Methods for the Segregation of Semi-Variable Costs (With Formula)

This article throws light upon the top seven methods for segregation of semi-variable costs. The methods are: 1. Comparison 2. High and Low Points 3. Equation 4. Average 5. Graphic (Scatter Diagram) 6. Least Squares 7. Analytical Approach.

Segregation of Semi-Variable Costs: Method # 1.

Comparison:

Under this method, the quantum of output at two different levels of activity is compared with corresponding amount of semi-variable costs.

As fixed cost remains constant, variable cost is determined by applying the following ratio:

Taking the level of activity of any two months (in the given illustration) say, April and May, the variable and fixed element of cost may be calculated as follows:

= 500/100 = Rs. 5 per unit

Therefore, Variable Element of Cost (for April) = 300 x 5 = Rs. 1,500

and, Fixed Element of Cost (for April) = Rs. 2,500 – 1,500 = Rs. 1,000

Similarly, Variable Cost (for May) = 400 × 5 = Rs. 2,000

and, Fixed Cost (for May) = Rs. 3,000 – 2,000 = Rs. 1,000

Segregation of Semi-Variable Costs: Method # 2.

High and Low Points:

This method is similar to the comparison method except that the data relating to the highest and lowest level of activity are considered.

In the given illustration 15, the highest level of activity is achieved in the month of June and the lowest in the month of February, and hence, the data of these two months is considered, as below:

= 1,750/350 = Rs. 5 per unit

For February 2011, Variable Element of Cost = 150’5 = Rs. 750

and, Fixed Element of Cost = Rs. 1,750-750 = Rs. 1,000

For June, 2011, Variable Element of Cost = 500’5 = Rs. 2,500

and, Fixed Element of Cost = Rs. 3,500 – 2,500 = Rs. 1,000

Segregation of Semi-Variable Costs: Method # 3.

Equation:

Under this method, variable and fixed element of semi-variable cost is determined by means of Straight Line Equation, which is as follows:

y = mx + c

Where, y = Total semi-variable cost

x = Output (in units)

m = Variable Cost per unit

c = Fixed Cost Element

Putting the figures of January and February in the above equation:

For January, the equation would be: Rs. 2,000 = 200m+c…(i)

and for February, the equation be : Rs. 1.750 = 150m+c…(ii)

Subtracting (ii) from (i), 250 = 50 m

or, m (variable cost-per unit) = Rs. 5

Now substituting the value of m in equation (i),

2,000 = 200 × 5 + c

or, c = Rs. 1,000

or, Fixed Cost = Rs. 1,000

Segregation of Semi-Variable Costs: Method # 4.

Average:

Under this method of segregation of fixed and variable elements of cost, first the average of the data relating to selected two levels of activity is calculated and then the equation method or range method is applied.

Taking data of first two and last two months from illustration 15, the cost is segregated as under:

Variable cost per unit = Change in Average S.V. Cost/ Change in Average Output

= 1,375/275

= Rs. 5 per unit

Therefore, Average Variable Cost for Jan. & Feb. = 175 × 5 = Rs. 875

and Fixed cost element = Rs. 1,875 – 875 = Rs. 1,000

Similarly, Variable Cost for May & June = 450 × 5 = Rs. 2,250

and, Fixed cost element = Rs. 3,250 – 2,250 = Rs. 1,000

Segregation of Semi-Variable Costs: Method # 5.

Graphic (Scatter Diagram):

Under this method of segregating semi-variable costs into fixed and variable elements, all relevant given data are plotted on a scatter graph, as given below:

(i) The volume of production is plotted on the horizontal axis and the semi-variable costs on the vertical axis.

(ii) Corresponding to the volume of production, points of semi-variable costs are drawn.

(iii) A line of best fit is then drawn from the plotted points in such a way that the fair average relationship between volume of production and cost is established. Points falling far away from the line of best fit are abnormal and, hence, should be ignored.

(iv) The point where the line of best fit (total semi-variable cost line) intercepts the vertical axis is the fixed cost. From this point, a line parallel to the horizontal axis is then drawn to show the fixed cost line.

(v) The slope of the total semi-variable cost line known as the line of best fit determines the variable element. The variable cost at any level of activity can be ascertained from the difference between the fixed cost line and total cost line.

Segregation of Semi-Variable Costs: Method # 6.

Least Squares:

This method is the most accurate method to segregate semi-variable costs into fixed and variable elements.

It is a statistical method based on the linear equations:

y = mx+c

or ∑y = m∑x + Nc………………………… (i)

and, ∑xy = m∑x² + c∑x………………………. (ii)

Where, y = Total Semi-variable cost

m = Variable cost per unit

x = Volume of output

C= Fixed cost element

N = Number of observations

Taking the data given in illustration 15, we compute the value of ∑x, ∑y, ∑x² and ∑xy as below:

Substituting the values in equation (i) and (ii), we get:

15,000 = 1,800m + 6c………………………….. (iii)

49,25,000 = 6,25,000m + 1,800c…………………….. (iv)

Multiplying (iv) by 300, we get

45,00,000m = 5,40,000m + 1,800c………………………… (v)

Subtracting (v) from (iv):

4,25,000 = 85,000m

or, m = 5

or, variable cost = Rs. 5 per unit

Now, substituting value of m = 5 in any equation, say (iii), We can ascertain he element of fixed cost:

15,000 = 1800 × 5 + 6c

or, 6c = 15,000 – 9,000

or, c = 1,000

or, Fixed Cost Element = Rs. 1,000

Segregation of Semi-Variable Costs: Method # 7.

Analytical Approach:

This method is based on ‘careful analysis of each item to determine how far the cost varies with volume.’ The analyst determines from the past experience as to what portion of semi-variable costs comprises of variable cost element and fixed cost element. Say, for instance, out of semi-variable cost of Rs. 5,000 the variable element is 80%, and then fixed cost would be Rs. 1,000, i.e. 5,000-80% of 5,000.

This method is simple but suffers from the subjectivity of the accountant or the analyst. Two different persons may determine different degree of variability and ascertain different element of fixed cost from the one given semi-variable cost.