Source: Cost Estimation and Regression Discussion Problems (Turner)
Difficulty: Introductory | Prerequisites: Basic understanding of fixed vs. variable costs and the concept of a cost function (Y = a + bX).
The high-low method is one of the simplest tools in managerial accounting for separating a mixed cost into its fixed and variable components. If you know that total cost = fixed cost + (variable rate x activity level), the high-low method uses just two data points to solve for the unknowns. It sits early in most cost accounting courses because it builds intuition for cost behaviour before you move on to regression, which uses all available data points. You should already be comfortable with the idea that some costs change with activity and some do not.
The high-low method estimates a cost equation by drawing a straight line through the highest and lowest activity points in a dataset. You calculate the variable cost per unit of activity from the slope between those two points, then back into the fixed cost. It is quick but rough, because it ignores every data point in between.
Mixed cost (semi-variable cost)
A cost that contains both a fixed component and a variable component. Total cost changes with activity, but not from zero, because there is a baseline amount incurred regardless of volume.
In simple terms, think of your phone bill: a flat monthly charge plus a per-gigabyte fee for data.
High-low method
A cost estimation technique that uses only the highest and lowest observed activity levels to calculate the variable cost rate and fixed cost. It fits a linear equation, Y = a + bX, from just two data points.
In simple terms, you pick the busiest period and the quietest period, then figure out how much cost changed per unit of activity between them.
Variable cost rate (slope, b)
The change in total cost divided by the change in activity between the high and low points. This is the per-unit cost that rises or falls with volume.
Fixed cost (intercept, a)
The portion of total cost that does not change with the level of activity. Calculated by subtracting total variable cost (at either the high or low point) from total cost at that point.
Cost driver (independent variable, X)
The activity or factor that causes the cost to change. In Problem 1 it is production volume; in Problem 2 it is direct labour costs. Choosing the right cost driver matters: the high-low method sorts data by this variable.
Dependent variable (Y)
The cost you are trying to estimate. In Problem 1 it is electricity costs; in Problem 2 it is overhead costs.
Identify the cost driver (X) and the cost to estimate (Y).
Find the periods with the highest and lowest activity levels for X. (Sort by the cost driver, not the cost itself.)
Calculate the variable rate: b = (Y_high − Y_low) / (X_high − X_low).
Calculate the fixed cost: a = Y_high − b × X_high (or equivalently, a = Y_low − b × X_low; both give the same answer).
Write the cost equation: Y = a + bX.
Data spans July to December. Production volume is the cost driver (X); electricity cost is the dependent variable (Y).
Highest activity: September, 3,200 units, $5,700.
Lowest activity: November, 1,200 units, $2,400.
Variable rate: b = (5,700 − 2,400) / (3,200 − 1,200) = 3,300 / 2,000 = $1.65 per unit.
Fixed cost: a = 5,700 − 1.65 × 3,200 = 5,700 − 5,280 = $420.
Cost equation: Y = $420 + $1.65X, where X is production volume.
Sanity check with another month (August): 420 + 1.65 × 2,800 = 420 + 4,620 = $5,040. The actual cost was $5,400, so there is a $360 gap. This is typical; the high-low method is an approximation.
Here the cost driver is direct labour costs (not units produced). The dependent variable is overhead costs.
Highest direct labour cost: $1,750 (210 units), overhead $2,910.
Lowest direct labour cost: $1,500 (120 units), overhead $2,570.
Variable rate: b = (2,910 − 2,570) / (1,750 − 1,500) = 340 / 250 = $1.36 per dollar of direct labour.
Fixed cost: a = 2,910 − 1.36 × 1,750 = 2,910 − 2,380 = $530.
Cost equation: Overhead = $530 + $1.36 × Direct Labour Costs.
Notice that b here is unitless (dollars of overhead per dollar of labour), not dollars per unit produced. The cost driver defines the unit of the slope.
Variable cost rate (slope):
b = (Y_high − Y_low) / (X_high − X_low)
Fixed cost (intercept):
a = Y_high − b × X_high
or equivalently: a = Y_low − b × X_low
Cost equation:
Y = a + bX
Where Y is total estimated cost, a is the fixed cost, b is the variable cost per unit of activity, and X is the level of activity.
Manufacturing managers use the high-low method for quick budgeting when they need a rough cost estimate but do not have time (or software) for a full regression analysis. A plant controller might use it to estimate next quarter's utilities cost based on planned production volume, accepting that the estimate is approximate. It is also a common first pass in consulting engagements before more sophisticated modelling begins.
Students often pick the highest and lowest cost values instead of the highest and lowest activity levels. The method sorts by the cost driver (X), not the cost (Y). In Problem 2, you sort by direct labour costs, not overhead costs and not units produced.
Students sometimes think the high-low method uses all data points. It does not. It uses exactly two, which is both its advantage (simplicity) and its weakness (it ignores useful information).
Some students assume the cost driver must always be units of production. It can be any measurable activity: machine hours, direct labour dollars, number of setups, or anything management believes causes the cost to change.
The high-low method can give misleading results if the high or low point is an outlier. If one of those months had an equipment failure or a shutdown, the estimate will be skewed.
⚠️ The high-low method is a staple exam question in AMIS 3300. You will almost certainly be asked to compute a cost equation from a small data table.
⚠️ Pay close attention to what the question names as the cost driver. If the problem says "the company believes overhead depends on direct labour costs," then direct labour costs is your X, even if units produced are also in the table.
⚠️ Know how to verify your answer by plugging a third data point into your equation. The predicted cost will not match perfectly (that is normal for the high-low method), but it should be in the right ballpark.
⚠️ Be ready to explain the limitation: because the method uses only two observations, it is sensitive to outliers and ignores the pattern in the rest of the data.
True or False: The high-low method selects the periods with the highest and lowest total cost.
Answer: False. It selects the periods with the highest and lowest activity level (cost driver).
Fill in the blank: The variable cost rate equals the change in ______ divided by the change in ______.
Answer: total cost; activity level.
True or False: If you solve for the fixed cost using the high point, you will get a different answer than if you use the low point.
Answer: False. Both should yield the same fixed cost.
True or False: The high-low method uses every available data point to estimate the cost equation.
Answer: False. It uses only two data points.
Q: Using the data from Problem 1, what is the variable cost per unit of production for electricity?
A: $1.65 per unit. Calculated as (5,700 − 2,400) / (3,200 − 1,200) = 3,300 / 2,000.
Q: In Problem 1, what is the fixed cost component of the electricity cost equation?
A: $420. Calculated as 5,700 − (1.65 × 3,200) = 5,700 − 5,280.
Q: Write the full cost equation for Problem 1.
A: Total Electricity Cost = $420 + $1.65 × Production Volume.
Q: In Problem 2, why is direct labour cost the cost driver rather than units produced?
A: Because the problem states that Smith Company believes overhead costs depend on direct labour costs. The company's assumption about what drives the cost determines the independent variable.
Q: Using the high-low method on Problem 2, what are the fixed and variable components of overhead?
A: Variable rate = $1.36 per dollar of direct labour. Fixed cost = $530. Overhead = $530 + $1.36 × Direct Labour Costs.
Q: If Smith Company expects direct labour costs of $1,650 next period, what is the estimated overhead using the high-low equation?
A: 530 + 1.36 × 1,650 = 530 + 2,244 = $2,774.
The high-low method connects directly to regression analysis (the next topic in AMIS 3300). Regression does the same job, separating fixed and variable costs, but it uses all available data points and provides statistical measures of fit (R², standard error). Understanding the high-low method first makes regression feel like the natural upgrade.
This also ties into cost-volume-profit (CVP) analysis later in the course. Once you have a cost equation, you can plug it into break-even calculations and contribution margin analysis.
Tags: high-low method, cost estimation, mixed costs, semi-variable costs, variable cost rate, fixed cost, cost equation, cost driver, independent variable, dependent variable, AMIS 3300, cost accounting, cost behaviour, Y = a + bX, slope intercept, Ohio State, Turner, managerial accounting, cost function estimation