Analyzing Mixed Costs Using Regression and High-Low Methods

 Introduction

In cost accounting, a mixed cost consists of both fixed and variable components. To separate these components, businesses use different techniques such as the High-Low Method and Regression Analysis. Understanding these methods helps in budgeting, forecasting, and decision-making.

1. High-Low Method

The High-Low Method is a simple way to estimate fixed and variable costs by using the highest and lowest levels of activity.

Steps to Apply the High-Low Method:

1. Identify the highest and lowest activity levels and their corresponding total costs.
2. Calculate the variable cost per unit: $VC = \frac{\text{Cost at High Activity} - \text{Cost at Low Activity}}{\text{High Activity Units} - \text{Low Activity Units}}$
3. Determine fixed cost by using the total cost equation: $\text{Total Cost} = \text{Fixed Cost} + (\text{Variable Cost per Unit} \times \text{Activity Level})$
4. Develop the cost function: $Y = a + bX$ where:
   • Y = Total Cost
   • a = Fixed Cost
   • b = Variable Cost per Unit
   • X = Activity Level

Numerical Example: High-Low Method

Activity Level (Units)	Total Cost ($)
10,000	50,000
25,000	80,000

1. Compute Variable Cost per Unit: $$VC = \frac{80,000 - 50,000}{25,000 - 10,000} = \frac{30,000}{15,000} = 2\text{ per unit}$$
2. Compute Fixed Cost using the cost function at the high level: $$80,000 = a + (2 \times 25,000)$$ $$a = 80,000 - 50,000 = 30,000$$ Cost equation: $Y = 30,000 + 2X$

2. Regression Analysis

Regression analysis provides a more accurate method to separate fixed and variable costs by using statistical techniques.

Steps to Apply Regression Analysis:

1. Collect historical cost data with different activity levels.
2. Use statistical software (Excel, SPSS, R) to run a linear regression.
3. The output provides:
   • Intercept (Fixed Cost) = Estimated fixed cost component.
   • Slope (Variable Cost per Unit) = Estimated variable cost per unit.

Numerical Example: Regression Analysis

Suppose regression analysis provides the following results:

• Intercept = $32,000 (Fixed Cost)
• Slope = $1.90 per unit (Variable Cost)
• Cost equation: Y = 32,000 + 1.90X

3. Comparison: High-Low vs. Regression Analysis

Criteria	High-Low Method	Regression Analysis
Accuracy	Less accurate (uses only two points)	More accurate (uses all data points)
Simplicity	Easy to compute manually	Requires statistical software
Data Requirement	Uses only extreme values	Uses all available data points
Sensitivity	Affected by outliers	Reduces outlier impact

Conclusion

• The High-Low Method is useful for quick estimations but is sensitive to extreme values.
• Regression Analysis provides more accurate results by considering all data points.
• In practice, businesses often prefer regression analysis for better decision-making, especially when large datasets are available.