# High-Low Method

High-Low method is one of the several mathematical techniques used in managerial accounting to split a mixed cost into its fixed and variable components. Given a set of data pairs of activity levels (i.e. units, labor hours, machine hours, etc.) and the corresponding total cost figures, high-low method only takes two extreme data pairs (i.e. the highest and the lowest) as inputs. These are then used to calculate the average variable cost per unit (b) and total fixed cost (a) to obtain a linear cost volume function:

y = a + bx

Where,
y is total cost; and
x is activity level.

Such a cost function may be used in budgeting to estimate the total cost at any given level of activity, assuming that past performance can reasonably be projected into future.

Although easy to understand, high low method may be unreliable because it ignores all the data except for the two extremes. It can be argued that activity-cost pairs (i.e. activity level and the corresponding total cost) which are not representative of the set of data should be excluded before using high-low method.

## Formulas

### Variable Cost per Unit

Variable cost per unit (b) is calculated using the following formula:

 Variable Cost per Unit = y2 − y1 x2 − x1

Where,
y2 is the total cost at highest activity level;
y1 is the total cost at lowest activity level;
x2 are the number of units/labor hours etc. at highest activity level; and
x1 are the number of units/labor hours etc. at lowest activity level.

The variable cost per unit is equal to the slope of the cost volume line (i.e. change in total cost ÷ change in number of units produced).

### Total Fixed Cost

Total fixed cost (a) is calculated by subtracting total variable cost from total cost at either highest or lowest activity level, thus:

Total Fixed Cost = y2 − bx2 = y1 − bx1

## Example

Company α wants to determine the cost-volume relation between its factory overhead cost and number of units produced. Use high-low method to split its factory overhead (FOH) costs into fixed and variable components and create a cost volume relation. The volume and the corresponding total cost information of the factory for past eight months are given below:

MonthUnitsFOH
11,520\$36,375
21,25038,000
31,75041,750
41,60042,360
52,35055,080
62,10048,100
73,00059,000
82,75056,800

### Solution:

We have,
at highest activity: x2 = 3,000; y2 = \$59,000
at lowest activity: x1 = 1,250; y1 = \$38,000

Variable Cost per Unit
= (\$59,000 − \$38,000) ÷ (3,000 − 1,250)
= \$12 per unit

Total Fixed Cost
= \$59,000 − (\$12 × 3,000)
= \$38,000 − (\$12 × 1,250)
= \$23,000

Cost Volume Formula:
y = \$23,000 + 12x

Due to its unreliability, high low method should be carefully used, usually in cases where the data is simple and not too scattered. For complex scenarios, alternate methods should be considered such as scatter-graph method and least-squares regression method.