Short-Term Decision-Making

Question: Another approach to identifying fixed and variable costs for cost estimation purposes is the high-low method. Accountants who use this approach are looking for a quick and easy way to estimate costs, and will follow up their analysis with other more accurate techniques. How is the high-low method used to estimate fixed and variable costs?

Answer: The high-low method uses historical information from several reporting periods to estimate costs. Assume Susan Wesley obtains monthly production cost information from the financial accounting department for the last 12 months. This information appears in Table 5.4 "Monthly Production Costs for Bikes Unlimited".

Table 5.4 Monthly Production Costs for Bikes Unlimited

All of the data points from Table 5.4 "Monthly Production Costs for Bikes Unlimited" are plotted on the graph shown in Figure 5.4 "Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method". Although a graph is not required using the high-low method, it is a helpful visual tool. Susan then draws a straight line using the high (April) and low (January) activity levels from these data. The goal of the high-low method is to describe this line mathematically in the form of an equation stated as Y = f + vX, which requires calculating both the total fixed costs amount (f) and per unit variable cost amount (v). Four steps are required to achieve this using the high-low method:

Step 1. Identify the high and low activity levels from the data set.

Step 2. Calculate the variable cost per unit (v).

Step 3. Calculate the total fixed cost (f).

Step 4. State the results in equation form Y = f + vX.

Figure 5.4 Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method

Question: How are the four steps of the high-low method used to estimate total fixed costs and per unit variable cost?

Answer: Each of the four steps is described next.

Step 1. Identify the high and low activity levels from the data set.

The highest level of activity (level of production) occurred in the month of April (5,900 units; $380,000 production costs), and the lowest level of activity occurred in the month of January (2,900 units; $200,000 production costs). Note that we are identifying the high and low activity levels rather than the high and low dollar levels – choosing the high and low dollar levels can result in incorrect high and low points.

Step 2. Calculate the variable cost per unit ( v).

Because the slope of the line shown in Figure 5.4 "Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method" represents the variable cost per unit, the goal here is to calculate the slope of the line using the high and low points identified in step 1 (the slope calculation is often referred to as "rise over run" in math courses). The calculation of the variable cost per unit for Bikes Unlimited is shown as follows:

\( \begin{aligned} \text { Unit variable cost }(v) &=\frac{\text { Cost at highest level - Cost at lowest level }}{\text { Highest activity level - Lowest activity level }} \\ &=\frac{\$ 380,000-\$ 200,000}{5,900 \text { units }-2,900 \text { units }} \\ &=\frac{\$ 180,000}{3,000 \text { units }} \\ &=\$ 60 \end{aligned} \)

Step 3. Calculate the total fixed cost (f).

After completing step 2, the equation to describe the line is partially complete and stated as Y = f + $60X. The goal of step 3 is to calculate a value for total fixed cost (f). Simply select either the high or low activity level, and fill in the data to solve for f (total fixed costs), as shown.

Using the low activity level of 2,900 units and $200,000,

\( \begin{aligned} \mathrm{Y} &=f+v \mathrm{X} \\ \$ 200,000 &=f+(\$ 60 \times 2,900 \text { units }) \\ f &=\$ 200,000-(\$ 60 \times 2,900 \text { units }) \\ f &=\$ 200,000-\$ 174,000 \\ f &=\$ 26,000 \end{aligned} \)

Thus total fixed costs total $26,000. (Try this using the high activity level of 5,900 units and $380,000. You will get the same result as long as the per unit variable cost is not rounded.)

Step 4. State the results in equation form Y = f + vX.

We know from step 2 that the variable cost per unit is $60, and from step 3 that total fixed cost is $26,000. Thus we can state the equation used to estimate total costs as

Y = $26,000 + $60X

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 $386,000:

\( \begin{aligned} \mathrm{Y} &=\$ 26,000+(\$ 60 \times 6,000 \text { units }) \\ \mathrm{Y} &=\$ 26,000+\$ 360,000 \\ \mathrm{Y} &=\$ 386,000 \end{aligned} \)

Question: Although the high-low method is relatively simple, it does have a potentially significant weakness. What is the potential weakness in using the high-low method?

Answer: In reviewing Figure 5.4 "Estimated Total Mixed Production Costs for Bikes Unlimited: High-Low Method", you will notice that this approach only considers the high and low activity levels in establishing an estimate of fixed and variable costs. The high and low data points may not represent the data set as a whole, and using these points can result in distorted estimates.

For example, the $380,000 in production costs incurred in April may be higher than normal because several production machines broke down resulting in costly repairs. Or perhaps several key employees left the company, resulting in higher than normal labor costs for the month because the remaining employees were paid overtime. Cost accountants will often throw out the high and low points for this reason and use the next highest and lowest points to perform this analysis. While the high-low method is most often used as a quick and easy way to estimate fixed and variable costs, other more sophisticated methods are most often used to refine the estimates developed from the high-low method.