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# Break-Even Analysis

The main objective of break-even analysis is to find the cut-off production volume from where a firm will make profit.

Break-Even Analysis

The main objective of break-even analysis is to find the cut-off production volume from where a firm will make profit.

Let

s       = selling price per unit v  = variable cost per unit FC  = fixed cost per period Q  = volume of production

The total sales revenue (S) of the firm is given by the following formula:

= s    Q

The total cost of the firm for a given production volume is given as

TC = Total variable cost + Fixed cost

= v    Q + FC

·        The linear plots of the above two equations are shown in Fig. .

·        The intersection point of the total sales revenue line and the total cost line is called the break-even point.

·        The corresponding volume of production on the X-axis is known as the break-even sales quantity.

·        At the intersection point, the total cost is equal to the total revenue. This point is also called the no-loss or no-gain situation.

·        For any production quantity which is less than the break-even quantity, the total cost is more than the total revenue.

·        Hence, the firm will be making loss. For any production quantity which is more than the break-even quantity, the total revenue will be more than the total cost. Hence, the firm will be making profit.

Profit  = Sales  (Fixed cost + Variable costs)

s    Q  (FC + v    Q)

The formulae to find the break-even quantity and break-even sales quantity

Break-even quantity =   [ Fixed cost ]  /  [ price/unit − Variable cost/unit ]         Selling

= FC/ s-v (in units)

Break-even sales =         [        Fixed cost   × Selling price/ unit − Variable cost  / unit ] x Selling price/ unit

=       [ FC / s − v ]         × s (Rs.) The contribution is the difference between the sales and the variable costs. The margin of safety (M.S.) is the sales over and above the break-even sales. The formulae to compute these values are

Contribution  = Sales  Variable costs

Contribution/unit  = Selling price/unit  Variable cost/unit

M.S.  = Actual sales  Break-even sales

= [ Profit / Contribution ] x sales

M.S. as a per cent of sales = (M.S./Sales) 100

P/ratio is a valid ratio which is useful for further analysis.

The different formulae for the P/V ratio are as follows:

P/V ratio =  Contribution / Sales       = Sales − Variable costs  /       Sales

The relationship between BEP and P/V ratio is as follows:

BEP  = Fixed cost / P/ratio

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Mechanical : Engineering Economics & Cost Analysis : Introduction to Economics : Break-Even Analysis |