The High-low Formula To Compute Total Costs Is:

The High-Low Method: A Comprehensive Guide to Calculating Total Costs

The high-low method is a simple technique used in cost accounting to estimate the fixed and variable components of a mixed cost. A mixed cost, also known as a semi-variable cost, contains both fixed and variable elements. Understanding these components is crucial for accurate budgeting, pricing decisions, and performance evaluation. This detailed guide will explore the high-low method, its applications, limitations, and alternatives.

Understanding Mixed Costs

Before diving into the high-low method, it's essential to grasp the concept of mixed costs. These costs exhibit characteristics of both fixed and variable costs.

• Fixed Costs: These costs remain constant regardless of the production volume or activity level. Examples include rent, salaries, and insurance premiums. They are incurred even if no goods are produced or services rendered.

• Variable Costs: These costs directly correlate with the production volume or activity level. As production increases, variable costs increase proportionally. Examples include raw materials, direct labor (in some cases), and packaging.

• Mixed Costs: These costs contain elements of both fixed and variable costs. A classic example is utilities. A base monthly charge (fixed cost) is incurred regardless of usage, while additional charges are added based on consumption (variable cost). Other examples include telephone bills, maintenance costs, and sales commissions with a base salary component.

The High-Low Method Formula: A Step-by-Step Approach

The high-low method uses the highest and lowest activity levels within a given period to separate the fixed and variable components of a mixed cost. Here's a step-by-step breakdown of the formula:

1. Identify the Highest and Lowest Activity Levels:

Begin by reviewing your cost data and identifying the periods with the highest and lowest activity levels. The "activity level" is the driver of the cost—it could be units produced, machine hours, labor hours, or sales revenue, depending on the specific cost you're analyzing.

2. Calculate the Variable Cost per Unit:

The formula for calculating the variable cost per unit is:

(Highest Cost – Lowest Cost) / (Highest Activity Level – Lowest Activity Level)

This formula determines the change in cost divided by the change in activity, giving you the variable cost per unit.

3. Calculate the Fixed Cost:

Once you've determined the variable cost per unit, you can calculate the fixed cost using either the highest or lowest activity level data. The formula is:

Total Cost – (Variable Cost per Unit * Activity Level)

Substitute the values from either the highest or lowest activity level into this formula. You should obtain the same fixed cost using either data point, barring any minor rounding errors.

4. Develop the Cost Formula:

Finally, express the relationship between total cost, variable cost, and fixed cost using a simple linear equation:

Total Cost = Fixed Cost + (Variable Cost per Unit * Activity Level)

This formula enables you to predict the total cost at various activity levels within the relevant range.

Example: Applying the High-Low Method

Let's illustrate the high-low method with a concrete example. Suppose a company's maintenance costs over the past five months are as follows:

Month	Activity Level (Machine Hours)	Total Maintenance Cost
January	500	$2,500
February	700	$3,100
March	900	$3,700
April	600	$2,900
May	1000	$4,300

1. Identify the Highest and Lowest Activity Levels:

• Highest Activity Level: 1000 machine hours (May)
• Lowest Activity Level: 500 machine hours (January)

2. Calculate the Variable Cost per Unit:

• ($4,300 – $2,500) / (1000 – 500) = $3.60 per machine hour

3. Calculate the Fixed Cost:

Using the highest activity level (May):

• $4,300 – ($3.60 * 1000) = $700

Using the lowest activity level (January):

• $2,500 – ($3.60 * 500) = $700

4. Develop the Cost Formula:

Total Maintenance Cost = $700 + ($3.60 * Machine Hours)

Strengths and Limitations of the High-Low Method

The high-low method offers several advantages:

• Simplicity: It's easy to understand and apply, requiring minimal mathematical expertise.
• Ease of Use: It requires readily available data, making it practical for quick cost estimations.
• Cost-Effectiveness: Its simplicity translates to low implementation costs.

However, the method also has significant limitations:

• Sensitivity to Outliers: The selection of the highest and lowest points can be significantly influenced by outliers, leading to inaccurate estimations if the chosen data points don't truly represent the typical cost behavior.
• Ignoring Data Points: The high-low method disregards all data points except the highest and lowest, potentially losing valuable information. This can lead to a less accurate representation of the cost relationship than more sophisticated methods.
• Assumption of Linearity: The high-low method assumes a perfectly linear relationship between cost and activity. In reality, cost behavior is often more complex and may exhibit non-linear patterns.
• Inaccuracy with Wide Data Ranges: The method's accuracy decreases as the range of activity levels increases. The broader the activity range, the more likely the relationship between activity and cost is non-linear.

Alternatives to the High-Low Method

Several alternative methods offer more accurate estimations of fixed and variable costs, addressing the limitations of the high-low method:

• Scattergraph Method: This visual technique plots all data points on a graph, allowing for a visual assessment of the relationship between cost and activity. A line of best fit is then drawn through the data points to estimate fixed and variable costs. While less precise than regression analysis, it provides a better understanding of the data's overall pattern than the high-low method.
• Least Squares Regression Analysis: This statistical technique provides a more accurate and reliable estimation of fixed and variable costs. It considers all data points and minimizes the sum of squared errors, providing a better fit than a simple visual estimation. While requiring more statistical expertise, it significantly improves accuracy.
• Account Analysis: This method involves carefully examining each cost item and classifying it as fixed, variable, or mixed based on its nature. This method is subjective and relies heavily on expertise but can provide valuable insights into cost behavior.

Conclusion: Choosing the Right Method

The high-low method, while simple and convenient, has limitations. For quick estimations and simple cost structures where the assumption of linearity holds reasonably well, it can be a useful tool. However, for more accurate and reliable cost estimations, especially when dealing with complex cost structures or when accuracy is crucial, the scattergraph method, least squares regression analysis, or account analysis might be more appropriate. Choosing the right method depends on the complexity of the cost structure, the available data, and the desired level of accuracy. Understanding the strengths and weaknesses of each method is crucial for making informed decisions about cost estimation. Always consider the context and limitations when interpreting results.