© 2009 Pearson Prentice Hall. All rights reserved. Determining How Costs Behave

© 2009 Pearson Prentice Hall. All rights reserved. COST BEHAVIOR PATTERNS Understanding cost behavior patterns (i.e., the relationship between cost and activity) is important to managers as they plan, control, and make decisions in the operation of their organizations. (For example, a manager must understand how costs behave across various levels of activity before a budget can be prepared.)

© 2009 Pearson Prentice Hall. All rights reserved. COST BEHAVIOR PATTERNS Cost Estimation: The process of determining cost behavior. Often focuses on historical data. Cost Behavior: The relationship between cost and activity. Cost Prediction: Using knowledge of cost behavior to forecast the level of cost at a particular level of activity. Focus is on the future. Cost estimation Cost behavior Cost prediction

© 2009 Pearson Prentice Hall. All rights reserved. Cost Terminology Variable Costs – costs that change in total in relation to some chosen activity or output (cost driver)  Example: the paper cost in giving exams varies with the number of students in a class. Step-variable costs are nearly variable, but such costs increase in small steps rather than in direct proportion to cost-driver changes.  Example: if a class is a bit larger than usual, an additional exam proctor may have to be hired. This increase in part-time hourly help increases by a step as the class size grows.

© 2009 Pearson Prentice Hall. All rights reserved. Cost Terminology Fixed Costs – costs that do not change in total in relation to some chosen activity or output  Example: a professor’s salary is fixed, and more students enrolled in his or her course will not affect salary. However, the salary cost per student will vary depending on class size. Step-fixed costs are fixed within a wide range of activity but will change outside that range  Example: if a course increases by a large number of students, it will be necessary to add another section and hire another instructor. The fixed cost then jumps to another step.

© 2009 Pearson Prentice Hall. All rights reserved. Cost Terminology Mixed Costs – costs that have both fixed and variable components; also called semivariable costs  Example: a printer’s fee for brochures, which includes a fixed set-up cost and a per-copy (i.e., variable) charge for running the total copies needed.

© 2009 Pearson Prentice Hall. All rights reserved. Cost Terminology An engineered cost is one that bears a definite physical relationship to the cost driver. Example: the food cost of a restaurant, as it is impossible to serve more meals without incurring more food cost. Committed costs result from an organization’s ownership or use of facilities and its basic organizational structure. These costs cannot be eliminated without endangering the entity’s overall health and existence. Examples: property taxes, depreciation on buildings and equipment, top management salaries.

© 2009 Pearson Prentice Hall. All rights reserved. Cost Terminology Discretionary costs exist as the result of a management decision. In comparison with committed costs, such costs are more easily changed in bad economic times without doing serious long-run harm to the entity.  Examples: a training program, an advertising campaign, corporate contributions. Fixed costs are becoming more prevalent in many industries because of automation and labor unions’ success in negotiating for a stable workforce. Costs that were once variable are becoming fixed, which makes a company less able to respond rapidly to changing economic conditions.

© 2009 Pearson Prentice Hall. All rights reserved. Cost Terminology A curvilinear cost function cannot be represented with a straight line but instead is represented with a curve that reflects either increasing or decreasing marginal costs. Relevant range— the range of activity within which managers expect a company to operate and within which managers can predict cost behavior with some certainty.  Within the relevant range, even curvilinear costs may behave in a linear fashion.

© 2009 Pearson Prentice Hall. All rights reserved. Cost Functions A cost function is a mathematical representation of how a cost changes with changes in the level of an activity relating to that cost Examples of activities are preparing setups for production runs and operating machines.

© 2009 Pearson Prentice Hall. All rights reserved. Cost Function Assumptions 1. Variations in the level of a single activity (the cost driver) explain the variations in the related total costs 2. Cost behavior is approximated by a linear cost function within the relevant range Graphically, the total cost versus the level of a single activity related to that cost is a straight line within the relevant range

© 2009 Pearson Prentice Hall. All rights reserved. Bridging Accounting & Statistical Terminology AccountingStatistics Variable CostSlope Fixed CostIntercept Mixed CostLinear Cost Function

© 2009 Pearson Prentice Hall. All rights reserved. The Linear Cost Function y = a + bX The Dependent Variable: The cost that is being predicted The Independent Variable: The cost driver The Intercept: Fixed Costs The slope of the line: variable cost per unit

© 2009 Pearson Prentice Hall. All rights reserved. Linear Cost Functions Illustrated

© 2009 Pearson Prentice Hall. All rights reserved. Criteria for Classifying Variable & Fixed Components of a Cost 1. Choice of Cost Object – different objects may result in different classification of the same cost 2. Time Horizon – the longer the period, the more likely the cost will be variable 3. Relevant Range – behavior is predictable only within this band of activity

© 2009 Pearson Prentice Hall. All rights reserved. The Relevant Range Illustrated

© 2009 Pearson Prentice Hall. All rights reserved. Cause & Effect as it relates to Cost Drivers The most important issue in estimating a cost function is determining whether a cause-and-effect relationship exists between the level of an activity and the costs related to that level of activity.

© 2009 Pearson Prentice Hall. All rights reserved. Cause & Effect as it relates to Cost Drivers A cause-and-effect relationship might arise as a result of: A physical relationship between the level of activity and costs A contractual agreement Knowledge of operations Note: a high correlation (connection) between activities and costs does not necessarily mean causality

© 2009 Pearson Prentice Hall. All rights reserved. Cost Estimation Methods 1. Industrial Engineering Method 2. Conference Method 3. Account Analysis Method 4. Quantitative Analysis Methods 1. High-Low Method 2. Regression Analysis

© 2009 Pearson Prentice Hall. All rights reserved. Industrial Engineering Method Estimates cost functions by analyzing the relationship between inputs and outputs in physical terms Includes time-and-motion studies Very thorough and detailed, but also costly and time- consuming Also called the Work-Measurement Method

© 2009 Pearson Prentice Hall. All rights reserved. Conference Method Estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of a company Pools expert knowledge Reliance on opinions still make this method subjective

© 2009 Pearson Prentice Hall. All rights reserved. Account Analysis Method The account-classification method (also called account analysis) requires the study of an account in the general ledger. The experienced analyst uses the account information as well as his or her own judgment to determine future cost behavior estimates cost functions by classifying various cost accounts as variable, fixed or mixed with respect to the identified level of activity Is reasonably accurate, cost-effective, and easy to use, but is subjective

© 2009 Pearson Prentice Hall. All rights reserved. Quantitative Analysis Method Uses a formal mathematical method to fit cost functions to past data observations Advantage: results are objective

© 2009 Pearson Prentice Hall. All rights reserved. Steps in Estimating a Cost Function Using Quantitative Analysis 1. Choose the dependent variable (the cost to be predicted) 2. Identify the independent variable or cost driver 3. Collect data on the dependent variable and the cost driver 4. Plot the data 5. Estimate the cost function using the High-Low Method or Regression Analysis 6. Evaluate the cost driver of the estimated cost function

© 2009 Pearson Prentice Hall. All rights reserved. AN EXAMPLE WeekCost Driver :Indirect Manufacturing: machine HoursLabor Costs ($) (X)(Y) 168 1, , , , , , , Total862 12,501

© 2009 Pearson Prentice Hall. All rights reserved. Visual-Fit method With the visual-fit method, an analyst examines a cost by plotting points on a graph (called a scatter diagram) and places a line through the points to yield a cost function. This method is more objective than the account- classification method, but it is still lacking because two cost analysts could visually fit different lines. The visual-fit method is useful because it helps spot nonrepresentative data points, or outliers.

© 2009 Pearson Prentice Hall. All rights reserved. Sample Cost – Activity Plot

© 2009 Pearson Prentice Hall. All rights reserved. High-Low Method Simplest method of quantitative analysis Uses only the highest and lowest observed values

(c) 2009 Pearson Prentice Hall. All rights reserved. Steps in the High-Low Method 1. Calculate variable cost per unit of activity

(c) 2009 Pearson Prentice Hall. All rights reserved. Steps in the High-Low Method 2. Calculate Total Fixed Costs 3. Summarize by writing a linear equation

© 2009 Pearson Prentice Hall. All rights reserved. AN EXAMPLE WeekCost Driver :Indirect Manufacturing: machine HoursLabor Costs ($) (X)(Y) 168 1, , , ,456 Highest Level 778 1, lowest level 982 1, , Total862 12,501

© 2009 Pearson Prentice Hall. All rights reserved. High low Method Cost Driver:Indirect Manufacturing Machine Hours (X)Labor Costs(Y) Highest observation of cost driver ( week 6) 96 1,456 lowest observation of cost driver ( week 8) Difference The Slope Co-efficient is calculated as: Difference between costs associated with Highest and Lowest observations of the cost driver Slope Co-efficient = ____________________________________________ Difference between Highest and Lowest observations of the cost driver = 746/50 Machine hours = $14.92 per machine-hour

© 2009 Pearson Prentice Hall. All rights reserved. High low Method At the highest observation of the cost driver, the constant, a, is calculated as : Constant= $1,456-($14.92 per machine hr * 96 Machine hrs) = $23.68 At the lowest observation of the cost driver Constant= $710-($14.92 per machine hr * 46 Machine hrs) = $23.68 Thus, the high-low estimate of the cost function is : Y= a + bX Y= $ ($14.92 per Machine Hr * Number of Machine Hrs)

© 2009 Pearson Prentice Hall. All rights reserved. High – Low Method Plot

© 2009 Pearson Prentice Hall. All rights reserved. Regression Analysis Regression analysis is a statistical method that measures the average amount of change in the dependent variable associated with a unit change in one or more independent variables Is more accurate than the High-Low method because the regression equation estimates costs using information from all observations; the High- Low method uses only two observations

© 2009 Pearson Prentice Hall. All rights reserved. Types of Regression Simple – estimates the relationship between the dependent variable and one independent variable Multiple – estimates the relationship between the dependent variable and two or more independent variables

© 2009 Pearson Prentice Hall. All rights reserved. AN EXAMPLE WeekCost Driver :Indirect Manufacturing: machine HoursLabor Costs ($) (X)(Y) 168 1, , , , , , , Total862 12,501

© 2009 Pearson Prentice Hall. All rights reserved. Sample Regression Model Plot

© 2009 Pearson Prentice Hall. All rights reserved. AN EXAMPLE MonthCost Driver :Indirect Manufacturing: Direct Labor HoursElectricity Costs ($) (X)(Y) January34, February30, March34, April39, May42, June32, July26, August26, September31, October35, November43, December48, Total420,000 6,840

© 2009 Pearson Prentice Hall. All rights reserved. Alternative Regression Model Plot

© 2009 Pearson Prentice Hall. All rights reserved. Terminology Goodness of Fit – indicates the strength of the relationship between the cost driver and costs Residual Term – measures the distance between actual cost and estimated cost for each observation

© 2009 Pearson Prentice Hall. All rights reserved. Criteria for Evaluating Alternative Cost Drivers 1. Economic Plausibility 2. Goodness of Fit 3. Significance of the Independent Variable

© 2009 Pearson Prentice Hall. All rights reserved. Nonlinear Cost Functions 1. Economies of Scale 2. Quantity Discounts 3. Step Cost Functions – resources increase in “lot- sizes”, not individual units 4. Learning Curves – labor hours consumed decrease as workers learn their jobs and become better at them 5. Experience Curve – broader application of learning curve that includes Downstream activities including marketing and distribution

© 2009 Pearson Prentice Hall. All rights reserved. Nonlinear Cost Functions Illustrated

© 2009 Pearson Prentice Hall. All rights reserved. A learning curve is a function that measures how labor-hours per unit decline as unit of production increase because workers are learning and becoming better at their jobs.

© 2009 Pearson Prentice Hall. All rights reserved. Types of Learning Curves Cumulative Average-Time Learning Model – cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced doubles. Rayburn has an 80% learning curve. Incremental Unit-Time Learning Model – incremental time needed to produce the last unit declines by a constant percentage each time the cumulative quantity of units produced doubles

© 2009 Pearson Prentice Hall. All rights reserved. Sample Cumulative Average-Time Model

© 2009 Pearson Prentice Hall. All rights reserved. Sample Incremental Unit-Time Model

© 2009 Pearson Prentice Hall. All rights reserved. Time Learning Model Comparative Plots

© 2009 Pearson Prentice Hall. All rights reserved. Predicting Costs Using Alternative Time Learning Models

© 2009 Pearson Prentice Hall. All rights reserved. The Ideal Database 1. The database should contain numerous reliably measured observations of the cost driver and the costs 2. In relation to the cost driver, the database should consider many values spanning a wide range

© 2009 Pearson Prentice Hall. All rights reserved. Data Problems The time period for measuring the dependent variable does not match the period for measuring the cost driver Fixed costs are allocated as if they are variable Data are either not available for all observations or are not uniformly reliable

© 2009 Pearson Prentice Hall. All rights reserved. Data Problems Extreme values of observations occur from errors in recording costs There is no homogeneous relationship between the cost driver and the individual cost items in the dependent variable-cost pool. A homogeneous relationship exists when each activity whose costs are included in the dependent variable has the same cost driver

© 2009 Pearson Prentice Hall. All rights reserved. Data Problems The relationship between the cost driver and the cost is not stationary Inflation has affected costs, the driver, or both

© 2009 Pearson Prentice Hall. All rights reserved.