Before costs can be effectively used in analysis, they should be segregated into purely fixed and purely variable costs. The easiest method to segregate mixed costs is the high-low method.

## The Cost Function

A mathematical equation known as cost function is used in analyzing costs. The cost function shows that the total cost is the sum of the total fixed costs and total variable costs. Total variable cost is equal to the variable cost per unit multiplied by the number of units. The cost function is presented as:

**y = a + bx**

where: y = total cost; a = total fixed costs; b = variable cost per level of activity (or units); x = level of activity (or number of units).

## Steps in Performing the High-Low Method

Cost figures are arranged in pairs of *x* and *y*. Data *x* represents the number of units while *y* represents the corresponding cost.

The high-low method can be done graphically by plotting and connecting the lowest point of activity and the highest point of activity. The y-intercept (value of *y* when *x* is zero) would be equal to the fixed cost. The high-low method can also be done mathematically for accurate computation.

If done mathematically, the following steps are followed:

- Determine the lowest point of activity (x1) and the corresponding cost (y1), and the highest point of activity (x2) and its corresponding cost (y2)
- Compute for the variable cost per unit or slope (b) using the formula:

b = y2 - y1 x2 - x1 - Determine the fixed cost (a) by substituting the slope in the cost equation

## Example

ABC Company wishes to relate total factory overhead costs to the number of units produced to develop a cost function (y = a + bx). The following data was gathered for five production runs.

Batch |
Units |
Total Cost |

1 |
680 |
$29,800 |

2 |
820 |
$34,000 |

3 |
570 |
$27,500 |

4 |
660 |
$29,000 |

5 |
750 |
$31,900 |

Solution:

Lowest point of activity (x1;y1) = 570 ; 18,000

Highest point of activity (x2;y2) = 820 ; 30,000

b = | y2 - y1 | = | 34,000 - 27,500 | = | 6,500 |

x2 - x1 | 820 - 570 | 250 |

**b = $26 per unit**

By substituting the amounts in the cost equation of the lowest point, we can determine the fixed cost (a).

y = a + bx

$27,500 = a + ($26 x 570 units)

$27,500 = a + $14,820

**a = $12,680**

The highest point of activity may also be used in computing for *a*. It will result in the same amount. The cost function for this particular set is: *y = $12,680 + $26x*.

## Conclusion

The high-low method is easy to use. Its drawback, however, is that not all data points are considered. Only the highest and lowest activity pairs are considered. Other methods such as the scattergraph method and linear regression address this flaw.