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2.3 The High-Low Method and Cost Prediction
CIMA BA2: Fundamentals of Management Accounting Exam
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1 Chapter 1: The Context of Management Accounting
1.1 The Need for Management Accounting, the GMAP Definition & Comparison with Financial Accounting 1.2 Qualities of Good Management Information: From Data to Decisions 1.3 Information for Operational, Managerial and Strategic Levels 1.4 The Role of the Management Accountant: CIMA's View, IFAC's Domain & Position in the Organisation 1.5 CIMA as a Professional Body: Members, Candidates, the Profession & Society
2 Chapter 2: Cost Identification, Classification and Behaviour
2.1 Cost Classification by Nature, Function, and Element 2.2 Cost Behaviour Patterns and Relevant Range 2.3 The High-Low Method and Cost Prediction 2.4 Scattergraph and Least-Squares Regression for Cost Estimation
3 Chapter 3: Overheads and Absorption Costing
3.1 Production Overheads: Allocation and Apportionment 3.2 Overhead Absorption Rates (OAR) & Under/Over-Absorption
4 Chapter 4: Marginal Costing, Profit Reconciliation and Cost-Based Pricing
4.1 Marginal Costing vs Absorption Costing Principles 4.2 Reconciling Marginal and Absorption Costing Operating Profits 4.3 Pricing with Cost Information: Full-Cost-Plus, Marginal-Cost-Plus, Mark-Ups, Margins and Return Targets
5 Chapter 5: Budget Preparation: Functional, Master and Cash Budgets
5.1 Purposes of Budgeting & The Budgeting Process 5.2 The Principal Budget Factor & Functional Budgets 5.3 The Master Budget: Budgeted Profit or Loss, Financial Position and Cash Flow 5.4 Cash Budgets & Cash Flow Forecasting
6 Chapter 6: Budgetary Control: Flexible Budgets, Behaviour and Budgeting Approaches
6.1 Fixed vs Flexible Budgeting and Budget Flexing 6.2 Budgetary Control Systems, Participation & Behavioural Aspects 6.3 Alternative Budgeting Approaches: Incremental, ZBB & Rolling Budgets
7 Chapter 7: Standard Costing and Cost Variances
7.1 Standard Costing Principles and Types of Standards 7.2 Direct Material Price and Usage Variances 7.3 Direct Labour Rate, Efficiency, and Idle Time Variances 7.4 Variable and Fixed Overhead Variances
8 Chapter 8: Sales Variances, Operating Statements and Interpreting Variances
8.1 Sales Variances and Operating Statements (Marginal and Absorption Formats) 8.2 Interpreting Variances: Causes, Interrelationships and Deciding What to Investigate
9 Chapter 9: Performance Measurement
9.1 The Need for Performance Measures: Responsibility Accounting, Controllability and Service Industries 9.2 Financial and Non-Financial Performance Measures in Manufacturing and Service Organisations
10 Chapter 10: Integrated Accounts, Job and Batch Costing and Management Reports
10.1 Integrating Cost and Financial Accounts: Control Accounts and the Manufacturing Account 10.2 Integrated Ledgers with Under- and Over-Absorption and Standard Cost Variances 10.3 Job and Batch Costing: Job Cost Cards, Job Accounts and Pricing a Job 10.4 Cost Reports for Manufacturing, Service and Not-for-Profit Organisations
11 Chapter 11: Risk, Probability and Statistics for Decision-Making
11.1 Risk, Uncertainty and Probability: Rules and Joint Probabilities for Decisions 11.2 Expected Values, Expected Value Tables and Their Limitations 11.3 Averages and Dispersion: Mean, Median, Mode, Range, Variance, Standard Deviation and Coefficient of Variation 11.4 The Normal Distribution: Z-Scores, Normal Distribution Tables and Business Probabilities
12 Chapter 12: Relevant Costing and Short-Term Decisions
12.1 Relevant Cost Concepts: Future, Incremental, and Opportunity Costs 12.2 Relevant Costs of Materials, Labour, and Overheads 12.3 Short-Term Operational Decisions: Make-or-Buy, Shutdowns, Special Orders
13 Chapter 13: Breakeven Analysis and Limiting Factor Analysis
13.1 Single-Product Break-Even Analysis & Margin of Safety 13.2 Target Profit Calculations, Operating Gearing & CVP Assumptions 13.3 Multi-Product CVP Analysis & Break-Even Charts 13.4 Limiting Factor Analysis (Key Factor Analysis)
14 Chapter 14: Long-Term Decisions: Time Value of Money, Payback, NPV and IRR
14.1 Time Value of Money: Compounding, Discounting, Annuities & Perpetuities 14.2 Payback Period Method: Constant and Uneven Cash Flows 14.3 Net Present Value (NPV): Methodology and Decision Rules 14.4 Internal Rate of Return (IRR) and Interpolation
2.3 The High-Low Method and Cost Prediction
Key Takeaways Explain This Topic AI
The high-low method separates semi-variable costs into fixed and variable components by analyzing the difference in costs between the highest and lowest activity levels.
Selection of observation periods must always be driven by activity volume (e.g., machine hours, units produced), never by the highest or lowest monetary cost.
Adjustments must be made prior to calculating unit variable rates when stepped fixed costs or price inflation affect data points across the observation window.
While simple and objective to apply, the method's primary limitation is relying on just two extreme data points while discarding all intermediate operational data.
Last updated: September 2026
In business operations, many overhead expenditures—such as plant maintenance, utility consumption, equipment servicing, and fleet transport—are semi-variable. To prepare operational budgets, determine contribution margins, and forecast total production expenditures at anticipated activity volumes, management accountants must decompose mixed costs into their distinct fixed and variable elements.
The high-low method is the standard mathematical technique taught and applied for separating semi-variable costs when historical volume and cost data are available.
Purpose and Principles of Cost Estimation
The fundamental premise of the high-low method rests on the linear cost equation: y = a + b x y = a + bx y = a + b x
Where:
- y = Total mixed cost y = \text{Total mixed cost} y = Total mixed cost
- a = Total fixed cost a = \text{Total fixed cost} a = Total fixed cost
b = Variable cost per unit of activity b = \text{Variable cost per unit of activity} b = Variable cost per unit of activity
x = Level of activity x = \text{Level of activity} x = Level of activity
Because total fixed costs ( a a a ) are assumed to remain constant between different activity levels within the relevant range, any change in total cost between two operating periods is assumed to be caused entirely by the variable cost associated with the difference in activity volume.
The Step-by-Step High-Low Methodology
Applying the high-low method involves a disciplined, multi-step calculation procedure:
Step 1: Identify Extreme Activity Levels
Review the historical operational records across all available observation periods. Select the period with the highest activity level ( x high x_{\text{high}} x high ) and the period with the lowest activity level ( x low x_{\text{low}} x low ), along with their corresponding total costs ( y high y_{\text{high}} y high and y low y_{\text{low}} y low ).
Important
The Golden Selection Rule: The two representative periods must be chosen based strictly on the level of activity , NEVER on the magnitude of the cost. If the period with the highest activity happens to have a lower cost than another period due to random operational variations, the highest activity period must still be selected.
Step 2: Calculate Variable Cost Per Unit ( b b b )
Compute the difference in cost ( Δ y \Delta y Δ y ) and the difference in activity ( Δ x \Delta x Δ x ) between the high and low points. The variable cost per unit ( b b b ) represents the slope of the cost line: b = Cost at highest activity − Cost at lowest activity Highest activity − Lowest activity = y high − y low x high − x low = Δ y Δ x b = \frac{\text{Cost at highest activity} - \text{Cost at lowest activity}}{\text{Highest activity} - \text{Lowest activity}} = \frac{y_{\text{high}} - y_{\text{low}}}{x_{\text{high}} - x_{\text{low}}} = \frac{\Delta y}{\Delta x} b = Highest activity − Lowest activity Cost at highest activity − Cost at lowest activity = x high − x low y high − y low = Δ x Δ y
Step 3: Calculate Total Fixed Costs ( a a a )
Substitute the calculated variable cost per unit ( b b b ) into either the highest or lowest activity data point and rearrange the equation to solve for a a a : a = y high − ( b × x high ) a = y_{\text{high}} - (b \times x_{\text{high}}) a = y high − ( b × x high ) or \text{or} or a = y low − ( b × x low ) a = y_{\text{low}} - (b \times x_{\text{low}}) a = y low − ( b × x low )
Both substitutions must yield the identical fixed cost value, providing an immediate arithmetic reconciliation check.
Step 4: Formulate the Forecasting Equation
Express the final cost function as y = a + b x y = a + bx y = a + b x . Management can now predict total cost for any desired future activity level ( x target x_{\text{target}} x target ) falling within the relevant range.
Comprehensive Standard Worked Example
Starlight Manufacturing records the following machine hours and total plant maintenance expenditures over a six-month period:
- Month Machine Hours ( x x x ) Total Maintenance Cost ( y y y )
- January 4,000 $38,000
- February 6,000 $48,000
- March (Lowest Activity) 3,500 $35,500
- April 5,000 $43,000
- May (Highest Activity) 7,500 $55,500
- June 6,500 $50,500
Calculation Walkthrough:
Identify High and Low Activity Points:
Highest Activity (May): x high = 7 , 500 hours x_{\text{high}} = 7,500 \text{ hours} x high = 7 , 500 hours ; y high = $ 55 , 500 y_{\text{high}} = \text{\textdollar}55,500 y high = $ 55 , 500
Lowest Activity (March): x low = 3 , 500 hours x_{\text{low}} = 3,500 \text{ hours} x low = 3 , 500 hours ; y low = $ 35 , 500 y_{\text{low}} = \text{\textdollar}35,500 y low = $ 35 , 500
Calculate Activity and Cost Differences:
Δ x = 7 , 500 − 3 , 500 = 4 , 000 machine hours \Delta x = 7,500 - 3,500 = 4,000 \text{ machine hours} Δ x = 7 , 500 − 3 , 500 = 4 , 000 machine hours
Δ y = $ 55 , 500 − $ 35 , 500 = $ 20 , 000 \Delta y = \text{\textdollar}55,500 - \text{\textdollar}35,500 = \text{\textdollar}20,000 Δ y = $ 55 , 500 − $ 35 , 500 = $ 20 , 000
Compute Variable Cost Per Machine Hour ( b b b ): b = $ 20 , 000 4 , 000 hours = $ 5.00 per machine hour b = \frac{\text{\textdollar}20,000}{4,000 \text{ hours}} = \text{\textdollar}5.00 \text{ per machine hour} b = 4 , 000 hours $ 20 , 000 = $ 5.00 per machine hour
Compute Total Fixed Cost ( a a a ):
Using the high point: a = $ 55 , 500 − ( $ 5.00 × 7 , 500 ) = $ 55 , 500 − $ 37 , 500 = $ 18 , 000 a = \text{\textdollar}55,500 - (\text{\textdollar}5.00 \times 7,500) = \text{\textdollar}55,500 - \text{\textdollar}37,500 = \text{\textdollar}18,000 a = $ 55 , 500 − ( $ 5.00 × 7 , 500 ) = $ 55 , 500 − $ 37 , 500 = $ 18 , 000
Validating at the low point: a = $ 35 , 500 − ( $ 5.00 × 3 , 500 ) = $ 35 , 500 − $ 17 , 500 = $ 18 , 000 a = \text{\textdollar}35,500 - (\text{\textdollar}5.00 \times 3,500) = \text{\textdollar}35,500 - \text{\textdollar}17,500 = \text{\textdollar}18,000 a = $ 35 , 500 − ( $ 5.00 × 3 , 500 ) = $ 35 , 500 − $ 17 , 500 = $ 18 , 000
Predict Cost at Future Activity: The resulting cost formula is: Total Cost = $ 18 , 000 + ( $ 5.00 × Machine Hours ) \text{Total Cost} = \text{\textdollar}18,000 + (\text{\textdollar}5.00 \times \text{Machine Hours}) Total Cost = $ 18 , 000 + ( $ 5.00 × Machine Hours ) .
If Starlight plans to operate 8,000 machine hours in July (within the relevant range): Forecasted Maintenance Cost = $ 18 , 000 + ( $ 5.00 × 8 , 000 ) = $ 18 , 000 + $ 40 , 000 = $ 58 , 000 \text{Forecasted Maintenance Cost} = \text{\textdollar}18,000 + (\text{\textdollar}5.00 \times 8,000) = \text{\textdollar}18,000 + \text{\textdollar}40,000 = \text{\textdollar}58,000 Forecasted Maintenance Cost = $ 18 , 000 + ( $ 5.00 × 8 , 000 ) = $ 18 , 000 + $ 40 , 000 = $ 58 , 000
Advanced High-Low: Stepped Fixed Cost Adjustments
In practical operations, fixed costs do not always remain flat across wide swings in volume. If an increase in activity crosses a capacity threshold, a stepped fixed cost will occur. When fixed costs differ between the highest and lowest activity points, applying the standard high-low formula without adjustment will distort the variable cost rate.
The Adjustment Technique
If fixed costs increase by a known stepped amount at higher activity volumes:
Either deduct the stepped fixed cost increase from the cost at the highest activity point before computing the cost difference;
Or add the stepped fixed cost increase to the lowest activity cost.
This adjustment isolates the change in cost attributable purely to variable operational activity.
Step-Cost Worked Numerical Demonstration
Highland Engineering records the following quarterly output and total production overheads:
- Lowest Activity (Quarter 1): 4,000 units produced; Total Cost = $47,000
- Highest Activity (Quarter 4): 9,000 units produced; Total Cost = $92,000
Condition: Plant records indicate that because production exceeded 6,500 units in Quarter 4, an additional supervisor was employed, stepping up total fixed overheads by $5,000 .
Step-by-Step Solution:
Adjust the High Activity Cost for the Step: Adjusted High Cost = $ 92 , 000 − $ 5 , 000 = $ 87 , 000 \text{Adjusted High Cost} = \text{\textdollar}92,000 - \text{\textdollar}5,000 = \text{\textdollar}87,000 Adjusted High Cost = $ 92 , 000 − $ 5 , 000 = $ 87 , 000
(This normalizes the high cost to the same fixed-cost baseline as the low activity period).
Calculate Variable Cost Per Unit ( b b b ): b = Adjusted High Cost − Low Cost High Activity − Low Activity = $ 87 , 000 − $ 47 , 000 9 , 000 − 4 , 000 = $ 40 , 000 5 , 000 units = $ 8.00 per unit b = \frac{\text{Adjusted High Cost} - \text{Low Cost}}{\text{High Activity} - \text{Low Activity}} = \frac{\text{\textdollar}87,000 - \text{\textdollar}47,000}{9,000 - 4,000} = \frac{\text{\textdollar}40,000}{5,000 \text{ units}} = \text{\textdollar}8.00 \text{ per unit} b = High Activity − Low Activity Adjusted High Cost − Low Cost = 9 , 000 − 4 , 000 $ 87 , 000 − $ 47 , 000 = 5 , 000 units $ 40 , 000 = $ 8.00 per unit
Calculate Baseline Fixed Cost ( a base a_{\text{base}} a base ):
Using the low activity point (Quarter 1, where the step has not occurred): a base = $ 47 , 000 − ( $ 8.00 × 4 , 000 ) = $ 47 , 000 − $ 32 , 000 = $ 15 , 000 a_{\text{base}} = \text{\textdollar}47,000 - (\text{\textdollar}8.00 \times 4,000) = \text{\textdollar}47,000 - \text{\textdollar}32,000 = \text{\textdollar}15,000 a base = $ 47 , 000 − ( $ 8.00 × 4 , 000 ) = $ 47 , 000 − $ 32 , 000 = $ 15 , 000
Define the Segmented Cost Functions:
For activity up to 6,500 units: Total Cost = $ 15 , 000 + ( $ 8.00 × x ) \text{Total Cost} = \text{\textdollar}15,000 + (\text{\textdollar}8.00 \times x) Total Cost = $ 15 , 000 + ( $ 8.00 × x )
For activity exceeding 6,500 units: Total Cost = ( $ 15 , 000 + $ 5 , 000 ) + ( $ 8.00 × x ) = $ 20 , 000 + ( $ 8.00 × x ) \text{Total Cost} = (\text{\textdollar}15,000 + \text{\textdollar}5,000) + (\text{\textdollar}8.00 \times x) = \text{\textdollar}20,000 + (\text{\textdollar}8.00 \times x) Total Cost = ( $ 15 , 000 + $ 5 , 000 ) + ( $ 8.00 × x ) = $ 20 , 000 + ( $ 8.00 × x )
Forecasting Example: If budgeted production for next quarter is 8,500 units : Forecasted Cost = $ 20 , 000 + ( $ 8.00 × 8 , 500 ) = $ 20 , 000 + $ 68 , 000 = $ 88 , 000 \text{Forecasted Cost} = \text{\textdollar}20,000 + (\text{\textdollar}8.00 \times 8,500) = \text{\textdollar}20,000 + \text{\textdollar}68,000 = \text{\textdollar}88,000 Forecasted Cost = $ 20 , 000 + ( $ 8.00 × 8 , 500 ) = $ 20 , 000 + $ 68 , 000 = $ 88 , 000
Advanced High-Low: Adjusting for Price Inflation and Wage Shifts
When observation periods span several quarters or years, general price inflation, utility tariff adjustments, or statutory wage increases can inflate costs in later periods. If historical costs reflect different price levels, applying the high-low formula directly will falsely inflate the variable cost slope.
Indexation Methodology
To correct for price changes:
Obtain the relevant cost price index for each period.
Convert all historical costs to a common price level (typically current period prices) prior to applying high-low: Standardized Cost = Historical Cost × Base Price Index Period Price Index \text{Standardized Cost} = \text{Historical Cost} \times \frac{\text{Base Price Index}}{\text{Period Price Index}} Standardized Cost = Historical Cost × Period Price Index Base Price Index
Apply the standard high-low calculation using the standardized costs.
Once the linear equation is derived, re-inflate the variable and fixed components to the expected price level of the future budgeting period.
Strategic Evaluation: Strengths and Technical Limitations
Management accountants must critically appraise the high-low method when selecting cost estimation tools for organizational forecasting:
Key Advantages
Simplicity and Speed: Requires only straightforward basic arithmetic. No specialized statistical software or complex matrix modeling is needed.
Objective and Replicable: Two analysts analyzing the same historical dataset will arrive at the exact same cost equation, eliminating subjective graphical bias.
Intuitive Presentation: Readily understood by non-financial operational directors, workshop supervisors, and commercial executives.
Critical Technical Limitations
Sensitivity to Outliers: Because the method relies entirely on the two extreme data points, any operational anomaly in those two periods—such as a machinery breakdown, an industrial strike, an adverse weather closure, or an unusual overtime surge—will severely distort the resulting cost formula.
Disregards Intermediate Data: The method completely discards all observations recorded between the highest and lowest activity points. Valuable operational intelligence from intermediate periods is ignored.
Assumption of Strict Linearity: Forces a straight-line relationship onto operational processes that may naturally follow a curved trajectory due to learning efficiencies or plant congestion.
Comparison with Linear Regression
Where accurate forecasting is paramount, linear regression analysis (the method of ordinary least squares) is superior to the high-low method. Regression utilizes every available historical observation, minimizes the sum of squared errors, and provides statistical measures of reliability (such as the coefficient of determination, R 2 R^2 R 2 ) to evaluate how well the cost equation fits the actual data.