## 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 visually on a graph.

The scatter-graph method requires that all recent, normal data observations be plotted on a cost (Y-axis) versus activity (X-axis) graph. The vertical axis of the graph represents the total costs and the horizontal axis shows the volume of related activity.

Let us again use the example of Friends Company and review their activities for the past six months (see Illustration 14 from the previous section). The first step is to plot the points on a graph. Then draw a line that most closely represents a straight line composed of all the data points. The graph using data points from Illustration 14 is shown in Illustration 15:

Illustration 15: Scatter graph

The point where this line intersects the vertical axis is the 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 valves will cost Friends Company \$75,000 and production of 25,000 valves will cost \$90,000. Knowing this information we can calculate the variable cost per unit:

 Y2 - Y1 = \$90,000 - \$75,000 = \$15,000 = \$3 X2 - X1 25,000 - 20,000 5,000

When the two variables become known, we can use them in the cost formula:

Y = F + V x X,

where F is the fixed cost, V is the variable cost per unit, and X is the production level.

So, the cost formula looks like this:

Y = \$14,000 + \$3 x X

Using this formula we can calculate the total costs of activity in the range of 10,000 to 28,000 valves per month and then separate them into fixed and variable components. For example, assume that production of 24,000 valves is planned for the next period. Using the formula we can determine that the total costs would be:

Y = \$14,000 + \$3 x 24,000 = \$86,000

\$14,000 is fixed and \$72,000 is variable, for a total of \$86,000 (\$14,000 + \$72,000).

This method is simple to use and provides clear representation of correlation between costs and the volume of activity. However, the disadvantage of this method is the difficulty in determining the location of the best-fit line.

## 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 30 or more past data observations for both the activity level (in units) and the total costs. 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 tutorial.

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