C 5 - COST BEHAVIOR: ANALYSIS AND USE notes-c5.doc Written by Professor Gregory M. Burbage, MBA, CPA, CMA, CFM

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1 C 5 - COST BEHAVIOR: ANALYSIS AND USE notes-c5.doc 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

2 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

3 C 5 - CONTRIBUTION MARGIN INCOME STATEMENT notes-c5.doc Instructor s Supplemental Information 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 Per Unit Percent Sales $ 900,000 $ Less variable costs: Cost of Goods Sold $ 360, Selling expenses 90, Administrative expenses 36, Total variable costs 486, Contribution Margin 414,000 $ ==== ==== Less fixed expenses: Cost of goods sold 124,000 Selling expenses 80,000 Administrative expenses 70,000 Total fixed costs 274,000 Net Income $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

4 C 5 - CONTRIBUTION MARGIN INCOME STATEMENT notes-c5.doc Instructor s Supplemental Information 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 Per Unit Percent Sales $ 900,000 $ Less variable costs: Direct material $ 162, Direct labor 135, Factory utilities 54, Indirect materials 9, Selling expenses 90, Administrative expenses 36, Total variable costs 486, Contribution Margin 414,000 $ ==== ==== Less fixed expenses: Supervisor salaries 85,000 Depreciation - factory 39,000 Sales salaries 62,000 Depreciation - delivery trucks 18,000 Administrative salaries 50,000 Insurance 20,000 Total fixed costs 274,000 Net Income $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

5 C 5 Homework Problem: Complete Prior to Class notes-c5.doc HIGH-LOW METHOD JAN FEB MAR Number of units sold Sales 6,250 10,000 7,500 Cost of Goods Sold 3,000 4,200 3,500 Gross Margin 3,250 5,800 4,000 Operating expenses 1,000 1,450 1,000 Net Income 2,250 4,350 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

6 C 5 Homework Problem: Complete Prior to Class notes-c5.doc HIGH-LOW METHOD AND CONTRIBUTION MARGIN Comparative Income Statement Four Months Ended July 31, 2002 Actual Projected April May June July Sales in units Sales revenue $22,800 $18,000 $27,000 $ Less Expense A 16,680 13,800 19,200 Gross Margin 6,120 4,200 7,800 Less operating expenses: Expense B 2,005 2,000 2,000 Expense C 3,420 2,700 4,050 Total expenses 5,425 4,700 6,050 Net Income $ 695 $ (500) $ 1,750 $ ======= ======= ======= ======= 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 circle one Expense B is a: FC VC MC circle one Expense C is a: FC VC MC 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