Prepared by Diane Tanner University of North Florida ACG Cost Estimation 4-1

Cost Behavior Unit cost remains the same amount at all activity levels 2 Fixed Costs Total cost is the same amount at all activity levels Variable Costs If a cost is neither fixed or variable, by default, it is a mixed cost. Mixed Costs Mixed costs must be separated into fixed and variable components using one of the cost estimation methods.

Cost Functions  Measured by determining a relationship (behavior) based on data from past costs and the related level of an activity  Goal is to determine a cause-and-effect relationship  Arises due to  A physical relationship between the activity and costs  A contractual agreement  Knowledge of operations  Understanding how costs behave enables managers to estimate future costs The key to planning

Cost Functions  Format of a linear cost function  TC = VCx + TFC  Y = mX + b  Y = a + bX  Dependent variable = y  Independent variable = x  Assumptions  Variations in the level of a single activity (cost driver) explain the variation in the related total cost  Costs behave in a linear manner within the relevant range of activity  A linear cost function is represented by a straight line 4 M = VC per unit = slope b = TFC = y -intercept Driver Predicted cost

Sample Cost Functions  Fixed cost function Y = 250  Variable cost function Y = 4.56x  Mixed cost function (semi-variable) Y = 4.56x TC = VCx + TFC Unit costs always displayed with 2 decimals Total costs always displayed with no decimals A note on ‘standard’ cost equation format…..

Cost Estimation Methods  Industrial engineering method  Estimates cost functions by analyzing the relationship between inputs and outputs in physical terms  Conference method  Estimates cost functions based on analysis and opinions about costs and their drivers gathered from various departments of a company  Account analysis method  Estimates cost functions by classifying various cost accounts with respect to the identified level of activity  Reasonably accurate, cost-effective, subjective  Quantitative analysis methods  Mathematical models – high-low, regression 6

Account Analysis Method  Requires considerable subjective judgment and insight  Most often used by accountants or managers who are familiar with the nature of costs within a general ledger account (often multiple accounts)  Managers examine costs and guess the most likely type of cost behavior  Is the only method to assess cost behavior when only one period of data is known.

Performing Account Analysis Step 1: Each cost is examined and separated into a fixed or variable pile based on a ‘best guess’ label of fixed or variable Step 2: All variable costs are totaled and divided by the number of cost object units Step 3: All fixed costs are totaled Step 4: Write the cost equation in standard form (replacing VC and FC with the correct amounts) TC = VCx + TFC

Quantitative Analysis of Cost Functions Step 1: Identify the dependent variable  The cost being estimated or predicted, Y Step 2: Identify the independent variable  The independent variable, i.e., the cost driver, X Step 3: Collect data Step 4: Plot the data - scattergraph Step 5: Estimate the function  Regression method or high-low method Step 6: Evaluate the cost driver 9

High-Low Method  Focuses on the highest and lowest activity levels of the data set  Based on ‘activity’ because activity drives costs  Advantages  Simple  Gives quick insight in cost-activity relationships  Disadvantages  Uses extreme data points  Ignores much of the data 10

High-Low Method Step 1: Choose high and low activity levels Step 2: Calculate the variable cost per unit. 11 [Cost of the highest activity level ― Cost of the lowest activity level] [Highest activity level ― Lowest activity level] Step 3: Calculate the total fixed costs. Total cost = [Variable cost per unit × Activity level] +TFC Choose the data of ONE of the two data points, and insert into the total cost equation. Step 4: Express in standard cost equation form. TC = VCx + TFC Solve for TFC.

High-Low Method Example High and low activity levels: January and April Variable cost per unit: 12 [$95,000 ― $92,000] [68,000― 60,000] $95,000 = [$0.375 × 68,000] + TFC Standard cost equation: TC = 0.38x + 69,500 Marx Inc. supplied the following data: MilesTotal Cost January 60,00092,000 February 65,00096,000 March 62,00090,000 April 68,00095,000 = $0.375 per unit Total fixed costs: TFC = $69,500

Linear Regression Analysis A statistical technique that measures the relationship between two sets of variables –Assesses how effective a cost driver is Uses all the data points Provides a more accurate cost estimation formula than the high-low method Excel ® generates linear regression output providing cost function components Three criterion used by accountants to assess cost drivers –Economic plausibility –Goodness of fit –Steepness of slope 13

Excel ® Regression Output 14 X-variable Y-intercept Cost equation: Y = 0.58x + 3,772 Cost equation: Y = 0.58x + 3,772 Wayco ran a regression of the the number of items shipped to customers and the shipping cost

Economic Plausibility 15 Does it make sense? It is logical to assume that as more packages are shipped, that total cost will increase. Does it make sense? It is logical to assume that as more packages are shipped, that total cost will increase. Cost equation: Y = 0.58x + 3,772 Cost equation: Y = 0.58x + 3,772

Goodness of Fit 16  A predictor of how good the cost driver is  Indicates the percentage of the total variation in the y-values (total cost) that is explained by the regression equation.  A predictor of how good the cost driver is  Indicates the percentage of the total variation in the y-values (total cost) that is explained by the regression equation. R2 Interpretation: About 98.2% of the variation in total cost is explained by the number of packages shipped

Steepness of Slope  Indicates the strength of the relationship between the cost driver and the costs incurred  Measures the significance of the independent variable  When comparing multiple drivers, drivers with steeper slopes are more reliable 17

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