A budget needs a cost for a level of activity that has never been run before: what will it cost to make 13,500 units next month when the last six months have been at different levels, and the ledger shows only total costs? To answer, the management accountant needs to know how much of each total is fixed and how much varies with output.
The high-low method does this with two figures: the total cost at the highest output and at the lowest. It is the simplest way of splitting a mixed cost, it can be done by hand in a minute, and it appears in examination questions in several forms: a plain split, a split with a step in fixed costs and a split with a change in variable cost per unit.
This topic explains the assumptions, the method, how to forecast with the resulting cost function, how to deal with a step in fixed cost (given in naira or as a percentage) and a change in the variable cost per unit, and the limits of the method. It builds on the earlier topic on participation, negotiation and ethics in budgeting.
The next topic covers correlation, regression and time series for budgeting and forecasting.
In 30 seconds
To prepare reliable budgets, total costs are analysed into fixed cost and variable cost per unit. Direct materials are normally 100% variable; direct labour may be variable, or fixed where there is a fixed workforce; overhead may be fixed, but for accuracy mixed overheads should be split.
The high-low method needs total costs at two activity levels and assumes that fixed cost is the same in total at both and variable cost per unit is constant. Variable cost per unit = (cost at high − cost at low) ÷ (high activity − low activity). Fixed cost = total cost − variable cost per unit × activity (at either level). The cost function is y = a + bx.
It can then forecast the cost of other levels. If there is a step in fixed costs given in naira, adjust one of the totals by the step so that both use the same fixed cost, then compute as usual; if given as a percentage, use a third level so that two levels lie on the same side of the step.
If the variable cost per unit changes at some level, use the two levels on the same side of the change. The method uses only two observations, which may not be typical. Full marks come from correct identification of high and low, the formula, the cost function and a forecast.
Fixed and variable costs, and the high-low method
Why costs must be split
Cost behaviour describes how total cost changes as activity changes. For budgeting it is normally assumed that total cost can be analysed into a fixed cost (the same in total whatever the activity, within a relevant range) and a variable cost per unit of activity (per unit of product or per hour of service). Some items are clear: direct materials are normally 100% variable.
Direct labour may be treated as variable, but where there is a fixed workforce it is budgeted as a fixed cost. Overheads may be treated as fixed, but for an accurate analysis the mixed overheads should be split into a fixed and a variable part, usually from an analysis of historical cost. Two techniques are standard: the high-low method and linear regression, which the next topic covers.
When the method can be used
High-low analysis can be used when (a) total cost is known at two different levels of activity; (b) fixed cost can be assumed to be the same in total at both levels; and (c) the variable cost per unit can be assumed constant at both levels. It uses two historical records: the highest recorded activity and its total cost, and the lowest and its total cost.
They are assumed to represent costs at all levels. The difference in total cost between the two levels is entirely variable cost, because the fixed cost is the same in both.
The method
- Select the highest and lowest activity levels and the total cost at each. Choose by activity, not by cost.
- Variable cost per unit = difference in total cost ÷ difference in activity.
- Fixed cost: substitute into the total cost at either level: fixed cost = total cost − (variable cost per unit × activity). The answer is the same from either level.
- Cost function: total cost = fixed cost + variable cost per unit × activity (y = a + bx).
- Forecast the cost of any planned level of activity from the function, preferably within or near the range of the data.
Steps, changes, and the limits of the method
A step increase in fixed costs given in naira
Sometimes fixed costs rise by a stated amount when activity reaches a certain level, which falls between the low and the high. The two totals then contain different fixed costs. To correct this, adjust one total by the step: add the step to the total at the lower activity, or deduct it from the total at the higher. The difference between the adjusted totals is then solely variable.
Calculate the variable cost per unit; calculate the fixed cost from the unadjusted pair; this gives the function on one side of the step; and the function on the other side is found by reversing the adjustment to the fixed cost.
A step in fixed costs given as a percentage
If the step is a percentage, the amount is unknown, so a third level of activity is needed. Choose the two levels that are on the same side of the step, where fixed cost is the same (unknown) amount, and compare them to find the variable cost per unit.
Find the fixed cost on that side by substitution, and the fixed cost on the other side by applying (or reversing) the percentage.
A change in variable cost per unit
If the variable cost per unit changes at some level of activity, for example a volume discount that reduces it by a percentage on all units, a third level is again needed.
Use the two levels on the same side of the change to find the variable cost per unit on that side and the fixed cost, and then apply the percentage to find the variable cost per unit on the other side.
Limits
- It uses only two observations, and these may not be typical: the highest and lowest may be unusual months.
- It assumes linear cost behaviour and a constant fixed cost, which hold only over a relevant range; forecasts far outside the data are unreliable.
- It cannot measure how reliable the result is. Linear regression uses all the data and gives a measure of reliability (the correlation coefficient), which is why it is better.
- Inflation or changes in method between periods can distort the data.
Layouts for the high-low method
- Table of highest and lowest activity, with costs, and the differences.
- Variable cost per unit = Δcost ÷ Δactivity.
- Fixed cost by substitution at one level; check with the other.
- Function and forecast.
- For steps and changes: adjusted totals, or the third level, as above; then the function on each side.
Money is in naira and each answer is rounded once, at the end.
Worked examples
Example 1: the plain split. Output and total cost for six months: 4,200 units ₦232,000; 5,100 ₦262,000; 6,000 ₦286,000; 4,800 ₦247,000; 5,500 ₦272,000; 3,600 ₦214,000. Required: the cost function, and the cost of 5,000 units.
- High and low. High 6,000 units ₦286,000; low 3,600 units ₦214,000. Differences: 2,400 units; ₦72,000.
- Variable cost.
72,000 ÷ 2,400 = ₦30 a unit. - Fixed cost.
286,000 − 30 × 6,000 = 286,000 − 180,000 = ₦106,000.
Check at the low: 214,000 − 30 × 3,600 = 214,000 − 108,000 = 106,000. - Function.
Total cost = 106,000 + 30x.
5,000 units: 106,000 + 150,000 = ₦256,000.
Example 2: a step in fixed costs given in naira. Fixed costs rise by ₦20,000 when output reaches 8,000 units or more. At 10,000 units total cost is ₦470,000; at 6,000 units it is ₦310,000. Required: the cost function on each side of the step.
- Adjust.
Add the step to the low total: 310,000 + 20,000 = 330,000. - Variable cost.
(470,000 − 330,000) ÷ (10,000 − 6,000) = 140,000 ÷ 4,000 = ₦35. - Fixed cost, above the step.
(unadjusted high): 470,000 − 35 × 10,000 = ₦120,000.
Below the step: 120,000 − 20,000 = ₦100,000.
Check at the low: 100,000 + 35 × 6,000 = 310,000. - Functions. Below 8,000 units: 100,000 + 35x. At or above: 120,000 + 35x.
Example 3: a step given as a percentage. Fixed costs rise by 25% at 12,000 units or more. Costs: 16,000 units ₦380,000; 13,000 units ₦335,000; 9,000 units ₦247,000. Required: the function on each side.
- Same side. 16,000 and 13,000 are both above 12,000.
- Variable cost.
(380,000 − 335,000) ÷ 3,000 = ₦15.
Fixed above the step: 380,000 − 15 × 16,000 = ₦140,000. - Fixed below the step:
140,000 ÷ 1.25 = ₦112,000.
Check at 9,000: 112,000 + 135,000 = 247,000.
Example 4: a change in variable cost. Fixed costs are constant, but the variable cost per unit falls by 20% on all units above 20,000 units. Costs: 28,000 units ₦304,000; 22,000 units ₦256,000; 16,000 units ₦240,000. Required: the functions.
- Same side. 28,000 and 22,000 are above 20,000.
Variable cost above: (304,000 − 256,000) ÷ 6,000 = ₦8. - Fixed cost.
304,000 − 8 × 28,000 = ₦80,000. - Variable cost below:
8 ÷ 0.80 = ₦10.
Check at 16,000: 80,000 + 160,000 = 240,000. - Functions. Above 20,000: 80,000 + 8x. At or below: 80,000 + 10x.
Expect variants: a table of six or twelve months, inflation adjustments, a step given at a level between observations, and a requirement to compare the result with regression.
Common mistakes
- Choosing the highest and lowest costs instead of the highest and lowest activity.
- Using a pair that straddles a step or change.
- Adjusting the wrong way for a step, or using the adjusted pair to find the fixed cost.
- Forgetting to reverse the adjustment for the function on the other side.
- Forecasting far outside the range.
- Omitting the limitations.
Quick revision
- b = Δcost ÷ Δactivity; a = cost − b × activity; y = a + bx.
- Step in naira: adjust one total, find b, find a from the unadjusted pair, reverse for the other side.
- Step in percentage or change in variable cost: third level, two levels on the same side.
- Limits: two points; linear; relevant range; no measure of reliability.
How the marks are earned
- Select the correct points and show the differences.
- Calculate b and a, with a check.
- Use and criticise the function.
Practice questions
These are original questions, written in the style of the Skills examination. Work each one before you open the answer.
Recall check: multiple choice
Question 1. The high-low method uses:
- The highest and lowest activity levels and their total costs
- All the data
- Only the highest cost
- The average cost
Show the answer
A. Choose by activity, not by cost.
Question 2. The variable cost per unit is:
- Total cost ÷ units
- Fixed cost ÷ units
- The difference in total cost ÷ the difference in activity
- The average of the two costs
Show the answer
C. The difference in cost is wholly variable.
Question 3. The fixed cost is found by:
- Halving the total cost
- Subtracting variable cost at that level from the total cost
- Adding the two costs
- Multiplying by units
Show the answer
B. Either level gives the same answer.
Question 4. The method assumes that:
- All costs are variable
- All costs are fixed
- Costs are random
- Fixed cost is constant in total and variable cost per unit is constant
Show the answer
D. Over the range observed.
Question 5. If fixed costs step up by a stated amount between the levels, you should:
- Adjust one total by the step before comparing
- Ignore the step
- Use the average
- Add the step to both totals
Show the answer
A. Both totals must contain the same fixed cost.
Question 6. If a step is given only as a percentage, you need:
- Nothing more
- The tax rate
- A third activity level
- The selling price
Show the answer
C. Two levels must lie on the same side of the step.
Question 7. The cost function can be used to forecast cost for:
- Any activity level at all
- Levels within or near the observed range
- Only the high level
- Only the low level
Show the answer
B. Far outside the range it is unreliable.
Question 8. A weakness of the high-low method is that it:
- Is too accurate
- Uses all the data
- Is too slow
- Uses only two observations that may not be typical
Show the answer
D. Regression uses all the data.
Question 9. If the variable cost per unit falls above a level, use the pair of observations:
- On the same side of that level
- On opposite sides
- With the highest cost
- With the lowest cost
Show the answer
A. Then apply the percentage to the other side.
Question 10. Direct material cost is normally treated as:
- Fixed
- Semi-fixed
- 100% variable
- A step cost
Show the answer
C. It varies with output.
Section B style: written questions
Question 11 (10 marks). (a) State the three conditions under which the high-low method can be used. (3 marks) (b) State the steps of the method. (4 marks) (c) State THREE limitations. (3 marks)
Question 12 (15 marks). Output and total cost for six months: 12,000 units ₦540,000; 15,000 ₦633,000; 18,000 ₦726,000; 10,000 ₦478,000; 14,000 ₦602,000; 16,000 ₦664,000.
(a) Identify the high and low points and calculate the variable cost per unit. (4 marks) (b) Calculate the fixed cost and state the cost function. (3 marks) (c) Forecast the cost of 13,500 units. (3 marks) (d) State THREE limitations. (3 marks) (e) State why regression is preferred. (2 marks)
Question 13 (20 marks). Fixed costs rise by ₦30,000 when output is 9,000 units or more. At 12,000 units total cost is ₦520,000; at 7,000 units it is ₦355,000.
(a) Calculate the variable cost per unit. (8 marks) (b) State the cost function on each side of the step. (4 marks) (c) Forecast the cost at 10,000 and at 8,000 units. (4 marks) (d) Explain when the high-low method is unreliable. (4 marks)
Model answers
Show the model answer to Question 11
(a) Total costs are known at two different activity levels; fixed cost is the same in total at both; variable cost per unit is constant at both (3).
(b) Select the highest and lowest activity levels and their costs; variable cost per unit = Δcost ÷ Δactivity; fixed cost = total cost − variable cost × activity; write the function and apply it (4).
(c) Any three: only two observations; may not be typical; assumes linearity; valid only in a relevant range; no measure of reliability; affected by inflation (1 each).
Show the model answer to Question 12
(a)
- High 18,000 units ₦726,000; low 10,000 units ₦478,000.
- Differences 8,000 units and ₦248,000.
- Variable cost 248,000 ÷ 8,000 = ₦31 a unit (4).
(b)
- Fixed cost 726,000 − 31 × 18,000 = 726,000 − 558,000 = ₦168,000.
- Check.
478,000 − 310,000 = 168,000. - Total cost = 168,000 + 31x (3).
(c) 168,000 + 31 × 13,500 = 168,000 + 418,500 = ₦586,500 (3).
(d) Any three limitations, as in Question 11 (3).
(e) Regression uses all the data and gives a measure of reliability (2).
Show the model answer to Question 13
(a)
- Add the step to the low total.
355,000 + 30,000 = 385,000. - Variable cost.
(520,000 − 385,000) ÷ (12,000 − 7,000) = 135,000 ÷ 5,000 = ₦27 (8).
(b)
- Fixed above the step.
520,000 − 27 × 12,000 = ₦196,000 - below.
196,000 − 30,000 = ₦166,000. - Functions: 196,000 + 27x at or above 9,000 units; 166,000 + 27x below (4).
(c)
- At 10,000: 196,000 + 270,000 = ₦466,000.
- At 8,000: 166,000 + 216,000 = ₦382,000 (4).
(d) When the two points are unusual; when cost is not linear; when there are steps or changes the data does not reveal; when the forecast is far outside the range (4).
Pathfinder on High-low method and cost estimation
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Expected selling prices; high-low unit variable cost; marginal profit statement; drop a product, price and shift changes; limits of sensitivity analysis.
Revise first: Layouts for the high-low method
Flexible budgets using high-low and step cost; variance report and follow-up.
Revise first: Layouts for the high-low method
High-low variable and fixed cost; demand function P=a-bx, MR=MC optimum price and profit; skimming conditions.
Revise first: Layouts for the high-low method
Flexible budgets from high-low cost split with step cost; budget report and variance follow-up.
Revise first: Layouts for the high-low method
Source: ICAN Pathfinder, Performance Management. Diets covered: March/July Diet, 2020 to May Diet, 2026. All 13 diets in the Pathfinder are mapped.
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