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)