unit variable cost 3,600 4,000 units
  0.90 per unit

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The High-Low Method

• Unit variable cost 3,600 4,000 units
  0.90 per unit
• Fixed cost Total cost Total variable cost
• Fixed cost 9,700 (0.90 per unit
  9,000 units)
• Fixed cost 9,700 8,100 1,600

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The High-Low Method

• Unit variable cost 3,600 4,000 units
  0.90 per unit
• Fixed cost Total cost Total variable cost
• Fixed cost 9,700 (0.90 per unit
  9,000 units)
• Fixed cost 9,700 8,100 1,600
• Total cost Fixed cost Variable cost (Y a
  bX) Y 1,600 0.90X

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The High-Low Method

• If sales salaries and commissions are 10,000
  when 80,000 units are sold and 14,000 when
  120,000 units are sold, 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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The High-Low Method

• If sales salaries and commissions are 10,000
  when 80,000 units are sold and 14,000 when
  120,000 units are sold, 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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The High-Low Method

• If sales salaries and commissions are 10,000
  when 80,000 units are sold and 14,000 when
  120,000 units are sold, 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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The High-Low Method

• If sales salaries and commissions are 10,000
  when 80,000 units are sold and 14,000 when
  120,000 units are sold, 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

• Accountants and managers may use computer
  software 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, calledthe adjusted R2, which is a
measure of the goodnessof fit of the regression
line to the data points.
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Least-Squares Regression Method

Y
20










Total Cost
10
0
X
0 1 2 3 4
Activity
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The Contribution Format
Lets put our knowledge of cost behaviour to work
by preparing a contribution format income
statement.
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The Contribution Format
The contribution margin format emphasizes cost
behaviour. Contribution margin covers fixed
costsand provides for income.
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The Contribution Format
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Least-Squares Regression Calculations
Appendix5A
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Least-Squares Regression

• This method provides the most objective and
  precise breakdown of mixed costs into variable
  and fixed components.
• This method also uses the most complex
  calculations. However, most business calculators
  and several computer software programs can
  quickly complete the calculations required.
• This method mathematically places the line in
  the most favourable location by ensuring that the
  total of the squares of all points off the line
  is minimized.

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Least-Squares Regression Calculations

• b n(?XY-(?X)(?Y)
• n(?X2) - (?X)2
• a (?Y) - b(?X)
• n
• where X the level of activity (Independent
  variable)
• Y the total mixed cost (dependent variable)
• a the total fixed cost (vertical intercept
  of line)
• b the variable cost per unit of activity
  (slope of line)
• n number of observations
• ? sum across all n observations

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End of Chapter 5