A two-month shortcut to the cost split every flexible budget needs, tested against the other ten months.
The high-low method takes the months with the highest and lowest activity and divides the change in cost by the change in activity to get the variable cost per unit; fixed cost is what remains. On an illustrative year of fulfilment costs it gives 9.21 an order and 212,508 a month fixed, where a regression on all twelve months gives 11.05 and 190,819. The two agree near the average and drift apart at the edges, and the high-low rate understates what each extra order costs by 17 per cent.
Worked in full in Financial Planning and Analysis by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A flexible budget, a forecast at a new volume or a price for extra business all need a cost split into what moves with activity and what does not. Ledgers do not record that split. It has to be estimated from history, and the quickest estimate, the high-low method, uses two months out of twelve.
| Month | Orders | Cost |
|---|---|---|
| Jan | 9,100 | 291,200 |
| Feb | 8,200 | 288,000 |
| Mar | 10,400 | 301,800 |
| Apr | 11,000 | 313,500 |
| May | 9,800 | 295,100 |
| Jun | 12,600 | 334,200 |
| Jul | 13,900 | 350,800 |
| Aug | 12,200 | 325,400 |
| Sep | 10,900 | 311,300 |
| Oct | 9,500 | 292,500 |
| Nov | 11,800 | 319,600 |
| Dec | 14,500 | 346,000 |
| Average | 11,158 | 314,117 |
Pick the months by activity, not by cost: December has the most orders, 14,500, and February the fewest, 8,200.
Variable cost per unit = (cost at high activity − cost at low activity) ÷ (high activity − low activity)
(346,000 − 288,000) ÷ (14,500 − 8,200) = 58,000 ÷ 6,300 = 9.21 an order
Fixed cost = cost at high activity − variable rate × high activity
346,000 − 9.21 × 14,500 = 212,508 a month. Using the low month instead gives the same answer by construction: 212,508 + 9.21 × 8,200 = 288,000.
A least-squares regression uses every month. In Excel it is two functions: =SLOPE(C2:C13,B2:B13) for the variable rate and =INTERCEPT(C2:C13,B2:B13) for the fixed cost, with =RSQ(C2:C13,B2:B13) for the fit.
| Method | Variable per order | Fixed a month |
|---|---|---|
| High-low, December and February | 9.21 | 212,508 |
| Regression, all months, R² 0.966 | 11.05 | 190,819 |
The two endpoints are the two least typical months. February's cost carried a one-off repair that has nothing to do with orders, and December was run without the usual temporary staff, with part of the work slipping into January, so its cost fell short of its volume. A high point pulled down and a low point pushed up flatten the line, so the high-low method reads too little cost as variable and too much as fixed. The regression is not fooled by two months because ten others outvote them.
Check the pair before you use it. Dropping December and February and taking the next pair, July at 13,900 orders and January at 9,100, gives 12.42 an order and 178,208 fixed. When the answer moves that much from one pair to the next, the method is measuring the noise in two months, not the cost behaviour.
| Orders | High-low | Regression | Difference |
|---|---|---|---|
| 8,000 | 286,159 | 279,218 | −6,941 |
| 10,000 | 304,571 | 301,317 | −3,254 |
| 12,000 | 322,984 | 323,417 | 433 |
| 14,000 | 341,397 | 345,517 | 4,120 |
| 16,000 | 359,810 | 367,616 | 7,807 |
Near the average month the two estimates are within 433 of each other, which is why the high-low split often looks fine in a review of the past. The error grows with the distance from the middle: at 16,000 orders, a peak-season forecast already beyond the observed range, the high-low budget allows 7,807 a month too little, and the operations manager will be reported as overspending against a flexed budget that was wrong. On a decision the gap is sharper still: 2,000 extra orders are costed at 18,413 by high-low and 22,100 by regression.
The high-low method is a two-point shortcut: (cost at high − cost at low) ÷ (high − low activity). Use it to get a first number, then check it against a regression on every month. Here it gives 9.21 an order against 11.05, a gap invisible at average volume and material at the edges. The flexed budget the split feeds is worked in how to calculate a flexible budget variance, and the wider question of which comparison a quarter should be judged against in the free workbooks for Financial Planning and Analysis.
Variable cost per unit equals the difference in cost between the highest and lowest activity periods divided by the difference in activity. With 346,000 at 14,500 orders and 288,000 at 8,200, that is 58,000 over 6,300, or 9.21 an order. Fixed cost is 346,000 less 9.21 times 14,500, which is 212,508.
Usually, because it uses every period instead of two. On the same twelve months, regression gives 11.05 an order and 190,819 fixed with an R-squared of 0.966. The high-low endpoints were both distorted months, so the high-low rate understates the variable cost by 17 per cent.
Because the method estimates how cost responds to the driver. Picking the most and least expensive months mixes in other causes such as repairs or overtime. Even chosen correctly, the two endpoints can be atypical: the next pair here, 13,900 and 9,100 orders, gives 12.42 an order instead of 9.21.
This article is one calculation from Financial Planning and Analysis. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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