# Calculating Break Even Point

Break even point may be determined in terms of physical units or in money terms i.e. sales value in rupees.

## Break-Even Point in Terms of Physical Units

Break even volume is the number of units of a product which must be sold to earn enough revenue just to cover all expenses. The break-even point (BEP) is reached when sufficient number of units has been sold so that the total contribution margin of the units sold is equal to the fixed costs.

$$B.E.P = \frac{Fixed\ costs}{Selling\ price - Variable\ costs\ per\ unit}$$

## Break-Even Point in Terms of Sales Value

Multi product firms are not in a position to measure the BEP in terms of any common unit of product. In these firms it is convenient to determine their BEP in terms of total rupee sales. In this case BEP would be the point where the contribution margin (Sales value Variable costs) would be equal to fixed costs contribution margin is expressed as a ratio to sales.

$$B.E.P. = \frac{Fixed\ costs}{Contribution\ ratio}$$

$$Where,\ Contribution\ ratio = \frac{Sales\ value - Variable\ costs}{Sales\ value}$$

## Margin of Safety

This is shown on the chart by the distance between B.E.P. and the output being produced. It shows that if this distance is short then a small decrease in output or sales will produce profit greatly. If the distance is long it means the business could still be making profit after a great reduction in output.

## Calculating Break Even Point

Example 1: Fixed costs of a firm are estimated as Rs. 5.0 lacs. The firm is selling a product manufactured by it at a rate of Rs. 50 per item. The variable cost / unit are estimated as Rs. 25. Determine the break-even point.

Solution:

$$Break-Even-Point = \frac{Fixed\ Cost}{Selling\ price - Variable\ cost\ or\ unit}$$

$$= \frac{500000}{50 - 25} = 20000\ units\ Ans.$$

Example 2: Determine the break-even point in Rupees for the firm of previous example.

Solution:

$$As\ B.E.P.\ (in Rs)\ = \frac{Fixed\ cost}{ 1 - (\frac{variable\ cost}{Selling\ price})}$$

$$= \frac{500000}{1 - (\frac{25}{50})}$$

= Rs. 10, 00, 000 = Rs. 10.0 lacs Ans.

Example 3: Fixed costs in a factory of Rs. 10000 per year, the variable costs are Rs. 2.00 per unit and the selling price is Rs. 4.00 per unit, calculate B.E.P.

Solution:

$$B.E.P\ = \frac{Fixed\ costs}{Contribution\ margin\ per\ unit}$$

$$= \frac{10000}{4 - 2} = 5000\ units.\ Ans.$$

Check

Sales = 5000 x 4 = Rs. 20000

Cost of goods sold = Variable cost + Fixed costs

5000 x 2 + 10000 = Rs. 20000

Therefore net profit = Nil.

Example 4: If in example 1 sales are 8000 units, calculate safety margin. If desired profit is Rs. 6000, Calculate target sales volume.

Solution. Safety margin.

$$= \frac{(Sales - BEP)}{ Sales} \times 100$$

$$= \frac{8000 - 5000}{8000} \times 100 = \frac{3}{8} \times 100 = 37.5 %\ Ans.$$

$$Target\ sales\ volume\ = \frac{10000 + 6000}{4 - 2}$$

= 8000 units. Ans.

## Angle of Incidence

By cutting sales line on to a total cost line an angle known as "Angle of Incidence" is formed. Chart shows that if the angle is large it is an indication of large profits and if it is small it shows that profits are being earned under less favorable conditions.

## Position of Break-Even Point

If B.E.P. is over to the left of the chart with a large angle of incidence it shows that output can be raised considerably. If B.E.P. is over to the right of the chart, the margin of safety is low, which means:

1. The fixed overheads are too great for the amount of sales being done, and

2. The fixed and variable costs are high while the profit is small.

If the production volume is below B.E.P., the company will be running in loss and beyond its profit can be had.

Break-even-point may be determined in terms of physical units or in money terms.

1. B.E.P. in terms of physical units. This is convenient for the single product firm. It represents the number of units of a product which must be sold to earn enough revenue just to cover all expenses.

2. B.E.P. in terms of sales value. Multi-product firm are not in a position to measure the B.E.P. in terms of any common unit of product. In these firms it is convenient to determine this B.E.P. in terms of total rupee sales.

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