8-Break Even Point

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BREAK EVEN ANLAYISIS

MANAGEMENT ACCOUNTING AND CONTROL

Rupesh Kumar KanaujiyaSanjeev Acharya

Satya Prakash RaoShubham Aggrawal

Shweta Dariyal

BY

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CONTENTS

Managerial Usage of Break Even Analysis

Graphical Method: Break Even

Cash and Composite Break-Even Charts

Algebraic Break Even Point

Introduction to Break-Even-Point

Margin of Safety

It is a management accounting tool.

In cost-volume-profit analysis an attempt is made to analyse the relationship between variation in cost with variation in volume.

The widely used technique to used cost volume profit analysis is Break Even Analysis

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Cost-volume-profit analysis

Cost-volume-profit relationship is of immense utility to management, it can be used to answer question such as-

How much sales should be made to avoid losses? How much should be the sales to earn a desired profit? What will be the effect of change in prices, costs and

volume on profits? Which product or product mix is most profitable? Should we manufacture or buy some product or

component?

4

Continued…

The Break even analysis shows the relationship between costs and profits with the sales volume.

The term “Break even analysis” is used in two senses- Broad sense- Relation between costs, volume and profit at

different levels of sales or production

Narrow sense- Refers to a technique of determining that level of operations where total revenue equal total expense, i.e., the point of no profit, no loss.

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Break Even Analysis

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Assumptions of Break-Even analysis

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Applications of BEP Analysis

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Limitations of Break Even Analysis

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Break even point

Break even point

Point of sales volume at which total revenue is equal to total cost.

It is the point of no profit, no loss.

At this point, contribution, i.e., sales minus marginal cost, equals the fixed costs.

This point is often called as ‘Critical Point’ or ‘Equilibrium point’ or ‘Balancing point’.

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1

The Algebraic Formula method

2

Graphic or Chart method

Computation of the break even point

Break even point can be computed by the following two methods:

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Algebraic Formula Method

1. Budget total or in terms of money value

2.Units of sales volume

3. As a percentage of estimated capacity

The break-even point can be computed in terms of:

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At the point of break-even, total contribution equal the total fixed costs.

Formula-

Break-Even point = fixed cost

selling price per unit-variable cost per unit

= fixed cost

contribution per unit

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(a) Break-Even points in units

Break-even points (in units) = fixed cost

selling price per unit- variable cost

= 20,000 = 20,000 = 2,000 units

30-20 10

Example 1

Calculate the break-even point in units: Output = 3,000

units Selling price per unit = Rs. 30 Variable cost per unit = Rs. 20 Total fixed cost = Rs. 20,000

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At break-even point:

Total sales= Total fixed cost + Total variable cost

S= F+V

(where S= sales, F= fixed cost & V=variable cost)

Or S-V = F

Or S-V F (dividing both sides by S-V)

S-V S - V

Or F

S-V

Or Fx S (multiplying both sides by S)

S-V

(b) Break even point in terms of budget-total or money value

=

=1

=Sx1

15

fixed cost

sales-variable cost

Fixed cost

P/V ratio

as contribution

sales

Continued…

x sales=Hence, break-even sales

With the use of P/V ratio, B.E.P. =

= P/V ratio

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Break-even point (in sales value) = fixed cost X sales

sales- variable cost

fixed cost = Rs. 20,000 (given)

sales = 3,000 x 30 = Rs. 90,000

variable cost = 3,000 x 20 = Rs. 60,000

Hence, B.E.P. (in sales value) = 20,000 x 90,000

90,000- 60,000

= 20,000 x 90,000 = Rs. 60,000

30,000

Example 2

Calculate the break-even point in Sales Value: Output = 3,000 units Selling price per unit = Rs. 30 Variable cost per unit = Rs. 20 Total fixed cost = Rs. 20,000

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P/V Ratio

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The P/V ratio shows the relationships of contribution to the sales volume.

Determinants of BEP

(BEP=FC/P-V ratio)Determinants of profits at given/budgeted

sales volume.Profit= (Actual sales-BEP Sales) X P/V Ratio Determinants of Sales volume to earn budgeted profits

Sales=(FC + Desired Profit)/P-V Ratio Determinants of the percentage of net profit with the help

of Margin of Safety ratio % of Net Profit =(P/V Ratio X MS Ratio)

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Applications of P/V Ratio

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From the following data, calculate:

(a) P/V ratio

(b) Break-even sales with the help of P/V ratio

(c) Sales required to earn a profit of Rs. 4,50,000

Fixed expenses = Rs. 90,000 Variable cost per unit:

Direct material = Rs. 5 Direct labor = Rs. 2 Direct overhead = 100% of direct labour Selling price per unit = Rs. 12

Example 3:

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Selling price per unit = 12 Rs 12 Less:

Direct material Rs. 5 Direct labor Rs. 2 Direct overhead Rs. 2

Rs. 9

Contribution per unit = (12 – 9) Rs. 3

(a)P/V ratio = contribution

sales

= 3

12

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Solution:

X 100 = 25%

X 100

(b) Break-even sales = Fixed expense

P/V ratio

= 90,000 = 90,000 x100

25 25

100

= Rs. 3,60,000

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Continued…

(c) Sales required to earn a profit of Rs. 4,50,000

= fixed expense + desired profit

P/V ratio

= 90,000 + 4,50,000 = 5,40,000

25% 25

100

= 5,40,000 x 100 = Rs. 21,60,000

25

23

Continued…

Break even point (as a percentage of estimated capacity or sales)

break even sales

estimated sales For example: if estimated capacity = 1,00,000 units

& break even sales = 50,000 units

then B.E.P. = 50% of estimated capacity And if total contribution at full capacity is available then

B.E.P. = fixed cost

total contribution

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(c) Break-even point as a Percentage of estimated capacity

=

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The cash break-even point may be defined as that point of sales volume at which total revenue is equal to total cash cost. At this point, cash contribution equals the cash fixed cost.

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CASH BREAK-EVEN POINT

This point enables the management to determine the level of activity below which the liquidity position of the firm would be adversely affected.

Cash Break-Even Point (in units) = Cash Fixed Cost Cash Contribution per unit

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CONTD..

ILLUSTRATION

From the following information, calculate the cash break-even

point.

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Rs.Selling Price per unit 40Variable cost per unit 30Depreciation included in above per unit 5Fixed Cost 1,00,000Depreciation included in fixed cost 25,000

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SOLUTION

Cash Fixed Cost = Rs. 1,00,000 – 25,000 = Rs. 75,000Cash contribution per unit = Rs. 40 – (30-5) = Rs. 15Cash Break-Even Point = Cash Fixed Cost Cash Contribution per unit = 75,000 = 5,000 units 15Cash Break-Even Point in sales value = Rs. 5,000 x 40 = Rs. 2,00,000

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COMPOSITE B-E POINT

We can also calculate the composite break-even point for a firm producing several products, as below:

Composite Break-Even Point (in Sales value) = Total Fixed Cost Composite P/V Ratio

And, Composite P/V Ratio = Total Contribution x 100 Total Sales

ILLUSTRATION

From the following information of a company producing three

products, you are required to compute(a) Composite P/V Ratio, and(b) Composite Break-Even Point.

Fixed costs : Rs. 50,000.

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Product Sales Revenue Variable Cost X Rs. 20,000 Rs. 10,000 Y 40,000 14,000 Z 60,000 36,000

SOLUTION

Product Sales Revenue

(Rs.)

Variable Cost

(Rs.)

Contribution

(S – V)

(Rs.)

P/V Ratio

X

Y

Z

20,000

40,000

60,000

10,000

14,000

36,000

10,000

26,000

24,000

50%

65%

40%

Total 1,20,000 60,000 60,000 50%

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CONTD..

(a) Composite P/V Ratio = Total Contribution x 100 Total Sales = 60,000 x 100 = 50% 1,20,000

(b) Composite Break-Even Point (in Sales value) = Total Fixed Cost Composite P/V Ratio = 50,000 = Rs. 1,00,000 50%

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Management Accounting and Control

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GRAPHIC METHOD

The break-even point can also be computed graphically with the help of Break-Even Charts.

A break-even chart is a graphical representation of marginal costing.

The break-even chart portrays a pictorial view of the relationship between costs, volume and profits.

It shows the break-even point and also indicates the estimated profit or loss at various levels of output.

The break-even point is the point (in the chart) at which the total cost line and the total sales line intersect.

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ILLUSTRATION

Plot the following data on a graph (break-even chart) and determine (a) break-even point (b) profit if the output is 25,000 units.

Output Variable Cost Total VC Fixed Total Cost SP Total(units) (per unit) Expenses (per unit) Sales Rs. Rs. Rs. Rs. Rs. Rs. 0 5 0 75,000 75,000 10 0 5,000 5 25,000 75,000 1,00,000 10 50,00010,000 5 50,000 75,000 1,25,000 10 1,00,00015,000 5 75,000 75,000 1,50,000 10 1,50,00020,000 5 1,00,000 75,000 1,75,000 10 2,00,00025,000 5 1,25,000 75,000 2,00,000 10 2,50,00030,000 5 1,50,000 75,000 2,25,000 10 3,00,000

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SOLUTION

FIRST METHOD:

Under this method following steps are taken to draw the break-even chart :

1. Volume of production/output or sales is plotted on horizontal axis i.e., X-axis. The volume of sales or production may be expressed in terms of rupees, units as a percentage of capacity.

2. Costs and sales revenue are represented on vertical axis, i.e. Y-axis.

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CONTD..

3. Fixed cost line is drawn parallel to X-axis. The line indicates that fixed expenses remain constant at all levels of activity.

4. Sales values at various levels of output are plotted and a line is drawn joining these plotted points. This line is called the sales (revenue) line.

5. The point of intersection of total cost line and sales (revenue) line is called the break-even point.

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300

250

200

150

100

50

350

0 5000 10000 15000 20000 25000 30000 Output in units

Cost andRevenues

(Rs, `000)

Profit

VariableExpenses

Fixed Expenses

BEP

Fixed cost line

Margin of safety

Profit Area

Loss Area

Total sales li

ne

Total cost line

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CONTD..

6. The number of units to be produced at break-even point can be determined by drawing a perpendicular to the X-axis from the point of intersection of cost and sales line.

7. The sales revenue at break-even point can be determined by drawing a perpendicular to the X-axis from the point of intersection of cost and sales line.

8. The area below the break-even point represents the loss area as the total sales is less than the total cost and the area above the break-even point indicates the area of profit as the sales revenue exceeds the total cost.

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GRAPHIC METHOD

SECOND METHOD:

The break-even chart can also be drawn by another method which is a variation of the first method.

Under this method, the variable cost line is drawn first and then total cost line is drawn over and parallel to the variable cost line

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300

250

200

150

100

50

350

0 5000 10000 15000 20000 25000 30000 Output in units

Cost and Revenues(Rs, `000)

Profit

Fixed Cost

Variable Cost

BEP

Margin of safety

Profit Area

Loss Area Variable cost line

Total cost line

Total sales li

ne

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CONTD..

This method is useful to the management for decision making because it reveals additional information:

(a) The variable costs are shown directly for various levels of output/sales.

(b) Marginal contribution at various levels of sales is indicated clearly by the difference between sales line and variable cost line.

(c) It indicates the recovery of fixed costs at various levels of production.

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CONTRIBUTION B-E CHART

THIRD METHOD:

This is a modified form of a simple break-even chart as shown in the first two methods.

Under this method, total cost line is not drawn, rather another line called contribution line is drawn from the origin and this line goes up with the increase in the level of output.

The fixed cost line is drawn parallel to the X-axis as in the first method. The sales line is also drawn as usual.

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300

250

200

150

100

50

350

0 5000 10000 15000 20000 25000 30000 Output in units

Cost andRevenues

(Rs, `000)

Variable Cost

Profit

Fixed Cost

BEP

Total sales li

ne

Fixed cost line

Contribution line

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CONTD..

In this method, the question of intersection of sales line with the total cost line does not arise because there is no cost line.

The break even point is that point where the contribution line crosses the fixed cost line. At this point, total contribution is equal to the total fixed cost and hence there is no profit or loss.

As the contribution increases more than the fixed cost, profit shall arise to the organisation and as contribution decreases from the fixed cost, there shall be loss to the organisation.

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CONTD..

The contribution break-even chart shows clearly the contribution at different levels of activity and indicates that all levels below the break-even point are unable to cover the fixed costs.

Note : In the above example, at level of output/sales of 25,000 units, there is a profit of Rs. 50,000 as indicated by break-even charts under the three methods.

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MARGIN OF SAFETY

The excess of actual or budgeted sales over the break-even is known as margin of safety.

It is the difference between actual sales minus the sales at break-even point.

It represents the amount by which sales revenue can fall before a loss is incurred

As at break-even point there is no profit no loss, sales beyond the break-even point represent margin of safety because any sales above the break-even point will give some profit.

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CONTD..

Margin of Safety = Total Sales – Sales at Break-Even Point

Margin of Safety Ratio = Margin of safety x 100 Sales = Actual Sales – Sales at B.E.P. x 100 Sales

Margin of Safety calculated in % terms is known as Margin of safety Ratio and can be expressed as:

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CONTD..

Margin of safety can also be calculated with the help of the following formula :

This is so because margin of safety is the volume of sales beyond break-even point and all sales above the break-even point give some profit which can be calculated as :

Margin of Safety (M.S.) = Profit P/V Ratio

Profit = Margin of Safety x P/V Ratio

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CONTD..

The size of margin of safety is an important indicator of the strength of a business.

The large margin of safety indicates that the business is sound and even if there is a substantial fall in sales, there will still be some profit.

On the other hand, small margin of safety indicates that position of the business is comparatively weak and even a small decline in sales would adversely affect the profit of the business and may result into losses.

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CONTD..

The margin of safety can be improved by taking the following steps :

a) By increasing the level of production.b) By increasing the selling price.c) By reducing the fixed costs.d) By reducing the variable cost.e) By substituting unprofitable products with profitable f) products.g) By increasing contribution by changing the sales mix.

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ANGLE OF INCIDENCE

The angle of incidence is the angle between the sales line and the total cost line formed at the break-even point where the sales line and the total cost line intersect each other.

The angle of incidence indicates the profit earning capacity of a business.

A large angle of incidence indicates a high rate of profit and, on the other hand, a small angle of incidence indicates a low rate of profit.

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CONTD..

Usually, the angle of incidence and margin of safety are considered together to indicate the soundness of a business.

A large angle of incidence with a high margin of safety indicates the most favourable position of a business.

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Managerial Usage of Break Even Analysis

Interpretation of CVP Graphs

Curvilinear Break-Even Analysis

CVP Graph: Cost-wise

Changes in Fixed and variable costs

Changes in sales and sales mix

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Curvilinear B-E Analysis

The marginal costing approach is based upon the basic assumption that selling price and variable cost per unit will remain constant at all levels of activity or in other words the cost-volume-profit relationship is linear.

However, in actual practice, the selling prices do not remain the same forever and for all levels of output due to competition and changes in general price level etc.

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Contd..

Further, it may not be possible to increase the sales volume without offering concessions in price to the customers.

In the same manner, variable cost per unit may also increase with the increase in level of production due to operating inefficiencies and the law of diminishing returns.

Thus, profit can be increased only upto a certain point and then it will decrease until it is converted into a loss.

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Contd..

The break-even chart will then become curvilinear instead of linear.

It might show more than one break-even point, one at a lower level of output and another at a higher level of output.

In such a case, increasing output/sales volume beyond the first break-even point will increase profit but increase in volume beyond the second break-even point will result in loss.

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Contd..

The optimum level of output shall be reached at the point where difference between the total revenue and the total cost is the highest.

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Costs/Revenue

Output/Sales

Total Costs

Total RevenueProfit Area

Loss

Loss

BEP1

BEP2

CBE Graph

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Interpretation of CVP Graphs

Like the algebraic break-even applications, the CVP graph can be used to analyse the cost-volume-profit planning.

CVP graphs can also be used to interpret the following: Distribution of various costs and taxes. Change in fixed costs Change in variable costs Change in selling price, and so on.

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Contd..

The following example illustrates the interpretation of Break-even chart (CVP graph).

The data of ABC Ltd. is given below:

Selling price per unit: Rs. 10

Fixed Costs: Rs. 60,000

Variable costs per unit: Rs. 5

Relevant Range (units): lower limit 6,000

: upper limit 20,000

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Contd..

Break up of variable costs per unit:

Direct Material: Rs. 2

Direct Labour: Rs. 1.50

Direct Expenses: Rs. 1

Selling Expenses: Rs. 0.50

Tax Rate: 50%

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CVP Graph, cost-wise

Lets calculate the various costs and selling price for 20000 units.

Selling price per unit = Rs. 10selling price for 20000 units = Rs. 200,000

Variable cost per unit = Rs. 5variable cost for 20000 units = Rs. 100,000direct material cost @ Rs. 2 = 40,000direct labour @ Rs. 1.50 = 30,000direct expenses @ Rs. 1 = 20,000selling expenses @ Rs. 0.50 = 10,000

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Contd..

Fixed cost = Rs. 60,000 So, Total cost for 20,000 units

= Variable cost + Fixed cost= 100,000 + 60,000= 160, 000

The graph shows the various costs separately.

Break even point = Rs. 120,000 for 20,000 units.

Taxes = 50% of total income = 20,000

Net Income (profit) = Rs. 20,000 Margin of Safety = 200,000 – 120,000 = 80,000

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240200160120 8040

280

0 4,000 8,000 12,000 16,000 20,000 24,000

0 40,000 80,000 120,000 160,000 200,000 240,000

Cost andRevenues

(Rs, `000)

Sales Volume

Sales Revenue

BEP

Sales line

Total cost line

Fixed cost line

CVP Graph

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240200160120 8040

280

0 4,000 8,000 12,000 16,000 20,000 24,000

0 40,000 80,000 120,000 160,000 200,000 240,000

Cost andRevenues

(Rs, `000)

Sales Volume

Sales Revenue

BEP1

Sales line

Fixed cost line

Total cost line

Selling Exp

Net Income

Direct ExpensesDirect LabourDirect

Material

Taxes

Cost-wise CVP graph

Change in fixed costs

Various parameters Actual values Decreasing fixed cost by 10,000

Increasing fixed cost by 10,000

a Selling price / unit 10 10 10

b Total selling price 200,000 200,000 200,000

c Fixed cost 60,000 50,000 70,000

d Variable cost / unit 5 5 5

e Variable cost 100,000 100,000 100,000

f Total cost (c + e) 160,000 100,000 170,000

g Break even point 120,000 100,000 140,000

h Margin of safety (b - g) 80,000 60,000 60,000

i Operating profit (b - f) 40,000 50,000 30,000

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Changing the fixed cost by Rs. 10,000.All values are corresponding to 20,000 units (in Rs.)

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240200160120 8040

280

0 4,000 8,000 12,000 16,000 20,000 24,000

0 40,000 80,000 120,000 160,000 200,000 240,000

Cost andRevenues

(Rs, `000)

Sales Volume

Sales Revenue

BEP1

BEP2

B

Sales line

Total cost lines

Fixed cost lines

Change in fixed cost: CVP graph

Change in variable costs

Various parameters Actual values Decreasing fixed cost by 10%

Increasing fixed cost by 10%



c Fixed cost 60,000 60,000 60,000

d Variable cost / unit 5 4 6

e Variable cost 100,000 80,000 120,000

f Total cost (c + e) 160,000 140,000 180,000


h Margin of safety (b – g) 80,000 100,000 50,000

i Operating profit (b – f) 40,000 60,000 20,000

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Changing the variable cost by 10%.All values are corresponding to 20,000 units (in Rs.)

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240200160120 8040

280

0 4,000 8,000 12,000 16,000 20,000 24,000

0 40,000 80,000 120,000 160,000 200,000 240,000

Cost andRevenues

(Rs, `000)

Sales Volume

Sales Revenue

BEP1

BEP2

Sales line

Total cost lines

Fixed cost line

CVP Graph: Change in variable cost

Change in selling price

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Changing the selling price per unit by 25%.

The impact of change in sales price is reflected indirectly in the variable cost line.

There is only one sales line in the CVP graph.

The following steps are followed:

Changing sales price per unit by 25%.Sales price/ unit = Rs. 10Increasing sales price by 25% = Rs. 12.5Decreasing sales price by 25% = Rs. 7.5Variable cost/ unit = Rs. 5

Contd..

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Changing the selling price per unit by 25%.

The impact of change in sales price is reflected indirectly in the variable cost line.

There is only one sales line in the CVP graph.

The following steps are followed:

Changing sales price per unit by 25%.Sales price/ unit = Rs. 10Increasing sales price by 25% = Rs. 12.5Decreasing sales price by 25% = Rs. 7.5Variable cost/ unit = Rs. 5

Actual Values

Selling price/ unit 12.5 7.5

Variable cost/ unit 5 5

Variable cost 100,000 100,000

Changed Values

Selling price/ unit 10 10

Variable cost/ unit 4 6.67

Variable cost 80,000 133,333.33

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Contd..

Changing the sales price to Rs. 10 per unit and reflecting the corresponding change in variable costs:

Contd..

Various parameters Actual values Change corresponding to sales price of Rs. 12.5

Change corresponding to sales price of Rs. 7.5



c Fixed cost 60,000 60,000 60,000

d Variable cost / unit 5 4 6.67

e Total variable cost 100,000 80,000 133,333.33

f Total cost 160,000 140,000 193,333.33


h Margin of safety 80,000 100,000 20,000

i Operating profit 40,000 60,000 6666.67

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Changing the selling price by 25%.All values are corresponding to 20,000 units (in Rs.)

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240

200

160

120

80

40

280

0 4,000 8,000 12,000 6,000 20,000 24,0000 40,000 80,000 120,000 160,000 200,000 240,000

Cost andRevenues

(Rs, `000)

Sales Volume

Sales Revenue

BEP1

BEP2

Sales line

Total cost lines

Fixed cost line

CVP Graph: Change In Selling Price

Change in Sales mix

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Many manufacturers make more than one kinds of products.

The relative proportion of each product sold in the aggregate sales is known as the sales mix.

A change in the mix of products sold affects the Break even point.

So the optimal strategy of the manufacturer is to chose the mix of products in a way so as to lower down the total costs and hence BEP.

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Costs/Revenue

Output/Sales

BEP3

BEP2

BEP1

Fixed cost line

Total sa

les lin

e

Total cost lines

(corresponding to

different sales m

ix)

CVP Graph: Change in sales mix

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References

Management Accountingby MY Khan, PK Jain

Management Accountingby Shashi K. Gupta, R.K. Sharma

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Documents

8-Break Even Point