The high-low method uses two formulas in sequence. The first divides the difference in cost between the highest and lowest activity levels by the difference in activity between them, which gives the variable cost per unit of activity. The second takes total cost at either of those two points and subtracts the variable component just calculated, which leaves the fixed cost. Together they split a mixed cost into the two parts a cost equation needs.
cost at highest activity - cost at lowest activity
Variable cost/unit = --------------------------------------------------------
units at highest activity - units at lowest activity
Fixed cost = total cost at that point - (variable cost/unit x units at that point)The method is a technique for separating the fixed and variable cost components of mixed costs, using the highest and lowest levels of activity and their associated costs (OpenStax, Principles of Accounting, Volume 2, Estimate a Variable and Fixed Cost Equation and Predict Future Costs). What the two outputs feed, and the other routes to a variable cost once the split exists, are in how to determine variable cost.
The First Formula Is a Slope
The variable rate is the rise over the run of a straight line through the two points, with cost as the dependent variable and activity as the independent one, so the calculation examines the change in cost relative to the change in activity (OpenStax, Estimate a Variable and Fixed Cost Equation and Predict Future Costs). That is why the answer is a rate per unit of activity rather than an amount, and why it only means anything if the underlying relationship really is linear.
The output slots into the total cost equation as its b term, alongside fixed cost as a and the activity level as x, which is the equation total cost formula sets out.
The Selection Rule Is the Whole Method
Both formulas are trivial arithmetic. The decision that determines whether the answer is usable happens before either of them runs, and it is the one people get wrong: always choose the highest and lowest activity and the costs that correspond with those levels of activity, even if they are not the highest and lowest costs (OpenStax, Estimate a Variable and Fixed Cost Equation and Predict Future Costs).
Activity drives the cost, so activity is what the endpoints have to be picked on. Sorting the column of dollar amounts instead picks whichever month happened to carry an unrelated charge, and the method has no way to know it did.
What Picking on Cost Actually Costs You
The figures below are stated for the illustration rather than taken from a real client. A firm holds twelve monthly software invoices set against returns filed, and one month carries an annual licence true-up on top of the usual charge.
Selected on activity, which is correct
Highest activity 320 returns 2,300
Lowest activity 70 returns 1,050
Variable rate (2,300 - 1,050) / (320 - 70) = 5.00 per return
Fixed cost 2,300 - (320 x 5.00) = 700
Check at the low 1,050 - (70 x 5.00) = 700
Selected on cost, which is wrong
Highest cost 245 returns 2,450
Lowest cost 70 returns 1,050
Variable rate (2,450 - 1,050) / (245 - 70) = 8.00 per return
Fixed cost 2,450 - (245 x 8.00) = 490
Check at the low 1,050 - (70 x 8.00) = 490
Predicting a 150-return month
From the correct split 700 + (150 x 5.00) = 1,450
From the wrong split 490 + (150 x 8.00) = 1,690Read the two blocks against each other. Selecting on cost overstates the variable rate, understates the fixed base by the same logic, and pushes the prediction for an ordinary mid-volume month well above what the firm will actually be billed. The true-up dollars were fixed, and the method has quietly reclassified them as variable.
Notice what the check line does in the second block. The fixed cost computed from the low point agrees exactly with the one computed from the high point, which is precisely what people treat as confirmation that the split is right. It confirms nothing. With two points the algebra forces agreement, because the second formula is just the first one rearranged, so both endpoints sit on the same line by construction. A high-low answer reconciles whether or not the two months you chose were the right ones.
What the Formulas Cannot Tell You
Two limits travel with the output, and neither shows up in the arithmetic.
The estimate rests on two observations out of however many the period produced, which is why it is not the most accurate approach to predicting future costs (OpenStax, Estimate a Variable and Fixed Cost Equation and Predict Future Costs). Where that matters, least-squares regression is the alternative, and how it and the scatter graph sit alongside this method is covered in how to determine variable cost.
The answer also holds only inside the band of activity the two points came from. Push the prediction past a level where a new supervisor gets hired or another licence tier begins, and the fixed component steps to a different figure, which is the relevant-range constraint set out in fixed expenses.
Common Questions
It is a pair, run in order. Change in cost divided by change in activity gives the variable rate, then total cost less the variable component at either endpoint gives the fixed cost. Written as one line, the result is the cost equation Y = a + bx, with a as the fixed cost and b as the rate the first formula produced.
No, and that is a property of the arithmetic rather than evidence about the data. The two endpoints define the line, so both must return the same intercept. Use whichever is easier and recompute at the other one purely as a check on your own multiplication.
Accountably places trained offshore accountants and tax preparers inside US CPA and EA firms, and a firm can put a block of its own recurring close and analysis work through a trial task so its reviewers stay on the judgment calls.
