Cost Behavior
9.8 Methods for separating mixed costs
Managers often need to know the fixed and variable components of mixed costs. 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: the high-low method, the scatter-graph method, and the method of least squares.
9.8.1 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 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 6 months:
Illustration 9-14: Total costs of Friends Corporation over the last 6 months
Month |
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 |
Since 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. In our case
Variable Cost per Unit = $54,000 / 18,000 units = $3
Now we know that the variable cost per unit is $3. We know that the fixed cost will be the same at both the highest and the lowest levels of production. 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
So we see that 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.
We just reviewed 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.
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