## Segregating Semi-Variable Costs into Fixed and Variable Components
Semi-variable costs have both fixed and variable elements. Five methods are used to separate them:
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### 1. Graphical Method
Steps:
1. Collect observations: total cost at various output levels.
2. Plot output (X-axis) vs total cost (Y-axis).
3. Draw a line of best-fit by visual judgment.
4. Where the line intersects the Y-axis = Fixed Cost.
5. Draw a horizontal line at that intercept = fixed cost line.
6. For any output level: Variable Cost = Total Cost − Fixed Cost.
Advantages: Simple; accessible to non-specialists; quick rough estimates.
Limitations: Subjective (line drawn by judgment); less precise; unreliable outside data range.
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### 2. High-Low Method
Formula:
$$\text{Variable Cost Rate} = \frac{\text{Cost at Highest Level} - \text{Cost at Lowest Level}}{\text{Output at Highest Level} - \text{Output at Lowest Level}}$$
Then: Fixed Cost = Total Cost at either level − (Variable Rate × Output at that level)
Advantage: Quick and simple.
Limitation: Uses only two extreme observations; ignores all other data points; distorted if extremes are outliers.
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### 3. Analytical Method
- Experienced cost accountant empirically estimates the variable proportion of each semi-variable item.
- e.g., Supervision cost: 20% variable, 80% fixed.
- Advantage: Easy to apply.
- Limitation: Highly subjective; relies on individual judgment.
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### 4. Comparison by Period / Level of Activity Method
- Compare two output levels and their corresponding costs.
- Since fixed element is constant, the difference in cost = difference in variable cost.
$$\text{Variable Cost per Unit} = \frac{\text{Change in Expense}}{\text{Change in Output}}$$
Then: Fixed Cost = Total Cost − (Variable Rate × Output)
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### 5. Least Squares Method (Best Method)
- Statistical method; finds the line of best fit using all data points (not just two extremes).
- Uses the linear equation:
$$y = mx + c$$
Where:
- $y$ = Total cost
- $x$ = Volume of output
- $m$ = Variable cost per unit
- $c$ = Total fixed cost
- Normal equations solved simultaneously to find $m$ and $c$.
- Most accurate because it uses all observations and minimises squared deviations.
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### Method Comparison
| Method | Data Used | Subjectivity | Accuracy |
|---|---|---|---|
| Graphical | All points (visual) | High | Low-Medium |
| High-Low | Only 2 points | Low | Low (outlier risk) |
| Analytical | Judgment | Very High | Depends on expertise |
| Comparison by Period | 2 selected levels | Low | Moderate |
| Least Squares | All points (statistical) | None | Highest |