We have 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 Corporation can produce from 10,000 to 50,000 valves per year. So, the relevant range for Friends Corporation is the range of normal activity from 10,000 to 50,000. Within this relevant range all fixed costs, such as rent, equipment depreciation, and administrative salaries remain constant. If Friends Corporation 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 production level is reduced, Friends Corporation has to reduce staff and rental expenses, so fixed costs will decrease.

Management usually needs to know what fixed and variable costs are included into 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

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 Corporation incurred the following costs during the last six months:

Illustration 14: Total costs of Friends Corporation over the last six months

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:

As the total fixed cost does not change with changes in volume of production, the difference in the total cost is the change in the total variable cost. So, if we divide the difference in total cost by difference in production, 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 the lowest levels of production because fixed costs stay constant. In order to estimate the fixed cost, 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 cost is equal to $14,000. Now, knowing the fixed cost and variable cost per unit we can estimate total cost for the planned production level using the formula below:

T = F + V x N,

where T is Total Cost, F is Fixed Cost, V is Variable Cost per Unit and N is number of units to be produced.

The above methodology 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 point often do not represent the rest of the points, which leads to possible inaccuracy of the final results. It 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.