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Break Even Analysis

Break Even Analysis

The break Even analysis (BEA) indicates at what level total costs and total revenue are in equilibrium. It is an analytical technique that is used to identify the level of output and sales volume at which the firm ‘breaks-even’ i.e. the revenues are sufficient to cover all costs.

BEA establishes the relationship among fixed and variable costs of production, value of output, sales value and profit. It is hence, also known as Cost Volume Project (CVP) analysis.

Three approaches are commonly used to solve the BE problems. They are; the graphical method, the equation method and the contribution margin method. We are going to discuss them in this chapter.

The Graphical Method or Break Even Chart

When the BEA is represented graphically, it is shown as the break even chart. The BEC shows the relationship of production costs and revenue to the volume of output. This relationship is determined by a BEP on a graph. The BEP is a specific level of output or volume of sales where total revenue and total costs of a firm are equal. It is the point of zero profit. This point is also known as no-profit, no loss or profit beginning point.

The graph represents a break even chart where the level of output is measured along the horizontal axis and revenue and costs on the vertical axis. The total revenue curve TR is drawn as a straight line, assuming that every level of output is sold at the same price. The fixed cost curve FC is drawn parallel to the horizontal axis. The variable costs are assumed as constant so that the total cost curve TC is also linear.

The point of equality B of TR and TC curves is the break even point. B is the point of no-profit no-loss at OQ level of output. When the firm expands its output beyond OQ, it starts making profit.

Thus the area to the right of point B is the profit zone. When the firm’s output falls below the OQ level, it incurs loss. So the area to the left of point B is the loss zone.

Margin of Safety

This type of BEA can be used to calculate the level of sales which most be attained to avoid less or to calculate the margin of safety MS. MS is the difference between the firm’s actual level of sales and sales at the BE point as represented in the above diagram. It is expressed as MS = Actual sales revenue – BE sales. Nevertheless, firms compute the MS in terms of ratio are:

MS Ratio =          MS
Actual Sales

The MS is an indicator of the strength of a firm. If the margin is large, it represents that the firm can make profit even it has to face difficulties. On the other hand, if the margin is small, a small reduction in sales can lead to loss. MS is nil at the point BE point for the reason that actual sales volume is equal to the cost.

The Equation Method

The same results can be arrived at by the equation method:

Profit       =          TR – TVC – TFC

Where         TR           =          Price x Quantity

TVC        =          AVC x Quantity

TFC is a constant

BE point is where profit = 0

And 0 = (Price x Quantity) – (AVC x Quantity) – TFC

Rearranging the above equation:

BE Quantity        =                      TFC
Price – AVC

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