Thescatterplot methodis a method of determining the equation of a line by plot- ting the data on a graph. The first step in applying the scatterplot method is to plot the data points so that the relationship between setup costs and activity level can be seen. This plot is referred to as a scattergraphand is shown in Exhibit 3-11. The vertical axis is total setup cost, and the horizontal axis is number of setup hours.
Inspecting Exhibit 3-11 gives us increased confidence that the assumption of a lin- ear relationship between setup costs and setup hours is reasonable for the indicated range of activity. Thus, one purpose of a scattergraph is to see whether or not an assumed linear relationship is reasonable. Additionally, inspecting the scattergraph may reveal several points that do not seem to fit the general pattern of behavior.
Upon investigation, it may be discovered that these points (the outliers) were due to some unusual occurrences. This knowledge may justify their elimination and per- haps lead to a better estimate of the underlying cost function.
A scattergraph can help provide insight concerning the relationship between cost and activity usage. In fact, a scattergraph allows one to visually fit a line to the points on the scattergraph. In doing so, the line chosen should be the one that appears to best fit the points. In making that choice, a manager or cost analyst is free to use past experience with the behavior of the cost item. Experience may provide a good intuitive sense of how setup costs behave; the scattergraph then becomes a useful tool to quantify this intuition. Fitting a line to the points in this
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C h a p t e r 3 / A c t i v i t y C o s t B e h a v i o r
Setup Cost
$4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500
100 200 300 400 500
Setup Hours
1 2
5
4 3
Exhibit 3-11
Scattergraph for Reddy Heaters, New Jersey Plantway is how the scatterplot method works. Keep in mind that the scattergraph and other statistical aids are tools that can help managers improve their judgment. Using the tools does not restrict the manager from using judgment to alter any of the esti- mates produced by formal methods.
Examine Exhibit 3-11 carefully. Based only on the information contained in the graph, how would you fit a line to the points in it? Suppose that you decide that a line passing through points 1 and 3 provides the best fit. If so, how could this deci- sion be used to compute the fixed cost and variable rate so that the fixed- and variable- cost components can be estimated?
Assuming your choice of the best-fitting line is the one passing through points 1 and 3, the variable cost per unit can be computed in the following way. First, let point 1 be designated by (100, $1,000) and point 3 by (300, $2,250). Next, use these two points to compute the slope:
Variable rate ($2,250 $1,000)/(300 100) $1,250/200
$6.25
Thus, the variable cost per setup hour is $6.25. Given the variable cost per unit, the final step is to compute the fixed-cost component. If we use point 3, the following equation results:
Fixed cost $2,250 ($6.25 300) $375
Of course, the fixed-cost component can also be computed using point 1, which produces the same result.
Fixed cost $1,000 ($6.25 100) $375
The fixed and variable components of setup cost have now been identified. The cost formula for the setup activity can be expressed as:
Total cost $375 ($6.25 Setup hours)
Using this formula, the total cost of setting up for between 100 and 500 setup hours can be predicted and then broken down into fixed and variable components. For example, assume that 350 setup hours are planned for June. Using the cost formula, the predicted cost is $2,562.50 [$375 ($6.25 350)]. Of this total cost, $375 is fixed and $2,187.50 is variable.
The cost formula for the setup activity was obtained by fitting a line to points 1 and 3 in Exhibit 3-11. Judgment was used to select the line. While one person may decide that the best-fitting line is the one that passes through points 1 and 3, others, using their own judgment, may decide that the line should pass through points 2 and 4, or points 1 and 5.
A significant advantage of the scatterplot method is that it allows us to see the data. Exhibit 3-12 gives examples of cost behavior situations that are not appropriate for a simple application of the high-low method. Graph A shows a nonlinear rela- tionship between activity cost and activity usage. An example of this might be a vol- ume discount given on direct materials or evidence of learning by workers (for example, as more hours are worked, the total cost increases at a decreasing rate due to the increased efficiency of the workers). Graph B shows an upward shift in cost if more than X1units are made. Perhaps this means that an additional supervisor must be hired or a second shift run. Graph C shows outliers that are not representative of the overall cost relationship.
The scatterplot method suffers from the lack of any objective criterion for choos- ing the best-fitting line. The quality of the cost formula depends on the quality of the subjective judgment of the analyst. The high-low method removes the subjectivity in the choice of the line. Regardless of who uses the method, the same line will result.
88 P a r t 2 / A c t i v i t y - B a s e d A c c o u n t i n g
The scatterplot and high-low methods produce equations with a large difference in fixed and variable components. Using these equations, the predicted setup cost for 350 setup hours is $2,562.50 according to the scatterplot method and $2,718.75 according to the high-low method. Which is “right”? Since the two methods can produce significantly different cost formulas, the question of which method is better naturally arises. Ideally, a method that is objective and, at the same time, produces the best-fitting line is needed. The method of least squares defines best fitting and is objective in the sense that using the method for a given set of data will produce the same cost formula.
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C h a p t e r 3 / A c t i v i t y C o s t B e h a v i o r
0 Activity Output
Activity Cost
Graph C––Presence of Outliers
0 Activity Output
Activity Cost
Graph B––Upward Shift in Cost Relationship
0 Activity Output
Activity Cost
Graph A––Nonlinear Relationship
X1
Exhibit 3-12
Cost Behavior Patterns90 P a r t 2 / A c t i v i t y - B a s e d A c c o u n t i n g
Setup Cost
$4,000 3,500 3,000 2,500 2,000 1,500 1,000 500
0 100 200 300 400 500
Setup Hours
5
4 3
2 1
5*