In this article we will discuss about:- 1. Definition of Break-Even Analysis 2. Formulae for Break-Even Analysis 3. Assumptions and Limitations of Break-Even Analysis 4. Profit-Volume Ratio 5. Margin of Safety 6. Profit Volume Ratio 7. Angle of Incidence 8. Relationship of BEP, Margin of Safety and Angle of Incidence.

**Definition of Break-Even Analysis****:**

Break-even analysis refers to ‘ascertainment of level of operations where total revenue equals to total costs’. It is an analysis used to determine the probable profit or loss at any level of operations. Break-even analysis is a method of studying the relationship among sales revenue, variable cost and fixed cost to determine the level of operation at which all the costs are equal to its sales revenue and it is the no profit no loss situation.

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This is an important technique used in profit planning and managerial decision making. Break-even analysis is made through graphical charts. Break-even chart indicates approximate profit or loss at different levels of sales volume within a limited range. The break-even charts show fixed and variable costs and sales revenue so that profit or loss at any given level of production or sales can be ascertained.

**Steps in Construction of Break-Even Chart****:**

**The following steps are involved in construction of a break-even chart: **

**Step 1: **

Select a scale for sales (units) on horizontal axis.

**Step 2: **

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Select a scale for costs and revenues on vertical axis.

**Step 3: **

Draw the fixed cost line parallel to the horizontal axis.

**Step 4: **

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Draw the total cost line, starting from the point on the vertical axis which represents fixed costs.

**Step 5: **

Draw the sales line, starting from the point of origin (zero) and finishing at point of maximum sales.

**Step 6: **

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The sales line will cut the total cost line at the point where the total cost equal to total revenues.

**Step 7: **

The point of intersection of two lines is called ‘break-even point’ i.e. the point of no profit no loss.

**Step 8: **

The lines drawn from intersection to horizontal axis and vertical axis give the sales value and number of units produced at break-even point.

**Step 9: **

The loss is shown if the production is less than the break-even point and profit is shown if the production is more than the break-even point.

**Step 10: **

The total sales minus break-even sales represent the margin of safety.

**Step 11: **

The angle which the sales line makes with total cost line, while intersecting it at breakeven point is called ‘angle of incidence’.

Break-even point helps in assessing the viability of the organization and to take decisions in profit planning and cost control. Break-even point is the point of zero net income i.e. the level of sales is just equal to its costs. Costs include both fixed and variable costs.

It is used as a useful tool in financial planning to recover costs and to maximize profits. The changes in operating condition such as, selling price, variable cost and fixed cost will change the break-even point. For calculation of break-even point, the costs need to be segregated into fixed cost and variable costs.

The basic assumption in ascertainment of break-even point is that the selling price per unit and variable cost per unit are constant and the fixed costs, in total, are constant. Break-even point indicates the level of operating capacity and sales to be achieved to recover all costs. Any further activity or sales beyond break-even point will lead to earn profit for the concern.

**Formulae for Break-Even Analysis****:**

**Assumptions and Limitations of Break-Even Analysis****:**

**The following assumptions and limitations are important considerations in break-even analysis: **

(a) The break-even analysis requires that all costs should be segregated into fixed and variable components. There is difficulty in segregation of semi-variable expenses into variable and fixed elements of costs accurately.

(b) It is assumed that all fixed costs remain constant at various levels of activity. But in practice, it may not be fixed in the long-run.

(c) Another assumption is that variable costs are really variable and changes in direct proportion to the volume of output. It means that variable cost per unit of product remains constant. In practice variable costs are not necessarily strictly variable with output.

(d) In break-even analysis, it is assumed that production units and sales units are equal and no inventory exists in the beginning or at the end of the period for which analysis is made. In practice there will always be existence of inventory.

(e) There will be no change in selling price and it remains constant at all levels of output and further assumed that there is no change in sales mix. In the real world situation, to increase the sales, it may necessitate to frequently change the selling prices and sales mix of the products.

(f) It is assumed that productivity, operating efficiency, product specifications and methods of manufacture and sale will not undergo any change. In actual situation, the operating efficiency and productivity depends upon the manpower, it is impractical to assume that these factors remain constant.

(g) A break-even chart can depict the position of only one product and fails to present various products in the sales mix in one chart and different charts are required to be drawn for different products.

(h) Break-even analysis ignores the capital employed in business, which is one of the important facts in determination of profitability of the company and its products.

(i) The break-even charts assumes that total cost and total revenue can be represented in straight lines. In practice, the function of costs and revenue are curvilinear in nature.

#### **Profit-Volume Ratio****:**

Profit-Volume Ratio (P/V) reveals the rate of contribution per product as a percentage of turnover. It indicates the relationship of the contribution to sales. It helps in knowing the profitability of business.

**This ratio is calculated as: **

P/V Ratio = Contribution/Sales x 100

**How to Improve P.V. Ratio?**

Better P.V. ratio is an index of sound financial health of company’s product. P.V. ratio can be improved, if contribution is improved.

**Contribution can be improved by taking any of the following steps: **

(a) Increase in selling price.

(b) Reduce marginal cost by efficient utilization of men, material and machines.

(c) Concentrate on the sale of products with relatively better P.V. ratio.

**Limitations: **

**The following limitations are to be borne in mind while using P.V. ratios in break-even analysis: **

(a) P.V. ratio heavily leans on excess of revenues over variable costs.

(b) P.V. ratio fails to take into consideration the capital outlays required by the additional productive capacity and the additional fixed costs that are added.

(c) It gives only an indication of relative profitability of product and product lines. It will not help to take a final decision.

(d) The fundamental prerequisite for comparing profitability through P.V. ratio is the proper segregation of costs into fixed and variable costs. Over simplification may lead to erroneous conclusion.

(e) Higher P.V. ratio per unit of sales or per unit of production will indicate the most profitable item only when other conditions are constant.

**Illustration 1****:**

**ABC Ltd. has provided the following information: **

Sales (@ Rs. 5 p.u.) – 20,000 units

Variable cost p.u. – Rs. 3

Fixed cost – Rs.8,000 p.a.

Calculate the p.v.ratio and the break-even sales of the company.

**Solution:**

**Illustration 2****:**

**You are required to calculate the break-even point from the following information: **

Selling price p.u. Rs. 20 Fixed cost p.a. Rs. 80,000

Variable cost p.u. P.s. 4 Sales for the year Rs. 2,00,000

The number of units involved coincides with expected volume of output.

**Solution**:

**Working notes: **

(a) Selling price p.u. – Variable cost p.u. = Contribution p.u.

= Rs. 20-Rs. 4 = Rs. 16

Contribution p.u. Rs. 16

(b) P.V.ratio = Contribution p.u./Selling price p.u. x 100 = Rs.16/Rs.20 x 100 = 80% or 0.80

At break-even sales, there is no profit no loss.

Verification

Break-even sales – Variable cost – Fixed cost = 0

(5,000 units x Rs. 20) – (5,000 units x Rs. 4) – Rs. 80,000 = 0

Rs. 1,00,000 – Rs. 20,000 – Rs. 80,000 = 0

**Margin of Safety****:**

The margin of safety refers to sales in excess of the break-even volume. It represents the difference between sales at a given activity level and sales at break-even point. It is important that there should be a reasonable margin of safety to run the operations of the company in profitable position.

A low margin of safety usually indicates high fixed overheads so that profits are not made until there is a high level of activity to absorb the fixed costs. A margin of safety provides strength and stability to a concern.

The margin of safety is an important measure, especially in times of receding sales, to know the real position to operate without incurring losses and to take steps to increase the margin of safety to improve the profitability.

**Margin of safety is calculated by using the following formulae: **

**How to Improve Margin of Safety?**

The higher the margin of safety, the better profitability of the product/product line.

**The margin of safety can be improved by adopting any of the following steps: **

(a) Keeping the break-even point at lowest level and try to maintain actual sales at highest level.

(b) Increase in sales volume.

(c) Increase in selling price.

(d) Change in product mix increasing contribution.

(e) Lowering fixed cost.

(f) Lowering variable cost.

(g) Discontinuance of unprofitable products in sales mix.

**Illustration 3: **

You are given the data of XYZ Ltd. for the year ended 31st March, 2009

Sales (@ Rs. 10) – 1,00,000 units Variable cost p.u. – Rs. 6 Fixed cost p.a. – Rs. 3,00,000

Calculate the margin of safety.

**Solution**:

Break-even Sales = Fixed cost/Contribution p.u. = Rs. 3,00,000/Rs. 4 = 75,000 units

Margin of Safety =

= Actual sales – Break-even sales

= 1,00,000 units – 75,000 units = 25,000 units

= 25,000 units x Rs. 10 = Rs. 2,50,000

**Angle of Incidence****:**

The angle which sales line makes with the total cost line is known as the ‘angle of incidence’. The larger the angle of incidence indicates the higher the margin of profit and vice versa. It is an indicator of profitability above the break-even point.

If the margin of safety and angle of incidence considered and studied together will provide significant information to the management about its profitability. A high margin of safety with wider angle of incidence will represent the most profitable position of the business concern and vice versa.

**Relationship of BEP, Margin of Safety and Angle of Incidence****:**

**The relationship among Break-even point, Margin of safety and Angle of incidence is summarized as follows: **

**Break-Even Level:**

It is the level of production or sales where there is no profit and no loss. At this point of sales, total cost is exactly equal to sales, so that, there is no profit no loss. The company starts earning profit only if actual sales are above break-even sales. A company with a lower break-even point is considered better than a company with a higher break-even point.

**Angle of Incidence: **

It is an angle formed by the intersection of total cost line and total revenue line in a break-even chart. Larger angle of incidence is a sign of higher profitability and a lower angle is a sign of lower profitability.

**Margin of Safety:**

It is the difference between actual sales and break-even point. Larger the margin of safety, the more sound is the position of the business in respect of profit earning. This means that larger margin of safety indicates larger amount of profit and vice versa.

**Impact of Selling Price, Fixed Cost and Variable Cost on BEP****:**

The selling price and variable cost has direct impact on the P.V. ratio, since P.V. ratio being a function of contribution to sales.

**The effects of changes in selling price, variable cost and fixed cost on P.V. ratio are explained below: **

(a) An increase in selling price increases the amount of contribution and resulting in improvement in P.V. ratio.

(b) The decrease in selling price of a product, result in decrease in contribution and lowering the P.V. ratio.

(c) The increase or decrease in fixed cost does not affect the P.V. ratio, even though it may increase or decrease the total profit.

(d) The increase in variable cost per unit will reduce the contribution and result in decrease of P.V. ratio.

(e) The decrease in variable cost per unit will result in improvement of contribution and simultaneously, the P.V. ratio will also increase.

(f) The increase in P.V. ratio means lower break-even point and higher margin of safety.

(g) The decrease in P.V. ratio result in increase of break-even point and lower margin of safety.