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## Lesson 37. PROFIT VOLUME ANALYSIS

*Module 6. Working capital management*

Lesson 37

PROFIT VOLUME ANALYSIS

**37.1 Introduction**

The profit volume analysis graph discloses the relationship of profit to volume. The P/V graph is also referred to as P/V chart. The utility of P/V graph is that it depicts the direct relationship between sales volume and quantum of profit fit different levels of activity. It is drawn on the basis of information as is required for the construction of break even chart.

The following steps are required to be adhered for the construction of P/V graph:

1. Profit and the fixed costs are represented on the vertical axis (Y) with appropriate scale. Total fixed costs are represented below the scale line on the left hand side of the vertical axis and the profits are shown on the right hand side above the sales line.

2. Sales are represented on the horizontal line (X) with appropriate scale. More precisely the horizontal line itself forms the sales line. This line is drawn in the middle of the graph so as to represent losses below this line and the profits above this line.

3. Points are plotted on the P/V graph for the required fixed costs and profits at two or three assigned sales levels. The points should be selected in such a manner that one point plotted must be below the sales line and the other must be above the sales line.

4. The origin of the curve (Profit line) would be a point of total fixed cost (treating the entire amount as loss) at zero sales level.

The P/V chart does not project the BEP alone. For it contains set of points whereby each point measures the amount of profit or loss in relation to sales volume.

37.2. Illustration

X Ltd. reports the following results for one year:

Particulars Sales Variable costs Fixed costs Net profits |
Rupees 2,00,000 1,20,000 50,000 30,000 |

37.3 Assumptions underlying CVP Analysis/ Break-Even Charts

1. All costs can be separated in to fixed and variable costs.

2. Fixed costs remain constant at every level and they do not Increase or decrease with change in output.

3. Variable cost fluctuates per unit of output. In other words they vary in the same proportion in which the volume of output or sales varies.

4. Selling price will remain constant even though there maybe competition or change in volume of production.

5. Cost and revenue depend only on volume and not on any other factor.

6. Production and sales figures are either identical or changes in the Inventory at the beginning and at the end of the accounting period are not significant. .

37.4 Advantages of Break Even Charts

1. Break even chart provides detailed and clearly understandable information to the management. Information provided by the break even chart can be understood by the management more easily than that contained in the profit and loss account and the cost estimates because it is the simple presentation of cost volume and profit structure of the company. It summarises a great mass of detailed information in a graph in such a way that its significance may be grasped even with a cursory glance.

2. Profitability of different products can be known with the help of break even charts, besides the level of no profit/no loss. The problem of managerial decision regarding temporary or permanent shut down of business or continuation at a Joss can be solved by break even analysis.

3. A break even chart is useful for studying the relationship of cost volume and profit. The effect of changes in fixed and variable costs at different levels of pr9duction can be demonstrated by the graph more legibly. Effect of changes in selling price can also be grasped quickly by the management by having a .look at the break even chart. Thus it is very much useful for quick managerial decisions.

4. A break even chart is a tool for cost control because it shows the relative importance of the fixed cost and the variable cost.

5. A break even chart is helpful for forecasting long term planning, growth and stability.

37.5 Limitations

1. A break even chart is based on a number of assumptions which may not hold good. Fixed costs very beyond 'a certain level of output. Variable costs do not vary proportionately if the law of diminishing or increasing returns is applicable in the business. Sales revenue do not vary proportionately with changes in volume of sales due to reduction in selling price as a result of competition or increased production:

2. Only a limited amount of information can be presented in a single break even chart. If we have to study the changes of fixed costs, variable costs and selling prices, a number of charts have to be drawn.

3. The effect of various product mixes on profits cannot be studied from a single break even chart.

37.6 Algebraic Method

The algebraic method of making CVP /BEP analysis is by the use of simple formula developed on the basis of the fundamental marginal costing equation, Sales -Variable cost = Fixed cost + Profit or S -V = F + P. This is the basic formula which is used to find out anyone of the factors when the other three are known.

Since contribution is the excess of sales revenue over marginal cost, the right hand side of the equation may be substituted by C. Accordingly, the equation becomes Sales -Variable Cost = Contribution or S-V=C.

At the breakeven point, profit is nil. Therefore

S-V=F+O

We can find out the sales volume required to break even by multiplying both sides of the equation by S. The 'equation will then be

S (S-V) = F x S

Since S – V = C the equation can also be written as

Since again fixed cost plus profit must be equal to contribution, the equation can be put as

The BEP can also be shown by the formula

If it is desired to find out the breakeven point in terms of units, the break even sales may be divided by the price per unit. Alternatively break even sales in terms of units can be found out by the formula,

37.7 Illustration

**From the following particulars, calculate the level of sales to break even**

Units sold Selling price Variable cost Fixed cost |
5000 Rs. 2 per unit Rs. 1.50 per unit Rs. 2000 |

Solution

Sales revenue for 4000 units at Rs. 2 per unit Rs. 8000

Less: Variable cost at Rs. 1.50 per unit Rs. 6000

Contribution 2000

Fixed cost 2000__ __

Profit/Loss NIL