Short-Term Decision-Making

Question: Many organizations prefer to use the scattergraph method to estimate costs. Accountants who use this approach are looking for an approach that does not simply use the highest and lowest data points. How is the scattergraph method used to estimate fixed and variable costs?

Answer: The scattergraph method considers all data points, not just the highest and lowest levels of activity. Again, the goal is to develop an estimate of fixed and variable costs stated in equation form Y = f + v X. Using the same data for Bikes Unlimited shown in Table 5.4 "Monthly Production Costs for Bikes Unlimited", we will follow the five steps associated with the scattergraph method:

Step 1. Plot the data points for each period on a graph.

Step 2. Visually fit a line to the data points and be sure the line touches one data point.

Step 3. Estimate the total fixed costs (f).

Step 4. Calculate the variable cost per unit (v).

Step 5. State the results in equation form Y = f + vX.

Question: How are the five steps of the scattergraph method used to estimate total fixed costs and per unit variable cost?

Answer: Each of the five steps is described next.

Step 1. Plot the data points for each period on a graph.

This step requires that each data point be plotted on a graph. The x-axis (horizontal axis) reflects the level of activity (units produced in this example), and the y-axis (vertical axis) reflects the total production cost. Figure 5.5 "Scattergraph of Total Mixed Production Costs for Bikes Unlimited" shows a scattergraph for Bikes Unlimited using the data points for 12 months, July through June.

Figure 5.5 Scattergraph of Total Mixed Production Costs for Bikes Unlimited

Step 2. Visually fit a line to the data points and be sure the line touches one data point.

Once the data points are plotted as described in step 1, draw a line through the points touching one data point and extending to the y-axis. The goal here is to minimize the distance from the data points to the line (i.e., to make the line as close to the data points as possible). Figure 5.6 "Estimated Total Mixed Production Costs for Bikes Unlimited: Scattergraph Method" shows the line through the data points. Notice that the line hits the data point for July (3,500 units produced and $230,000 total cost).

Figure 5.6 Estimated Total Mixed Production Costs for Bikes Unlimited: Scattergraph Method

Step 3. Estimate the total fixed costs (f).

The total fixed costs are simply the point at which the line drawn in step 2 meets the y-axis. This is often called the y-intercept. Remember, the line meets the y-axis when the activity level (units produced in this example) is zero. Fixed costs remain the same in total regardless of level of production, and variable costs change in total with changes in levels of production. Since variable costs are zero when no units are produced, the costs reflected on the graph at the y-intercept must represent total fixed costs. The graph in Figure 5.6 "Estimated Total Mixed Production Costs for Bikes Unlimited: Scattergraph Method" indicates total fixed costs of approximately $45,000. (Note that the y-intercept will always be an approximation.)

Step 4. Calculate the variable cost per unit (v).

After completing step 3, the equation to describe the line is partially complete and stated as Y = $45,000 + vX. The goal of step 4 is to calculate a value for variable cost per unit (v). Simply use the data point the line intersects (July: 3,500 units produced and $230,000 total cost), and fill in the data to solve for v (variable cost per unit) as follows:

\( \begin{aligned} \mathrm{Y} &=f+v \mathrm{X} \\ \$ 230,000 &=\$ 45,000+(v \times 3,500) \\ \$ 230,000-\$ 45,000 &=v \times 3,500 \\ \$ 185,000 &=v \times 3,500 \\ v &=\$ 185,000 \div 3,500 \\ v &=\$ 52.86 \text { (rounded) } \end{aligned} \)

Thus variable cost per unit is $52.86.

Step 5. State the results in equation form Y = f + vX.

We know from step 3 that the total fixed costs are $45,000, and from step 4 that the variable cost per unit is $52.86. Thus the equation used to estimate total costs looks like this:

Y = $45,000 + $52.86X

Now it is possible to estimate total production costs given a certain level of production (X). For example, if Bikes Unlimited expects to produce 6,000 units during August, total production costs are estimated to be $362,160:

\( \begin{aligned} \mathrm{Y} &=\$ 45,000+(\$ 52.86 \times 6,000 \text { units }) \\ \mathrm{Y} &=\$ 45,000+\$ 317,160 \\ \mathrm{Y} &=\$ 362,160 \end{aligned} \)

Question: Remember that the key weakness of the high-low method discussed previously is that it considers only two data points in estimating fixed and variable costs. How does the scattergraph method mitigate this weakness?

Answer: The scattergraph method mitigates this weakness by considering all data points in estimating fixed and variable costs. The scattergraph method gives us an opportunity to review all data points in the data set when we plot these data points in a graph in step 1. If certain data points seem unusual (statistics books often call these points outliers), we can exclude them from the data set when drawing the best-fitting line. In fact, many organizations use a scattergraph to identify outliers and then use regression analysis to estimate the cost equation Y = f + vX. We discuss regression analysis in the next section.

Although the scattergraph method tends to yield more accurate results than the high-low method, the final cost equation is still based on estimates. The line is drawn using our best judgment and a bit of guesswork, and the resulting y-intercept (fixed cost estimate) is based on this line. This approach is not an exact science! However, the next approach to estimating fixed and variable costs – regression analysis – uses mathematical equations to find the best-fitting line.