1Chapter 10Determining How Costs BehaveOmit section on Learning Curves pp 349-362Online Quiz: omit MC #10,11,12Topics Cost Behavior Assumptions Linear Cost Functions Non-linear cost functions Cost-estimation methods Learning curves-OMIT Data CollectionCost Behavior Assumptions Lineary = bx + a ory = mx + bslope and y intercept One cost driverCost Functions Variable Fixed Mixed Step CurvilinearVariable Costs Total costs increase directly with volume Unit cost remain constant as volume changesCostvolumeEquation for a straight lineY = mx + bm = slope = (y2-y1) / (x2-x1) b = y interceptb = y2–mx2 or b = y1–mx12Example (cont)Slope = 10y = mxm = slope = variable cost per unitb = zeroy=10xFixed Costs Total cost remains constant as volume changes Unit cost varies inversely with changes in volumeCOSTFixed Cost Equation: y = bExample : graphSlope = 01000y=1000Mixed costs Contain both a fixed and variable component Increases with volume but not proportionately Example:  pay a base salary plus a commission Rent is a set fee per month plus a percent of salesMixed cost equationy = mx + bm = variable component per unitb = fixed costSlope = variable cost per unitIntercept = fixed costsWhat if cost function is curvilinear?3What if cost function is curvilinear?Relevant rangeEstimate with a mixed cost functionWhat if the cost is a step fixed cost?step fixed coststep fixed costEstimate with a fixed cost functionstep fixed costRelevant rangeEstimate with a fixed cost functionOr estimate with a mixed cost functionEstimate with a mixed cost functionMethods to Estimate Cost Function Account analysis  Engineering analysis Conference Method High Low  Scatter Graph  RegressionMethods (cont) Account analysis Review accounts and based on prior experience, classify as fixed or variable Depreciation is fixed, cost of goods sold is variable Total costs are mixed Problem: rough estimate  Quick Conference Method Opinions from various departments4Methods (cont.) Engineering analysis Work measurement method Observe, measure Example: weigh raw material, price per unitmeasure the number of DL hours, determine hourly rateProblem: not practical for all costsMethods (cont.) High low method Collect data points from historical records Select 2 points to determine equation Problem May select outliers Not all data points are usedMethods (cont) Scatter graph (visual fit) Collect data points from historical records Graph all the data points Draw a line that “Best fits” Select 2 points from the line, compute the equation Problem: need graph paper, not preciseMethods (cont.) Linear regression Collect data points from historical records Use a mathematical model that computes an equation based on all points Problem:  very complex formulas very precise but not necessarily accurate uses outliersExample: Estimate shipping cost functionMonthUnits ShippedActual Shipping CostJan 3 18$ Feb 6 23$ Mar 4 17$ Apr 5 20$ May 7 23$ Jun 8 27$ Jul 2 12$ Historical Data: Graph of Actual Data Points01020300510UnitsCostActual ShippingCost5High Low example Select high and low data points: High: Low:MonthUnits ShippedActual Shipping CostJan 3 18$ Feb 6 23$ Mar 4 17$ Apr 5 20$ May 7 23$ Jun 8 27$ Jul 2 12$ High Low example Select high and low data points: High: June (8,27) Low: July (2, 12)MonthUnits ShippedActual Shipping CostJan 3 18$ Feb 6 23$ Mar 4 17$ Apr 5 20$ May 7 23$ Jun 8 27$ Jul 2 12$ High Low exampleDevelop the equation y = mx + bm = slope = (y2-y1) / (x2-x1) b = y intercept = y2–mx2 or y1–mx1High low example (continued)m = (27-12) / (8-2)= 15/6 = 2.5b = 27-8*2.5= 27 – 20 = 7y = 2.5 x + 7High: June (8,27)Low: July (2, 12)b=12-(2)*(2.5) = 7HiLow vrs. Actua lJulJanMa rAprFeb MayJun051015202530012345678Units ShippedAc tual Shipping CostHi Low Shipping example:Scatter graph Graph of Actual Data Points01020300510UnitsCostActual ShippingCost6Draw a line that “best fits”Scatter Graph01020300510UnitsCostActu alShippingCostScatterSelect any 2 points that fall on the lineScatter Graph01020300510UnitsCostActu alShippingCostScatter4, 18 7,254,187,25Develop the equation from the 2 points (4,18) and (7,25)m =b =y =Develop the equation from the 2 points (4,18) and (7,25)m = (25-18) / (7-4) = 7 /3 =2.333b = 25 – 2.33 * 7 = 25 –16.33 =8.667y = 2.33 x + 8.67Shipping example: regression Use EXCEL Enter data points in adjacent columns click on Tools Data Analysis, Regression May have to load ADD INS Select the x range, y range, output rangeY = 2.18 x + 9.117Regression Analysis: Coefficient of Determination  R2 Goodness of Fit Proportion of the variation in y explained by x 0 to 1 1Îperfect explanatory power Good fit if R2>30%Standard Error of the estimated coefficientindicates how much of the estimated value is likely to be affected by random factors T Stat: indicates how large the value of the estimated coefficient is relative to its standard error; the larger the better (>2.5 for small samples)Re g re ss vrs HL vrs S c a t t vrs Actu a l0510152025300123456789Actual Shipping CostHi LowScatterRegressionRecap High low: y = 2.5x + 7 Scatter y = 2.333x + 8.67 Regression y = 2.179x + 9.107Outliers: same data except June is 8,40 instead of 8,27Re gr e ss vrs HL vr s S ca tt vr s Ac tu a l051015202530354045012345678Actual ShiHi LowScatterRegressioData Collection Many observations of cost and cost driver Collect a wide range of cost driver observations Problems: Time periods for cost and cost driver do not match Fixed costs are unitized Observations from outside the relevant range Missing observations Costs are not homogeneous  Relationship between cost and cost driver is not stationary