Performance Management · Budgetary systems and types of budget

High-Low Method, Time Series and Learning Curve for ACCA PM

Updated 11 October 2026 · Fact-checked

These techniques turn past data into budget estimates. The high-low method splits cost into variable and fixed parts using the highest and lowest activity levels. Regression fits a best-fit line, time series separates trend from seasonal variation, and the learning curve predicts falling labour time per unit as cumulative output doubles.

Understand Quantitative Techniques: Forecasting, High-Low and Learning Curve

A budget needs numbers for the future: costs at a given activity level, next year's sales, and the labour time for a new product. You get them by studying past data and projecting it forward. Each technique answers a slightly different question.

The high-low method assumes a cost has a fixed part and a variable part. You take only two points, the highest and lowest activity levels. The change in cost between them, divided by the change in activity, gives the variable cost per unit. What is left is the fixed cost. It is quick but uses just two observations, so it is rough. Linear regression does the same job using all the data points. It fits the line y = a + bx that minimises the squared gaps from the points. The correlation coefficient r tells you how well the line fits.

Time series analysis looks at data over time, such as quarterly sales. You split it into a trend (the long-run direction), seasonal variations (regular repeating patterns), and random variations. You find the trend with moving averages. You then work out the seasonal variation as the gap between actual and trend. The additive model uses differences. The multiplicative model uses ratios, and suits seasonal swings that grow with the trend. To forecast, project the trend forward and adjust it for the season.

The learning curve says that when people repeat a task, they get faster. Each time cumulative output doubles, the cumulative average time per unit falls to a fixed percentage of its previous value. An 80% curve means the average falls to 80% each time output doubles. The effect fades once workers are fully skilled, at the steady state. It applies mainly to labour-intensive, new or complex work. In budgeting it lowers expected labour hours and cost, so ignoring it overstates the budget.

Key rules to remember

High-low variable cost per unit: Variable cost per unit = (Cost at high activity − Cost at low activity) ÷ (High activity − Low activity); Use the highest and lowest activity levels, not the highest and lowest costs. Take the costs that belong to those activity levels.
High-low fixed cost: Fixed cost = Total cost at either point − (Variable cost per unit × Activity at that point); Check by calculating at the other point. You should get the same fixed cost.
Regression line: y = a + bx; y is the dependent variable (cost or sales), x is the independent variable (activity or time period). b is the slope and a is the intercept.
Regression slope and intercept: b = (nΣxy − ΣxΣy) ÷ (nΣx² − (Σx)²); a = (Σy − bΣx) ÷ n; n is the number of pairs of data. Work out b first, then a.
Correlation coefficient and coefficient of determination: r lies between −1 and +1; r² = proportion of the variation in y explained by x; The closer r is to +1 or −1, the stronger the linear relationship. A value near 0 means a weak linear relationship.
Time series models: Additive: Y = T + S + R. Multiplicative: Y = T × S × R; Y is actual, T is trend, S is seasonal, R is random. Seasonal variations should add to zero (additive) or average 1 (multiplicative) over a full cycle, so adjust the averages if they do not.
Seasonal variation from the trend: Additive: S = Actual − Trend. Multiplicative: S = Actual ÷ Trend; Average the figures for each season over all cycles, then adjust so the total is correct. Forecast = Projected trend + S (additive) or Projected trend × S (multiplicative).
Learning curve (cumulative average time model): Y = aX^b, where b = log r ÷ log 2; Y is cumulative average time per unit for X units, a is time for the first unit, r is the learning rate as a decimal. For an 80% curve, b ≈ −0.322.
Total and incremental time: Total time for X units = X × Y. Time for later units = Total for X units − Total for earlier units; Always work with totals before subtracting. Never subtract averages.

How to solve Quantitative Techniques: Forecasting, High-Low and Learning Curve questions

Start by naming the technique the question wants. Then apply its steps in order and finish with a result in the form the budget needs.

1Identify the data and the target: cost at a new activity level, sales for a future period, or labour time for a batch.
2For high-low, pick the highest and lowest activity levels. Find the variable cost per unit from the difference in cost and activity. Then find the fixed cost.
3For regression, set up columns for x, y, xy and x², total them, then calculate b and a. Write the equation and substitute the forecast value of x.
4For time series, calculate the moving average trend, find the seasonal variation for each season, average and adjust the variations, then project the trend and add or multiply the seasonal factor.
5For the learning curve, find the cumulative average time for the target number of units from the rate. Multiply by the units to get total time. Subtract earlier totals to isolate the batch.
6Convert hours to money using the labour rate. Add or adjust other costs as the question requires.
7State the answer with units and add one line on reliability: extrapolation, few data points, or the learning rate assumption.

Quickest way: Doubling shortcut and two-point check

When to use it: Use it when output is 2, 4, 8, 16 and so on times the first unit, and for any high-low question under time pressure.

Learning curve: multiply the first-unit time by the rate once for each doubling. For 8 units at 80% that is 80% × 80% × 80% = 51.2% of the first-unit time.
Multiply the cumulative average by the units to get total time. Subtract totals to get any later batch.
If output is not a doubling, use Y = aX^b with your calculator and b = log r ÷ log 2.
High-low: write the two points in two lines, subtract, divide to get the variable rate, then find fixed cost from the high point.
Check high-low by recalculating the low point. If it does not match, you have mixed up the pairs.

Common mistakes in Quantitative Techniques: Forecasting, High-Low and Learning Curve

Using the highest and lowest costs rather than the highest and lowest activity levels in high-low.
Students scan the cost column for the extremes and ignore the activity column.
Fix: Select the rows by activity. Take the cost that sits beside each activity figure, even if it is not the highest or lowest cost.
Subtracting cumulative average times to find the time for a later batch.
The numbers look like times per unit, so subtraction feels natural.
Fix: Convert to totals first (average × units), then subtract the total for the earlier units from the total for the larger number.
Applying the learning rate to each unit instead of each doubling of cumulative output.
Students read 80% as meaning every unit takes 80% of the previous unit.
Fix: Apply it only when cumulative output doubles: 1 to 2, 2 to 4, 4 to 8. The rate acts on the cumulative average.
Not adjusting seasonal variations so they sum to zero (additive) or to the number of periods (multiplicative).
Students stop once they have averaged the raw variations.
Fix: Add up the averaged variations. Share any difference equally across the seasons, then use the adjusted figures in the forecast.
Forecasting with regression or the trend far outside the data range and presenting the result as reliable.
The formula gives a number, so students treat it as precise.
Fix: Give the figure, then note that extrapolation is less reliable than interpolation and depends on r and on conditions staying the same.
Forgetting that high-low gives a fixed cost that holds only within the relevant range, and using it for activity far outside the data.
Students treat the fixed cost as fixed at every level.
Fix: State that the result holds within the activity range observed and may include step costs or inflation effects.

Worked examples

Example 1

A factory's monthly overhead cost was ₹1,25,000 at its lowest activity of 5,000 units and ₹1,85,000 at its highest activity of 9,000 units. Using the high-low method, estimate the overhead cost for a month with 7,500 units.

Show the solution

Change in cost = ₹1,85,000 − ₹1,25,000 = ₹60,000.
Change in activity = 9,000 − 5,000 = 4,000 units.
Variable cost per unit = ₹60,000 ÷ 4,000 = ₹15.
Fixed cost = ₹1,85,000 − (9,000 × ₹15) = ₹1,85,000 − ₹1,35,000 = ₹50,000.
Check at the low point: (5,000 × ₹15) + ₹50,000 = ₹1,25,000. This matches.
Cost at 7,500 units = (7,500 × ₹15) + ₹50,000 = ₹1,12,500 + ₹50,000 = ₹1,62,500.

Answer: Estimated overhead for 7,500 units is ₹1,62,500 (variable ₹15 per unit, fixed ₹50,000 per month).

Example 2

The first unit of a new product takes 100 labour hours. An 80% learning curve applies and the cumulative average time model is used. Labour costs ₹300 per hour. Calculate the labour cost of making units 5 to 8.

Show the solution

Units 1 to 4 involve two doublings (1 to 2, 2 to 4). Cumulative average time for 4 units = 100 × 0.8 × 0.8 = 64 hours.
Total time for 4 units = 4 × 64 = 256 hours.
Units 1 to 8 involve three doublings. Cumulative average time for 8 units = 100 × 0.8 × 0.8 × 0.8 = 51.2 hours.
Total time for 8 units = 8 × 51.2 = 409.6 hours.
Time for units 5 to 8 = 409.6 − 256 = 153.6 hours.
Labour cost = 153.6 × ₹300 = ₹46,080.

Answer: Units 5 to 8 take 153.6 hours, costing ₹46,080 in labour.

Exam tips

In objective test questions, one wrong step gives zero marks. Write each line of working on the scratchpad and do the high-low check at the second point.
Check whether the question uses the cumulative average time model. PM questions state the model, so use that and do not mix it with other approaches.
In Section C, set out the table of x, y, xy and x² neatly, show the formulas and label every figure. You can earn marks for method even if the arithmetic slips.
When asked to comment, give two or three points: the data range, the strength of r, and that learning effects end at the steady state or that seasonal patterns may change.
Read whether the trend is additive or multiplicative before you start, and use the matching adjustment for the seasonal variations.

Practice questions from Budgetary systems and types of budget

Quantitative Techniques: Forecasting, High-Low and Learning Curve in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

ACCA Applied KnowledgeLinear Regression and High-Low Method

Quantitative Techniques: Forecasting, High-Low and Learning Curve: frequently asked questions

How do I answer high-low method questions in ACCA PM?

Pick the highest and lowest activity levels and the costs beside them. Divide the cost difference by the activity difference to get the variable cost per unit. Then find the fixed cost from either point and forecast at the required activity.

How do I calculate the learning curve cumulative average time?

Multiply the first-unit time by the learning rate once for each doubling of cumulative output. For other volumes use Y = aX^b with b = log r ÷ log 2. Multiply the average by the units to get the total time.

What is the difference between additive and multiplicative time series?

The additive model treats seasonal variation as a fixed amount added to the trend. The multiplicative model treats it as a proportion of the trend. Use multiplicative when the seasonal swings grow as the trend rises.

When does the learning curve stop applying?

It stops at the steady state, when workers are fully skilled and time per unit no longer falls. It also does not suit highly automated or very short-run tasks. Questions usually tell you if a steady state applies.