# Profit-Volume Relationships

Revenue of a firm is affected by the policies adopted by the competitors, by the firms pricing policy and changes in market demand for the product and services rendered by the firm. Factors that affect the expenses include the prices paid for inputs, business volume and the efficiency of translating the raw material resources and resources into a product.

The study of the profit-volume relationship of a business helps to identify a point at which a business moves from loss to profit position is termed as a break-even analysis. Break-even analysis is a tool which finds the point, either in monetary terms or in terms of a number of units, at which total costs equal revenues. The point is called the break-even point.

Break-even analysis requires a knowledge of fixed costs, variable costs and revenue.

### Steps Involved in Break Even Analysis:

1. Identify the fixed costs (FC) and sum them.
2. Estimate the variable cost (VC) associated with the production of each unit.
3. Fixed costs are drawn on the vertical line representing cost.
4. Variable costs are then drawn originating from the vertical axis at the point where fixed costs end as shown in the figure below. These are indicated as an incrementally increasing cost with the change in volume as we move to the right on the volume (horizontal) axis.
5. Revenue line, beginning at the origin and proceeding upward to the right, i.e., increasing by the selling of each unit is plotted. The point at which the revenue line intersects the total cost line is called the break-even point as shown in the above figure. Areas of the graph enclosed between the two lines, below and above the break-even point, are termed as loss corridor and profit corridor respectively.

Mathematically, it can be calculated as follows:

We can use the below notations to terms for easy understanding.
BEPR = Break-even point in monetary units
BEPx = Break-even point in units of product
P = Price per unit
x = Number of units produced
T.R = Total revenue = P × x
F = Fixed costs
V = Variable costs per unit
T.C = Total costs = F + V × x

At the break-even point,

Total Revenue = Total Cost

P × x = F + V × x

Profit = T.R – T.C
= P × x – (F + V × x)
= P × x – F – V × x Profit = (Difference in fixed and variable cost) × No. of units produced – Fixed Costs

With these equations, we can directly solve for break-even point and profitability for units to be produced. Break-even analysis helps to identify processes with the lowest total cost for the expected volume. It also identifies the largest profit corridor and thus helps in addressing two major issues with which a process decision be made successful.