C5-
COST BEHAVIOR: ANALYSIS AND USE
notes-c5.doc
Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM ©
CHAPTER LEARNING OBJECTIVES:
MAJOR:
- Use the High-Low method to determine and calculate the structure of a cost.
- Define, explain and use variable, fixed and mixed costs in problems.
- Use regression line cost formula to determine total and per unit cost.
- Prepare a Contribution Margin income statement.
MINOR:
- Explain the Scatter graph and Least Squares methods – Appendix 5A.
NOT IMPORTANT:
- Memorize least squares formula – Appendix 5A.
ACTIVITY OR ACTIVITY BASE is that thing which we are comparing to a cost to see if that cost changes
as the activity changes. The usual activity base in this class is production or sales.
RELEVANT RANGE is that range of activity (production/sales) within which assumptions relative to cost
behavior are valid.
COST BEHAVIOR (variable or fixed) is how costs change or don't change as activity changes.
FIXED COSTs remain constant in total dollar amount but varies inversely on a per unit basis as activity
changes. E.g., IDL, factory insurance, depreciation (SL method).
VARIABLE COSTs remain constant on a per unit basis but varies directly in total as activity changes.
E.g., DM, DL, factory utilities & freight-out
STEP VARIABLE costs can only be obtained in large chunks and increase/decrease only in response to
wide changes in activity. E.g., IDL (supervision).
CURVILINEAR COST is a cost that is not linear, i.e., does not graph as a straight line. Accountants will
use a straight line in place of the true line in the area of the relevant range, so as to treat the cost as either
fixed, variable or mixed.
COMMITTED FIXED COST - related to the basic organizational structure, and plant and equipment (very
long-term planning) and can't be reduced substantially, even for a short period of time, without great harm
to the company.
DISCRETIONARY FIXED COST (Managed Fixed Cost) are determined annually (usually) by
management. E.g., advertising, R&D, training, etc. These can be reduced substantially, even to zero, for
short periods of time without great harm to the company.
COST STRUCTURE is the relative proportion of fixed, variable and mixed cost found within an
organization.
COST FORMULA is the summarized Cost Structure for a company, product, department, etc.
FORMULA is: Y = a + bX, where Y = TC <-- Dependent Variable
Where a = FC;
b = UVC;
X = activity <-- Independent variable
1
COST BEHAVIOR APPROXIMATION METHODS:
HIGH-LOW formula uses only two examples of activity and related cost. It is the least accurate of the
three methods but is the quickest and easiest to do. There are really two calculations necessary.
The first is:
(change in cost / change in activity) which calculates the Variable Rate.
The second uses the regression line formula to determine the Fixed Cost in total.
SCATTER GRAPH uses all examples of activity and related cost plotted on graph paper. Then a straight
line is visually fitted to approximate the FC and Variable Rate (Variable Cost Per Unit). This method is
more accurate than the High-Low method and it takes longer prepare.
LEAST SQUARES uses statistical analysis (mathematical equations) to approximate the FC and
Variable Rate of a cost. It is the most accurate but is hardest to calculate without the use of a computer.
When a particular cost graphs as a straight line each of the above three cost approximation
methods will result in the same answer. This is because the cost is linear. This means there is a
set determinable fixed amount and a set determinable variable component. When a particular
cost graphs as a curvilinear line (in effect, it does not graph as a straight line) the three cost
approximation methods will result in different answers. This is because the cost is not linear. A
non-linear cost does not have a set fixed component nor does it have a set variable component.
Therefore, to speed the information flow to managers and reduce undue tedious calculations
(which would not change the answer materially) a cost is ASSUMED to be linear within the relevant
range.
CONTRIBUTION INCOME STATEMENT - See examples on next two pages. Study thoroughly!
APPENDIX - READ ONLY (LEAST-SQUARES METHOD)
2
C5-
CONTRIBUTION MARGIN INCOME STATEMENT
Instructor’s Supplemental Information
notes-c5.doc
Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM ©
EXAMPLE OF A
CONTRIBUTION INCOME STATEMENT WITH APPLICABLE UNIT COST DATA
SUMMARIZED FORM
BOBO’S BIKE BUILDING BARN
Contribution Income Statement
Three Months Ended May 31, 2003
Sales
Less variable costs:
Cost of Goods Sold
Selling expenses
Administrative expenses
Total variable costs
Contribution Margin
Less fixed expenses:
Cost of goods sold
Selling expenses
Administrative expenses
Total fixed costs
Net Income
$ 900,000
$ 360,000
90,000
36,000
486,000
414,000
Per Unit
$ 500
Percent
100.0
200
50
20
270
$ 230
====
40.0
10.0
4.0
54.0
46.0
====
124,000
80,000
70,000
274,000
$140,000
======
NOTE TO STUDENTS:
- As this statement is in summarized form the COGS, selling and administrative expense totals are
shown, not the compete details (all accounts). As a CM I/S is for internal use only, this statement would
probably be for upper management, who does not need full details. The statement on the next page
would be directed towards middle level management who would need more information.
- COGS is a Mixed Cost in a manufacturing company, therefore, is broken into its Variable and Fixed
components. In a merchandising (retail) company COGS would be variable only. Service type companies
don't have COGS.
- MEMORIZE THIS STATEMENT FORMAT!
- LEARN HOW TO IDENTIFY AND CALCULATE VARIABLE, FIXED AND MIXED COSTS!
3
C5-
CONTRIBUTION MARGIN INCOME STATEMENT
Instructor’s Supplemental Information
notes-c5.doc
Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM ©
EXAMPLE OF
CONTRIBUTION INCOME STATEMENT WITH APPLICABLE UNIT COST DATA
DETAILED FORM
BOBO’S BIKE BUILDING BARN
Contribution Income Statement
Three Months Ended May 31, 2003
Sales
Less variable costs:
Direct material
Direct labor
Factory utilities
Indirect materials
Selling expenses
Administrative expenses
Total variable costs
Contribution Margin
Less fixed expenses:
Supervisor salaries
Depreciation - factory
Sales salaries
Depreciation - delivery trucks
Administrative salaries
Insurance
Total fixed costs
Net Income
$ 900,000
$ 162,000
135,000
54,000
9,000
90,000
36,000
486,000
414,000
Per Unit
$ 500
Percent
100.0
90
75
30
5
50
20
270
$ 230
====
18.0
15.0
6.0
1.0
10.0
4.0
54.0
46.0
====
85,000
39,000
62,000
18,000
50,000
20,000
274,000
$140,000
======
NOTE TO STUDENTS:
- ALWAYS PREPARE CONTRIBUTION MARGIN INCOME STATEMENTS SHOWING FULL DETAILS
FOR HOMEWORK, QUIZZES OR TESTS. Always use the form that your employer wants on the job. If
that is in summary form, make sure you have the full details as a back-up schedule or have the detailed
information in your records.
- MEMORIZE THIS STATEMENT FORMAT FOR TESTING PURPOSES!
- LEARN HOW TO IDENTIFY AND CALCULATE VARIABLE, FIXED AND MIXED COSTS!
4
C5–
Homework Problem: Complete Prior to Class
HIGH-LOW METHOD
notes-c5.doc
Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM ©
Number of units sold
Sales
Cost of Goods Sold
Gross Margin
Operating expenses
Net Income
JAN
250
6,250
3,000
3,250
1,000
2,250
=====
FEB
400
MAR
300
10,000
4,200
5,800
1,450
4,350
======
7,500
3,500
4,000
1,000
3,000
=====
Using the High-Low method, calculate the:
1. Variable cost per unit for COGS
___________
2. Variable cost per unit for Operating expenses
___________
3. Variable cost per unit for all the expenses combined
___________
4. Fixed cost portion for COGS
___________
5. Fixed cost portion for Operating expenses
___________
6. Fixed cost in total for January
___________
7. Fixed cost in total for February
___________
8. Contribution margin for January
___________
9. Contribution margin for February
___________
5
C5–
Homework Problem: Complete Prior to Class
HIGH-LOW METHOD AND CONTRIBUTION MARGIN
notes-C5.doc
Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM ©
Comparative Income Statement
Four Months Ended July 31, 2002
Actual
May
300
April
380
Sales in units
Sales revenue
Less Expense A
Gross Margin
Less operating expenses:
Expense B
Expense C
Total expenses
Net Income
June
450
$22,800
16,680
------6,120
-------
$18,000
13,800
------4,200
-------
$27,000
19,200
------7,800
-------
2,005
3,420
------5,425
------$
695
=======
2,000
2,700
------4,700
------$ (500)
=======
2,000
4,050
------6,050
------$ 1,750
=======
Projected
July
350
$
-------------
------------$
=======
THIS PROBLEM REQUIRES THE USE THE HIGH-LOW METHOD
1.
What type of income statement format is shown above?
a. Traditional (Organized by cost function; GAAP based; external use.).
b. Contribution (Organized by cost behavior; not GAAP; internal use).
2. Using the Y = a + bx format, show the Cost Formula for each cost and for
the company in total.
Y
=
a
+
b
x
Expense A:
Y
=
Expense B:
Y
=
Expense C:
Y
=
COMPANY TOTALS:
Y
=
4.
Based upon your analysis identify each expense as a FC, VC or MC.
Expense A is a:
FC
VC
MC
Å circle one
Expense B is a:
FC
VC
MC
Å circle one
Expense C is a:
FC
VC
MC
Å circle one
5.
Using your cost formulas fill in all the numerical data for July above.
6. On a separate sheet of paper, prepare a Comparative Contribution Margin
Income Statement for the three months (May - July), including the Per Unit
information AND percentages.
Statement Format Should Be:
May
June
July
Per Unit
Percent
6