1. Cost Accounting Dr. Baldwin University of Arkansas – Fort Smith Fall 2010

2. 2 Chapter 10 Determining How Costs Behave

3. 3 Why understand cost behavior? Managers need to understand cost behavior in order to make decisions about strategy and about operations. For example –Product decisions Apple  iPod, iPhone, iPad Amazon  Kindle –Other decisions Fort Smith administration  enrollment

4. 4 What do we already know about the nature of costs? Variable Cost Fixed Cost Mixed Cost Cost Volume of Activity

5. 5 Assumptions Costs are linear – or approximated by linear functions Each cost has a single cost driver Are these always true? Not always! We generally assume they are true within the relevant range. Exercise 18.

6. 6 Relevant Range The range of the activity in which total cost and the level of activity are related.

7. 7 How to understand cost behavior? A cost function is a mathematical description of how a cost changes with changes in the volume of its cost driver activity. Variable Cost Fixed Cost Mixed Cost Cost Volume of Activity

8. 8 Linear Cost Functions example Let’s assume you are a spin class instructor and you have to provide your own music for class. You spend a lot of time and money downloading songs to use in class. uTunes is providing three different payment options. –Let’s look at the options and identify the cost function for each.

9. 9 Linear Cost Functions example Option A –Pay $5 per song downloaded Option B –Pay $100 per month for unlimited downloads Option C –Pay $50 per month plus $0.50 per download Create a cost function for each option using the generic linear cost function formula.

10. 10 Create a Linear Cost Function Formula:Y = a + bX Where: –Y = total costs –a = fixed costs –b = variable cost per unit of cost driver –X = cost driver Option A:Y = $0 + $5X Option B: Y = $100 + $0X Option C: Y = $50 + $0.50X

11. 11 How to understand cost behavior? Option A:Y = $0 + $5X Option B: Y = $100 + $0X Option C: Y = $50 + $0.50X Variable Cost Fixed Cost Mixed Cost Cost Volume of Activity (downloads) A B C

12. 12 Calculate Total Cost of Each Option Which option is least expensive? Assuming 40 downloads a month, what is the total cost per month for each option? Option A:Y = $0 + $5 * 40 = $200 Option B: Y = $100 + $0*40 = $100 Option C: Y = $50 + $0.50*40 = $70 What happens if you download more or less than 40? 100? 200?

13. 13 How to understand cost behavior? Option A:Y = $0 + $5X Option B: Y = $100 + $0X Option C: Y = $50 + $0.50X Variable Cost Fixed Cost Mixed Cost Cost Volume of Activity (downloads) A B C 10 100 20

14. 14 How to understand cost behavior? Cost Estimation Methods Many methods to estimate costs Potential problems in cost estimation –Availability of historical data –Accuracy of data –The estimates are only as good as the data on which they are based.

15. 15 How to understand cost behavior? Cost Estimation Methods Industrial Engineering –Time and motion studies Conference –Consensus of estimates  Account Analysis Quantitative Analysis –High-Low Method –Regression

16. 16 Account Analysis Method Use knowledge of operations to Classify cost accounts according to their relationship with the cost driver activity: –variable, fixed, or mixed Estimate the cost/driver relationship Example: Lorenzo’s Car Wash (Exercise 20)

17. 17 Lorenzo’s Car Wash example Incoming cars are put on a conveyor belt. Cars are washed as they are carried by the conveyor belt from start to finish. The cars are then dried manually. Workers clean and vacuum car inside. They are managed by a single supervisor. Lorenzo serviced 80,000 cars in 2009, for which he reports the following costs:

18. 18 Lorenzo’s Car Wash example Use knowledge of operations to Classify cost accounts according to their relationship with the cost driver activity: –variable, fixed, or mixed Estimate the costs if 90,000 cars are washed in 2010.

19. 19 Lorenzo’s Car Wash example Classify: variable, fixed, or mixed Variable Fixed $412,000 $110,000

20. 20 Lorenzo’s Car Wash example Variable Costs for 2009 $ 412,000 80,000 cars = $5.15 per car Fixed Costs $110,000 Total average cost per car = (412,000 + 110,000) 80,000 cars= $6.53 per car

21. 21 Lorenzo’s Car Wash example Estimate Lorenzo’s 2010 costs (90,000 washes) Variable Costs 90,000 cars * $5.15 per car = $463,500 Fixed Costs $110,000 Total costs = $463,500 + $110,000 = $573,500

22. 22 How to understand cost behavior? Cost Estimation Methods Industrial Engineering –Time and motion studies Conference –Consensus of estimates Account Analysis Quantitative Analysis –High-Low Method –Regression 

23. 23 Quantitative Analysis Uses formal mathematical methods to fit cost functions to past data observations. Remember, a cost function is a mathematical description of how a cost changes with changes in the level of its cost driver activity. –Total costs = FC + VC UNIT * activity –Lorenzo’s cost function: $110,000 + $5.15 per car * number of cars

24. 24 Estimate a Linear Cost Function Formula:Y = a + bX Where: –Y = total costs –a = fixed costs –b = variable cost per unit of cost driver –X = cost driver Two methods –High-Low Method –Regression Analysis

25. 25 High-Low Method Uses two points (the high and the low) to find the equation of the cost line y = a + bx –slope = b = change in y/change in x –intercept = a = y - bx Strengths –Simple to compute –Easy to understand Weaknesses –Only two points used - what if they are not representative of normal relationship? Exercise 16.

26. 26 Regression Analysis Uses all the observations to find the equation of the cost line y = a + bx –slope = change in y/change in x –intercept = a = y - bx Regression minimizes the sum of the squared differences between the observed data and the predicted line Strengths –More accurate than the high-low method

27. 27 Statistical Output Provides estimates of the two parameters in the cost function: Y = a + bX –a = intercept = fixed costs –b = slope = variable costs per unit Measures of goodness of fit –Co-efficient of determination = r 2 Measures the % variation in Y explained by X –T-statistic = b/standard error of estimated co-efficient t tells us if b is different from zero Larger is better

28. 28 Statistical Output What do we do with it? Check goodness of fit measures –Want r 2 .3 (or perhaps even higher) –Want t  2 Compare cost drivers to see which is best Estimate Y (total costs) for future period.

29. 29 Non-Linear Functions Costs are not always linear! For example: Quantity discounts –Costs decrease as volume increases Step cost functions –Costs increase by discrete amounts over narrow ranges Step fixed-cost functions –Cost remain the same over wider intervals Learning curves 

30. 30 Learning Curves A learning curve is a function that measures how labor- hours per unit decline as unites of production increase because workers are learning and becoming better at their jobs. Two types: Cumulative average-time learning model –Average time per unit declines at a constant rate Incremental unit-time learning model –Time to produce last unit decreases at a constant rate Learning curves are given as a percentage

31. 31 Learning Curves Formula:Y = pX q Where: –Y = cumulative average time or incremental time –p = labor hours on first unit –X = cumulative # of units –q reflects the learning rate (log of learning curve)

32. 32 Learning Curves Learning is faster in which model? –(cumulative model) Which of these models will predict higher costs? – (incremental model) Which of these models is better? –It depends! Case by case basis decision.

33. 33 Learning Curves What are implications for product costing? –Charge more initially and decrease price as time to produce declines? Will the customers put up with that? –Price down the learning curve - set price based on what we expect costs to be in the future Why might companies do this?

34. 34 Summary 1 Managers have to understand cost behavior in order to make decisions about strategy and about operations. Most of the time we assume costs are linear and each has single cost driver. A cost function is a mathematical description of how a cost changes with changes in the level of its cost driver activity. –Formula:Y = a + bX Costs are not always linear (e.g. learning curves).

35. 35 Summary 2 Cost Estimation Methods help us understand cost behavior. Industrial Engineering (Time & motion studies) Conference (consenses) Account Analysis Quantitative Analysis –High-Low Method –Regression

36. 36 Summary 3 Many methods to estimate costs Potential problems in cost estimation –Availability of historical data –Accuracy of data –The estimates are only as good as the data on which they are based. Don’t forget to read the appendix which discusses regression.