Determining How Costs Behave

1. Determining HowCosts Behave Chapter 10

2. Overview • Assumptions • Model: Y = a + bX • Determinates of Fixed vs. Variable costs • Cost Estimation Industrial Engineering Conference Method Account Analysis Quantitative Analysis: H-L & OLS 5) Non-linear cost functions

3. Two assumptions frequently used in cost-behavior estimation 1. Changes in total costs can be explained by changes in the level of a single activity. 2. Cost behavior can adequately be approximated by a linear function of the activity level within the relevant range.

4. Cost Function What is a cost function? It is a mathematical expression describing how costs change with changes in the level of an activity.

5. Cost Function—variable cost La Playa Hotel offers an airline three alternative cost structures to accommodate its crew overnight: 1. $60 per night per room usage y = $60x The slope of the cost function is $60.

6. Cost Function

7. Cost Function—fixed cost 2. $8,000 per month y = $8,000 $8,000 is called a constant or intercept. The slope of the cost function is zero.

8. Cost Function

9. Cost Function—mixed cost 3. $3,000 per month plus $24 per room This is an example of a mixed cost. y = $3,000 + $24x y = a + bx

10. Cost Function

11. Cost Classificationand Estimation Function Choice of cost object Time span Relevant range

12. Choice of Cost Object Example If the total cost to operate all taxis owned by a taxi company is the cost object, annual taxi registration and license fees would be variable costs (number of taxis). If the cost to operate a particular taxi is the cost object, registration and license fees for that taxi are fixed costs.

13. Time Span Whether a cost is variable or fixed with respect to a particular activity depends on the time span. More costs are variable with longer time spans.

14. Relevant Range Variable and fixed cost behavior patterns are valid for linear cost functions only within the given relevant range. Costs may behave nonlinear outside the range.

15. Cost Estimation What is cost estimation? It is the attempt to measure a past cost relationship between costs and the level of an activity. Past cost-behavior functions can help managers make more accurate cost predictions.

16. The Cause-and-Effect CriterionIn Choosing Cost Drivers Physical relationship Contractual agreements Implicitly established by logic

17. Cost Estimation Approaches Industrial engineering method Conference method Account analysis method Quantitative analysis methods

18. Steps In EstimatingA Cost Function Step 1: Choose the dependent variable. Step 2: Identify the independent variable cost driver(s). Step 3: Collect data on the dependent variable and the cost driver(s).

19. Steps In Estimating A Cost Function Step 4: Plot the data. Step 5: Estimate the cost function. Step 6: Evaluate the estimated cost function.

20. High-Low Method Example(A quantitative analysis method) High capacity December: 55,000 machine-hours Cost of electricity: $80,450 Low capacity September: 30,000 machine-hours Cost of electricity: $64,200 What is the variable rate?

21. High-Low Method Example ($80,450 – $64,200) ÷ (55,000 – 30,000) $16,250 ÷ 25,000 = $0.65 What is the fixed cost?

22. High-Low Method Example $80,450 = Fixed cost + (55,000 × $0.65) Fixed cost = $80,450 – $35,750 = $44,700 $64,200 = Fixed cost + (30,000 × $0.65) Fixed cost = $64,200 – $19,500 = $44,700 y = a + bx y = $44,700 + ($0.65 × Machine-hours)

23. Regression Analysis--OLS(A quantitative analysis method) It is used to measure the average amount of change in a dependent variable, such as electricity, that is associated with unit increases in the amounts of one or more independent variables, such as machine-hours. Regression analysis uses all available data to estimate the cost function.

24. Regression Analysis Simple regression analysis estimates the relationship between the dependent variable and one independent variable. Multiple regression analysis estimates the relationship between the dependent variable and multiple independent variables.

25. Regression Analysis The regression equation and regression line are derived using the least-squares technique. The objective of least-squares is to develop estimates of the parameters aand b.

26. Regression Analysis The vertical difference (residual term) measures the distance between the actual cost and the estimated cost for each observation. The regression method is more accurate than the high-low method.

27. Criteria to Evaluate andChoose Cost Drivers Economic plausibility Goodness of fit Slope of the regression line

28. Goodness of Fit The coefficient of determination (r2) expresses the extent to which the changes in (x) explain the variation in (y). An (r2) of 0.80 indicates that 80% of the change in the dependent variable can be explained by the change in the independent variable.

29. Slope of Regression Line Everything else equal: A relatively steep slope indicates a strong relationship between the cost driver and costs. A relatively flat regression line indicates a weak relationship between the cost driver and costs.

30. Slope of Regression Line The closer the value of the correlation coefficient (r) is to ±1, the stronger the statistical relation between the variables.

31. Excel Regression--Data

32. Excel Regression--results • Interpret Excel regression output (in class)

33. Non-linear Cost Functions A nonlinear cost function is a cost function in which the graph of total costs versus the level of a single activity is not a straight line within the relevant range. Economies of scale Quantity discounts Step cost functions

34. Concave Cost Functions Learning versus experience curves

35. Data Issues Data problems encountered in estimating cost functions.