Cost Behavior
9.8.2 Scatter-graph method
The scatter graph method (also called scatter plot or scatter chart method) involves estimating the fixed and variable elements of a mixed cost by a visual process.
The scatter-graph method requires that all recent, normal data observations be plotted on a cost (Y-axis) versus activity (X-axis) graph. Vertical axis of graph represents total costs and horizontal axis shows the volume of related activity.
Let us again use the example of Friends Corporation and review their activities for the last 6 months (see Illustration 9-14 from the previous section). First step is to plot the points, according to given data. Then a line that most closely represents a straight line composed of all the data points should be drawn. The graph is shown on Illustration 9-15.
Illustration 9-15: Scatter graph
The point where this line intersects the vertical axis is our fixed costs, or $14,000 in our case. The angle (slope) of the line can be calculated to give a fairly accurate estimate of the variable cost per unit. We can see from the graph that production of 20,000 DVDs will cost us $75,000 and production of 25,000 DVDs will cost $90,000. Knowing this information we can calculate the variable cost per unit.
X2-X1 |
= |
$90,000 - $75,000 |
= |
$15,000 |
= |
$3 |
Y2-Y1 |
25,000 – 20,000 |
5,000 |
When two variables are known, we may use them in the regression formula:
Y = F + V x X, where F is fixed costs and V is variable cost per unit.
So, the cost formula for activity looks like this:
Y = $14,000 + $3 x X
Using this formula we can predict the total cost of activity in the range of 10,000 to 28,000 DVDs per month and then separate them into fixed and variable components. For example, assume that production of 24,000 DVDs is planned for the next period. Using the formula we can predict that total costs would be equal to:
Y = $14,000 + $3 x 24,000 = $86,000
Of this total cost, $14,000 is fixed and $72,000 is variable.
This method is simple to use and provides clear representation of correlation between costs and volume of activity. However, the disadvantage of this method is difficulties that may appear when determining the location of the best-fit line.
9.8.3 Method of least squares
The most robust method of separating mixed costs is the least-squares regression method. This method requires the use of thirty or more past data observations, both the activity level in units produced and the total production cost for each. The method of least squares identifies the line that best fits the data points (the sum of the squared deviations is minimized). This method is the most sophisticated and provides the user with a measure of the goodness of fit, which can be used to assess the usefulness of the cost formula. Usually this method requires the use of software packages, and therefore will not be discussed in this lecture.
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