Break-Even Analysis

The break-even analysis is the study of revenues and costs of a firm in relation to its volume of sales and specially the determination of that volume at which its costs and revenues are equal to each other.

The break-even point (BEP) may be defined as that level of sales of a firm at which its total revenues are equal to its total costs and hence its net income is zero.

BEP is also known as “no profit and no loss point”.

Determination of BEP

The BEP of a firm can be determined in two ways. They are:

In terms of physical units i.e volume of output.

In terms of money value i. e the value of sales.

(1) BEP in terms of Physical Units

This method is convenient for a firm producing a single product. The BEP is the no of units of the commodity that should be sold to earn enough revenue just to cover all the expenses of production.

The revenue covers all the cost – variable as well as fixed. The firm does not earn any profit nor does it incur any loss.

The table given above shows that ,when the output is zero the TFC is RS.1000 and this will be the TC.

When the output is 10 units, the TC consisting of TFC is Rs.1000 and TVC is Rs.1000,is totally Rs.2000. The TR is Rs.1500,since the price is Rs.150/- unit the firm incurs a loss of Rs.500 at this point.

When the output is 20 units, the TC is Rs.3000 and the TR is also Rs.3000 and hence TR = TC. At this level the firm is working at a point where there is no profit and no loss. This is called the BEP.

From this level of output the firm starts earning profit.

Alternative method to find out BEP in terms of Physical units

There is another method of finding out BEP in terms of physical units of output. This is by means of formula. We adopt AR and AVC instead of TR and TC.

The BEP is that level of output at which the price of the product (AR) covers the AC. The price should be sufficient to cover not only the AVC but also some portion of AC.

The excess of selling price over AVC goes towards meeting some portion of the FC. The excess is called contribution margin.

BEP = TFC

Contribution margin per unit

Where contribution margin = selling price – average variable cost

CM = SP – AVC

Therefore , BEP = TFC

SP – AVC

Example:

Suppose the TFC of a firm is Rs.10000 per annum. The variable cost per unit i.e. AVC is Rs.6 and the selling price is Rs.10 per unit. Find the BEP in terms of physical units.

BEP = 10000 = 2500 units

10 – 6

Thus the company would not make any profit or loss when the output is 2500 units.

Verification:

Total revenue = 2500 x 10 = Rs.25000

TVC = 2500 x 6 = 15000

TFC = +10000

TC = 25000

So TC = TR. Hence BEP = 2500 units.

BEP in terms of Money Value Or Sales Value

If a firm is producing many products the BEP has to be approached only in terms of money value of goods sold or total sales revenue.

Here also total contribution margin (SP-AVC) would be equal to the TFC. But the contribution margin is expressed as a ratio to sales.

This ratio is also known as “profit – volume ratio” or P/V ratio.

Contribution ratio = TR –TVC / TR

BEP = TFC / CR

Ex 1: Total sales = Rs. 3000

TVC = Rs. 2000

Fixed cost = Rs.1000

CR = 3000 – 2000 / 3000 = 1/3

Now to find out BEP, BEP = TFC = 1000 = Rs. 3000

CR 1/3

TR = Rs. 3000

TFC = Rs. 1000 3000 = TR

TVC = RS. 2000

In this way TR of Rs. 3000 = TC of Rs. 3000. Therefore no profit or no loss.

EX:2 Given:Total Sales Revenue : Rs 10,000Total Variable Costs : Rs 6,000Total Variable Costs : Rs 3,000

Find BEP

BEP = TFC/Contribution Ratio(CR)where, CR= TR-TVC/TRCR = 10,000-6,000/10,000 = 2/5BEP = 3000/2/5 3000*5/2 = 15000/2 = 7500VERIFY :FOR 10000 TVC Rs 6000FOR 7500 6000/10000*7500

TVC = 4500TR =7500TC= TFC 3000 + TVC 4500 = 7500HENCE, TR=TC

Margin Of Safety (or) Safety Margin

That amount of sales which is over and above the break-even sales value is known as margin of safety.

Safety Margin = Total sales – sales at BEP

MS = TS – BES

Or

MS = NP

CR

The margin of safety indicates the extent to which the sales may fall before the firm suffer loss. Larger the margin of safety, safer the firm.

Illustrations

TS = Rs.20,000

BES = 15,000

MS = TS — BES

= 20,000 – 15,000 = 5,000

Margin of safety can also be expressed as % of total sales.

MS = margin of safety x 100

total sales

= 5,000 x 100

20,000

= 25%

To find out MS:

Total sales = 1,50,000

Variable cost = 75,000

Fixed cost = 50,000

CR = TR – TVC = 1,50,000 – 75,000 = 1

TR 1,50,000 2

BES = TFC = 50,000 = 1,00,000

CR ½

MS = TR – BES

=1,50,000 – 1,00,000

= Rs. 50,000

Break–Even Point as a % of Full Capacity

The term full capacity means maximum possible volume that can be produced with the firm’s existing capital equipment and operating policies and practices. This is also expressed as % of full capacity.

For ex, if the full capacity is 10,000 units and BEP is 4000 units then the BEP can be expressed as 40% of full capacity.

Assumptions of Break Even Analysis

The quantity produced and sold are equal.

The FC remains constant at different levels of output.

The VC goes on increasing by a fixed amount.

The price per unit remains constant and does not change.

The TR goes on increasing proportionately to the output.

Managerial Uses of Break-Even Analysis

Microscopic View

Profit Target

Contribution Margin per unit = SP –VC per unit

1= 4-3

Target sales volume = FC + Target profit / Contribution margin per unit

= 300 + 200 /1

= 500 units

To determine the value of sales to maintain the profit level

Safety Margin

To expand the production capacity

Profit Projections

Make or Buy decisions

Illustration:Given Selling Price : Rs. 10/- each

TFC & AVC is Rs 12000 & Rs 4. Should a firm make or buy?

BEP = 12000/10 – 4

= 12000/6

= 2000 components

If the firms requirements is less than 2000 then it is profitable to buy than to manufacture them