Mixed Cost Analysis

1. Mixed Cost Analysis

2. The Analysis of . . . Mixed Costs

3. Fixed And Variable CostsCost Behavior – Mixed Costs y y y y = a a Cost Cost Cost x x x Activity level Activity level Activity level y = a + bx y = bx a Fixed cost y = a + bx since b = 0 y = a Variable cost y = a + bx since a = 0 y = bx Mixed cost y = a + bx 3

4. Methods of Analysis Visual fit of a scatter diagram High-low method Linear regression analysis 4

5. Y 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced Scatter Graph Method Plot the data points on a graph (total cost vs. activity)

6. Quick-and-Dirty Method Draw a line through the data points with about anequal numbers of points above and below the line. Y 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 Intercept is the estimated fixed cost = $10,000 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced

7. Advantages One of the principal advantages of this method is that it lets us “see” the data. What are the advantages of “seeing” the data?

8. Nonlinear Relationship Activity Cost * * * * * 0 Activity Output

9. Upward Shift in Cost Relationship Activity Cost * * * * * * 0 Activity Output

10. Presence of Outliers Activity Cost * * * * * * 0 Activity Output

11. Scatter Graph Example The sales manager for Hinds Wholesale Supply Company needs to estimate the expected delivery vehicle operating cost (maintenance) for 2005.

12. Scatter Graph Example Truck Number Miles Driven Packages Delivered Maintenance Cost 202 204 205 301 422 460 520 15,000 11,000 24,000 30,000 31,000 26,000 20,000 1,200 1,000 1,500 1,500 500 1,000 2,000 $2,000 $1,600 $2,200 $2,400 $2,600 $2,200 $2,000 Vehicle Data for 2004:

13. Scatter Graph Example Estimated Line Maintenance Cost and Miles Driven

14. Scatter Graph Example Maintenance Cost and Miles Driven Y = a + bx $15,000= ($1,100 x 7) + bx Total Miles Driven (x) = 157,000 b = $7,300 / 157,000 = $0.0465 or 4.7 cents per mile

15. Scatter Graph Example Maintenance Cost and Miles Driven Vehicle maintenance cost (y) = $1,100 (a) + $0.047 (b) per mile driven (x) What is the estimated maintenance cost for a truck that will be driven 28,000 miles? $1,100 + ($0.047 × 28,000) = $2,416

16. The high-low method involves taking the two observations with the highest and lowest level of activity to calculate the cost function High Low Method 16

17. High-low method ~ step 1 Cost Identify the highest and lowest activity levels. Volume of Activity 17

18. High-low Method ~ step 2 Cost Determine the differences between the high and low points coordinates. Volume of Activity 18

19. High-low method ~ step 3 Cost Variable cost per unit = slope of the line between the two points (which reflect total mixed costs). Variable Cost per Unit Rise = Run Volume of Activity 19

20. High-low method ~ step 4 Cost To find fixed costs, use slope and co-ordinates of one point in y = bx + a Rise Variable Cost per Unit  in cost  in units = Run Volume of Activity 20

21. High-low method ~ step 5 Select one of the two point Substitute into y = bx + a, where y = y coordinate of point x = x coordinate of point b = step 4 calculations Find a, ie total fixed costs 21

22. High-Low Method Example Maintenance Cost and Miles Driven Truck Number Miles Driven Packages Delivered Maintenance Cost 202 204 205 301 422 460 520 15,000 11,000 24,000 30,000 31,000 26,000 20,000 1,200 1,000 1,500 1,500 500 1,000 2,000 $2,000 $1,600 $2,200 $2,400 $2,600 $2,200 $2,000

23. High-Low Method Example ($2,600 – $1,600) (31,000 – 11,000) = $1,000 20,000 = $0.05 Maintenance Cost and Miles Driven What is the fixed cost element?

24. High-Low Method Example Maintenance Cost and Miles Driven: High Observation $2,600 = Fixed cost + (31,000 × $0.05) Fixed cost = $2,600 – $1,550 = $1,050 $1,050 is the fixed cost element.

25. High-Low Method Example Maintenance Cost and Miles Driven: Low Observation $1,600 = Fixed cost + (11,000 × $0.05) Fixed cost = $1,600 – $550 = $1,050 What is the estimated maintenance cost for a truck to be driven 28,000 miles? $1,050 + (28,000 × $0.05) = $2,450

26. Some Important Considerations We have used historical cost to arrive at the cost equation. Therefore, we have to be careful in how we use the formula. Never forget the relevant range.

27. Relevant Range 11,000 31,000 $ 11,000 to 31,000 activity level Volume (Activity Base)

28. Strengths of High-Low Method Simple to use Easy to understand

29. Weaknesses of High-Low Only two data points are used in the analysis. Can be problematic if either (or both) high or low are extreme (i.e., Outliers). Other months may not yield the same formula.

30. Extreme values - not necessarily representative . . . . . . . . . . . . . . . Representative High/Low Values

31. Regression Analysis A statistical technique used to separate mixed costs into fixed and variable components. All observations are used to fit a regression line which represents the average of all data points.

32. Regression Analysis Requires the simultaneous solution of two linear equations So that the squared deviations from the regression line of each of the plotted points cancel out (are equal to zero).

33. Simple Regression with one Independent Variable VC Per Unit (Slope) Total Costs y = a + bX Fixed Cost (Intercept) Level of Activity

34. Simple Regression with one Independent Variable Dependent Variable VC Per Unit (Slope) y = a + bX Fixed Cost (Intercept) Independent Variable

35. Regression Analysis With this equation and given a set of data. Two simultaneous linear equations can be developed that will fit a regression line to the data.

36. Estimating the Regression Line

37. Excel and Regression Analysis An Illustration of Regression Analysis Using Microsoft Excel

40. Dependent variable Independent variable

41. y = $3,998.25 + 2.09x Prediction equation Variable Cost per Unit Number of Units Fixed Cost

42. Slope of regression line Fixed Cost $3,998.25

43. Coefficient of Correlation The multiple R (called the coefficient of correlation) is a measure of the proximity of the data points to the regression line. Can range from 0 (no relationship) to 1 or -1 (Perfect Relationship). Positive correlation means the variables move together. Negative correlation means they move in opposite directions. In this case, there is a positive correlation between the number of pizzas produced (independent variable) and the total overhead costs (dependent variable).

44. A coefficient of correlation of 1 would indicate that all data observations fall on the regression line.

45. Coefficient of Determination The R Square (R2) called the Coefficient of Determination is a measure of goodness of fit (how well the regression line “fits” the data). R2 can be interpreted as the proportion of variation in the dependent variable (overhead costs) that is explained by changes in the independent variable (the number of pizzas). The R2 may range from 0 to 1. An R2 of less than one indicates that other independent variable might have an impact on the dependent variable.

46. Positive Correlation Machine Hours Utility Costs Machine Hours Utility Costs r approaches +1

47. r approaches +1

48. r Equals +1

49. Negative Correlation Hours of Safety Training Industrial Accidents Hours of Safety Training Industrial Accidents r approaches -1

50. r approaches -1