Cost Behavior: Analysis and Use Mar 3, 2004 Chapter 5

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Cost Behavior How a cost will react or change as the level of business activity changes Cost can be either variable, fixed or mixed Understanding cost behavior allows managers to predict what costs will be at various business activity levels This information is essential for managing your business efficiently

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Recall the summary of our cost behavior discussion from Chapter 2. Types of Cost Behavior Patterns

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Activity Base A measure of the event that causes the incurrence of a variable cost – a cost driver Units produce d Miles driven Labor hours Machine hours

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Minutes Talked Total Long Distance Telephone Bill True Variable Cost Example Your total long distance telephone bill is based on how many minutes you talk.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Minutes Talked Per Minute Telephone Charge Variable Cost Per Unit Example The cost per minute talked is constant. For example, 10 cents per minute.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Step-Variable Costs Activity Cost Total cost remains constant within a narrow range of activity.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Step-Variable Costs Activity Cost Total cost increases to a new higher cost for the next higher range of activity. i.e., hiring an additional supervisor or maintenance worker.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Relevant Range A range of business activity within which the assumptions made about cost behavior are valid. Variable costs on a per unit basis remain the same within the relevant range, and in total vary directly with the level of activity Fixed costs in total remain fixed within the relevant range, but will change on a per unit basis as the level of activity changes

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Number of Local Calls Monthly Basic Telephone Bill Total Fixed Cost Example Your monthly basic telephone bill is probably fixed and does not change when you make more local calls. Exh. 5-5

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Number of Local Calls Monthly Basic Telephone Bill per Local Call Fixed Cost Per Unit Example The fixed cost per local call decreases as more local calls are made. Exh. 5-5

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Cost Behavior - Examples Merchandisers Cost of Goods Sold Merchandisers Cost of Goods Sold Manufacturers Direct Material, Direct Labor, and Variable Manufacturing Overhead Manufacturers Direct Material, Direct Labor, and Variable Manufacturing Overhead Merchandisers and Manufacturers Sales commissions and shipping costs Merchandisers and Manufacturers Sales commissions and shipping costs Service Organizations Supplies and travel Service Organizations Supplies and travel Examples of normally variable costs Examples of normally fixed costs Merchandisers, manufacturers, and service organizations Real estate taxes, Insurance, Sales salaries, Depreciation, Advertising Merchandisers, manufacturers, and service organizations Real estate taxes, Insurance, Sales salaries, Depreciation, Advertising

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Examples Advertising and Research and Development Examples Advertising and Research and Development Examples Depreciation on Buildings and Equipment, Property Taxes Examples Depreciation on Buildings and Equipment, Property Taxes Types of Fixed Costs Discretionary May be altered in the short-term by current managerial decisions Discretionary May be altered in the short-term by current managerial decisions Committed Long-term, cannot be reduced in the short term. Committed Long-term, cannot be reduced in the short term.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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. Fixed Costs and Relevant Range Continue

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Rent Cost in Thousands of Dollars 0 1,000 2,000 3,000 Rented Area (Square Feet) Fixed Costs and Relevant Range 90 Relevant Range 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. Exh. 5-6

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin How does this type of fixed cost differ from a step-variable cost? Step-variable costs can be adjusted more quickly and... The width of the activity steps is much wider for the fixed cost. Fixed Costs and Relevant Range

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check Which of the following statements about cost behavior are true? aFixed costs per unit vary with the level of activity. bVariable costs per unit are constant within the relevant range. cTotal fixed costs are constant within the relevant range. dTotal variable costs are constant within the relevant range. Which of the following statements about cost behavior are true? aFixed costs per unit vary with the level of activity. bVariable costs per unit are constant within the relevant range. cTotal fixed costs are constant within the relevant range. dTotal variable costs are constant within the relevant range.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Fixed Monthly Utility Charge Variable Cost per KW Activity (Kilowatt Hours) Total Utility Cost X Y A mixed cost has both fixed and variable components. Consider the example of utility cost. Mixed Costs Total mixed cost

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Fixed Monthly Utility Charge Variable Cost per KW Activity (Kilowatt Hours) Total Utility Cost X Y Mixed Costs Total mixed cost Y = a + bX

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Separating Variable and Fixed Costs There are a number of methods for separating variable and fixed costs for a mixed cost total Scattergraph High-Low Method Least Squares Regression

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Plot the data points on a graph (total cost vs. activity) * Total Cost in 1,000’s of Dollars * * * * * * * * * Activity, 1,000’s of Units Produced X Y The Scattergraph Method

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin * Total Cost in 1,000’s of Dollars * * * * * * * * * Activity, 1,000’s of Units Produced X Y Quick-and-Dirty Method Intercept is the estimated fixed cost = $10,000 Draw a line through the data points with about an equal numbers of points above and below the line.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin * Total Cost in 1,000’s of Dollars * * * * * * * * * Activity, 1,000’s of Units Produced X Y Quick-and-Dirty Method The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units Vertical distance is the change in cost. Horizontal distance is the change in activity.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Calculating the Total Cost Y = a + bX “a” is the intersection of the slope line and the y axis (fixed cost) To find “b”, find a data point on the slope line, and determine the level of activity (x axis) and total cost (y axis) Solve for b using the above equation See example on page Disadvantages: Outliers, accuracy of line drawn through the dots

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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. The High-Low Method (Use example on page 204)

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Change  in cost Change in units The High-Low Method  Variable cost per unit = Change in cost ÷ change in units

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The High-Low Method  Variable cost per unit = $2,400 ÷ 3,000 units = $0.80 per unit

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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 (or do the same calculation with the low activity level)

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin  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 The High-Low Method

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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 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 Quick Check $4,000 ÷ 40,000 units = $0.10 per unit

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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 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 Quick Check

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Mixed Cost Equation If variable cost per unit is $.10 and fixed cost is $2,000 then what is the Total cost equation? Y = $2,000 + $.10(X)

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Hi-Lo Disadvantages Utilizes only two data points out of the entire data base; not enough for accurate results in cost analysis Outliers could cause a major discrepancy if they are selected as a high or low

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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 Method Least-squares regression also provides a statistic, called the R 2, that is a measure of the goodness of fit of the regression line to the data points.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Total Cost Activity * * * * * * * * * * Least-Squares Regression Method R 2 is the percentage of the variation in total cost explained by the activity. R 2 for this relationship is near 100% since the data points are very close to the regression line. X Y

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Total Cost Formula using Least Squares Method Use the data provided by the least squares for points a and b See example on page 210 Result of least squares method: Y = $3,431 + $0.759(X)

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Least Squares Disadvantages Outliers can also cause least squares to come up with a wrong answer. Always use least squares on conjunction with scatter grade to identify, and eliminate if necessary, outliers that may erroneously impact the results.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Comparison of Methods Scatter Graph Y = $3,300 + $0.79(X) High Low Y = $3,400 + $0.80(X) Least Squares Y = $3,431 + $0.759(X) Which one would you choose? Why?

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Let’s put our knowledge of cost behavior to work by preparing a contribution format income statement.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Contribution Margin Approach Provides the internal manager with an income statement geared directly to cost behavior; can predict future results Contribution margin is what is left after you subtract variable costs from sales This allows you to determine if you are selling enough product to cover your fixed costs and, therefore, earn a profit Provides ability to analyze profitability by product line, operation, etc.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Contribution Format ( Requires Segregation of variable and fixed cost) The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs and provides for income.

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The Contribution Format Used primarily for external reporting. Used primarily by management. Not GAAP

© The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin End of Chapter 5