• The high‑low method separates mixed costs into a fixed component and a variable-per‑unit component using only the highest and lowest activity observations.
– Steps: identify the high and low activity levels, compute variable cost per unit from the change in cost divided by the change in activity, solve for fixed cost, then form the total cost equation.
– It’s simple and fast but relies on only two points, so it can be sensitive to outliers and may be less accurate than regression techniques that use all available data.
– Best used for quick estimates or when data are limited; use regression or more robust methods when precision is important.
What is the high‑low method?
The high‑low method is a basic cost‑accounting technique used to split a mixed cost (one with both fixed and variable components) into:
– a fixed cost component that does not change with activity, and
– a variable cost per unit that changes proportionally with activity.
It uses only two observations: the period with the highest activity and the period with the lowest activity. The method assumes a linear relationship between total cost and activity and that fixed costs remain constant over the range of observed activity.
Practical steps — how to apply the high‑low method
1. Select the high and low activity periods
• Identify the observation with the highest activity (units produced, sales volume, machine hours, etc.) and the observation with the lowest activity.
• Use the total costs observed in those same periods. Note: choose high/low by activity level, not by cost amount.
2. Calculate variable cost per unit
• Formula: Variable cost per unit = (Cost at high activity − Cost at low activity) / (High activity units − Low activity units)
• This gives the change in cost per one unit of activity.
3. Solve for total fixed cost
• Choose either the high or low observation and plug into: Total cost = (Variable cost per unit × Units) + Fixed cost
• Rearranged: Fixed cost = Total cost − (Variable cost per unit × Units)
4. Form the cost equation
• Total cost = Fixed cost + (Variable cost per unit × Activity units)
• Use this equation to estimate total cost at any activity level within (or near) the observed range.
Worked example (bakery)
Data (monthly):
– Highest activity: October — 125 cakes, total cost = $5,550
– Lowest activity: August — 70 cakes, total cost = $3,750
Step 1: Variable cost per cake
Variable cost = (5,550 − 3,750) / (125 − 70) = 1,800 / 55 = 32.7273 ≈ $32.73 per cake
Step 2: Fixed cost
Use the high point: Fixed cost = 5,550 − (32.7273 × 125) = 5,550 − 4,090.91 ≈ $1,459.09
Step 3: Cost equation
Total cost = $1,459.09 + ($32.73 × number of cakes)
Example prediction:
– For 100 cakes: Total cost ≈ 1,459.09 + 32.73 × 100 = 1,459.09 + 3,273 = $4,732.09 (rounded)
What the high‑low method tells you
– The method yields an estimate of the per‑unit variable cost and an estimate of total fixed cost, enabling quick cost forecasts and break‑even calculations when data are limited.
– It provides a simple linear cost function over the observed activity range.
Difference between the high‑low method and regression analysis
– High‑low uses only two observations (the extremes) and computes a slope and intercept from them.
– Regression (ordinary least squares) uses all available observations to estimate the best‑fit line minimizing overall errors; it gives statistics (R², standard errors) for assessing fit.
– Regression is generally more accurate and less affected by random variation, but requires more computation and (ideally) more data.
Limitations and reasons the high‑low method can be unreliable
– Uses only two data points: ignores all other observations, so results can be skewed by atypical high/low months.
– Sensitive to outliers: if the high or low point is irregular (e.g., one‑time event or data error), the estimates will be misleading.
– Assumes linearity and constant fixed costs across the activity range—may not hold if there are step costs, economies of scale, or nonlinearity.
– Does not provide measures of statistical fit or confidence in the estimates.
When and how to use the high‑low method
– Appropriate for quick, rough estimates when only limited data are available or when a fast approximation is acceptable.
– Use as an initial diagnostic: calculate high‑low, then check results against a plot of cost vs. activity or perform regression if more precision is needed.
– If you suspect outliers, consider removing known abnormal periods (e.g., one‑time shutdowns) or use median/robust methods before applying regression.
Practical tips to improve reliability
– Verify that the high and low observations reflect normal operations; if not, consider choosing the next-most extreme normal observations or flagging outliers.
– Plot cost vs. activity to visually assess linearity and identify outliers.
– If you have more than a few observations, run a simple linear regression to get a more robust estimate and goodness‑of‑fit measures.
– When forecasting beyond the observed range (extrapolation), be cautious—relationship may change outside the observed region.
Bottom line
The high‑low method is a straightforward, easy-to-apply technique to split mixed costs into fixed and variable components using just two points. It’s useful for quick estimates or when data are scarce, but because it relies on only the highest and lowest activity points and assumes linearity, its estimates can be imprecise. For more reliable results, especially when accuracy matters or when more data are available, use regression analysis and inspect the data for outliers or nonlinear patterns.
Source
– Investopedia: “High‑Low Method” by Joules Garcia —
(Continuing from the bakery calculation where the variable cost was $32.72 per cake and total fixed cost was $1,460.)
PREDICTING COSTS USING THE HIGH-LOW RESULTS
– Cost equation derived: Total Cost = Fixed Cost + (Variable Cost × Units) = $1,460 + $32.72 × Units.
– Example prediction: For 90 cakes, Total Cost = $1,460 + ($32.72 × 90) = $1,460 + $2,944.80 = $4,404.80.
– Per-cake average cost at 90 cakes = $4,404.80 / 90 ≈ $48.94 per cake.
ADDITIONAL EXAMPLE — COMPARING HIGH-LOW TO SIMPLE REGRESSION
Use the same three months of data (units, total cost): (70, $3,750), (90, $4,400), (125, $5,550).
1) High-low:
– High point: (125, $5,550); Low point: (70, $3,750)
– Variable cost per unit = (5,550 − 3,750) / (125 − 70) = 1,800 / 55 = $32.72 per unit
– Fixed cost = 5,550 − (32.72 × 125) = $1,460
– Equation: Cost = $1,460 + $32.72 × Units
2) Ordinary least squares (OLS) regression using all three points:
– Slope (variable cost per unit) ≈ $32.74
– Intercept (fixed cost) ≈ $1,455.68
– Equation: Cost ≈ $1,455.68 + $32.74 × Units
Comparison:
– Predictions are close (e.g., at 90 units OLS predicts ≈ $4,402.46 vs high-low $4,404.80). Regression used all data and minimizes overall error; high-low uses only two extreme activity levels, making it more sensitive to the chosen points.
PRACTICAL STEP-BY-STEP: HOW TO APPLY THE HIGH-LOW METHOD
1. Collect data
• Gather period-by-period data of activity levels (units, hours, etc.) and the corresponding total mixed costs.
2. Identify the high and low activity periods
• Choose the period with the highest activity level and the one with the lowest activity level (not the highest/lowest cost).
3. Compute variable cost per unit
• Variable cost/unit = (Total cost at high activity − Total cost at low activity) / (Units at high activity − Units at low activity).
4. Compute fixed cost
• Fixed cost = Total cost at either the high or low activity − (Variable cost/unit × Units in that period).
5. Formulate cost equation
• Total cost = Fixed cost + (Variable cost/unit × Units).
6. Validate the estimate
• Check the equation against other data points; create a scatter plot of costs vs activity to see fit.
7. Use with caution
• If extremes are outliers or if costs appear nonlinear, consider alternative methods (e.g., regression).
WHEN AND WHY THE HIGH-LOW METHOD IS USED
– Good for quick, simple estimates when data are limited.
– Useful for rough budgeting, preliminary cost-behavior analysis, and teaching cost separation concepts.
– Fast and requires minimal computation — attractive when a quick answer matters more than precision.
ADVANTAGES
– Simplicity: needs only two observations.
– Transparency: results are easy to explain and compute.
– Speed: useful for rapid, preliminary decision-making.
LIMITATIONS AND POTENTIAL PROBLEMS
– Uses only two points: discards information contained in other data points.
– Sensitive to outliers: an abnormal high or low activity period skews the estimates.
– Assumes linear cost behavior: variable cost per unit and fixed costs are constant across range — not valid for step costs or capacity constraints.
– Assumes same fixed cost at both chosen activity levels — may be false if there are step-fixed costs or cost structure changes.
– Yields less statistically rigorous estimates than regression (no goodness-of-fit measures or standard errors).
ALTERNATIVES AND IMPROVEMENTS
– Simple linear regression (OLS): uses all data and produces best-fit slope and intercept; provides statistics (R², standard errors).
– Visual inspection/scatter plots: spot nonlinearity or outliers before estimating.
– Account analysis (judgmental): review accounts line by line to classify costs as fixed, variable, or mixed.
– Engineering/“bottom-up” approach: estimate costs from first principles (material, labor standards) when data are poor.
PRACTICAL GUIDELINES / BEST PRACTICES
– Don’t pick extreme months that are one-off (sales promotions, equipment downtime). If extreme activity points are outliers, exclude them or use another method.
– Plot data first. A scatter plot of cost vs activity helps confirm linearity and spot anomalies.
– If you have more than two points, prefer regression to obtain a more reliable estimate.
– Use high-low as a first pass, then refine with regression or account analysis if accuracy matters.
– Document assumptions (why you chose the high and low periods) so users understand limitations.
ADDITIONAL EXAMPLE — SERVICE BUSINESS (TECH SUPPORT)
Data (monthly active tickets, total support cost):
Month A: 200 tickets — $12,000
Month B: 400 tickets — $19,000
Using high-low:
– Variable cost per ticket = (19,000 − 12,000) / (400 − 200) = 7,000 / 200 = $35.00 per ticket
– Fixed cost = 19,000 − (35 × 400) = 19,000 − 14,000 = $5,000
– Cost equation: Cost = $5,000 + $35 × Tickets
– Use to budget support cost for expected ticket volumes; check by comparing to other months.
CONCLUDING SUMMARY
The high-low method is a fast, straightforward technique to split mixed costs into fixed and variable components by using only the highest and lowest activity observations. It’s best used for quick estimates or when data are sparse. However, because it relies on only two points and assumes linearity and constant fixed costs, it can be sensitive to outliers and less accurate than regression-based methods. For more reliable estimates when multiple data points exist, use linear regression or supplement the high-low estimate with account-level analysis and visual inspection of the data.
Source: Investopedia, “High-Low Method”