Cost Behavior: Variable vs. Fixed

1. Cost Behavior: Variable vs. Fixed

2. Types of Cost Behavior Patterns  activity level and relevant range

3. Unitsproduced Machine hours Miles driven Labor hours The Activity Base A measure of what causes the incurrence of a variable cost

4. A straight line closely approximates a curvilinear variable cost line within the relevant range. RelevantRange Accountant’s Straight-Line Approximation (constant unit variable cost) The Linearity Assumption and the Relevant Range Economist’sCurvilinear Cost Function Total Cost Activity

5. The Trend Toward Fixed Costs The trend in many industries is toward greater fixed costs relative to variable costs. As machines take overmany mundane taskspreviously performedby humans, “knowledge workers”are demanded fortheir minds ratherthan their muscles. Knowledge workerstend to be salaried,highly-trained anddifficult to replace. Thecost to compensatethese valued employeesis relatively fixedrather than variable.

6. Example: Office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows, more space is rented, increasing the total cost. Fixed Costs and Relevant Range The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat.

7. Fixed Costs and Relevant Range 90 Total cost doesn’t change for a wide range of activity, and then jumps to a new higher cost for the next higher range of activity. Relevant Range 60 Rent Cost in Thousands of Dollars 30 0 0 1,000 2,000 3,000 Rented Area (Square Feet)

8. Which of the following statements about cost behavior are true? Fixed costs per unit vary with the level of activity. Variable costs per unit are constant within the relevant range. Total fixed costs are constant within the relevant range. Total variable costs are constant within the relevant range. Quick Check 

9. Which of the following statements about cost behavior are true? Fixed costs per unit vary with the level of activity. Variable costs per unit are constant within the relevant range. Total fixed costs are constant within the relevant range. Total variable costs are constant within the relevant range. Quick Check 

10. Y X Mixed Costs A mixed cost has both fixed and variablecomponents. Consider the example of utility cost. Total mixed cost Total Utility Cost Variable Cost per KW Fixed MonthlyUtility Charge Activity (Kilowatt Hours)

11. Y X Mixed Costs Total mixed cost Total Utility Cost Variable Cost per KW Fixed MonthlyUtility Charge Activity (Kilowatt Hours)

12. Y = a + bX Y = $40 + ($0.03 × 2,000) Y = $100 Mixed Costs Example If your fixed monthly utility charge is $40, your variable cost is $0.03 per kilowatt hour, and your monthly activity level is 2,000 kilowatt hours, what is the amount of your utility bill?

13. Learning Objective 2 Use a scattergraph plot to diagnose cost behavior.

14. Y 20 * * * * * * * * Maintenance Cost1,000’s of Dollars * * 10 0 X 0 1 2 3 4 Patient-days in 1,000’s The Scattergraph Method Plot the data points on a graph (total cost vs. activity).

15. Y 20 * * * * * * * * Maintenance Cost1,000’s of Dollars * * 10 0 X 0 1 2 3 4 Patient-days in 1,000’s The Scattergraph Method Draw a line through the data points with about anequal numbers of points above and below the line.

16. Learning Objective 3 Analyze a mixed cost using the high-low method.

17. Assume the following hours of maintenance work and the total maintenance costs for six months. The High-Low Method

18. $2,400300 =$8.00/hour The High-Low Method The variable cost per hour of maintenance is equal to the change in cost divided by the change in hours.

19. Total Fixed Cost = $9,800 – $6,400 Total Fixed Cost = $3,400 The High-Low Method Total Fixed Cost = Total Cost – Total Variable Cost Total Fixed Cost = $9,800 – ($8/hour × 800 hours)

20. The Cost Equation for Maintenance Y = $3,400 + $8.00X The High-Low Method

21. Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, 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 Quick Check 

22. Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, 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 $4,000 ÷ 40,000 units = $0.10 per unit Quick Check 

23. Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Quick Check 

24. Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Quick Check 

25. Least-Squares Regression Method A method used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables. This method uses all of thedata points to estimatethe fixed and variablecost components of amixed cost. The goal of this method isto fit a straight line to thedata that minimizes thesum of the squared errors.

26. Software can be used to fit a regression line through the data points. The cost analysis objective is the same: Y = a + bX Least-Squares Regression Method Least-squares regression also provides a statistic, called the R2, which is a measure of the goodnessof fit of the regression line to the data points.

27. Least-Squares Regression Method R2 is the percentage of the variation in total cost explained by the activity. Y 20 * * * * * * * * * * Total Cost 10 R2 varies from 0% to 100%, andthe higher the percentage the better. 0 X 0 1 2 3 4 Activity

28. Learning Objective 4 Prepare an income statement using the contribution format.

29. The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs and provides for income. The Contribution Format

30. Used primarily forexternal reporting. Used primarily bymanagement. The Contribution Format

31. Uses of the Contribution Format • The contribution income statement format is used as an internal planning and decision making tool. We will use this approach for: • Cost-volume-profit analysis. • Budgeting. • Segmented reporting of profit data. • Special decisions such as pricing and make-or-buy analysis.

32. Cost-Volume-Profit (CVP) Relationships

33. Learning Objective 1 Explain how changes in activity affect contribution margin and net operating income.

34. Basics of Cost-Volume-Profit Analysis Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

35. Basics of Cost-Volume-Profit Analysis CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.

36. The Contribution Approach Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit.

37. The Contribution Approach Each month, Racing must generate at least $80,000 in total CM to break even.

38. The Contribution Approach If Racing sells 400 unitsin a month, it will be operating at the break-even point.

39. The Contribution Approach If Racing sells one more bike (401 bikes), net operating income will increase by $200.

40. The Contribution Approach We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. If Racing sells 430 bikes, its net income will be $6,000.

41. Learning Objective 2 Prepare and interpret a cost-volume-profit (CVP) graph.

42. CVP Graph Dollars In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Units

43. Fixed Expenses CVP Graph Dollars Units

44. Total Expenses Fixed Expenses CVP Graph Dollars Units

45. Total Sales Total Expenses Fixed Expenses CVP Graph Dollars Units

46. Break-even point(400 units or $200,000 in sales) CVP Graph Profit Area Dollars Loss Area Units

47. CVP Relationships in Graphic Form The relation among revenue, cost, and profit can be expressed graphically by preparing a CVP graph. Racing developed contribution margin income statements at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph.

48. Profit Equation Profit = Sales – VC – FC = pq – vq – FC =(p – v)q – FC = UCM x q – FC Draw the profit equation and interpret it.

49. Learning Objective 3 Use the contribution margin ratio (CM ratio) to compute changes in contribution margin and net operating income resulting from changes in sales volume.

50. Total CM Total sales CM Ratio = $80,000 $200,000 = 40% Contribution Margin Ratio The contribution margin ratio is:For Racing Bicycle Company the ratio is: Each $1.00 increase in sales results in a total contribution margin increase of 40¢.