## 7. Relevant range

We mentioned a relevant range before when we talked about step-variable costs:

Relevant range is the volume of activity, over which cost behavior stays valid.

Friends Company can produce from 10,000 to 50,000 valves per year. So, the relevant range for Friends Company is the range of normal activity from 10,000 to 50,000 units. Within this relevant range all fixed costs, such as rent, equipment depreciation, and administrative salaries remain constant. If Friends Company decides to produce more valves, they have to hire additional staff and rent more equipment, which will result in an increase of fixed costs. On the contrary, if the production level is reduced, Friends Company has to reduce staff and rental expenses, so fixed costs will decrease.

## 8. Methods for separating mixed costs

Management usually needs to know what fixed and variable costs are included in mixed costs. This is required for budgeting and planning purposes, among others. Using the total costs and the associated activity level, it is possible to break out the fixed and variable components. There are three methods for separating a mixed cost into its fixed and variable components:

• High-low method
• Scatter-graph method
• Method of least squares

## 8.1. High-low method

When using the high-low method, the highest point and the lowest point are used to create the cost formula. The high point is defined as the point with the highest activity and the low point is defined as the point with the lowest activity. Using the lowest and highest activity levels, it is possible to estimate the variable cost per unit and the fixed cost component of mixed costs.

Let us assume that Friends Company incurred the following costs during the past six months:

Illustration 14: Total costs of Friends Company over the past six months

 Month Vales Production Total Cost July 10,000 \$44,000 August 15,000 \$60,000 September 23,000 \$85,000 October 21,000 \$75,000 November 19,000 \$70,000 December 28,000 \$98,000

The lowest level of production was in July and the highest level of production was in December. The difference between the number of units produced and the difference between the total cost at the highest and lowest levels of production are shown below:

 Production Total Cost Highest Level 28,000 units \$98,000 Lowest Level 10,000 units \$44,000 Difference 18,000 units \$54,000

As the total fixed cost does not change with changes in the production volume, the difference in the total costs represents the change in the total variable costs. So, if we divide the difference in the total costs by the difference in the production levels, we will have an estimate of the variable cost per unit:

Variable Cost per Unit = \$54,000 ÷ 18,000 units = \$3

The variable cost per unit is \$3. The fixed cost will be the same at both the highest and lowest levels of production because fixed costs don't change. In order to estimate the fixed costs, we have to subtract the estimated total variable cost from the total cost:

 Total Cost = Variable Cost per Unit x Units of Production + Fixed Cost

Highest level:

\$98,000 = \$3 x 28,000 + Fixed Cost

Fixed Cost = \$14,000

Lowest level:

\$44,000 = \$3 x 10,000 + Fixed Cost

Fixed Cost = \$14,000

The fixed costs equal \$14,000. Knowing the fixed costs and the variable cost per unit we can estimate the total costs for the planned production level by using the formula below:

T = F + V x N,

where T is the total cost, F is the fixed cost, V is the variable cost per unit, and N is the number of units to be produced.

Using the formula presented above and the fixed cost and variable cost per unit, we obtain the following formula for our example:

T = \$14,000 + \$3 x N

The methodology presented above is the high-low method of separating mixed costs. The advantage of this method is its simplicity. However, this method ignores all data points other than the highest and the lowest activity levels. The highest and the lowest activity points often do not represent the rest of the points, which leads to a possible inaccuracy of the final results. This is the main disadvantage of this method.

In order to get more precise results, it is better to use the scatter-graph method or the method of least squares.

Not a member?