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, forecasting, and pricing decisions. This in-depth guide will walk you through the high-low method, its applications, limitations, and offer alternative methods for a more comprehensive cost analysis.

Understanding Mixed Costs

Before diving into the high-low method, let's define mixed costs. These costs exhibit characteristics of both fixed and variable costs.

• Fixed Costs: Remain constant regardless of the production volume or activity level. Examples include rent, salaries, and insurance premiums.
• Variable Costs: Change proportionally with the production volume or activity level. Examples include direct materials, direct labor (in some cases), and sales commissions.
• Mixed Costs: Contain elements of both fixed and variable costs. Examples include utilities (a fixed base charge plus a variable charge based on consumption), maintenance costs (fixed preventative maintenance plus variable reactive maintenance based on usage), and telephone expenses (a fixed line rental plus variable call charges).

The High-Low Method Formula

The high-low method uses the highest and lowest activity levels within a given period to separate the fixed and variable cost components. The formula is based on the following logic:

Change in Cost / Change in Activity = Variable Cost per Unit

Once the variable cost per unit is determined, the fixed cost can be calculated by substituting the values into the cost equation:

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

Let's break down the steps:

1. Identify the highest and lowest activity levels: Review your historical data to find the periods with the highest and lowest activity levels. Activity levels can be measured in various units, depending on your business: production units, machine hours, miles driven, etc. It's crucial to choose a consistent measure across all data points.

2. Determine the corresponding total costs: For each of the identified highest and lowest activity levels, note the total costs incurred during those periods. This data should include both fixed and variable costs.

3. Calculate the change in cost: Subtract the total cost at the lowest activity level from the total cost at the highest activity level.

4. Calculate the change in activity: Subtract the lowest activity level from the highest activity level.

5. Calculate the variable cost per unit: Divide the change in cost by the change in activity. This gives you the variable cost associated with each unit of activity.

6. Calculate the fixed cost: Substitute the variable cost per unit, the total cost at either the highest or lowest activity level, and the corresponding activity level into the total cost equation. Solve for the fixed cost.

Example: Applying the High-Low Method

Let's illustrate with an example. Suppose a company tracks its total monthly maintenance costs and machine hours over a six-month period:

1. Identify Highest and Lowest Activity Levels:

• Highest Activity: 1000 machine hours (May)
• Lowest Activity: 300 machine hours (June)

2. Determine Corresponding Total Costs:

• Highest Cost: $4,300 (May)
• Lowest Cost: $1,900 (June)

3. Calculate the Change in Cost:

$4,300 - $1,900 = $2,400

4. Calculate the Change in Activity:

1000 - 300 = 700 machine hours

5. Calculate the Variable Cost per Unit:

$2,400 / 700 = $3.43 per machine hour

6. Calculate the Fixed Cost:

Using the data from May (highest activity):

$4,300 = Fixed Cost + ($3.43 * 1000)

Fixed Cost = $4,300 - $3,430 = $870

Therefore, the estimated cost equation is:

Total Maintenance Cost = $870 + ($3.43 * Machine Hours)

Limitations of the High-Low Method

While the high-low method is straightforward, it has several limitations:

• Sensitivity to Outliers: The method relies heavily on only two data points (highest and lowest). Outliers or unusual data points in these two selected months can significantly skew the results and lead to inaccurate estimations of fixed and variable costs. A single unusually high or low data point can dramatically change the calculated variable cost per unit and fixed costs.

• Ignoring Other Data Points: The high-low method ignores the remaining data points, potentially discarding valuable information and leading to a less accurate estimation. More sophisticated methods consider all data points for a more robust analysis.

• Assumption of Linearity: The high-low method assumes a linear relationship between cost and activity. In reality, this relationship might be curvilinear, especially at very high or low activity levels. A non-linear relationship will produce inaccurate results.

• Lack of Consideration for External Factors: The method doesn't account for external factors that might influence costs, such as changes in material prices, technological advancements, or economic conditions.

Alternative Methods for Cost Estimation

More robust methods exist for determining the fixed and variable components of mixed costs. These methods offer greater accuracy by considering all available data points:

• Scattergraph Method: This visual method plots the historical cost and activity data on a graph. A line of best fit is drawn through the plotted points, visually estimating the fixed and variable costs. This method is less precise than regression analysis but offers a quick visual assessment.

• Regression Analysis: This statistical method uses all data points to determine the line of best fit using mathematical calculations. It provides a more precise estimate of fixed and variable costs than the high-low method and accounts for the variability in the data.

• Least Squares Regression: A specific type of regression analysis that minimizes the sum of the squared differences between observed and predicted values. This yields the most statistically accurate estimation of the cost equation.

Conclusion

The high-low method provides a simple and easy-to-understand approach to estimating fixed and variable costs. However, its limitations should be carefully considered. For increased accuracy, especially in situations with a large amount of data or suspected non-linear relationships, employing more sophisticated methods like regression analysis is recommended. The choice of method depends on the data availability, complexity of the cost relationship, and the desired level of accuracy. Understanding these methods and their limitations is essential for effective cost management and decision-making in any organization. Remember to always carefully review and interpret your results, considering potential external factors that might impact your cost structure.