Break-Even Point
| Author | Karen Brown, Laurie Hillstrom |
| Pages | 45-49 |
Page 45
A company's break-even point is the amount of sales or revenues that it must generate in order to equal its expenses. In other words, it is the point at which the company neither makes a profit nor suffers a loss. Calculating the break-even point (through break-even analysis) can provide a simple, yet powerful quantitative tool for managers. In its simplest form, break-even 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. Managers can use this information in making a wide range of business decisions, including setting prices, preparing competitive bids, and applying for loans.
The break-even point has its origins in the economic concept of the "point of indifference." From an economic perspective, this point indicates the quantity of some good at which the decision maker would be indifferent, i.e., would be satisfied, without reason to celebrate or to opine. At this quantity, the costs and benefits are precisely balanced.
Similarly, the managerial concept of break-even analysis seeks to find the quantity of output that just covers all costs so that no loss is generated. Managers can determine the minimum quantity of sales at which the company would avoid a loss in the production of a given good. If a product cannot cover its own costs, it inherently reduces the profitability of the firm.
Typically the scenario is developed and graphed in linear terms. Revenue is assumed to be equal for each unit sold, without the complication of quantity discounts. If no units are sold, there is no total revenue ($0). However, total costs are considered from two perspectives. Variable costs are those that increase with the quantity produced; for example, more materials will be required as more units are produced. Fixed costs, however, are those that will be incurred by the company even if no units are produced. In a company that produces a single good or service, this would include all costs necessary to provide the production environment, such as administrative costs, depreciation of equipment, and regulatory fees. In a multi-product company, fixed costs are usually allocations of such costs to a particular product, although some fixed costs (such as a specific supervisor's salary) may be totally attributable to the product.
Figure 1 displays the standard break-even analysis framework. Units of output are measured on the horizontal axis, whereas total dollars (both revenues and costs) are the vertical units of measure. Total revenues are nonexistent ($0) if no units are sold. However, the fixed costs provide a floor for total costs; above this floor, variable costs are tracked on a per-unit basis. Without the inclusion of fixed costs, all products for which marginal revenue exceeds marginal costs would appear to be profitable.
Figure 1
Simple Break-Even Analysis: Total Revenues and Total Costs
In Figure 1, the break-even point illustrates the quantity at which total revenues and total costs are equal; it is the point of intersection for these two totals. Above this quantity, total revenues will be greater than total costs, generating a profit for the company. Below this quantity, total costs will exceed total revenues, creating a loss.
To find this break-even quantity, the manager uses the standard profit equation, where profit is the difference between total revenues and total costs. Predetermining the profit to be $0, he/she then solves for the quantity that makes this equation true, as follows:
Let TR = Total revenues
TC = Total costs
P = Selling price
F = Fixed costs
V = Variable costs
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Q = Quantity of output
TR = P× Q
TC = F + V × Q
TR − TC = profit
Because there is no profit ($0) at the break-even point, TR − TC = 0, and then P× Q − (F + V× Q) = 0. Finally, Q = F(P − V).
This is typically known as the contribution margin model, as it defines the break-even quantity (Q) as the number of times the company must generate the unit contribution margin (P − V), or selling price minus variable costs, to cover the fixed costs. It is particularly interesting to note that the higher the fixed costs, the higher the break-even point. Thus, companies with large investments in equipment and/or high administrative-line ratios may require greater sales to break even.
As an example, if fixed costs are $100, price per unit is $10, and variable costs per unit are $6, then the...
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