In this article we will discuss about:- 1. Introduction to Break-Even Analysis 2. Margin of Safety 3. Chart 4. Concept of Contribution.

#### Introduction to Break-Even Analysis:

The study of cost-volume-profit relationship is often referred to as ‘break-even analysis’. The term ‘break-even analysis’ is interpreted in narrow as well as broad sense. In its narrow sense, it is concerned with finding out the break-even point.

Break-even point is the point at which total revenue is equal to total cost, it is the point of no profit no loss. In its broad sense, break-even analysis refers to a system of analysis that can be used to determine the probable profit at any level of production. It may be shown both graphically as well as algebraically.

Break-even point can be calculated in the following ways:

#### Margin of Safety:

Definition:

The margin of safety is the difference between actual sales or output and the break­even sales or production. It may also be expressed in percentage. A greater margin of safety reflect the soundness of the business. If the margin of safety is small, any fall in sales value, may even result in loss.

The margin of safety can be rectified by the management, by lowering fixed or variable costs, by increasing selling price or volume of sales, by substituting unprofitable product by profitable ones.

It may be expressed as:

Margin of Safety = Actual Sales or output – Break-even sales or productions

#### Break-Even Chart:

The break-even chart is the graphic presentation that shows the varying costs along with varying sales revenue. It depicts the point of production at which neither profit nor loss can result (i.e., the break-even point) and also shows the estimated profit or loss at different levels of production.

Construction of Break-Even Chart:

There are three methods of drawing a break-even chart.

These have been explained as follows:

First Method:

On the X-axis (i.e., on the horizontal line) of the graph is plotted the volume of production; and on the Y-axis (i.e., on the vertical line) the cost and sales revenue are shown. Plot the fixed cost on the vertical axis and draw fixed cost line passing through this “point parallel to horizontal axis. This is so because fixed cost remains the same with any volume of production.

The variable cost line is shown above the fixed cost line. This line can be considered as a total cost line because it begins from the point where certain fixed cost has been incurred and variable cost at that point is zero.

The sales revenue line is drawn from the point where there are no sales (Zero intersection of horizontal and vertical sales) and it goes upward, thereby depicting the increasing sales revenue due to increasing sale. The total costs and total sales line intersect each other at a point which is known as break-even point.

To the left of this point there is a loss and to the right of it there is profit. This chart shows clearly the fixed Costs, Variable Costs, Profit and Margin of Safety, etc.

Second Method:

Under this method, the fixed costs line is shown above the variable cost. This method has the advantage because of the fact that it reveals more clearly the recovery of fixed costs at various levels of production before profits are realized.

This chart depicts the contribution at different levels of production more clearly than the previous one. The graph is drawn in a similar way except that variable cost line is drawn first, then fixed cost and sales lines are drawn.

Third Method:

This method is known as Analysis (Detailed), Break-even chart. It is prepared showing various details of variable costs under various elements of costs, such as direct material cost, direct labour cost. Variable factory overhead, variable administration, selling and distribution overheads etc. Similarly, appropriation of profit to taxes, dividends, reserves etc., is also depicted.

Profit Volume Chart:

Besides the above three methods of showing break-even point another variation of the Break-Even Chart is profit volume chart. In this chart the sales volume is depicted on the horizontal line and profit or loss on the vertical line.

The profit line is plotted by determining the Profit or Loss (i.e., difference between sales revenue and total cost) at each volume. The point where the profit line intersects the horizontal line is the Break-Event Point.

Angle of Incidence:

This is an angle at which sales line intersects the total cost line. If the angle of incidence is large it is an indication that profits are being earned at high rate. Taken in conjunction with the margin of safety, it can be said that a large angle of incidence with high margin of safety indicates an extremely favourable position. On the other hand, if the angle of incidence is small, it indicates low rate of earning.

Assumptions Underlying Break-Even Chart:

The break-even analysis is drawn within a given capacity to produce and sell, and is generally based on the following assumptions:

(a) Fixed costs remain unchanged at all levels of activity.

(b) Variable cost change in direct proportion to the volume of output.

(c) All indirect costs can be classified into fixed and variable elements.

(d) Selling price remains constant irrespective of volume of production or sales changes.

(e) Prices of raw materials, labour rate etc., remain constant.

The break-even charts offer many advantages, more important of which have been summarised as follows:

1. It is easy to compile and to understand:

It presents the information very clearly. A look or a glance shall give a detailed picture of the whole affairs.

2. Useful tool to guide management in studying the relationship of cost, volume and profits. The chart may depict the effect of changes in costs and sales price because of changes in fixed costs, variable costs.

3. Ascertainment of strength of the business and the profit earning capacity:

By the study of Margin of Safety and angle of incidence together, many important policy decisions can be taken.

Policy decisions like:

(a) To increase the selling price;

(b) To reduce the costs;

(c) To increase the level of production;

(d) To substitute the less profitable products by more profitable products may be taken on the basis of Margin of Safety and Angle of Incidence in the Break-even Chart.

4. It helps identifying product and sale-mix:

It helps in selecting the most profitable product mix or sales-mix in making maximum profits.

Limitations of Break-Even Chart:

1. The assumptions on the basis of which Break-even chart is drawn are unrealistic for the following reasons:

(a) It is not possible to separate or segregate all indirect costs into fixed costs and variable component accurately.

(b) Fixed costs are constant only in the short period; in the long period they are subject to change.

(c) Certain items of variable costs may not change in direct proportion to volume but may reduce on account of economies of bulk buying etc.

(d) The selling price does not also remain constant. Any increase or decrease in output is likely to have an influence on the selling price.

2. When a number of products are manufactured, separate break-even charts will have to be drawn up. This surely poses problem of apportionment of fixed expenses to each product.

3. Break-even chart does not take into account the amount of capital employed—which is one of the vital factors in the determination of profitability.

It appears from the graph that for demand below Rs.1,50,000 sales, A.B. Ltd. will earn greater profit than C.D. Ltd. At value of Rs.1,50,000 both will earn same profit.

Since the rate of profit earning in case of C.D. Ltd. is greater than that of A.B. Ltd. (vide angle incidence), for volume above Rs.1,50,000 C.D. Ltd. will earn more profit than A.B. Ltd. Thus, in case of heavy demand, C.D. Ltd. will earn greater profits; while A.B. Ltd. will earn greater profits in condition of low demand for the product.

#### Concept of Contribution in Break-Even Analysis:

Contribution is the difference between selling price and variable cost. If selling price is Rs.20 and its variable cost is Rs.10, then contribution is Rs.20 – Rs.10 = Rs.10. Otherwise we can say that contribution = Fixed Cost + Profit.

Thus, Contribution = Selling Price – Variable Cost = Fixed Cost + Profit. Profit = Contribution margin – Fixed Cost.

= Selling price – Variable Cost – Fixed Cost.

Benefits of Contribution:

The knowledge of contribution margin is of great importance to the management as it acts as an aid to management in making various decisions.

A few benefits are discussed below:

1. While considering the question of acceptance or rejection of any new order, contribution margin is of considerable help to the management in taking correct decision.

2. While choosing from among alternative methods of production, the method which yields the greatest contribution is to be adopted.

3. Contribution margin helps a lot in the selection of a product mix keeping in view that the products which give the minimum contribution margin are to be retained.

Contribution = S – V, or, Sales – Variable Cost

or,

Fixed Cost + Profit

Fixed Cost = S – V – Profit

Profit = S – V – FC