The below mentioned short article provides a finish overview on Break-Even Analysis.

Break-Even Analysis:

Break-even analysis seeks to inspection the in­terrelationships amongst a firm’s sales revenue or to­tal turnover, cost, and also profits together they relate to al­ternate level of output. A profit-maximizing firm’s initial objective is to cover all costs, and also thus to reach the break-even point, and also make net profit thereafter.

The break-even suggest refers to the level of calculation at which full revenue equals full cost. Monitoring is no doubt interested in this level of output. How­ever, it is much more interested in the vast question that what happens to earnings (or losses) at assorted rates that output.

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Therefore, the major objective of making use of break-even charts as an analytical an equipment is to examine the impacts of changes in output and sales on total revenue, complete cost, and also ultimately on complete profit. Break-even analysis is a very generalized ap­proach for taking care of a wide selection of questions connected with profit planning and also forecasting.

The complying with list seeks to highlight few of the much more practical applications the break-even analysis:

1. What happens to all at once profitability as soon as a brand-new product is introduced?

2. What level the sales is essential to cover all costs and earn, say, Rs. 1, 00,000 benefit or a 12% price of return?


3. What happens to revenues and costs if the price of one of a company’s products is changed?

4. What happens to as whole profitability if a com­pany purchases new capital equipment or in­curs greater or reduced fixed or change costs?

5. In between two different investments, which one supplies the greater margin of benefit (safety)?

6. What are the revenue and cost ramifications of an altering the process of production?


7. Have to one make, buy, or lease capital equip­ment?

Our basic objective right here is to present the gen­eral break-even model, in both graphical and alge­braic forms, and to discover the useful use the the model. It may be noted at the outset the although the model has actually some limitations, if offered properly, it can administer management with some an useful guide­lines in making certain strategic decisions. After pre­senting the design these constraints will be lugged into focus.

Graphical Presentation that Break-Even Model:

Figure 21.1 presents the simplest and most com­mon graphical depiction of break-even analysis. The horizontal axis procedures the price of output, and also revenues and also costs, measured in rupees, are shown on the vertical axis. Figure 21.1 combine an in­verted U-shaped complete revenue (TR) curve and the familiar S-shaped short run complete cost curve (TC).

The curvi­linear shape of the full revenue curve adheres to from the assumption that the firm deals with a downward-slop­ing need curve and also must mitigate its price to have the ability to sell more. The legislation of diminishing returns accounts for the curvilinear form of the full cost curve.

The upright distance in between TR and TC mea­sures the benefit or loss associated with any specific level the output. To the left of Qa and also to the best of Qb full costs exceed full revenues, and there are losses.

So there space two break-even points. In between these two points, revenues are positive due to the fact that TR ex­ceeds TC. The point at which revenues are maximized (that is, the allude at i beg your pardon the vertical distance be­tween TR and also TC is the largest) is shown as Qc.

The generalised model in number 21.1 is usually simplified to a direct break-even chart, such together that in number 21.2. Linearity in the total revenue role implies that the certain is offering in a perfectly competi­tive market, and hence is a pure price taker and also does not need to reduce that price to sell more.

Conversely, linearity in the situation of the total cost curve means that the certain can expand output without transforming its variable expense per unit an extremely much. For a relatively narrow calculation range, this is no doubt a reasonable assumption.

Moreover, we make this linearity as­sumption to make our analysis simple, and thus to carry out management with basic profit guidelines, no to suggest precise answers to specific problems. These qualifications apart, there is much to -be claimed for utilizing the direct break-even version in the actual commercial world.


The break-even suggest is the allude where total revenue = complete cost, or price per unit = cost per unit. In number 21.1 the for sure breaks also at two various points B and B’. At both the points over there is neither benefit nor loss.


In number 21.2 the suggest at which TR equates to TC, allude QA, is the break-even level the output. Come the left that this suggest the firm occurs losses be­cause TC over TR. But in number 21.1 over there were 2 break-even points. In the decision-making procedure managers frequently employ a modified break­even model.

This modification follows indigenous the no­tion that administration may not necessarily think of benefit in the financial sense of full revenues, mi­nus full costs. When provided for short-run decision making, where a section of the firm’s financial re­source has already been clogged in the acquisition of addressed capital, a much more appropriate measure well-known as the contribution margin or contribution to profit is used.


In the short-run a firm’s initial target is come cover variable cost. If this can not be covered, a for sure would favor to close under its to work com­pletely and attempt to minimization its losses. If the price the the product exceeds variable cost, the firm would attempt to expand production with a watch to covering addressed cost and also make profit subsequently. So output will increase if price exceeds median vari­able costs.

The difference between the 2 (i.e., p — AVC) is called the donation margin per unit, or typical contribution margin. This mirrors the contribution of the product toward the restore of fixed cost and toward net profit. If that is multi­plied by the sales volume (Q), us arrive at the total contribution margin.

In short, contribution margin refers to the differ­ence between total revenue and also total variable cost. Because that example, if a product sells for Rs. 5 every unit, and overall variable expense is Rs. 3 per unit, each unit sold provides a contribution of Rs. 2 toward the restore of addressed cost.

Figure 21.3 illustrates a donation margin break-even chart based upon linear cost and also revenue curves. Here full net profit TNP, is the difference in between TR and also TC.


Total contribution margin (or profit) TCM is expressed as:



Contribution together a Decision Criterion:

The difference in between the revenue created from sale of a product, and also its production and also selling cost, is the contribution towards solved costs and also to the ultimate network profit. This contribution concept is regularly used for decision-making purposes.

There is hardly any reason, however, why every product-line made and also marketed by the firm must be intended to make the exact same contribution. By contrast, over there is a situation for assuming the preference must be given to those product-lines which market the opportunity of do the largest contribution.


An important element of cost-volume-profit analysis is the marginal income ratio or profit-volume ratio, defined as “the percentage of the sales i m sorry is obtainable as a donation to addressed costs and profits after direct prices are deducted.”

It is expressed as:



One may comparison this technique with the of ‘full cost’. Intend that a hypothetical firm is con­sidering the family member merits of 2 products, X and Y.

Initially, it viewpoints the problem by means of full cost and also produces some such statement as the following:


It may apparently seem, native this example, that both assets yield the same percent profit ~ above sales and also that over there is nothing come choose between them.

If, however, one focusses top top the dubious na­ture the the cost allocation embodied in the over figures, an alternate presentation might be make on the following lines:


Now we acquire a fully different picture. Each unit the X marketed produces a higher cash con­tribution and a higher rate of contribution towards resolved costs and also profit. It would certainly surely merit the at­tention the the monitoring in choice to product Y. The partnership is shown in number 21.4.


In order to embrace this type of approach, one must relate the prices directly to the production and also marketing that the product—the expenses which could be avoided through not developing the item. Clearly, the sell­ing price should generate adequate revenue to cover these in the typical course of business.


If the com­pany is mainly a ‘price taker’, having to expropriate the prevailing industry price, the over cost data have the right to be supplied to identify the product mix which will certainly yield the maximum donation for the least sales rev­enue. If, however, the agency is a ‘price maker’ v some degree of independence in price fixing, it have the right to use the data together the beginning point in price deter­mination.

In a multi-product firm, that is not enough merely to identify the product mix through a see to the maximization of contribution. The firm will be fitted with production facilities, few of which might be specific to offered products, whilst others deserve to be offered for much more than one product, though the de­mands do on castle in regards to time will vary from one product to another.

Thus, in settling for a provided pattern of contribution, the manufacturer have to make certain that this does no make him suffer from ca­pacity constraints.

As a guide to the solution of this difficulty it may appear necessary come evolve some yardstick to permit a decision to it is in made as to which product-line or stimulate is to it is in discarded, when particular production infrastructure are overburdened.

Consider the following example:


The stimulate B contributes Rs. 20,000 to fixed charges and also profit as versus the Rs. 10,000 noted by order A. Yet its case on production framework if 25 times as great. The an outcome is the the donation per basic hour is Rs. 200 as against Rs. 250.

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If ca­pacity is inadequate, speak 60 hours, come undertake both orders, and also if part orders cannot be taken, climate the monitoring may be constrained to refuse order B. Thus, if the volume of production which the firm can sell above the currently capacity, the optimal outcomes will be derived by producing those order which do the maximum contribution per basic hour in the area where the bottleneck occurs.

Example 1:

A firm produces two commodities X and Y. The complying with facts are given regarding them:




Since the production hour is the limiting factor, product X, which makes higher contribution every hour, will certainly be accorded priority.

Therefore, optimum product mix will certainly be together under:


The continuing to be 500 hours will it is in utilised for the production of Y, i.e., 500/2 = 250 units of Y deserve to be produced in the remaining hours.


We understand that typical net profit, i.e., ANP = P- ATC = P- AVC – AFC or ANP + AFC = ns — AVC = ACM or mean contribution margin. Currently at the break-even allude ANP = 0. Therefore, AFC = ACM. Therefore the break-even point can be determined by finding the end the level of sales in ~ which AFC = ACM. See figure 21.5.

Algebra of Break-Even Analysis:

Let us proceed to assume direct cost and also rev­enue functions. We might now specify the symbols usually provided in break-even analysis:




Three Alternatives:

The breakeven point may now be computed in one of three different but interrelated ways:

(1) as a number of units mat must be sold,

(2) Money worth of sales, or

(3) together a percentage of plant capacity.

To illustrate, assume that we have a manufacturing facility that can develop a best of 20,000 units of output per month. These 20,000 units deserve to be sold at a price that Rs. 100 per unit. Variable expenses are Rs. 20 every unit and also the total fixed expenses are Rs. 2, 00,000.

1. By a straight application that Eq. (2) we can com­pute the number of units that have to be marketed to rest even:


2. If one is to identify the break-even level mea­sured in terms of rupee sales, Eq. (2) has to be slightly modified to yield where Sb denotes the breakeven sales level.


The denominator in equation (3a) carry out a measure up of the contribution made by the product to recover fixed costs. Because that our example, the breakeven level in rupee sales is i m sorry is the same result that can be acquired by multiply the break-even amount by unit price.


In equation (3), the contribution margin is calculation on a per unit communication from the proportion of AVC come price. In equation (3a), the contribution margin is calculate on a total sales revenue basis from the ratio of TVC come TR. The ratio is the exact same in each case and in both the instances the calculated ratio is subtracted from 1 to yield the percent of revenue the contributes to restore of fixed prices or overhead.

3. In stimulate to identify the breakeven suggest in state of percentage utilization of plant capacity (%B), (or load element to it is in achieved) Eq. (2) needs to be modified as follows:


which indicates that the firm have the right to break even by us­ing just 12.5% that its capacity.

Example 2:

Indian Airlines has a volume to bring a maxi­mum the 10,000 passengers every month from Calcutta to Guwahati at a fare of Rs. 500. Variable expenses are Rs. 100 every passenger, and also fixed prices are Rs. 3, 00,000 every month. How many passengers should be brought per month to break even? What load element (i.e., average percentage of seating volume filled) should be got to to break even?

We may note that p – AVC = Rs. 500 – Rs. 100 = Rs. 400. Then, by equation (7) or (7a) we gain


Obtaining Information crucial for Break­-Even Models:

To construct break-even charts or models we have to study a solitary time period’s income and also ex­pense accounts. Through the income and also expense state­ments in hand we have to then categorise the vari­ous costs as either fixed or variable. We may then continue to build our model. The primary ad­vantage that this strategy is the it highlights the duty of every of the expense categories affect profits.

Alternatively one can compare a collection of in­come and also expense account over numerous time peri­ods in i m sorry management has been differing both cost and output levels. This details may then be utilized to come at an calculation of one empirical cost role (usually, via regression), which, when merged with the revenue functions, provides in­formation on breakeven levels.

This approach has one obvious benefit that an ext information is in­corporated into the model. But the major problem with this technique is that enough data might not be obtainable to enable us to estimate either the expense or revenue functions.

Applications that Break-Even Analysis:

The break-even analysis can throw light top top a number of real (commercial) human being problems. We might now see exactly how break-even evaluation can be offered as a device to assist management in making decisions. We continue to assume that the linear cost and also rev­enue curves room a close sufficient approximation so regarding make the results valuable to management.

Adding one MBA Programme:

Suppose the Pro-Vice-Chancellor (Academy) that Calcutta college is contemplating the enhancement of a distinct weekend MBA programme for functioning ex­ecutives. Two different proposals have actually been put be­fore the Pro-Vice-Chancellor.

In the very first alternative, the college would incur a fixed prices of Rs. 75,000 for microcomputers dedicated to the weekend pro­gramme, and also experience an median variable price of Rs. 20 per lecture hour come cover earnings for ad­ditional faculty and the incidental incremental ex­penses associated with it.

In the second alternative, Rs. 50,000 would certainly be invested to raise the volume of the university’s present mainframe computer, and variable price per unit is meant to be Rs. 30 every lecture hour.

The P.V.C. Is now faced with two certain ques­tions. First, what should the enrolment be for the college to break even with one of two people alternative, if the tuition fee is set at Rs. 70 every lecture hour? Sec­ond, how high will certainly the volume (lecture hours) need to be prior to the benefit level that the high invest project equates to the profit level of the low investment alternative?

The P.V.C’s an initial question contains all of the relevant info which can be summarized as follows:

Project 1:

TFC = Rs. 75,000

AVC = Rs. 20 every lecture hour

P = Rs. 70/per great hour

Project 2:

TFC = Rs. 50,000

AVC = Rs. 30 per lecture hour

P = Rs. 70 every lecture hour

Substituting these values right into Eq. (7) and solv­ing because that the break-even quantities (Q1 and also Q2, respec­tively), we obtain

Q1 = Rs.75, 000/ (Rs.70 – 20)

= 1500 lecture hours

Q2 = Rs.50, 000/ (Rs.70 – 30)

= 1250 great hours.

Thus the first project would show up to it is in riskier because it has higher fixed prices and higher break­even level. The is, it requires a larger number of lecture hrs to cover all of its costs. Top top the con­trary, the contribution margin on a per-unit communication from the project is Rs. 50 every lecture hour versus just Rs. 40 because that the 2nd project.

The P.V.C.’s second request to be to identify the output level in ~ which the benefit from the first project equates to that that the 2nd project. This be­comes a crucial issue due to the fact that the 2nd project have the right to break even at 1250 hours and earn a benefit of Rs. 10,000 in ~ 1500 hours, conversely, the 2nd project have to reach 1500 hours before breaking even.


To discover the volume level in ~ which π1 equates to π2, us simply set Eq. (16) and (17) same to each other and then solve for Q:

50Q = 75,000 = 40Q – 50,000

10Q = 25,000

Q = 2500 class hours.

Output will have to reach 2500 lecture hours for job 1 to be as lucrative as job 2. Beyond 2500 hours, the comparative profitability of project 1 i do not care greater because of the higher contribution every unit. Conversely, below 2500 hours, task 2 be­comes preferable. V this information, the P.V.C. Might be interested in estimating the likely number of lecture hrs to be generated by the brand-new MBA programme.

Break-Even Models and also Planning because that Profit:

The break-even allude represents the volume the sales at which profits equal expenses; that is, at which benefit is zero. Computationally, the break­even volume is landed on by splitting fixed costs (costs that execute not vary with output) by the contribu­tion margin per unit, i.e., selling price minus variable expenses (costs that vary directly with output).

In cer­tain situations, and especially in the factor to consider of multi-products, break-even volume is measure in terms of rupee sales value quite than units.

This is excellent by separating the fixed expenses or overheads through the donation margin-ratio (contribution margin separated by offering price). Generally, in these varieties of computations, the preferred profit is added to the fixed prices in the molecule in order to ascertain the sales volume important for producing the target profit.

If management plans because that a details profit, climate revenues essential to covering all prices plus the wanted profit is


This information deserve to be displayed graphically, as in figure 21.6. In this example, fixed prices are Rs. 1, 00, 000 and also variable prices are Rs. 12.50 every unit. The price fee is Rs. 25.00 every unit and the break­even allude occurs in ~ 8,000 units of manufacturing (ver­ify this using the formula). If management wants a benefit of Rs. 50,000, they will need to produce and also sell 12,000 systems (again, you should verify this).


To amount up, a break-even point can be discovered by calculating every fixed prices for a period, calculating the variable prices per unit, including the fixed and variable costs, and also deciding on the price of the product or ser­vice (or earnings per unit).

It have the right to be provided for multi- product situations if the product mix is constant and if different revenues and costs can be developed for every product, back this typically presents a prob­lem due to the fact that separating these expenses is no doubt difficult in practice.

Instead that focusing solely on the break­even level of output, administration may at times be interested in estimating the volume (QT) needed to earn sufficient not just to cover every costs yet earn a’’ target “(PRT).

If this is the objective, the break- also equations have to be modified together follows:


To show this process, we go back to the ex­ample provided in our discussion of the direct break­even model.

The necessary information is offered be­low:

Qcap = 2000,

P = Rs.100,

AVC = Rs.20,

TFC = Rs.200, 000

Qb = 2500 units,

Sb = Rs.250, 000,

%B = 12.5.

Now suppose that monitoring wants to knife a target profit of Rs. 50,000. Do the proper substitution into Eqns. (6) v (8) we acquire the new levels the Qb = 321,500 and also %B = 15,625. If we include this target profit to the fixed prices we watch that the break-even level of all three determinants get increased.

The information in this example could be expanded so regarding make provisions because that such factors as payment of counting or because that payment of any other fixed responsibilities that could be associated with the fixed costs (such as interest payments on bond or debentures supplied to finance one investment).

Example 3:

Suppose the target of Indian airlines is to make a profit of Rs. 2, 00,000 every month. The ques­tion is: how many passengers need to be brought per month to reach the profit target? One last question is: What is the maximum amount of benefit that have the right to be made by Indian Airlines?

Now come answer to very first question we can use the adhering to expression:



which is the maximum quantity of profit that can be deserve by Indian airline by fully utilizing its capacity (i.e., through 10,000 passengers every month).

Example 4:

To show the case of break-even evaluation with taxation, mean that r represents the tax rate per­centage, pat is earnings after taxes, and PBT is profits before taxes. The relationship in between PAT and PBT deserve to be displayed to it is in

PAT = (1 – r) PBT (9)

Or, PBT = play (1-r) (10)

Consider the situation when the tax price is 50%. One after-tax profit of Rs. 50,000 would call for a before- tax profit that

PBT= Rs.50, 000 / (1-0-5) = 100,000

This number of Rs. 1, 00,000 would certainly then it is in intro­duced into the molecule of the break-even ratio, together was done in Eq. (6) through Eq. (8). Essentially, the advent of taxes or various other fixed duties will result in boosting the break-even level of output in numbers, rupees sales, and capacity.

Break-Even chart Alternatives:

The break-even amount is not a addressed number. Management can alter the quantity by changing the controlled variables. Since plant capacity is lim­ited in the quick run, profits have the right to be increased only by changing the break-even allude to a lower level of production or sales which deserve to be achieved by manipulating three variables: resolved costs, variable costs, or price. Herein lies an essential application that break-even charts in profit planning, control, and also forecasting.

To illustrate this situation, suppose that us have gathered the adhering to information (all tabulated ~ above a every month basis):


Figure 21.7 depicts the impact of manipulating the 3 variables on the break-even level of output. Dashboard (a) illustrates the original case where the break-even level of calculation is 100 units and total revenue and cost same Rs. 1,500. Panel (b) depicts the affect of reduce fixed costs from Rs. 600 to Rs. 200.

The shaded portion on the graph provides a measure up of the initial profits, and also the crosshatched area provides a measure of the boost of profits.


If the fixed costs can be reduced to Rs. 200, the break­even level of output deserve to be carried down come approx­imately 33 units, and break-even costs and also revenues to around Rs. 497. The impact of reduce variable prices to Rs. 5 is shown in panel (c).

In this situation, costs and also revenue both fall to Rs. 900 and also the break-even calculation level of 60 devices is reached. Dashboard (d) gift the final option of raising the industry price that the product come Rs. 17 every unit.

When the price is increased, the slope of the full revenue curve changes, while the break-even level the output falls to 75 units. A to compare of the 3 alter­native methods of transforming the break-even quantity shows that the most promising, in terms of prof­itability, is the situation where the fixed prices are diminished to Rs. 200.

Example 5:

Suppose you have actually the complying with information around a theoretical company:

Plant capacity =100 devices

AVC = Rs.7per unit

P = Rs.12 per unit

TFC = Rs.400

Qb = 80 devices

TR (at capacity) = Rs.1,200

TC (at capacity) = Rs.1, 100

Suggest alternative ways of to reduce the break­even amount by 50%.

There space three methods of to reduce the break-even quantity:

(a) Reducing complete fixed cost,

(b) Reducing complete vari­able cost and

(c) raising product price,

(a) In the example, if total fixed expense is diminished to Rs. 200, we can reduce the break-even quantity to 40, or


(b) Alternatively, reduction of the break-even quan­tity come 40 may be accomplished by a reduction in AVC. For this reason


Thus a 50% reduction in break-even amount re­quires an ext than 70% palliation in total variable expense (from Rs. 7 to Rs. 2).

(c) Finally, the price of the product may be raised to attain the brand-new break-even quantity thus:


It might be listed that with rise in price, a decrease in sales might be expected, yet even with decreased sales, a sizable increase in profit could re­sult.

The Margin of safety and security (Profit):

So lengthy only one of the controllable variables (price, or resolved or change costs) to be changed, however in practice monitoring may have actually the strength to adjust all 3 of lock simultaneously. In order to have the ability to assess the influence of changing more than one of the variables us often take on a modified version of break-even analysis.

This modification looks in ~ the proportion of full net benefit to total fixed cost. By fo­cussing ~ above this ratio, we room virtually focussing top top the margin of profit that the firm is at this time mak­ing, and also the casualty it would certainly incur in instance sales fall listed below the break-even level.

The larger the proportion of profits to full fixed costs, the far better it is for the firm (from the standpoint of safety). Hence this ratio is called the margin of safety or the margin of profit.

The margin of safety can be express as:


where Qs refers to the number of units in reality sold.

Example 6:

We might now illustrate the applications of the margin of safety in performing the marketing func­tion, and also we mean that we have actually the adhering to information:


The manufacturing manager has argued a adjust in a production an approach that will rise variable expenses by Rs. 5 per unit. The new item will sell for Rs. 15 much less than the old one and also the mar­keting manager estimates that this price palliation will boost sales come 775 units.

However, he likewise suggests the Rs. 10,000 will have to be invested on ad­vertising to educate potential customers of the price reduction.

Management has now to decision which that four options is to it is in preferred:

(1) Maintain­ing the condition quo,

(2) Adopting the production tech­nique, reduce price and also undertaking the advertis­ing project ,

(3) keeping profits there is no un­dertaking the declaring programme, and

(4) not reducing the selling price but conducting the adver­tising programme. The computations for these four alternative are gift below:

1. Maintain status quo:


2. Undertake every one of the options:

Suppose the new production method is adopted; variable expenses increase to Rs. 175 every unit; price is decreased to Rs. 285 and sales boost to 775 units; and Rs. 5,000 is invested on advertising:


3. If the exact same level the sales is maintained as in op­tion 2 yet without the advertising programme, we have actually the adhering to results:


It is come be noted that the projected sales space lower below than with the 2nd option since of not un­dertaking the heralding programme.


4. If the exact same level that profit together in choice 2 is main­tained but price is not lowered and also the adver­tising programme is undertaken, we have actually the complying with results:


Example 7:

Suppose a firm produces three-wheelers for sale come commercial customers at Rs. 35,000 each. The tree is at this time operating in ~ 60% that its volume of 80 devices per year, at a total fixed price of Rs. 6, 00,000 and also an mean variable cost of Rs. 20,000 every unit.

The for sure is contemplating a readjust in product de­sign the will rise the median variable prices by Rs. 1,000. Also an advertising project will be introduced at a price of Rs. 1, 20,000, come announce that the new improved version will market for Rs. 2,000 less than the old one.

The marketing manager estimates that these actions will increase sales come 90% of tree capacity. Assuming that the marketing man­ager is correct, what will be the results of all these alters on the break-even sales volumes and on an­nual profits?


In the existing case the break-even sales volume is




The margin that safety clearly indicates the the third option is preferable. The implication of this higher margin of security is the management have the right to un­dertake this choice with the knowledge that it have the right to come closer to incurring its fixed costs even if the meant level the sales stops working to materialize.

Applications the Break-Even Charts:

Comparison of various Production Techniques:

One of the primary jobs of the manufacturing man­ager is to make decisions such the production costs are minimized. Break-even analysis can be fruit­fully used by management in making expense com­parisons among production methods that involve different fixed and also variable cost structures.

As a gen­eral rule, more capital-intensive approaches involve a cost structure with greater fixed and lower change costs. By contrast, labour-intensive manufacturing tech­niques usually suggest lower solved and higher vari­able costs. Thus the cost advantage of every of these two production techniques depends top top the level of output.

In most production procedures it is observed that the higher the level that output, the more effi­cient will be the capital-intensive technique, and also the lower the level of projected output the much more efficient will be the labour-intensive technique.

This allude may currently be illustrated.

Suppose that the manufacturing analyst has acquired the follow­ing two expense functions for various production tech­niques:

TCa = Rs. 170 + Rs. 1.40Q

TCb = Rs.520 + Rs. 0.85Q.

Technique (a) is the labour-intensive production an approach and an approach (b) is the capital-intensive method.

The first step in this form of practical instance is to determine the level of output at i m sorry the 2 production techniques are equally efficient. To carry out this, us simply collection the full cost features equal to each other and solve for Q as follows:

TCa = TCb

Rs. 170 + 1.40Q = Rs. 520 + Rs. 0.85Q

Rs. 1.40Q- Re. 0.85Q = Rs. 520- Rs. 170

or, Q — 636 (approx.).

For any kind of output level which is less than 636 units, production an approach (a) is an ext efficient, and also for any output level above this initial quantity, produc­tion technique (b) will involve a lower cost.

If this type of details in available, the pro­duction analyst may contact the marketing manager about the projected level of sales. The marketing manager argues that the many probable level that sales is 700 units with deviation of 250 units and that the distribution of sales is roughly a common distribution.

This info may currently be summa­rized in one graph displayed is number 21.8. Now the pertinent question confronted by the production analyst is this: What is the probability the sales equalling or exceeding the break-even level that 636 units? This corresponds to the shaded area under the typical probability curve as presented in figure 21.8.


To arrive at the exactly answer come the question, the first step is come compute the appropriate Z value as follows:


The suitable percentage that the typical prob­ability curve that corresponds to this Z value is given in any type of standard textbook of statistics. Corre­sponding come the Z value of 0.26 is the entrance 0.1026.

Because 50% the area of the regular curve lies come the appropriate of the mean, the shaded area amounts to 60.26% (obtained by summing 50% and 10.26%). Through this information, the production manager have the right to now bring the information to the an alert of top administration that over there is roughly a 60% probability that the capital-intensive tree will cause a lower cost per unit.

We deserve to use exactly the same kind of method to advice such inquiries as the following:

Should us buy or lease a item of equipment?

Should we make or purchase a part?

Should the plant dimension be expanded?

The level of operating Leverage:

Linear cost-volume-profit analysis can likewise be provided for analysing the financial qualities of dif­ficult manufacturing processes. Through using linear break­even charts we can ascertain how complete costs and profits vary v output together the for sure uses an ext and more capital-intensive methods of production, and also thus elevating the relationship of solved costs and reducing the of change costs.

Operating leverage “reflects that extent to which fixed manufacturing facilities, as opposed to variable production facilities, are used in operations.” The relation between operating leverage and also profit vari­ation is displayed if figure 21.9, in which us compare three firms, X, Y, and also Z each having actually a different de­gree the leverage. The fixed expenses of operations in firm Y are considered to be the most representative the all.

It uses devices with which one operator can turn out a couple of or numerous units in ~ the same work cost, to about the same level as the average firm in the industry. For sure X provides less resources equipment in the production process and has lower addressed costs.

But X’s variable price increases much more sharply than that that Y. Certain X breaks also at a lower operation price than go Firm Y. In figure 21.9, in ~ a produc­tion level of 40,000 units, Y is losing Rs. 8,000, but X division even.

Here for sure Z is having the highest possible fixed costs since its uses modern, advanced and for this reason costly machines that require very small labour every unit of output. V such an operation, its variable expenses rise really slowly.

Because the the high overhead resulting from charges associated with the high value machinery, Z’s break-even suggest is greater than that of one of two people X or Y. When firm Z get its break­even point, however, its earnings rise much faster than carry out those of X and Y.

The degree of operation leverage has actually been defined as the percentage adjust in benefit that outcomes from a 1 every cent adjust in units sold. The shows how a given readjust in volume affects profits.

This may be exactly expressed as:


where π is profit and also Q is the quantity of calculation in units.

Since the degree of operating leverage is a ra­tio the two portion changes, it is not fundamen­tally different from an elasticity concept. It has actually been dubbed by Pappas the operating leverage elasticity that profits. In situation of direct cost and also revenue curves, this elasticity measure will vary depending upon the particular part of the breakeven chart that is under consideration.

For instance, the degree of operat­ing leverage is always really close come the break-even point, where a very tiny change in sales volume can create a very big percentage boost in profits, simply due to the fact that the base revenues are close to zero near the break-even point.



For certain Y, in number 21.9(b) the degree of oper­ating leverage at 100,000 devices of output is 2.0. This is calculated together follows:


We arbitrarily assume that the change in Q (∆Q) = 2,000. If us assume any other ∆Q, for example, ∆Q = 1,000 or ∆Q = 4,000 the degree of operation leverage will certainly still revolve out to be 2, since we proceed to use linear cost and also revenue curves. However if we select a base various from 100,000 units, the degree of operation leverage (DOL) will certainly be uncovered to be different from 2.


For straight revenue and cost relations, it is pos­sible to calculation the level of operation leverage for any kind of level of output Q: The change in output is characterized as ∆Q. Fixed expenses are held continuous so the change in profit is ∆Q(P — AVC). Whereby all the terms have their normal meanings.

The initial level of profit is Q (P – AVC) – TFC, and the percentage change in the is:


The percentage change in output is ∆Q/Q, for this reason the ratio of the percentage readjust in profits to the per­centage change in output might be expressed as:


A tiny manipulation will yield the adhering to


Using Equation (16), we find Y’s level of op­erating leverage at 1,00,000 systems of output to be:


Equation (16) can additionally be applied to this firm X and Z. If this is done, X’s level of operating leverage at 100,000 units end up being 1.67; Z’s is 2.5. Thus with a 10 every cent rise in volume, Z (the firm through the most operating leverage) will experience a profit increase of 25 percent. Because that the same 10 percent sales gain, X the firm with the the very least leverage, will certainly expe­rience only a 1.67 percent profit gain.

The calculate of the level of operating lever­age with equation (13) and also (16) reflects the very same thing that number 21.8 shows graphically; that the earnings of for sure Z, the agency with the most op­erating leverage, is many responsive to changes in sales volume, while those of for sure X, which has only a small amount of operation leverage, is reasonably less responsive come volume changes.

Firm Y, with an intermediate level of leverage, lies in-between the two too much situations.

Evaluation that Break-Even Models:

Break-even models are reasonably simple to con­struct and to translate by both experts and manage­ment. Furthermore, they are inexpensive, particularly when contrasted to more complicated models and, offered their extensive applicability, castle confer signifi­cant expense advantages.

In general, the data required to use break-even evaluation are conveniently available, and the cost of such data repertoire is nominal. How­ever, break-even evaluation is not totally free from defects. It is topic to abuse and also misinterpretation.

So one who uses this method of benefit planning have to be conscious of the adhering to limitations and also qualifica­tions linked with break-even models:

1. Prima facie, because most the the data made use of to build break-even charts and models room de­rived from accounting records and also statements, financial experts must be aware of the limita­tions of audit data.

In particular, together Bails and Peppers have actually cautioned that “the cost es­timates and also functions should be readjusted to con­sider latent costs, depreciation estimates, and inappropriate assignment the overhead costs. This is, one must ensure the the measures of total cost represent only those expenses that are in­curred as a result of the decision being consid­ered, and also that the does not include expenses that will be incurred by the firm nevertheless of the deci­sion made around the difficulty at hand”.

2. Secondly, so far we have concentrated on direct ap­plications of the break-even model. However, the same evaluation could be expanded with curvi­linear cost and also revenue functions. Yet in such situations we get two break-event points, no one. True enough, straight cost-volume-profit analysis is really weak with regard come costs.

The linear relations indicated by the chart execute not organize at all calculation levels. With rise in sales, exist­ing plant and equipment space worked beyond capacity, for this reason reducing your productivity. This case results in a need for additional work­ers and also frequently longer working days, which may require the payment the overtime wages.

All this factors cause variable prices to rise really sharply. Added plant and equipment might be required, raising fixed costs. Further­more, over an extended duration of time the prod­ucts sold by the firm readjust in quality and also quantity. Such transforms in optimum product mix influence both the level and also the slope of the expense function.

3. Thirdly, the assignment that selling and also market­ing costs can be difficult and might require some kind of subjective decision making. This follows from the reality that the relationship in between out­put and selling prices is a one-sided one. More­over, over there is fixed anything to show that the relationship in between output and marketing expenses is particularly stable in time or over var­ious calculation ranges.

4. Moreover, we implicitly assumed so far that the for sure was involved with only one product. Yet in practice we observed that many firms are multi-product firms. The most common approa­ch because that a heterogeneous product mix is come mea­sure calculation in terms of rupee sales volume. However, this approach does not totally overcome the problems connected with multi­ple products.

5. Direct cost-volume-profit evaluation is especially weak in what that implies about the sales possibil­ities for the firm. Any given linear-cost-volume profit chart is based on a fixed selling price. Therefore, with a view to researching profit possi­bilities under alternative prices, a whole series of charts is necessary, one chart for each price. Non-linear cost-volume-profit evaluation can be supplied as a preferable alternative.

6. Over there are several other troubles with break­even analysis, however, which usually typical it deserve to only administer a rough approximation for planning decisions:

(a) Usually, the cost and also revenue calculations are much more facility than the basic examples provided here. Frequently managers do not understand what this fixed and also variable prices are.

(b) it is difficult, if no impossible, to estimate what sales will be at various price levels, or to accu­rately project complete revenues.

(c) Materials and other variable costs may shake widely. Choose prices, they room not constant over time. Similarly, that is not clear which fixed costs (like overhead costs) need to be included. Because that example, what component of the president’s value is to be contained for a offered product?

A considerable amount of judgement is required to classify the costs as either resolved or variable. If fixed costs are overstated, the break-even point is overstated, which might lead to missed opportuni­ties due to the fact that that sales level is thought about unattainable.

If fixed prices are understated, the break-even suggest is understated, which can lead come a commit­ment of resources to acquire an undesirable level of sales. If variable expenses are overstated, addressed ex­penses space understated (and vice-versa) bring about the two preceding situations.

7. In fact, cost behaviour is the an answer of expense to a variety of influences. Therefore, as soon as work­ing out a cost-volume-profit analysis, we should take right into account any type of factor which may have an effect on the results, and also realize that the break­even graph is only a pictorial expression i m sorry relates costs and also profit to activity. The graph tends to over-simplify the real instance as there space other effects besides sales volume.

(a) Cost and also revenues are displayed as right lines. Yet in practice, selling prices perform not necessarily continue to be fixed, and also the revenue may readjust de­pending top top the quantities of items sold directly, offered through agents and sold at a discount. The slope of the graph will certainly not be continuous in prac­tice. The will vary under different circumstances.

(b) Variable prices may not be proportional to vol­ume for various reasons such together overtime work­ing, to reduce in the price of products when mass discounts are negotiated, or since of rise in price of materials when demand out­strips supply. If sales are made end a wider area, marketing expenses tend to rise sharply.

(c) Fixed costs do not constantly remain constant dur­ing the duration of activity.

(d) The effectiveness of production or a change in pro­duction techniques is most likely to have an effect on variable costs.

(e) The assorted quantities of different goods marketed (the sales mix) might not readjust the full sales worth considerably yet they may adjust the quantum the profit relying on the proportion of low and high-margin items sold.

For this reasons, break-even analysis is a crit­ical planning tool that can provide a manager with useful insights about the dynamic relationships among expenses, volumes and profits. But, like various other planning techniques, it have to be offered with treatment with a see to staying clear of the hazard of make inappro­priate decisions.

Implications because that Managers:

For organizations that are came to with prof­its or costs, gaue won planning approaches are the ba­sis because that all other tactical planning. Break-even anal­ysis is in ~ the heart of many tactical planning. One firm to be actually selling every item it developed at a loss since it did not go with this exercise. The losses on this product were covered by revenues on various other lines.

Later, when a break-even analysis was done, the instance was rapidly (and profitably) corrected. In practice, friend will have some difficulties in classifying prices as fixed or variable, or also in assigning them to a particular product. Again, make the attempt will uncover problems and opportuni­ties and also give girlfriend planning insights girlfriend didn’t have before.