 # High-Low Method By Yuriy Smirnov Ph.D.

## Definition

The high-low method is one of several techniques used in managerial accounting to split mixed cost into fixed components and variable components. Actually, it uses two sets of numbers:

• The dollar amount of mixed cost at the highest level of business activity during a relevant period
• The dollar amount of mixed cost at the lowest level of business activity during a relevant period

The high-low method assumes that the fixed component is constant regardless of the business activity level, and any change in total cost is caused by the variable component.

## Formula

Application of the high-low method makes it possible to describe the behavior of mixed cost as a linear function. In general, the equation can be written as follows,

TC = a + b × Q

where “a” is a fixed component of mixed cost, “b” is the per unit amount of variable component of mixed cost, and “Q” is the production level in units.

The variable cost per unit is calculated as follows,

 b = TC2 - TC1 Q2 - Q1

where TC2 is the total amount of mixed cost at the maximum production level, TC1 is the total amount of mixed cost at the minimum production level, Q2 is the maximum production level in units, and Q1 is the minimum production level in units.

The total fixed cost can then be calculated as shown below.

a = TC2 - b × Q2

or

a = TC1 - b × Q1

### Example

Estro-X LLC management is going to split overhead costs into fixed components and variable components using the high-low method. Information about actual production output and overhead cost during last year is shown in the table below. The minimum production output of 780 units was in February, and the maximum production output of 960 units was in May. The relevant overhead costs were \$124,000 and \$148,000. Let’s put this data into the formula above.

 b = \$148,000 - \$124,000 = \$133.33 960 - 780

a = \$148,000 - \$133.33 × 960 = \$20,000

The variable component of overhead costs is \$133.33 per unit, and the fixed component of overhead cost is \$20,000.

### Graph

The equation describing the behavior of overhead costs is as follows:

TC = \$20,000 + \$133.33 × Q

Let’s plot the graph combining actual values of overhead costs and projected values under a linear function. As we can see, the actual values are close enough to the TC-line, so using the high-low method gives a quite accurate estimation of overhead costs behavior.

## Disadvantages of the high-low method

Using the high-low method is advisable if costs are relatively stable; otherwise, the result of cost split will be inaccurate because that technique assumes using only two boundary points and ignores all other data in a set. After the linear function describing mixed cost behavior is determined, it is strongly recommended to check whether or not it accurately describes the relationship between the production level and costs.

An example when this method should not be used is shown in the graph below. As we can see, all actual values of costs are well above the TC-line. In this case, using the high-low method will lead to an undervaluation of total costs and an inaccurate split into variable components and fixed components.