What happens when the high-low method ends up with a negative amount?

The high-low method of determining the fixed and variable portions of a mixed cost relies on only two sets of data: 1) the costs at the highest level of activity, and 2) the costs at the lowest level of activity. If either set of data is flawed, the calculation can result in an unreasonable, negative amount of fixed cost.

To illustrate the problem, let's assume that the total cost is $1,200 when there are 100 units of product manufactured, and $6,000 when there are 400 units of product are manufactured. The high-low method computes the variable cost rate by dividing the change in the total costs by the change in the number of units of manufactured. In other words, the $4,800 change in total costs is divided by the change in units of 300 to yield the variable cost rate of $16 per unit of product. Since the fixed costs are the total costs minus the variable costs, the fixed costs will be calculated to a negative $400. This unacceptable answer results from total costs of $1,200 at the low point minus the variable costs of $1,600 (100 units times $16), or total costs of $6,000 at the high point minus the variable costs of $6,400 (400 units times $16).

The negative amount of fixed costs is not realistic and leads me to believe that either the total costs at either the high point or at the low point are not representative. This brings to light the importance of plotting or graphing all of the points of activity and their related costs before using the high-low method. (The number of units uses the scale on the x-axis and the related total cost at each level of activity uses the scale on the y-axis.) It is possible that at the highest point of activity the costs were out of line from the normal relationship—referred to as an outlier. You may decide to use the second highest level of activity, if the related costs are more representative.

If the $6,000 of cost at the 400 units of activity is an outlier, you might select the next highest activity of 380 units having total costs of $4,000. Now the variable rate will be the change in total costs of $2,800 ($4,000 minus $1,200) divided by the change in the units manufactured of 280 (380 minus 100) for a variable rate of $10 per unit of product. Using the variable rate of $10 per unit manufactured will result in the fixed costs being a positive $200. The positive $200 of fixed costs is calculated at either 1) the low activity: total costs of $1,200 minus the variable costs of $1,000 (100 units at $10); or at 2) the high activity: total costs of $4,000 minus the variable costs of $3,800 (380 units at $10).