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Chapter 5

Chapter 5. Cost Behavior. Cost Behavior Patterns. Cost behavior describes the way total cost behaves, or changes, when some measure of activity changes . . The range of activity within which assumptions about cost behavior hold true is the relevant range . .

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Chapter 5

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  1. Chapter 5 Cost Behavior

  2. Cost Behavior Patterns Cost behavior describes the way total cost behaves, or changes, when some measure of activity changes. The range of activity within which assumptions about cost behavior hold true is the relevant range. Unit variable costsremain unchanged. Total fixed costsremain unchanged.

  3. Learning Objective 5-1 Identify costs as variable, fixed, step, or mixed.

  4. Variable Costs Total variable costsincrease asactivity increases. Variable cost per unit isconstant asactivity increases.

  5. Fixed Costs Total fixed costs remain constant as activity increases. Cost per cupdeclines asactivity increases.

  6. Cost Behavior Summary

  7. Step Costs Step-variable costsrise in multiple steps across the relevant range. Step-fixed costs are fixed over a fairly wide range of activities.

  8. Mixed Costs Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases withusage. Utilities typically behave in this manner. Total mixed cost Total Utility Cost Variable Cost per KW Fixed MonthlyUtility Charge Activity (Kilowatt Hours)

  9. Mixed Costs Total mixed costs increase asactivity increases. Per unit mixed costsdecrease asactivity increases.

  10. Linear Approaches to Analyzing Mixed Costs y= total cost, which is plotted on the vertical axis, and is called the dependent variable. a= total fixed cost, an amount that will be incurred regardless of the activity level, and is called the intercept or the constant. b = Slope y = Total Costs b= the slope of the line, the unit variable cost,which tells us how much the total cost (y) willincrease for each unit increase in activity (x). a = Intercept x= the activity that causes total cost (y) to change. Activity (x) is also called the cost driver, or the independent variable. x = Activity

  11. Linear Approaches to Analyzing Mixed Costs • There are three different methods to analyze mixed costs, all using the linear assumption as a base. • Scattergraph:A graph that provides a visual representation of the relationship between total cost (y) and activity level (x). A scattergraph is a useful first step in analyzing cost behavior because it helps determine the nature of the relationship and whether the linearity assumption is valid. • High-low method: A simple approach that uses the two most extreme data points to determine the slope of the line (variable cost per unit) and the intercept (total fixed cost). • Least-squares regression:A statistical technique for finding the best fitting line based on historical data. The slope of the line provides an estimate of the variable cost per unit, while the intercept provides an estimate of the total fixed cost.

  12. Learning Objective 5-2 Prepare a scattergraph to illustrate the relationship between total cost and activity.

  13. Scattergraph A scattergraph is a graph with total cost plotted on the vertical (Y) axis and some measure of activity on the horizontal (X) axis.

  14. Preparing a Scattergraph • A scattergraph can be created by manually plotting data points ongraph-paper, or by using a the following steps in Excel: • Enter the data in Excel, and highlight the data that you want to plot. • 2. Select the Chart Wizard from the toolbar. • 3. Select XY (Scatter) as the chart type. Be sure total cost is on the Y axis, with the activity driver on the X axis. • 4. Add a chart title and labels for the X and Y axes. To apply these steps, consider the following data showing the total overhead cost (Y) of running our hypothetical Starbucks location, along with the number of customers served (X).

  15. Preparing a Scattergraph

  16. Learning Objective 5-3 Use the high-low method to analyze mixed costs.

  17. High-Low Method

  18. High-Low Method _ = Total Fixed Cost Total Cost Variable Cost per Unit × Activity May Estimate February Estimate _ _ Total Fixed Cost = = $13,250 $15,750 $0.25 × 5,000 $0.25 × 15,000 = Total Fixed Cost $12,000 $12,000 Total Fixed Cost = Total Fixed Cost

  19. High-Low Method

  20. Learning Objective 5-4 Use least-squares regression to analyze mixed costs.

  21. Least-Squares Regression Method A statistical method used to analyze mixed costs. } Error The goal of this method is to minimize the sum of the squared errors.

  22. Software such as Excel 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 The output from the regression analysis can be used to create an equation that enables you to estimate total costs at any activity level.

  23. Least-Squares Regression Method

  24. Least-Squares Regression Method R2 tell us how closely we can explain the relationship between our two variables. In our example, the number of customers explains about 64% of the overhead costs. The intercept and x coefficient, respectively, are estimated total fixed cost and variable cost per unit.

  25. Least-Squares Regression Method TotalCost Total Fixed Cost Total Variable Cost(Variable Cost per Unit × X) + = Using our regression output, if Starbucks expected to serve 8,000 customers in July, we would estimate total overhead costs as follows: $0.32 × 8,000 =$2,560 $11,181 $13,741 + =

  26. Summary of Linear Methods

  27. Learning Objective 5-5 Prepare and interpret a contribution margin income statement.

  28. Contribution Margin Approach Contribution margin is the difference between sales revenue and variable costs.

  29. Contribution Margin Ratio Contribution Margin Formula Contribution Margin Ratio Contribution Margin Ratio Contribution MarginSales Revenue = Contribution Margin Sales Revenue Variable Costs = ‒

  30. Contribution Margin Unitcontributionmargin Contribution margin ratio

  31. Contribution Margin

  32. Supplement 5A Variable Versus Full Absorption Costing

  33. Learning Objective 5-S1 Compare variable costing to full absorption costing.

  34. Variable Versus Full Absorption Costing

  35. Reconciling Variable and Full Absorption Costing

  36. Full Absorption Costing Income Statement

  37. Variable Costing Income Statement Variable costs only. All fixed manufacturing overhead is expensed.

  38. Reconciling Variable and Full Absorption Costing Difference between Full Absorption and Variable Costing Income Change in Units in Ending Inventory (Production ‒ Sales) Fixed Manufacturing Overhead Cost per Unit = × = × $40,000 2,000 units $20 per unit

  39. Effect of Changes in Inventory Under Full Absorption and Variable Costing

  40. End of Chapter 5

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