University:
Kentucky State University
Course:
ECO 302 | Macroeconomics
Academic year:

2024
Views:

186

Pages:

65
Author:

Apolenajz

Cost Behavior: Analysis and Use Chapter Five 5-2 Learning Objective 1 Understand how fixed and variable costs behave and how to use them to predict costs. 5-3 Types of Cost Behavior Patterns Recall the summary of our cost behavior discussion from an earlier chapter. Summary of Variable and Fixed Cost Behavior Cost In Total Per Unit Variable Total variable cost is proportional to the activity level within the relevant range. Variable cost per unit remains the same over wide ranges of activity. Total fixed cost remains the same even when the activity level changes within the relevant range. Fixed cost per unit goes down as activity level goes up. Fixed 5-4 The Activity Base Units produce d Machine hours A measure of what causes the incurrence of a variable cost Miles driven Labor hours 5-5 True Variable Cost Example Total Long Distance Telephone Bill A variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level. Your total long distance telephone bill is based on how many minutes you talk. Minutes Talked 5-6 Types of Cost Behavior Patterns Recall the summary of our cost behavior discussion from an earlier chapter. Summary of Variable and Fixed Cost Behavior Cost In Total Per Unit Variable Total variable cost is proportional to the activity level within the relevant range. Variable cost per unit remains the same over wide ranges of activity. Total fixed cost remains the same even when the activity level changes within the relevant range. Fixed cost per unit goes down as activity level goes up. Fixed 5-7 Variable Cost Per Unit Example Per Minute Telephone Charge A variable cost remains constant if expressed on a per unit basis. The cost per minute talked is constant. For example, 10 cents per minute. Minutes Talked 5-8 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. A merchandising company usually will have a high proportion of variable costs, like cost of sales. 5-9 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. 5-10 True Variable Cost 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. Volume 5-11 Step-Variable Costs Cost A resource that is obtainable only in large chunks (such as maintenance workers) and whose costs increase or decrease only in response to fairly wide changes in activity is known as a step-variable cost. Volume 5-12 Step-Variable Costs Cost Small changes in the level of production are not likely to have any effect on the number of maintenance workers employed. Volume 5-13 Step-Variable Costs Cost Only fairly wide changes in the activity level will cause a change in the number of maintenance workers employed Volume 5-14 The Linearity Assumption and the Relevant Range Total Cost A straight line Economist’s closely Curvilinear Cost approximates a Function curvilinear Relevant Range variable cost line within the relevant range. Accountant’s Straight-Line Approximation (constant unit variable cost) Activity 5-15 Types of Cost Behavior Patterns Let’s look at fixed cost behavior on the next screens. Summary of Variable and Fixed Cost Behavior Cost In Total Per Unit Variable Total variable cost is proportional to the activity level within the relevant range. Variable cost per unit remains the same over wide ranges of activity. Total fixed cost remains the same even when the activity level changes within the relevant range. Fixed cost per unit goes down as activity level goes up. Fixed 5-16 Total Fixed Cost Example Monthly Basic Telephone Bill A fixed cost is a cost whose total dollar amount remains constant as the activity level changes. Your monthly basic telephone bill is probably fixed and does not change when you make more local calls. Number of Local Calls 5-17 Types of Cost Behavior Patterns Recall the summary of our cost behavior discussion from an earlier chapter. Summary of Variable and Fixed Cost Behavior Cost In Total Per Unit Variable Total variable cost is proportional to the activity level within the relevant range. Variable cost per unit remains the same over wide ranges of activity. Total fixed cost remains the same even when the activity level changes within the relevant range. Fixed cost per unit goes down as activity level goes up. Fixed 5-18 Fixed Cost Per Unit Example Monthly Basic Telephone Bill per Local Call Average fixed costs per unit decrease as the activity level increases. The fixed cost per local call decreases as more local calls are made. Number of Local Calls - 5-19 Types of Fixed Costs Committed Discretionary Long-term, cannot be significantly reduced in the short term. May be altered in the short-term by current managerial decisions Examples Examples Depreciation on Equipment and Real Estate Taxes Advertising and Research and Development 5-20 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. 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. 5-21 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. 5-22 Rent Cost in Thousands of Dollars Fixed Costs and Relevant Range 90 Relevant 60 Range 30 0 0 Total cost doesn’t change for a wide range of activity, and then jumps to a new higher cost for the next higher range of activity. 1,000 2,000 3,000 Rented Area (Square Feet) 5-23 Fixed Costs and Relevant Range The relevant range of activity for a fixed cost is the range of activity over which the graph of the cost is flat. Example: Office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows, more space is rented, increasing the total cost. - - 5-24 Fixed Costs and Relevant Range How does this type of fixed cost differ from a stepvariable cost? Step-variable costs can be adjusted more quickly and . . . The width of the activity steps is much wider for the fixed cost. 5-25 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. - 5-26 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. 5-27 Mixed Costs A mixed cost has both fixed and variable components. Consider the example of utility cost. Total Utility Cost Y Variable Cost per KW X Activity (Kilowatt Hours) Fixed Monthly Utility Charge - 5-28 Mixed Costs The tota l m ix e d cost line ca n be e x pre sse d a s a n e qua tion: Y = a + bX W he re : Total Utility Cost Y Variable Cost per KW X Activity (Kilowatt Hours) - Y = the tota l m ix e d cost a = the tota l fix e d cost (the ve rtica l inte rce pt of the line ) b = the va ria ble cost pe r unit of a ctivity (the slope of the line ) X = the le ve l of a ctivity Fixed Monthly Utility Charge - 5-29 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? Y = a + bX Y = $40 + ($0.03 × 2,000) Y = $100 5-30 Analysis of Mixed Costs Account Analysis and the Engineering Approach Each account is classified as either variable or fixed based on the analyst’s knowledge of how the account behaves. Cost estimates are based on an evaluation of production methods, and material, labor and overhead requirements. 5-31 Learning Objective 2 Use a scattergraph plot to diagnose cost behavior. 5-32 The Scattergraph Method Plot the data points on a graph (total cost vs. activity). Maintenance Cost 1,000’s of Dollars Y 20 * * * * 10 0 0 1 2 * ** * ** 3 4 X Patient-days in 1,000’s - 5-33 The Scattergraph Method Draw a line through the data points with about an equal numbers of points above and below the line. Maintenance Cost 1,000’s of Dollars Y 20 * * * * 10 0 0 1 2 * ** * ** 3 4 X Patient-days in 1,000’s - 5-34 The Scattergraph Method Maintenance Cost 1,000’s of Dollars Use one data point to estimate the total level of activity and the total cost. Y Total maintenance cost = $11,000 20 * * * * 10 * ** * ** Intercept = Fixed cost: $10,000 0 0 1 2 3 4 Patient-days in 1,000’s Patient days = 800 X 5-35 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 Variable cost per unit = $1,000 800 $ 11,000 10,000 $ 1,000 = $1.25/patient-day Y = $10,000 + $1.25X Total maintenance cost - Number of patient days - 5-36 Learning Objective 3 Analyze a mixed cost using the high-low method. - 5-37 The High-Low Method Assume the following hours of maintenance work and the total maintenance costs for six months. - 5-38 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 5-39 The High-Low Method Total Fixed Cost = Total Cost – Total Variable Cost Total Fixed Cost = $9,800 – ($8/hour × 800 hours) Total Fixed Cost = $9,800 – $6,400 Total Fixed Cost = $3,400 5-40 The High-Low Method The Cost Equation for Maintenance Y = $3,400 + $8.00X - 5-41 Quick Check ✓ Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? a. $0.08 per unit b. $0.10 per unit c. $0.12 per unit d. $0.125 per unit 5-42 Quick Check ✓ Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the variable portion of sales salaries and commission? Units Cost a. $0.08 per unit High level 120,000 $ 14,000 b. $0.10 per unit Low level 80,000 10,000 40,000 $ 4,000 c. $0.12 per unit Change d. $0.125 per unit $4,000 ÷ 40,000 units = $0.10 per unit 5-43 Quick Check ✓ Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 5-44 Quick Check ✓ Sales salaries and commissions are $10,000 when 80,000 units are sold, and $14,000 when 120,000 units are sold. Using the high-low method, what is the fixed portion of sales salaries and commissions? Total cost = Total fixed cost + a. $ 2,000 Total variable cost b. $ 4,000 $14,000 = Total fixed cost + c. $10,000 ($0.10 × 120,000 units) d. $12,000 Total fixed cost = $14,000 - $12,000 Total fixed cost = $2,000 5-45 Least-Squares Regression Method A method used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables. This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost. The goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors. 5-46 Least-Squares Regression Method • Software 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 also provides a statistic, called the R2, which is a measure of the goodness of fit of the regression line to the data points. 5-47 Least-Squares Regression Method R2 is the percentage of the variation in total cost explained by the activity. Y Total Cost 20 * * * *2 10 * ** * ** R varies from 0% to 100%, and the higher the percentage the better. 0 0 1 2 3 Activity 4 X 5-48 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. - 5-49 Learning Objective 4 Prepare an income statement using the contribution format. - 5-50 The Contribution Format Let’s put our knowledge of cost behavior to work by preparing a contribution format income statement. - 5-51 The Contribution Format Sales Revenue Less: Variable costs Contribution margin Total $ 100,000 60,000 $ 40,000 Less: Fixed costs Net operating income 30,000 $ 10,000 Unit $ 50 30 $ 20 The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs and provides for income. - 5-52 Uses of the Contribution Format The contribution income statement format is used as an internal planning and decision making tool. We will use this approach for: 1. Cost-volume-profit analysis (Chapter 6). 2. Budgeting (Chapter 9). 3. Segmented reporting of profit data (Chapter 12). 4. Special decisions such as pricing and make-orbuy analysis (Chapter 13). - 5-53 The Contribution Format Used primarily for external reporting. Used primarily by management. Least Squares Regression Using Microsoft Excel Appendix 5A 5-55 Learning Objective 5 Analyze a mixed cost using the least-squares regression method. 5-56 Simple Regression Analysis Example Matrix, Inc. wants to know its average fixed cost and variable cost per unit. Using the data to the right, let’s see how to do a regression using Microsoft Excel. 5-57 Simple Regression Using Excel You will need three pieces of information from your regression analysis: 1. Estimated Variable Cost per Unit (line slope) 2. Estimated Fixed Costs (line intercept) 3. Goodness of fit, or R2 To get these three pieces information we will need to use three different Excel functions. LINEST, INTERCEPT, & RSQ 5-58 Simple Regression Using Excel Place your cursor in cell F4 and press the = key. Click on the pull down menu and scroll down to “More Functions . . .” 5-59 Simple Regression Using Excel Scroll down to the “Statistical”, functions. Now scroll down the statistical functions until you highlight “SLOPE” - 5-60 Simple Regression Using Excel 1. In the Known_y’s box, enter C4:C19 for the range. 2. In the Known_x’s box, enter D4:D19 for the range. - - 5-61 Simple Regression Using Excel Here is the estimate of the slope of the line. 1. In the Known_y’s box, enter, C4:C19 for the range. 2. In the Known_x’s box, enter, D4:D19 for the range. - - 5-62 Simple Regression Using Excel With your cursor in cell F5, press the = key and go to the pull down menu for special functions. Select Statistical and scroll down to highlight the INTERCEPT function. - 5-63 Simple Regression Using Excel Here is the estimate of the fixed costs. 1. In the Known_y’s box, enter C4:C19 for the range. 2. In the Known_x’s box, enter D4:D19 for the range. - - 5-64 Simple Regression Using Excel Finally, we will determine the “goodness of fit”, or R2, by using the RSQ function. - - 5-65 Simple Regression Using Excel Here is the estimate of R2. 1. In the Known_y’s box, enter C4:C19 for the range. 2. In the Known_x’s box, enter D4:D19 for the range. - -

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