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Cost Accounting : Determining How Cost Behaves

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Cost Accounting : Determining How Cost Behaves

  1. 1. Determining How Costs Behave
  2. 2. Introduction <ul><li>How do managers know what price to charge, whether to make or buy, or other questions related to costs. </li></ul><ul><li>They need to have an understanding of how costs change in relation to various factors. </li></ul><ul><li>This chapter will focus on how to determine cost behavior. </li></ul>
  3. 3. Learning Objectives <ul><li>Explain the two assumptions frequently used in cost-behavior estimation </li></ul><ul><li>Describe linear cost functions and three common ways in which they behave </li></ul><ul><li>Understand various methods of cost estimation </li></ul>
  4. 4. Learning Objectives <ul><li>Outline six steps in estimating a cost function on the basis of current or past cost relationships </li></ul><ul><li>Describe three criteria to evaluate and choose cost drivers </li></ul><ul><li>Explain and give examples of nonlinear cost functions </li></ul>
  5. 5. Learning Objectives <ul><li>Distinguish the cumulative average-time learning model and incremental unit-time model </li></ul><ul><li>Be aware of data problems encountered in estimation cost functions </li></ul>
  6. 6. Learning Objective 1 <ul><li>Explain the two assumptions frequently used in cost-behavior estimation </li></ul>
  7. 7. Cost Function... <ul><li>is a mathematical expression describing how costs change with changes in the level of an activity. </li></ul><ul><li>Output produced </li></ul><ul><li>Direct manufacturing labor hours </li></ul><ul><li>Machine hours </li></ul><ul><li>Batches of production </li></ul>
  8. 8. Assumptions in Cost-Behavior Estimation <ul><li>Managers often estimate cost functions base on two assumptions: </li></ul><ul><li>Changes in total costs can be explained by changes in the level of a single activity. </li></ul><ul><li>Variation in machine hours can explain variations in total cost . </li></ul><ul><li>Variation in labor hours can explain variations in total cost. </li></ul>
  9. 9. Assumptions in Cost-Behavior Estimation <ul><li>Cost behavior can adequately be approximated by a linear function of the activity level within the relevant range. </li></ul><ul><li>A linear cost function is a cost function in which the graph of total cost versus the level of a single activity is a straight line. </li></ul>
  10. 10. Learning Objective 2 <ul><li>Describe linear cost functions and three common ways in which they behave </li></ul>
  11. 11. Cost Function <ul><li>La Bella Hotel offers Happy Airline three alternative cost structures to accommodate its crew overnight: </li></ul><ul><li>$60 per night per room usage </li></ul><ul><li>Total room usage is the only factor whose change causes a change in total costs. </li></ul><ul><li>The cost is variable. </li></ul>
  12. 12. Cost Function <ul><li>y = $60 x </li></ul><ul><li>y measures the total costs of the rooms used. </li></ul><ul><li>x refers to the actual number of rooms used. </li></ul><ul><li>The slope of the cost function is $60. </li></ul>
  13. 13. Cost Function <ul><li>y = cost y x x = number of rooms </li></ul>
  14. 14. Cost Function <ul><li>$8,000 per month </li></ul><ul><li>The total cost will be $8,000 per month regardless of room usage. </li></ul><ul><li>The cost is fixed, not variable. </li></ul><ul><li>What is the cost function? </li></ul>
  15. 15. Cost Function <ul><li>y = $8,000 </li></ul><ul><li>$8,000 is called a constant or intercept. </li></ul><ul><li>The slope of the cost function is zero. </li></ul>
  16. 16. Cost Function <ul><li>y = cost y $8,000 x x = number of rooms </li></ul>
  17. 17. Cost Function <ul><li>$3,000 per month plus $24 per room </li></ul><ul><li>This is an example of a mixed cost. </li></ul><ul><li>y = $3,000 + $24 x </li></ul><ul><li>y = a + bx </li></ul>
  18. 18. Cost Function <ul><li>y = cost y $3,000 x x = number of rooms </li></ul>
  19. 19. Learning Objective 3 <ul><li>Understand various methods of cost estimation </li></ul>
  20. 20. Cost Estimation... <ul><li>is the attempt to measure a past cost relationship between costs and the level of an activity. </li></ul><ul><li>Managers are interested in estimating past cost-behavior functions primarily because these estimates can help them make more accurate cost predictions . </li></ul>
  21. 21. Cost Estimation Approaches <ul><li>Industrial engineering method </li></ul><ul><li>Conference method </li></ul><ul><li>Account analysis method </li></ul><ul><li>Quantitative analysis methods </li></ul>
  22. 22. Industrial Engineering Method... <ul><li>is also called the work-measurement method . </li></ul><ul><li>It estimates cost functions by analyzing the relationship between inputs and outputs in physical terms. </li></ul>
  23. 23. Conference Method... <ul><li>estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various sources. </li></ul><ul><li>This method involves the pooling of expert knowledge. </li></ul>
  24. 24. Account Analysis... <ul><li>estimates cost functions by classifying cost accounts in the ledger as variable, fixed, or mixed with respect to the identified activity. </li></ul><ul><li>Typically, managers use qualitative rather than quantitative analysis when making these cost-classification decisions. </li></ul>
  25. 25. Quantitative Analysis Methods <ul><li>Quantitative analysis uses a formal mathematical method to fit linear cost functions to past data observations. </li></ul>
  26. 26. Learning Objective 4 <ul><li>Outline six steps in estimating a cost function on the basis of current or past cost relationships </li></ul>
  27. 27. Steps In Estimating A Cost Function <ul><li>Choose the dependent variable. </li></ul><ul><li>Identify the independent variable, or cost driver. </li></ul><ul><li>Collect data on the dependent variable and the cost driver. </li></ul><ul><li>Plot the data. </li></ul><ul><li>Estimate the cost function. </li></ul><ul><li>Evaluate the cost driver of the estimated cost function. </li></ul>
  28. 28. High-Low Method <ul><li>Choose the highest and lowest value of the cost driver and their respective costs. </li></ul><ul><li>Determine a and b using algebra. </li></ul>
  29. 29. High-Low Method <ul><li>High capacity December: 55,000 machine hours </li></ul><ul><li>Cost of electricity: $80,450 </li></ul><ul><li>Low capacity September: 30,000 machine hours </li></ul><ul><li>Cost of electricity: $64,200 </li></ul><ul><li>What is the variable rate? </li></ul>
  30. 30. High-Low Method <ul><li>($80,450 – $64,200) ÷ (55,000 – 30,000) </li></ul><ul><li>$16,250 ÷ 25,000 = $0.65 </li></ul><ul><li>What is the fixed cost? </li></ul>
  31. 31. High-Low Method <ul><li>$80,450 = Fixed cost + 55,000 – $0.65 </li></ul><ul><li>Fixed cost = $80,450 – $35,750 = $44,700 </li></ul><ul><li>$64,200 = Fixed cost + 30,000 x $0.65 </li></ul><ul><li>Fixed cost = $64,200 – $19,500 = $44,700 </li></ul><ul><li>y = a + bx </li></ul><ul><li>y = $44,700 + ($0.65 × Machine-hours) </li></ul>
  32. 32. Learning Objective 5 <ul><li>Describe three criteria to evaluate and choose cost drivers </li></ul>
  33. 33. Criteria to Evaluate and Choose Cost Drivers <ul><li>Economic plausibility </li></ul><ul><li>Goodness of fit </li></ul><ul><li>Slope of the regression line </li></ul>
  34. 34. Goodness of Fit <ul><li>The coefficient of determination (r 2 ) expresses the extent to which the changes in (x) explain the variation in (y) . </li></ul><ul><li>An (r 2 ) of 0.80 indicates that more than 80 percent of the change in the dependent variable can be explained by the change in the independent variable. </li></ul>
  35. 35. Slope of Regression Line <ul><li>A relatively steep slope indicates a strong relationship between the cost driver and costs. </li></ul><ul><li>A relatively flat regression line indicates a weak relationship between the cost driver and costs. </li></ul>
  36. 36. Slope of Regression Line <ul><li>The closer the value of the correlation coefficient (r) to ±1, the stronger the statistical relation between the variables. </li></ul><ul><li>As (r) approaches +1, a positive relationship is implied, meaning the dependent variable (y) increases as the independent variable (x) increases. </li></ul>
  37. 37. Slope of Regression Line <ul><li>As (r) approaches –1, a negative, or inverse, relationship is implied, meaning the dependent variable (y) decreases as the independent variable (x) increases. </li></ul>
  38. 38. Learning Objective 6 <ul><li>Explain and give examples of nonlinear cost functions </li></ul>
  39. 39. Nonlinearity and Cost Functions <ul><li>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. </li></ul><ul><li>Economies of scale </li></ul><ul><li>Quantity discounts </li></ul><ul><li>Step cost functions </li></ul>
  40. 40. Nonlinearity and Cost Functions <ul><li>Economies of scale in advertising may enable an advertising agency to double the number of advertisements for less than double the cost. </li></ul>
  41. 41. Nonlinearity and Cost Functions <ul><li>Quantity discounts on direct materials purchases produce a lower cost per unit purchased with larger orders. </li></ul>
  42. 42. Nonlinearity and Cost Functions <ul><li>A step function is a cost function in which the cost is constant over various ranges of the level of activity, but the cost increases by discrete amounts as the level of activity changes from one range to the next. </li></ul>
  43. 43. Learning Objective 7 <ul><li>Distinguish between the cumulative average-time learning model and incremental unit-time model </li></ul>
  44. 44. Learning Curves <ul><li>A learning curve is a function that shows how labor-hours per unit decline as units of output increase. </li></ul>
  45. 45. Experience Curve... <ul><li>is a function that shows how the costs per unit in various value chain areas decline as units produced and sold increase. </li></ul>
  46. 46. Cumulative Average-Time Learning Model <ul><li>Cumulative average time per unit is reduced by a constant percentage each time the cumulative quantity of units produced is doubled. </li></ul>
  47. 47. Incremental Unit-Time Learning Model <ul><li>The time needed to produce the last unit is reduced by a constant percentage each time the cumulative quantity of units produced is doubled. </li></ul>
  48. 48. Learning Objective 8 <ul><li>Be aware of data problems encountered in estimation cost functions </li></ul>
  49. 49. Data Collection and Adjustment Issues <ul><li>The ideal database for cost estimation has two characteristics: </li></ul><ul><li>It contains numerous reliably measured observations of the cost driver(s) and the cost that is the dependent variable. </li></ul><ul><li>It considers many values for the cost driver that span a wide range. </li></ul>
  50. 50. Data Collection and Adjustment Issues <ul><li>Time periods do not match. </li></ul><ul><li>Fixed costs are allocated as if they were variable. </li></ul><ul><li>Data are either not available or not reliable. </li></ul><ul><li>Inflation may play a role. </li></ul>
  51. 51. Data Collection and Adjustment Issues <ul><li>Extreme values of observations occur from errors in recording costs. </li></ul><ul><li>Analysts should adjust or eliminate unusual observations before estimating a cost relationship. </li></ul><ul><li>There is no homogeneous relationship. </li></ul><ul><li>The relationship between the cost driver and the cost is not stationary. </li></ul>
  52. 52. Data Collection and Adjustment Issues <ul><li>The most difficult task in cost estimation is collecting high-quality, reliably measured data on the dependent variable and the cost driver(s). </li></ul>

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