BREAK-EVEN ANALYSIS

INTRODUCTION

• The signs of a healthy business include making a profit consistent with the various risks that it has to face.

• A firm is faced with a number of uncertainties. • These uncertainties are created by the dynamic nature

of consumer needs, the diverse nature of competition, the uncontrollable nature of most elements of cost, and the continuous technological developments.

• So far as demand is concerned, save for the basic needs essential for survival, consumer preferences are highly subjective and, therefore, most unpredictable.

• The nature of competition may be related to either product or price or to both simultaneously.

• It is said that normally the degree of risk involved in product competition is greater than in price competition.

• In period of continuously rising prices, no firm can be certain of its own internal cost structure.

• Continuous technological developments may make today’s established commercial production completely obsolete in course of time.

• However, if it does not have access to the improved process; it may have to go out of business altogether.

• Unless a firm is prepared to face the uncertainties created by these risks, its profits would be left to chance.

• Naturally, the firm will have to plan for profits. • In this respect, a through understanding of the

relationship of cost, price and volume is extremely helpful to business executives.

• The most important method of determining the cost-volume-profit relationship is that of break-even analysis.

Break-Even PointBreak-Even Point• The break-even analysis established a

relationship between revenues and costs with respect to volume.

• It indicates the level of sales at which costs and revenues are in equilibrium.

• The equilibrium point is commonly known as the break-even pointbreak-even point.

Definition Definition • The break-even pointbreak-even point may be defined as that

level of sales at which total revenues equal total costs and the net income is equal to zero.

• It is a no-profit, no-loss point. It should be noted, however, that the break-even point is just incidental in cost-volume-profit studies.

• The main objective of the break-even point, but to develop an understanding of the relationships of cost, price and volume within a company’s practical range of operations.

Basic Assumptions

1. The behaviour of costs in predictable

• The conventional cost-volume profit-model is based on the assumption that the costs of the firm are divisible into two components: fixed costs and variable costs.

• Fixed costs remain unchanged for all ranges of output; variable costs very proportionately to volume. Hence the behaviour of costs is predictable.

2. The selling price per unit is constant• For firms which have a strong market for their

products, this assumption is quite valid. • For other firms, however, it may not be so.

3. The firm manufactures a stable product-mix

• In the case of a multi-product firm, the cost-volume-profit model assumes that the product-mix of the firm remains stable.

4. Inventory changes are nil

• A final assumption underlying the conventional cost-volume-profit model is that the volume of sales is equal to the volume of production during an accounting period.

• One of the important prerequisites for using the break-even analysis is that costs can be separated as fixed and variable.

• Fixed costs arise as a result of capacity creation and are invariant with respect to variations of activity (Capacity utilization).

• They may represent depreciation charges, property tax, insurance and rent which arise because the firm owns plant and equipment and hires factory premises; they may consist of salaries paid to managerial and supervisory staff; they may consist of interest burden on long-term debt.

• Several important elements of cost vary directly with output. For example, the total material cost, the cost of power, labour charges and other utilities may vary directly with output are referred to as variable costs.

• Break-even analysis may be carried out graphically or algebraically. We first deal with the graphical analysis and then with the algebraic

Graphical Analysis

• [BEA is very commonly presented by means of break-even charts, also known as profit-charts]

5 10 15 20 25 30 35 40 4550 55 60

CO

ST

S A

ND

R

EV

EN

UE

(R

S.

CR

OR

ES

)

60

55

50

45

40

35

30

25

20

15

10

5

0

BREAK-EVEN SALES (PHYSICAL UNITS) ‘000 UNITSBREAK-EVEN PERCENTAGE OF CAPACITY

BREAK – EVEN POINT

SALES LINE

FIXED COST LINE

MARGIN OF SAFETY

TOTAL COST LINE

LOSS ZONE

Profit Zone

Total Variable Costs

Total Fixed Costs

ALGEBRAIC ANALYSIS:For algebraic analysis of break-even point, we may use the following symbols.F = Total Fixed CostQ = Quantity Produced and Sold

V = Unit Variable Cost

(1)

TVC = Total Variable Costs = QXVP = Unit Selling PriceTR = Total Revenue = QXPΠ = ProfitΠ = QXP – QXV – F

Q

TVCAVC

Break-Even Quantity The break-even quantity is the value of

quantity (Q) for which the profit (Π) is Zero. Setting Π equal to zero in e.g. (1) we get:

Break-even quantity (QB) (2)

In e.g. (2), (P-V), which represents the difference between unit selling price and unit variable cost, is called the contribution margin.

VP

F

Break-even Sales in Rupees It is simply break-even quantity X unit selling price. The following

equation, derived from E.g.(2) can be employed to calculate more directly the break-even sales in rupees.

Break-even sales in Rupees (SB) (3)

Break-even Percentage of Capacity

Break-even point in terms of percentage of plant capacity can be expressed as;

Break-even percentage capacity (%B)

(4)

P

VF

1

100

QMaximumVP

F

Profit for a given Quantity The profit (Π) for a given quantity level is obtained by

putting the value of quantity (Q) on the right-hand side of E.g. (1) i.e.,

Π = Q (P-V) – F (5)

Volume needed to attain Target Profit Break-even analysis may be utilized for the purpose of

determining the volume of sales necessary to achieve a target profit.

Target Sales Volume

where ΠT is target profit. VP

FT

Margin of Safety

It is the excess of actual sales (or budgeted sales) over the break-even sales volume.

(7)100

QActual

QBQActualM S

Problem Solving

A manufacturing unit undertakes the production of a certain commodity withSelling Price per unit = Rs.20Variable Cost per unit = Rs.12Total Fixed Costs = Rs.5,60,000

• What is the break-even output?• What is the break-even sales in rupees?• What is the profit earned when the output is

1,00,000 units.?• What should be the output to achieve a target

profit of Rs.4,00,000?

Solution

(a) The Break-even Output is

70,000 Units

(b) The Break-even sales in Rupees is

= Rs.14,00,000

VP

FQ

1220

000,60,5

P

VF

1

20

121

000,60,5

The Profit earned when the output is 1,00,000 units

Π = Q (P-V) – F

= 1,00,000 (20 – 12) 5,60,000

Π = Rs.2,40,000

The output required for achieving a target profit of Rs.4,00,000 is:

= 1,20,000 Units

Vp

FT

1220

000,60,5000,00,4

Examples

A firm has purchased a plant to manufacture a new product, the cost data for which is given below:

Estimated Annual Sales : 24,000 unitsEstimates Costs –

Material : Rs.4/- per unitDirect Labour : Rs.0.60 per unitOverhead : 24,000 per yearAdministration Expenses : 28,800 per yearSelling Expenses : 15% of Sales

(i) Calculate the selling price, if profit per unit is Rs.1.02; (ii) Find out the break-even point in terms of units of output.

Solution (i) Estimated cost of production for 24,000 units –

Material at Rs.4 per unit : Rs.96,000/-Direct Labour : Rs.14,400/-Administrative Expenses : Rs.28,800/-Overheads : Rs.24,000/-

----------------Total Cost of Production : Rs.1,63,200/-

=========TC = TCP + Total Selling Cost

= 1,63,200 + 15% of salesΠ on 24,000 units at Rs.1.02 = Rs.24,480/-Let the sales volume = Rs. XThen Rs. X = TC + Π

Rs.24,480

= 1,87,680

= Rs. 1,87,680

= 1,87,680

100

15200,63,1

100

15

100

151

100

85

Rs. 2,20,800

The Values of Sales Volume = Rs.2,20,800

Value of Sales Volume

Selling Price = ------------------------------

Sales Volume

85

100187680

000,24

800,20,2

Selling Price = 9.20

(ii) AT BEP: TR – TC = 0

OR TR = TC

Units Sold X Selling Price = TC

Q BEP ..PS

TC

20.9

800,20,2%15200,63,1 of

20.9

800,20,2100

15200,63,1

20.9

320,96,1 21,339.130 Units

OR QBEP = 21,340 Units

The following information is available for Sulthan Mfg. Co. Ltd.

Cost Element V. C. (% Sales) F. C. (R.S)

Direct Materials 32.8 - - -

Direct Labour 28.4 - - -

Factory Overheads 12.6 1,89,900

Distribution Overheads 4.1 58,400

General Administration 1.1 66,700

Budgeted Sales are Rs.18,50,000. You are required to determine:•The BE Sales Volume.•The profit at the Budgeted Sales Volume.•The profit if actual sales drop by 10% and increase by 5% from budgeted sales.

Solution:

(i) The BE Sales Volume:

In order to find the break-even point in terms of rupee volume of sales, we need to express the contribution margin as the fraction of price/ revenue that contributes to payments of fixed costs and profit:

Break-even Sales Volume PAVC

TFC

/1

Break-even Sales Volume

Note: Both e.g.s. Yield the same result.

From the given information, TFC = Rs.3,15,000 and TVC is 79% of budgeted sales

i.e. = Rs.14,61,500

Substituting the values

TRTVC

TFC

/1

100

79000,50,18

000,50,18

500,61,141

000,15,3

= Rs.15,00,000

21.0

000,15,3

(i) The Profit at the Budgeted Sales Volume:

TVCTFCTR

500,61,14000,15,3000,50,18

500,73.Rs

(ii)The Profit of Actual Sales Drop by 10%:

)TVCTFCTR 350,15,13000,15,3000,65,16

650,34.Rs

100

10000,50,18

TR000,65,16

The profit if actual sales increase by 5% when actual sales increase by 5% budgeted ales will increase to Rs.19,42,500.

000,65,16100

79TVC

350,15,13TVC

TVCTFCTR 100

5000,50,18

575,34,15000,15,3500,42,19

= 92,500

Then 18,50,000 + 92,500

= Rs.19,42,500

925,92.RsTVC = 79% of sales

100

79500,42,19..

ei

= 15,34,575

3. For a firm, total sales value is Rs.10,00,000 where total direct cost is Rs.6,70,000 and total fixed cost is Rs.2,30,000. Find the B.E. condition of the firm.

Solution: BEP (Rupees) VRatioP

FixedCosts

/

(Note that the contribution ratio is also known as P/V ratio)where P represents profit as an equivalent of contribution

and V represents volume as an equivalent of sales.

33.0000,00,10

000,30,3

Sales Variable Costs Contribution P/V Ratio

Rs.10,00,000 Rs.6,70,000 3,30,000

i.e. 33% BEP 33.0

000,30,2

= Rs.6,96,969.696

OR BEP = 6,96,970

4. From the following data you are required to calculate break-even point and net sales value at this point.

Direct Material Cost per unit : Rs.8

Direct Labour Cost per unit : Rs.5

Fixed Overheads :Rs.24,000

Variable Overhead @60% on direct labour:Rs.3/-

Selling Price per unit : Rs.25/-

Trade Discount : 4 per cent

Solution:

Selling price Rs.25

Trade Discount 4% 1.100

425. RsRs

Net realization per unit sold = Rs.25 – 1 = Rs.24/-.V.C D.M.C. = Rs.8

D.L.C. = Rs.5 3.100

605. RsRs

V. Overhead = Rs.3----------------------------------Total = Rs.16=====================

Contribution margin = SP – VC = Rs.24 – Rs.16 = Rs.8

FC 24,0001) BEP Sales Units = ----------------- = ----------- = 3,000 units

C.M. per unit Rs.82) Net Sales Value at BE Sales Value = Units sold X S.P.

= 3,000 x Rs.25 = Rs.75,000

Net Sales Value at BE Sales Value = Units sold X S.P.

= 3,000 x Rs.25 = Rs.75,000

Trade Discount of 4% 100

4000,75 =Rs.3,000

(75,000-3,000) i.e., Rs.72,000

Net Sale Value = Rs.72,000/-

5. Deccan Airline has the monthly sealing capacity of 20,000 passengers on one of its routes at a fare of Rs.170/-. Variable cost is Rs.20 per passenger and fixed cost is Rs.6,00,000. FindB E Quantity?Solution:

Maximum number of passengers that can be carried on the route per month is 20,000. Fare is 170 per passenger, TFC is 6,00,000. V. C. per passenger is Rs.20.

TVC = 20,000 x 20 = Rs.4,00,000

(i) BEP (Quantity)

AVCP

TFC

20170.

000,00,6.

Rs

Rs

150

000,00,6

BEP = 4,000 passenger

(ii) BEP (In Sales) onRatioContributi

TFC Contribution Ratio

TSR

TVCTSR

Contribution Ration 000,00,34

000,00,4000,00,34 TSR

170 x 20,000

000,00,34

000,00,30

17

15 = 0.8823 TVC

8823.0

000,00,6 = Rs.6,80,040 20 x 20,00,000

OR 4,000 x 170 -------------- 6,80,000 ========

(iii) BEP % of Capacity

100max

QAVCP

TFC %20

000,2020170

100000,00,6

(iv) Suppose that management sets a profit target of the route at Rs.4,00,000/-. What would be the required profit before tax to achieve this profit target (tax rate = 30%)? Profit after tax = profit before tax – r (profit before tax). rPBTPAT 1

70.0

000,00,4

30.01

000,00,4

1

r

PATPBT

PBT = Rs.5,71,428

6.BE production of a firm is 5,000 units. Its fixed cost is Rs.50,000; the VC per unit is Rs.25. Find out the price of the product. How much the firm should produce to earn a profit of Rs.25,000?

(i) QBEP AVCP

FC

5,000 25.

000,50.

RsP

Rs

5000 P – 5000 x 25 = Rs.50,000 5000 P = 50,000 + 1,25,000

35.5000

000,75,1RsP

FC (ii) QBEP = ------------------------------------ Contribution margin per unit

AVCice

FC

Pr

25.35.

000,25000,50

RsRs

QBEP 500,710

000,75 units

7. Suppose the fixed costs of a factory are Rs.10,000 per year, the variable costs are Rs.2 per unit and the selling price is Rs.4 per unit. Find out the break-even point would be:

BEP 000,524

000,10

units

In other words, the company would not make any loss or profit at a sales volume of 5,000 units as shown below: [Sales Rs.20,000

Cost of goods sold Variable cost @Rs.200 Rs.10,000 Fixed costs Rs.10,000 Rs.20,000 ------------- NIL ]

(b) Find out the safety margin by assuring sales as 8,000 units.

Safety Margin

%5.37000,8

100000,5000,8

[Safety margin reveals the percentage increase in sales necessary to reach the BEP so as at least to avoid losses].

If the desired profit is Rs.6,000, calculated the target sales volume:

000,82

000,6000,10

units

8. A manufacturer sells his product at Rs.5 each. Variable costs are Rs.2 per unit and the fixed costs amount to Rs.60,000.

(i) Calculate the Break-even point. (ii) What would be the profit if the firm sells

30,000 units? (iii) What would be the BEP if the firm spends

Rs.3,000 on advertising? (iv) How much should the manufacturer sell to

make a profit of Rs.30,000 after spending Rs.3,000 for advertisement.

Solution:

(i) BEP 000,2025

000,60

VCSp

FC units

(ii) Profit = Total Revenue – Fixed Cost – Variable Cost

= (5 x 30,000) – 60,000 – (2 x 30,000) = 1,50,000 – 60,000 – 60,000 = Rs.30,000

(i) If the firm spends Rs.3,000 on advertising, fixed costs would rise by Rs.3,000 i.e., Rs.63,000. Hence, BEP would be:

000,2125

000,63

VCSp

FCBEP units

(i) The formula for finding out the volume of sales necessary to achieve the target profit is:

Fixed Costs + Target Profit Total Sales Volume = --------------------------------- Contribution Margin

000,313

000,93

3

000,30000,63

units

9. Bionics International Manufactures a certain product. Its current financial and production figures are as follows:

Unit Selling Price = Rs.45 Unit Variable Cost = Rs.20 Fixed Costs = Rs.4,00,000 Output = 24,000 units

(1) What is Bionics current level of profit? (2) What will be the percentage change in profit for the following changes

(i) a 10 per cent increase in output (ii) a 12 per cent increase in unit selling price (iii) a 5 per cent decrease in unit variable cost

Solution: (1) The current level of profit for bionics is:

Q(P-V)-F = 24,000 (45-20) – 4,00,000 = Rs.2,00,000

(2) (i) A 10 per cent increase in output will raise the profit to:

26,400 (45-20) – 4,00,000 = Rs.2,60,000 Hence, the percentage increase in profit works out to.

%30100000,00,2

000,00,2000,60,2

(ii) A 12 per cent increase in unit selling price will raise the profit to 24,000 (50.4-20)-4,00,000 = Rs.3,29,600.

Hence, the percentage increase in profit works out to

%8.64100000,00,2

000,00,2000,29,3

(iii) A 5 per cent decrease in unit variable cost will raise the profit to: 24,000(45 – 19) – 4,00,000 = Rs.2,24,000 Hence, the percentage increase in profit works out to

%12100000,00,2

000,00,2000,24,2

Limitations: Break-even analysis is a useful tool of profit planning. However, it suffers from several limitations arising out of the following:

(1) Break-even analysis is static in Character:

The assumptions of the break-even analysis make it a static measure of a dynamic process. The break-even chart used for analysis represents static sales and costs line which fail to predict future revenues and costs. It is unrealistic to assume that price level is constant and that whatever is manufactured in a period is sold.

(1) Multiple Products:

Break-even analysis is perhaps best suited for a firm producing a single product. Its usefulness varies from industry to industry. Industries suffering from frequent, volatile changes in input prices, rapid technological changes and constant shifts in product mix will not benefit much from break-even analysis. Although the break-even analysis suffers number of limitations yet it remains an important of profit planning. What is needed is that the financial analyst should understand the underlying assumptions on their corresponding limitations, and adjust his data appropriately to suit his needs. Finally, break-even analysis should be viewed as a guide to decision making and not as a substitute for judgment, logical thinking or commonsense.

Economist’s Model of Break-Even Analysis: An Economist’s model of BEA assumes that costs and revenues are curvilinear. The revenue curve is expected to indicate that the firm is able to sell increasing quantities only by reducing prices. The cost curve is expected to indicate that total costs rise steeply as the firm operates at the lower levels of the volume range, level out and then rise less steeply as the operating efficiency of the plant picks up. If the activity level goes beyond a certain point, costs again rise steeply as the per unit cost would go up. The economist’s view point thus results in a break-even chart as follows:

As can be seen from the above chart in comparison to the chart presented earlier as the accountant’s BE Chart, the following characteristics can be distinguished.

PROFIT

VARIABLE COST

C

TR

TC

B2 R

CO

ST

S A

ND

RE

VE

NU

E (

RS

.)

0

Y

X E

FIXED COST OPTIMAL LEVEL

TFC

LO

SS

B1

LOSS

LEVEL OF ACTIVITY OUTPUT

a) Economists treat costs and revenues as curvilinear functions, whereas accountants treat them as linear.

b) Economist’s break-even chart indicates two break-even points, whereas accountant’s

break-even chart shows only on.

c) From the profit range shown in the economist’s break-even chart, an optimum level of operations can be found the level at which the firm makes maximum profits. This is not possible from an accountant’s break-even chart.

Conclusion:Break-even analysis is a specific way of presenting

and studying the inter-relationship between costs, volume and profits. It provides information to management in most lucid and precise manner. It is an effective and efficient financial reporting system.

Application: Managerial uses of Break-Even Analysis: The break-even analysis can be used for the following purposes: 1) Margin of Safety: It reflects the difference between the actual volume of sales and the break-even volume of sales. It reveals the percentage increase in sales necessary to reach the BEP so as atleast to avoid losses. 2) Volume needed to Attain Target Profit: BEA may be utilized for the purpose of determining the volume of sales necessary to achieve a target profit. 3) Change in Price: BEA will help the management to know the required volume of sales to maintain the previous level of profit. And on the basis of its knowledge and experience, it will be much easier for the management to judge whether the required increase in sales will be feasible

4) Change in Costs: BEA helps the management to decide the total sales volume to maintain present profits without any change in price even if variable cost or fixed cost changes. 5) To Expand Capacity or Not: The management might often be interested in knowing whether to expand production capacity or not through the installation of additional equipment. Through break-even analysis, it would be possible to examine the various implications of this proposal. 6) Effect of Alternative Prices: The BE chart can be modified to show the profit position at different price levels. 7) Drop and/ or Add Decision: BEA is helps the management in taking decision about the addition of a new product or dropping of a particular product and it also helps to know consequent effects on revenue and cost.

8) Make or Buy Decision: Many business firms often have the option of making certain components or ingredients which are part of their finished products or purchasing them from outside suppliers. BEA helps in taking right decision. 9) Choosing Promotion-Mix: Sellers often use several modes of sales promotion e.g. personal selling, advertising etc. BEA helps to select the right mode of promotion mix. 10) Equipment Selection: BEA analysis can also be used to compare different ways of doing jobs.

11) Production Planning: BEA can also help in production planning to as to give maximum contribution towards profit and fixed costs. 12) Improving Profit Performance: There are 4 specific ways in which profit performance of a business can be improved: (a) Increasing the volume of sales (b) Increasing the selling price (c) Reducing variable cost per unit (d) Reducing the fixed cost.