High-Low Method

The high-low method is a cost accounting technique used to separate a mixed cost, one that contains both a fixed and a variable element, into its two components. It does this by looking at only two data points: the period with the highest level of activity and the period with the lowest. The change in cost between those two periods is assumed to be caused entirely by the change in activity, which gives the variable cost per unit. The fixed cost is then whatever is left over.

Understanding cost behavior is essential for budgeting, pricing and break-even analysis, but many real costs, such as utilities, maintenance and delivery costs, do not fall neatly into fixed costs or variable costs. The high-low method is the quickest way to estimate the split, which is why it appears in most introductory management accounting courses, although more accurate statistical methods are usually preferred in practice.

The variable cost per unit is calculated first:

Here $\text{Cost at highest activity}$ and $\text{Cost at lowest activity}$ are the total costs in the periods with the most and least activity, and $\text{Highest activity}$ and $\text{Lowest activity}$ are the activity levels, such as units produced or machine hours, in those periods. The points are chosen by activity level, not by cost.

The fixed cost is then found by substituting into either period:

A printing company records its monthly maintenance cost and machine hours for six months:

• January: 1,200 hours and $9,400.
• February: 1,500 hours and $10,300.
• March: 900 hours and $8,200.
• April: 1,800 hours and $11,800.
• May: 1,100 hours and $9,100.
• June: 1,400 hours and $10,200.

The highest activity is April, with 1,800 hours and $11,800, and the lowest is March, with 900 hours and $8,200. The variable cost per hour is ($11,800 minus $8,200) divided by (1,800 minus 900), which is $3,600 divided by 900, or $4.00 per machine hour. Using April, the fixed cost is $11,800 minus (1,800 times $4.00), which equals $4,600 a month. Checking with March gives $8,200 minus $3,600, also $4,600. The cost formula is therefore $4,600 plus $4.00 per machine hour. If the company expects 1,600 machine hours next month, its budget for maintenance would be $4,600 plus $6,400, or $11,000.

Once a cost is split, the results can be used in several ways. Managers can build budgets that adjust automatically for activity, estimate the contribution margin of products and services, and carry out cost-volume-profit analysis, including calculating the break-even point. The method is also handy for a quick estimate when only limited records are available, such as in a small business or early in a project, or as a reasonableness check on a more detailed analysis.

The method's simplicity is also its main weakness. Because it relies on just two observations, it ignores all the other data, and those two points may not be typical. The highest and lowest activity months may include unusual events, such as a one-off repair, a strike or a holiday shutdown, which would distort the result. In the example above, January and June fall exactly on the line implied by the two extreme points, but February is $300 below it and May $100 above it, so the formula does not fit every month exactly.

The method also assumes that the relationship between cost and activity is linear across the whole range, which may not hold if, for example, overtime rates or bulk discounts apply at higher volumes. Estimates should only be used within the range of activity observed. For more reliable results, accountants use the scatter-graph method, which plots all the data visually, or least-squares regression, which uses every observation and gives a statistical measure of how well the line fits. The high-low method remains useful as a first approximation in cost accounting and when weighing the marginal cost of extra output.