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Behavior: Cost Analysis and Use Chapter Five McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Types of Cost Behavior Patterns Summary of Variable and Fixed Cost Behavior Cost Variable In Total Total variable cost is proportional to the activity level within the relevant range. Total fixed cost remains the same even when the activity level changes within the relevant range. Per Unit Variable cost per unit remains the same over wide ranges of activity. Fixed cost per unit goes down as activity level goes up. Fixed McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Extent of Variable Costs The proportion of variable costs differs across organizations. For example . . . A public utility with large investments in equipment will tend to have fewer variable costs. A manufacturing company will often have many variable costs. A service company will normally have a high proportion of variable costs. McGraw-Hill/Irwin A merchandising company usually will have a high proportion of variable costs like cost of sales. Copyright 2006, The McGraw-Hill Companies, Inc. Examples of Variable Costs 1. Merchandising companies cost of goods sold. 2. Manufacturing companies direct materials, direct labor, and variable overhead. 3. Merchandising and manufacturing companies commissions, shipping costs, and clerical costs such as invoicing. 4. Service companies supplies, travel, and clerical. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. True Variable Cost Direct materials is a true or proportionately variable cost because the amount used during a period will vary in direct proportion to the level of production activity. Cost Volume McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Step-Variable Costs Define step-variable cost Cost Volume McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. The Linearity Assumption and the Relevant Range A straight line Economist's closely Curvilinear Cost approximates a Function curvilinear Total Cost Relevant Range variable cost line within the relevant range. Accountant's Straight-Line Approximation (constant unit variable cost) Activity McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Types of Fixed Costs Committed Long-term, cannot be significantly reduced in the short term. Discretionary May be altered in the short-term by current managerial decisions Examples Depreciation on Equipment and Real Estate Taxes McGraw-Hill/Irwin Examples Advertising and Research and Development Copyright 2006, The McGraw-Hill Companies, Inc. The Trend Toward Fixed Costs The trend in many industries is toward greater fixed costs relative to variable costs. As machines take over many mundane tasks previously performed by humans, "knowledge workers" are demanded for their minds rather than their muscles McGraw-Hill/Irwin Knowledge workers tend to be salaried, highly-trained and difficult to replace. The cost to compensate these valued employees is relatively fixed rather than variable. Copyright 2006, The McGraw-Hill Companies, Inc. Is Labor a Variable or a Fixed Cost? The behavior of wage and salary costs can differ across countries, depending on labor regulations, labor contracts, and custom. In France, Germany, China, and Japan management has little flexibility in adjusting the size of the labor force. Labor costs are more fixed in nature. In the United States and the United Kingdom management has greater latitude. Labor costs are more variable in nature. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Fixed Costs and Relevant Range Rent Cost in Thousands of Dollars 90 Relevant Total cost doesn't change for a wide range of activity. 60 Range 30 0 0 How does this differ from step-variable costs? 1,000 2,000 3,000 Rented Area (Square Feet) Copyright 2006, The McGraw-Hill Companies, Inc. McGraw-Hill/Irwin Quick Check Which of the following statements about cost behavior are true? 1. Fixed costs per unit vary with the level of activity. 2. Variable costs per unit are constant within the relevant range. 3. Total fixed costs are constant within the relevant range. 4. Total variable costs are constant within the relevant range. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Mixed Costs The total mixed cost line can be expressed as an equation: Y = a + bX Where: Y = the total mixed cost a = the total fixed cost (the vertical intercept of the line) b = the variable cost per unit of activity (the slope of the line) X = the level of activity Y Total Utility Cost Variable Cost per KW X Activity (Kilowatt Hours) Fixed Monthly Utility Charge Copyright 2006, The McGraw-Hill Companies, Inc. McGraw-Hill/Irwin Mixed Costs Example If your fixed monthly utility charge is $40, your variable cost is $0.03 per kilowatt hour, and your monthly activity level is 2,000 kilowatt hours, what is the amount of your utility bill? McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Analysis of Mixed Costs: (1) The Scattergraph Method Plot the data points on a graph (total cost vs. activity). Y Maintenance Cost 1,000's of Dollars 20 10 * * * * 0 1 2 * ** * ** X 0 3 4 Patient-days in 1,000's McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. (1) The Scattergraph Method Draw a line through the data points with about an equal numbers of points above and below the line. Y Maintenance Cost 1,000's of Dollars 20 10 * * * * 0 1 2 * ** * ** X 0 3 4 Patient-days in 1,000's McGraw-Hill/Irwin Copyright 2006, The Companies, McGraw-Hill Inc. (1) The Scattergraph Method Use one data point to estimate the total level of activity and the total cost. Maintenance Cost 1,000's of Dollars Y Total maintenance cost = $11,000 20 10 * * * * 0 1 2 * ** * ** X Intercept = Fixed cost: $10,000 0 3 4 Patient-days in 1,000's Patient days = 800 McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. (2) The Scattergraph Method Make a quick estimate of variable cost per unit and determine the cost equation. Total maintenance at 800 patients Less: Fixed cost Estimated total variable cost for 800 patients $1,000 800 $ 11,000 10,000 $ 1,000 Variable cost per unit = = $1.25/patient-day Y = $10,000 + $1.25X Total maintenance cost McGraw-Hill/Irwin Number of patient days Copyright 2006, The McGraw-Hill Companies, Inc. (2) The High-Low Method Assume the following hours of maintenance work and the total maintenance costs for six months. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. (2) The High-Low Method The variable cost per hour of maintenance is equal to the change in cost divided by the change in hours. $2,400 = $8.00/hour 300 McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. (2) The High-Low Method Total Fixed Cost = Total Cost Total Variable Cost Total Fixed Cost = $9,800 ($8/hour Total Fixed Cost = $9,800 $6,400 Total Fixed Cost = $3,400 McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. 800 hours) (2) The High-Low Method The Cost Equation for Maintenance Y = $3,400 + $8.00X McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Exercise 5-8 High-Low Method; Predicting Cost The Lakeshore Hotel's guest-days of occupancy and custodial supplies expense over the last seven months were: Month March April May June July August September Guest-days of occupancy 4,000 6,500 8,000 10,500 12,000 9,000 7,500 Custodial Supplies Expense $ 7,500 8,250 10,500 12,000 13,500 10,750 $ 9,750 Guest-days is a measure of the overall activity at the hotel. For e.g., a guest who stays at the hotel for 3 days is counted as 3 guest-days Required: 1. Using the high-low method, estimate a cost formula for custodial supplies expense. 2. Using the cost formula, what amount of custodial supplies expense would you expect to be incurred at an occupancy level of 11,000 guest-days? McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. (3) Least-Squares Regression Method Software can be used to fit a regression line through the data points. Uses all the data points. Fits a straight line to the data that minimizes the sum of the squared errors. The cost analysis objective is the same: Y = a + bX Least-squares regression also provides a statistic, called the R2, that is a measure of the goodness of fit of the regression line to the data points. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. (3) Least-Squares Regression Method R2 is the percentage of the variation in total cost explained by the activity. Y 20 Total Cost 10 * * * * 2 0 1 * ** * ** R varies from 0% to 100% 0 2 3 Activity 4 X McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Comparing Results From the Three Methods The three methods just discussed provide slightly different estimates of the fixed and variable cost components of the mixed cost. This is to be expected because each method uses differing amounts of the data points to provide estimates. Least-squares regression provides the most accurate estimate because it uses all the data points. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. The Contribution Income Statement Total $ 100,000 60,000 $ 40,000 30,000 $ 10,000 Unit $ 50 30 $ 20 Sales Revenue Less: Variable costs Contribution margin Less: Fixed costs Net operating income The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs and provides for income. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. The Contribution Income Statement Used primarily for external reporting. McGraw-Hill/Irwin Used primarily by management. Copyright 2006, The McGraw-Hill Companies, Inc. Problem 5-13 Cost Behavior; High-Low Method; Contribution Format Income Statement Morrisey & Brown, LTd., of Sydney is a merchandising company that is the sole distributor of a product that is increasing in popularity among Australian consumers. The company's income statements for the 3 most recent months follow: July August September Sales in Units 4,000 4,500 5,000 Sales Revenue A$400,000 A$450,000 A$500,000 Less CGS 240,000 270,000 300,000 Gross Margin 160,000 180,000 200,000 Less Operating Expenses: Advertising Expense 21,000 21,000 21,000 Shipping Expense 34,000 36,000 38,000 Salaries and commissions 78,000 84,000 90,000 Insurance expense 6,000 6,000 6,000 Depreciation expense 15,000 15,000 15,000 Total operating expenses 154,000 162,000 170,000 Net operating income A$6,000 A$18,000 A$30,000 1. Identify each of the company's expenses as either variable, fixed, or mixed. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. Problem 5-13 Cost Behavior; High-Low Method; Contribution Format Income Statement (con't) 2. Using the high-low method, separate each mixed expense into variable and fixed elements. State the cost formula for each mixed expense. 3. Redo the company's income statement at the 5,000 unit level of activity using the contribution format. McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc. End of Chapter 5 McGraw-Hill/Irwin Copyright 2006, The McGraw-Hill Companies, Inc.

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