ALGEBRAIC ANALYSIS

The supposition of linear cost behavior allows use of straight-line graphs and simple linear algebra in cost-volume study.

The net cost is a semi-variable cost—few of the costs are fixed, a number of costs are variable, and others are semi-variable. In study, the fixed component of a semi-variable cost can be treated similar to any other fixed cost. The variable component can be treated similar to any other variable cost. As an outcome, we can state that:

Total Cost = Fixed Cost + Variable Cost
          
By using symbols:
               
C = F + V


Here:

C = Total cost
F = Fixed cost
V = Variable cost

Net variable cost based on two elements:

Variable Cost = Variable Cost per Unit x Volume Produced
           
By using symbols:

V = Vu (Q)

Here:

VU = Variable cost per unit
Q   = Quantity (volume) produced

Replacing this variable cost information into the fundamental total cost equation, we have the equation employed in cost-volume study:

C = F + VU (Q)