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Chapter: Civil : Engineering Economics and Cost analysis : Cost And Break Even Analyses

Break even Analysis

An enterprise, whether or not a profit maximizer, often finds it useful to know what price (or output level) must be for total revenue just equal total cost.

Break-even Analysis


An enterprise, whether or not a profit maximizer, often finds it useful to know what price (or output level) must be for total revenue just equal total cost. This can be done with a breakeven analysis. Strictly speaking, this analysis is to determine the minimum level of output that allows the firm to break even, but it could be used for some other tasks. In this Appendix, we introduce:


-  The algebra of break-even analysis


-  Break-even diagram


Operating leverage

One of the important indicators of success of the start-up company is the time from starting the business till the moment when revenues of product sales equals the total costs associated


with the sale of product - it is also called break-even point. In other words profit = 0. Breakeven analysis is accounting tool to help plan and control the business operations.


Break-even point represents the volume of business, where company's total revenues (money coming into a business) are equal to its total expenses (total costs). In its simplest form, breakeven


analysis provides insight into whether or not revenue from a product or service has the ability to cover the relevant costs of production of that product or service.




Let QBE denote the break-even output level. By definition TR (at QBE) = TC (at QBE)


or TR (at QBE) = TFC + TVC (at QBE) (1)


The break-even condition (1) holds true for any cost and demand functions. Hence, in general, when costs and demand are complex, the analysis of this condition might not be any simpler than the analysis of profit maximization. Yet, what is widely known in business as break-even analysis is indeed much easier than


profit analysis, although it also starts with the above identity, because it makes a very important assumption: that price and average variable cost do not change with output level.


Break-even analysis is based on categorizing production costs between those which are:


           VARIABLE cost that do vary with the number of units produced and sold (raw


materials, fuel, direct labor, revenue-related costs), and those that are


FIXED costs that don't vary with the number of units produced and sold (salaries, rent and rates, depreciation, marketing costs, administration costs, R&R, insurance)


Calculating Break-even Point


To calculate break-even point we need to know following information:


         The price that the company is charging,


         variable costs (direct costs) of each unit and


         fixed costs (or indirect costs/overheads).


1.     TR = Total revenue


2.     P = Selling price


3.     Q = Number of units sold


4.     TC = Total costs


5.     F = Fixed costs


6.     V = Variable costs


7.     FC = Total fixed costs

8.     VC = Total variable costs


Financial Feasibility Study


A financial feasibility study is an assessment of the financial aspects of something. If this case, for starting and running a business. It considers many things including start-up capital, expenses, revenues, and investor income and disbursements. Other portions of a complete feasibility study will also contribute data to your basic financial study.


A financial feasibility study can focus on one particular project or area, or on a group of projects (such as advertising campaigns). However, for the purpose of establishing a business or attracting investors, you should include at least three key things in your comprehensive financial feasibility study:


Start-Up Capital Requirements,


Start-Up Capital Sources, and


Potential Returns for Investors.




         All costs are classified as either fixed or variable. If not impossible or impractical, dividing costs into the variable and fixed cost elements as an extremely difficult job. This is attributable to the inherent nature or characteristics of the cost per se.


         Fixed costs remain constant within the relevant range. Fixed costs remain unchanged at any level of activity within the relevant range, even at the zero level.


         The behavior of total revenues and total costs will be linear over the relevant range, i.e. will appear as a straight line on the BE chart. This is based on the idea that variable costs vary in direct proportion to volume; the fixed costs remain unchanged, hence drawn as a straight horizontal line on the graph within the relevant range; and that selling price is constant.


         In case of multiple product companies, the selling prices, costs and proportion of units (sales mix) sold will not change. This cannot always be correct. Sales mix ratio may be due to the change in the consuming habits of customers. Selling prices of the individual products may likewise change due to competition, popularity and salability of the products, etc.


         There is no significant change in the inventory levels during the period under review. Stated in another way, production volume is assumed to be almost (if not exactly) equal to the sales volume, which causes an immaterial (or none at all) difference between the beginning and ending inventories.


Managerial Uses of Break-Even Analysis:


To the management, the utility of break-even analysis lies in the fact that it presents a microscopic picture of the profit structure of a business enterprise. The break-even analysis not only highlights the area of economic strength and weakness in the firm but also sharpens the focus on certain leverages which can be operated upon to enhance its profitability.


It guides the management to take effective decision in the context of changes in government policies of taxation and subsidies.


The break-even analysis can be used for the following purposes:


(i) Safety Margin:


The break-even chart helps the management to know at a glance the profits generated at the various levels of sales. The safety margin refers to the extent to which the firm can afford a decline before it starts incurring losses.


The formula to determine the sales safety margin is:

Safety  Margin=  (Sales  -  BEP)/


Sales x 100


From the numerical example at the level of 250 units of output and sales, the firm is earning profit, the safety margin can be found out by applying the formula


Safety Margin = 250- 150 / 250 x 100 =40%


This means that the firm which is now selling 250 units of the product can afford to decline sales upto 40 per cent. The margin of safety may be negative as well, if the firm is incurring any loss. In that case, the percentage tells the extent of sales that should be increased in order to reach the point where there will be no loss.


(ii) Target




The break-even analysis can be utilised for the purpose of calculating the volume of sales necessary to achieve a target profit.


When a firm has some target profit, this analysis will help in finding out the extent of increase in sales by using the following formula:


Target Sales Volume = Fixed Cost + Target Profit / Contribution Margin per unit


By way of illustration, we can take Table 1 given above. Suppose the firm fixes the profit as Rs.


100, then the volume of output and sales should be 250 units. Only at this level, it gets a profit of


Rs. 100. By using the formula, the same result will be obtained.


(iii)   Change

in Price:


The management is often faced with a problem of whether to reduce prices or not. Before taking a decision on this question, the management will have to consider a profit. A reduction in price leads to a reduction in the contribution margin.


This means that the volume of sales will have to be increased even to maintain the previous level of profit. The higher the reduction in the contribution margin, the higher is the increase in sales needed to ensure the previous profit.


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