# Cost Volume Profit Analysis, Linear Break Even Analysis

The break even analysis is also supportive for ascertaining the degree of productivity necessary to make specified target volume of profits. Presume if the industry fixes a target amount of profits for a period equal to 10 million dollars then the degree of productivity needed to be manufactured and sold to access the given target volume of profit surpasses the break even level.

The above condition is presented in the diagram above to realise target amount of profits π or ET, the level of productivity required to be manufactured and sold enhances to VT.

__Linear Break Even Analysis in Algebraic Method:__

Even though graphic method of break even analysis is useful method of illustrating cost-productivity revenue-productivity and profit-productivity associations break even analysis through algebraic model is of great support in decision making difficulties by an industry.

Let P = Price per unit of Article Sold

V = Volume
Manufactured and Sold

TFC = Total
Fixed Cost

AVC = Average Variable Cost per unit of Productivity

π = Profits

Summon up that profit π is the disparity among total revenue TR and Total Cost TC. To write in symbolic terms

π = TR – TC

Total revenue TR is equal to the price P per unit of the article times the volume of productivity sold.

Thus,

TR = P.V …..Equation (1)

Alternatively, total cost is the sum of total variable cost TVC and total fixed cost TFC. Total Variable Cost is the variable cost per unit multiplied by the sold produce i.e. TVC = AVC.V. Therefore,

TC = TVC + TFC

TC = AVC.V + TFC …..Equation (2)

As described above, break even volume of productivity manufactured and sold happens at the level at which total revenue TR parities total cost TC.

Let VB denote the break even volume. From Equation (1) and (2) above, at the break even volume VB, we have

TR = TC

P.VB = TFC + AVC.VB

P.VB – AVC.VB = TFC

(P – AVC).VB = TFC

VB = __ TFC __

P – AVC …..Equation
(3)

The disparity among price and average variable cost that is P-AVC in Equation (3) is termed as the contribution margin per unit which measures how much each unit of productivity manufactured and sold makes contribution to cover total fixed cost and provide for profits. From Equation (3) it adopts that break even volume of productivity manufactured and sold is ascertained by Total Fixed Cost (TFC), Price of Productivity (P) and Average Variable Cost (AVC).

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**Other topics under Theory of Production and Cost analysis:**

- Break Even and Leverage Analysis
- Concept of Cost
- Elasticity of Supply and Its Function
- Establishment of Cost Function Analysis
- Establishment of Short Run Cost Function
- Estimation of Returns To Scale
- Isoquants, Equal Product Curves
- Linearity Assumptions and Choice of Product and Process
- Long Run average Cost Curve
- Optimum Input Combination
- Production Function with Two Variable Inputs
- Short Run Cost Function
- Survival Technique
- Theory of Production - Returns to One Variable Factor