1、Chapter 10 Determining How Costs Behave,Cost Functions,Basic linear cost function equation: y = a + bx where: y = total costa = fixed cost componentb = slope coefficient (variable cost rate)x = the volume of the cost driver,Pages 355 - 356,Volume (x),Total Cost (y)a,Slope = b,Estimating Cost Functio
2、ns,Assume variations in total cost are explained by a single cost driver Assume that cost behaviour can be explained adequately assuming a linear cost function within the relevant rangeHow a cost is classified depends on: the cost object selected the time span under consideration the relevant rangeA
3、lways look for a cause-effect relationship when selecting a cost driver,Pages 357 - 358,Cost Estimation Approaches,1. Industrial Engineering Method also called work measurement analyze the input-output relationship in physical terms 2. Conference Method speak to managers familiar with how costs are
4、incurred 3. Account Analysis analyze accounting data directly 4. Quantitative Analyses high-low method linear regression,Pages 359 - 361,Steps in Estimating a Cost Function,1. Choose the dependent variable (the cost to be predicted using the cost function) 2. Identify the cost driver (x in the equat
5、ion y = a + bx) 3. Collect data 4. Plot the data and eliminate “extreme” observations 5. Estimate the cost function 6. Evaluate the estimated cost function,Pages 361 - 362,High-Low Method of Cost Estimation,Indirect $1,456LabourCosts$ $710,Pages 363 - 364,46 96 Machine Hours,xx x x xx x x,Variable c
6、ost = Change in cost / Change in volume= ($1,456 - $710) / (96 - 46) = $14.92 per MHFixed cost = Mixed cost at high point - variable cost= $1,456 - (96 x $14.92)= $23.68 per week,Regression Analysis Method,Regression analysis is a statistical method that measures the average amount of change in the
7、dependent variable (x) that is associated with a unit change in one or more independent variable (s) Simple linear regression - one independent variable Multiple regression - more than one independent variable Allows for the evaluation of the quality of the cost function Coefficient of determination
8、 (R-Squared) measures the goodness of fit of the line to the underlying data t-value measures the potential error of the estimated variables,Pages 364 - 366,Evaluating and Choosing Cost Drivers,In evaluating a cost driver look for:1. Economic plausibility Does it make sense that the cost driver woul
9、d explain changes in the cost2. Goodness of fit Does the cost equation match the underlying data3. Slope of the regression line A flat regression line (small amount of slope) indicates a weak relationship between the dependent and independent variables,Pages 366 - 357,Step Cost Function,Step Cost Fu
10、nction a cost function in which the cost is constant over various ranges of the cost driver, but increases in discrete amounts (or steps) as the cost driver moves from one range to the next,Pages 368 - 370,$,Volume,Step Variable Cost Function,$,Volume,Step Fixed Cost Function,Nonlinearity Cost Funct
11、ion,Nonlinear cost function a cost function in which the graph of total costs versus a single cost driver does not form a straight line within the relevant range,Pages 370 - 374,Time,Cumulative Total Volume,Nonlinear Cost Function (Learning Curve),Data “Problems”,Collection periods for variables dif
12、fer Some “variable” costs are actually allocated fixed costs Missing data points Errors in recording data points Lack of a homogeneous relationship between the dependent variable pool and cost driver Relationship between cost and cost driver is unstable Impact of inflation on data points over time,Pages 374 - 375,
