Cost Behavior: Analysis and Use Chapter 5 Cost Behavior: Analysis and Use

Types of Cost Behavior Patterns Recall the summary of our cost behavior discussion from Chapter 2.

The Activity Base Units produced Miles driven Labor hours Machine hours A measure of the event that causes the incurrence of a variable cost – a cost driver

True Variable Cost Example Your total long distance telephone bill is based on how many minutes you talk. Total Long Distance Telephone Bill Minutes Talked

Variable Cost Per Unit Example The cost per minute talked is constant. For example, 10 cents per minute. Per Minute Telephone Charge Minutes Talked

Total cost remains constant within a narrow range of activity. Step-Variable Costs Total cost remains constant within a narrow range of activity. Cost Activity

Step-Variable Costs Total cost increases to a new higher cost for the next higher range of activity. Cost Activity

The Linearity Assumption and the Relevant Range Exh. 5-4 The Linearity Assumption and the Relevant Range Relevant Range A straight line closely approximates a curvilinear variable cost line within the relevant range. Economist’s Curvilinear Cost Function Total Cost Accountant’s Straight-Line Approximation (constant unit variable cost) Activity

Total Fixed Cost Example Exh. 5-5 Total Fixed Cost Example Your monthly basic telephone bill is probably fixed and does not change when you make more local calls. Monthly Basic Telephone Bill Number of Local Calls

Fixed Cost Per Unit Example Exh. 5-5 Fixed Cost Per Unit Example The fixed cost per local call decreases as more local calls are made. Monthly Basic Telephone Bill per Local Call Number of Local Calls

Cost Behavior Examples of normally variable costs Merchandisers Cost of Goods Sold Service Organizations Supplies and travel Manufacturers Direct Material, Direct Labor, and Variable Manufacturing Overhead Merchandisers and Manufacturers Sales commissions and shipping costs Examples of normally fixed costs Merchandisers, manufacturers, and service organizations Real estate taxes, Insurance, Sales salaries Depreciation, Advertising

Types of Fixed Costs Committed Discretionary Examples Examples Long-term, cannot be reduced in the short term. Discretionary May be altered in the short-term by current managerial decisions Examples Depreciation on Buildings and Equipment Examples Advertising and Research and Development

Fixed Costs and Relevant Range 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. Continue

Fixed Costs and Relevant Range Exh. 5-6 Fixed Costs and Relevant Range 90 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. Relevant Range 60 Rent Cost in Thousands of Dollars 30 0 1,000 2,000 3,000 Rented Area (Square Feet)

Fixed Costs and Relevant Range Step-variable costs can be adjusted more quickly and . . . The width of the activity steps is much wider for the fixed cost. How does this type of fixed cost differ from a step-variable cost?

Which of the following statements about cost behavior are true? Quick Check  Which of the following statements about cost behavior are true? Fixed costs per unit vary with the level of activity. Variable costs per unit are constant within the relevant range. Total fixed costs are constant within the relevant range. Total variable costs are constant within the relevant range.

Fixed Monthly Utility Charge Mixed Costs A mixed cost has both fixed and variable components. Consider the example of utility cost. X Y Total mixed cost Total Utility Cost Variable Cost per KW Fixed Monthly Utility Charge Activity (Kilowatt Hours)

Fixed Monthly Utility Charge Mixed Costs X Y Total mixed cost Y = a + bX Total Utility Cost Variable Cost per KW Fixed Monthly Utility Charge Activity (Kilowatt Hours)

The Analysis of Mixed Costs Account Analysis Engineering Approach Scattergraph Plot High-Low Method Least-Square Regression Method

Account Analysis & Engineering Estimates 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.

The Scattergraph Method Plot the data points on a graph (total cost vs. activity). 0 1 2 3 4 * Total Cost in 1,000’s of Dollars 10 20 Activity, 1,000’s of Units Produced X Y

Quick-and-Dirty Method Draw a line through the data points with about an equal numbers of points above and below the line. Y 20 * * * * * * * * Total Cost in 1,000’s of Dollars * * 10 Intercept is the estimated fixed cost = $10,000 X 0 1 2 3 4 Activity, 1,000’s of Units Produced

Quick-and-Dirty Method The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units Y 20 * * * * * * * * Total Cost in 1,000’s of Dollars * * 10 Horizontal distance is the change in activity. Vertical distance is the change in cost. X 0 1 2 3 4 Activity, 1,000’s of Units Produced

The High-Low Method WiseCo recorded the following production activity and maintenance costs for two months: Using these two levels of activity, compute: the variable cost per unit; the fixed cost; and then express the costs in equation form Y = a + bX.

Changein cost Change in units The High-Low Method Variable cost per unit = Change in cost ÷ change in units Changein cost Change in units

The High-Low Method Variable cost per unit = $2,400 ÷ 3,000 units

The High-Low Method Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit Fixed cost = Total cost – Total variable cost Fixed cost = $9,800 – ($0.80 per unit × 8,000 units) Fixed cost = $9,800 – $6,400 = $3,400

The High-Low Method Variable cost = $2,400 ÷ 3,000 units = $0.80 per unit Fixed cost = Total cost – Total variable cost Fixed cost = $9,800 – ($0.80 per unit × 8,000 units) Fixed cost = $9,800 – $6,400 = $3,400 Total cost = Fixed cost + Variable cost (Y = a + bX) Y = $3,400 + $0.80X

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 $4,000 ÷ 40,000 units = $0.10 per unit

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

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, that is a measure of the goodness of fit of the regression line to the data points.

Least-Squares Regression Method R2 is the percentage of the variation in total cost explained by the activity. Y 20 * * * * * * * * * * Total Cost 10 R2 for this relationship is near 100% since the data points are very close to the regression line. X 0 1 2 3 4 Activity

Cost Estimation Methods Regression Analysis A statistical method used to create an equation relating independent (or X) variables to dependent (or Y) variables. Past data is used to estimate relationships between costs and activities. Dependent variables are caused by the independent variables. Independent variables are the cost drivers that are correlated with the dependent variables.

Cost Estimation Methods Regression Analysis The simple cost model is actually a regression model: TC = F + VX Caution: Before doing the analysis, take time to determine if a logical relationship between the variables exists. This model will only be useful within a relevant range of activity.

Cost Estimation Methods Regression Analysis A set of data can be regressed using several techniques: Manual computations SPSS or SAS Statistical Software Excel or other spreadsheet The result of the regression process is a regression model: TC = F + VX Each regression model has an R-square (R2) measure of how good the model is. Range of R2 = 0 to 1.0

Simple Regression Analysis Example Fasco wants to know it’s average fixed cost and variable cost per unit. Using the data to the right, let’s see how to do a regression using Excel.

Simple Regression Analysis Example You will need three pieces of information from your regression analysis: Estimated Variable Cost per Unit (line slope) Estimated Fixed Costs (line intercept) Goodness of fit, or R2 To get these three pieces of information we will need to use THREE different excel functions. LINEST, INTERCEPT, & RSQ

Simple Regression Using Excel 2000 First, open the excel file with your data and click on “Insert” and “Function”

Simple Regression Using Excel 2000 When the function box opens, click on “Statistical”, then on “LINEST”

Simple Regression Using Excel 2000 By clicking on the buttons to the left, you can highlight the desired cells directly from the spreadsheet. 1. Enter the cell range for the cost amounts in the “Known_y’s” box. 2. Enter the cell range for the quantity amounts in the “Known_x’s” box.

Simple Regression Using Excel 2000 The Slope, or estimated variable cost per unit, is identified here. Click OK to put this value on your spreadsheet.

Simple Regression Using Excel 2000 Repeat the procedure using “Intercept”, to estimate fixed cost.

Simple Regression Using Excel 2000 As previously, enter the appropriate cell ranges in their appropriate places. The estimated fixed cost is identified here.

Simple Regression Using Excel 2000 Finally, determine the “goodness of fit”, or R2, by using the RSQ function.

Simple Regression Using Excel 2000 As previously, enter the appropriate cell ranges in their appropriate places. The estimated R2 for your estimated cost function is identified here.

Let’s put our knowledge of cost behavior to work by preparing a contribution format income statement.

The Contribution Format The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs and provides for income.

The Contribution Format Used primarily for external reporting. Used primarily by management.

End of Chapter 5