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 the relevant data, the fixed and variable cost components can be determined from specific points on the graph.
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).
| b = | y2 - y1 |
| x2 - x1 |
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.
Step 2: Estimate the 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.
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).
The scatter-graph method is a graphical approach in calculating fixed and variable costs. By plotting data points on a graph, we can determine the cost function line; whereby the fixed and variable cost values can easily be derived.
