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Scatter Graph Method

Introduction

The scatter graph method is used to segregate mixed costs and is more accurate than the high-low method. Scatter-graph method segregates costs visually. By plotting relevant data points in a graph, the fixed and variable cost components can be determined.

What's in Here

In this tutorial, we will learn step by step how to use the scatter-graph method in calculating fixed and variable costs.

Cost Function

Like all other methods of cost segregation, the scatter graph method follows the same cost function:

y = a + bx

where: y = total cost; a = total fixed costs; b = variable cost per level of activity (or units); x = level of activity (or number of units).

Steps in Performing the Scatter Graph Method

  1. Plot the data points in a graph. The level of activity is placed on the x-axis (independent variable) and the total cost on the y-axis (dependent variable).
  2. Draw a straight line that estimates the line of best fit. The line of best fit is a line that represents all the data points in a given set. This line will be used in estimating the fixed costs and variable costs.
  3. The total fixed cost is equal to the y-intercept (the value of y at x=0, or the point where the line crosses the y-axis).
  4. The variable cost per unit or slope (b) can be computed using any two coordinates in the line of best fit.
    b = y2 - y1
      x2 - x1

Example

The following data was gathered for five production runs of ABC Company. Estimate the cost function using the scatter graph method.

Batch Units (x) Total Cost (y)
1 680 $29,800
2 820 $34,000
3 570 $27,500
4 660 $29,000
5 750 $31,900

Solution:

Step 1: Plot the data points in a graph.

Plotting data points on a graph

Step 2: Estimate the line of best fit.

Drawing line of best fit

Step 3: Determine the total fixed costs.

The total fixed cost is equal to the y-intercept. Based on the graph above, the line of best fit crosses the y-axis at approximately $12,000, hence total fixed costs is equal to $12,000.

a = $12,000

Step 4: Compute for the variable cost per unit.

The variable cost per unit or slope is computed using any two data points in the line of best fit. Let us use coordinates that we can easily determine: x=0, y=12,000 and x=900, y=36,000 (approximately).

b = y2 - y1 = 36,000 - 12,000 = 24,000
  x2 - x1   900 - 0   900

b = $ 26.67 per unit

Again, any two points found in the line of best fit can be used (e.g., at x=300, y=20,000; or at x=700, y=33,000.) It is advisable to use two data points whose values can be easily approximated or determined.

The cost function for this particular set using the scatter graph method is:
y = $12,000 + $26.67x.

Conclusion

Compared to the high-low method which considers the highest level and lowest level of activity only, the scatter graph method is more reliable since it considers all data points. However, drawing the line of best fit involves some estimation. This issue is addressed by an even more accurate method: computing for the fixed and variable costs mathematically through linear regression (next lesson).

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