High-Low Method

What Is the High-Low Method?

In cost accounting, the high-low method is a way of attempting to separate out fixed and variable costs given a limited amount of data. The high-low method involves taking the highest level of activity and the lowest level of activity and comparing the total costs at each level.

If the variable cost is a fixed charge per unit and fixed costs remain the same, it is possible to determine the fixed and variable costs by solving the system of equations. It is worth being cautious when using the High-Low Method, however, as it can yield more or less accurate results depending on the distribution of values between the highest and lowest dollar amounts or quantities.

Understanding the High-Low Method

Calculating the outcome for the high-low method requires a few formula steps. First, you must calculate the variable cost component and then the fixed cost component, and then plug the results into the cost model formula.

First, determine the variable cost component:

Variable Cost = HAC − Lowest Activity Cost HAUs − Lowest Activity Units where: HAC = Highest activity cost HAUs = Highest activity units Variable cost is per unit \begin{aligned} &\text{Variable Cost} = \frac { \text{HAC} - \text{Lowest Activity Cost} }{ \text{HAUs} - \text{Lowest Activity Units} } \\ &\textbf{where:} \\ &\text{HAC} = \text{Highest activity cost} \\ &\text{HAUs} = \text{Highest activity units} \\ &\text{Variable cost is per unit} \\ \end{aligned} Variable Cost=HAUs−Lowest Activity UnitsHAC−Lowest Activity Costwhere:HAC=Highest activity costHAUs=Highest activity unitsVariable cost is per unit

Next, use the following formula to determine the fixed cost component:

Fixed Cost = HAC − ( Variable Cost × HAUs ) \begin{aligned} &\text{Fixed Cost} = \text{HAC} - ( \text{Variable Cost} \times \text{HAUs} ) \\ \end{aligned} Fixed Cost=HAC−(Variable Cost×HAUs)

Use the results of the first two formulas to calculate the high-low cost result using the following formula:

High-Low Cost = Fixed Cost + ( Variable Cost × UA ) where: UA = Unit activity \begin{aligned} &\text{High-Low Cost} = \text{Fixed Cost} + ( \text{Variable Cost} \times \text{UA} ) \\ &\textbf{where:} \\ &\text{UA} = \text{Unit activity} \\ \end{aligned} High-Low Cost=Fixed Cost+(Variable Cost×UA)where:UA=Unit activity

What Does the High-Low Method Tell You?

The costs associated with a product, product line, equipment, store, geographic sales region, or subsidiary, consist of both variable costs and fixed costs. To determine both cost components of the total cost, an analyst or accountant can use a technique known as the high-low method.

The high-low method is used to calculate the variable and fixed cost of a product or entity with mixed costs. It takes two factors into consideration. It considers the total dollars of the mixed costs at the highest volume of activity and the total dollars of the mixed costs at the lowest volume of activity. The total amount of fixed costs is assumed to be the same at both points of activity. The change in the total costs is thus the variable cost rate times the change in the number of units of activity.

Example of How to Use the High-Low Method

For example, the table below depicts the activity for a cake bakery for each of the 12 months of a given year.

Below is an example of the high-low method of cost accounting:

Cakes Baked (units)

Total Cost ($)

October

The highest activity for the bakery occurred in October when it baked the highest number of cakes, while August had the lowest activity level with only 70 cakes baked at a cost of $3,750. The cost amounts adjacent to these activity levels will be used in the high-low method, even though these cost amounts are not necessarily the highest and lowest costs for the year.

We calculate the fixed and variable costs using the following steps:

1. Calculate variable cost per unit using identified high and low activity levels

Variable Cost = TCHA − Total Cost of Low Activity HAU − Lowest Activity Unit Variable Cost = $ 5 , 5 5 0 − $ 3 , 7 5 0 1 2 5 − 7 0 Variable Cost = $ 1 , 8 0 0 5 5 = $ 3 2 . 7 2  per Cake where: TCHA = Total cost of high activity HAU = Highest activity unit \begin{aligned} &\text{Variable Cost} = \frac{ \text{TCHA} - \text{Total Cost of Low Activity} }{ \text{HAU} - \text{Lowest Activity Unit} } \\ &\text{Variable Cost} = \frac { \$5,550 - \$3,750 }{ 125 - 70 } \\ &\text{Variable Cost} = \frac { \$1,800 }{ 55 } = \$32.72 \text{ per Cake} \\ &\textbf{where:} \\ &\text{TCHA} = \text{Total cost of high activity} \\ &\text{HAU} = \text{Highest activity unit} \\ \end{aligned} Variable Cost=HAU−Lowest Activity UnitTCHA−Total Cost of Low ActivityVariable Cost=125−70$5,550−$3,750Variable Cost=55$1,800=$32.72 per Cakewhere:TCHA=Total cost of high activityHAU=Highest activity unit

2. Solve for fixed costs

To calculate the total fixed costs, plug either the high or low cost and the variable cost into the total cost formula:

Total Cost = ( VC × Units Produced ) + Total Fixed Cost $ 5 , 5 5 0 = ( $ 3 2 . 7 2 × 1 2 5 ) + Total Fixed Cost $ 5 , 5 5 0 = $ 4 , 0 9 0 + Total Fixed Cost Total Fixed Cost = $ 5 , 5 5 0 − $ 4 , 0 9 0 = $ 1 , 4 6 0 where: VC = Variable cost per unit \begin{aligned} &\text{Total Cost} = ( \text{VC} \times \text{Units Produced} ) + \text{Total Fixed Cost} \\ &\$5,550 = ( \$32.72 \times 125 ) + \text{Total Fixed Cost} \\ &\$5,550 = \$4,090 + \text{Total Fixed Cost} \\ &\text{Total Fixed Cost} = \$5,550 - \$4,090 = \$1,460 \\ &\textbf{where:} \\ &\text{VC} = \text{Variable cost per unit} \\ \end{aligned} Total Cost=(VC×Units Produced)+Total Fixed Cost$5,550=($32.72×125)+Total Fixed Cost$5,550=$4,090+Total Fixed CostTotal Fixed Cost=$5,550−$4,090=$1,460where:VC=Variable cost per unit

3. Construct total cost equation based on high-low calculations above

Using all of the information above, the total cost equation is as follows:

Total Cost = Total Fixed Cost + ( VC × Units Produced ) Total Cost = $ 1 , 4 6 0 + ( $ 3 2 . 7 2 × 1 2 5 ) = $ 5 , 5 5 0 \begin{aligned} &\text{Total Cost} = \text{Total Fixed Cost} + ( \text{VC} \times \text{Units Produced} ) \\ &\text{Total Cost} = \$1,460 + ( \$32.72 \times 125 ) = \$5,550 \\ \end{aligned} Total Cost=Total Fixed Cost+(VC×Units Produced)Total Cost=$1,460+($32.72×125)=$5,550

This can be used to calculate the total cost of various units for the bakery.

The Difference Between the High-Low Method and Regression Analysis

The high-low method is a simple analysis that takes less calculation work. It only requires the high and low points of the data and can be worked through with a simple calculator. It also gives analysts a way to estimate future unit costs. However, the formula does not take inflation into consideration and provides a very rough estimation because it only considers the extreme high and low values, and excludes the influence of any outliers.

Regression analysis helps forecast costs as well, by comparing the influence of one predictive variable upon another value or criteria. It also considers outlying values that help refine the results. However, regression analysis is only as good as the set of data points used, and the results suffer when the data set is incomplete.

It's also possible to draw incorrect conclusions by assuming that just because two sets of data correlate with each other, one must cause changes in the other. Regression analysis is also best performed using a spreadsheet program or statistics program.

Limitations of the High-Low Method

The high-low method is relatively unreliable because it only takes two extreme activity levels into consideration. The high or low points used for the calculation may not be representative of the costs normally incurred at those volume levels due to outlier costs that are higher or lower than would normally be incurred. In this case, the high-low method will produce inaccurate results.

The high-low method is generally not preferred as it can yield an incorrect understanding of the data if there are changes in variable or fixed cost rates over time or if a tiered pricing system is employed. In most real-world cases, it should be possible to obtain more information so the variable and fixed costs can be determined directly. Thus, the high-low method should only be used when it is not possible to obtain actual billing data.