# Break-even (economics)

In economics, the breakeven point, also benefit threshold ( engl. break-even point ) is the point at which revenues and costs of production ( or product ) are the same high and thus neither loss nor profit is earned. To put it simply, that the contribution of all products sold is identical to the fixed costs at the breakeven point. If the earnings threshold is exceeded, one makes profits, it is below, you make losses. The breakeven point can for a product ( single-product approach) or several products (multi - product approach) can be calculated.

Economy Mathematically the breakeven point is how the profit limit a zero of the profit function. In both places revenues and costs are equal. However, below the break, the lower and is understood to be the income limit, the upper zero: from reaching the breakeven profit is made, from reaching the income limit losses to be written.

The starting point of breakeven analysis are the following questions:

- How many products must be produced and sold to cover the fixed costs? ( Single-product approach)
- How much revenue must be generated by the products under consideration, in order to cover the fixed costs? ( More product analysis)

The breakeven analysis ( break-even analysis) is an important tool for corporate planning. It helps to analyze the impact of changes in the cost structure and to determine the requirements for sales volume.

## Break- even analysis

The break-even analysis is essential for a company to determine at which sales amount (also called turnover ) just a full cost recovery occurs. This full- cost recovery (short BEP), also called break- even point break-even point or minimum sales.

A break-even analysis can only be performed when a breakdown of costs is in the fixed and variable costs and the contribution margin (short DB) is known. The BEP is an operational measure that shows how much can go back at constant prices of the paragraph, so just the overall costs are still being met.

## Calculation of the break - even point in general

The question of the break- even point is: At what amount of profit is equal to 0?

Generally calculated from the revenues minus the costs.

You can find the BEP, by equating both of the above equations. The result is

The BEP therefore is the point where income is equal to total costs. Equating and paste the individual lines of the respective functions results in the formula shown above. This formula can ultimately be converted to the minimum sales amount.

At the break- even point of the proceeds is equal to the cost

The function of the proceeds () is the unit price times the pieces were sold or the number of pieces

The total costs consist of the fixed and variable costs together

When equating the formulas for the proceeds, there is the point of intersection, which is the BEP

After the minimum sales amount dissolved arises

The contribution margin per unit () is equal to the price per unit minus the variable cost per unit.

- Price per Unit
- Variable costs per unit
- Total fixed costs
- Minimum sales amount.

For companies with more than one product of the minimum conversion is determined by value.

- Value-based minimum turnover
- Total fixed costs
- The contribution margin as a percent of sales

The break- even point is a tool for the entrepreneur. Therefore, there is a certain degree of freedom, from which costs and revenues (or positive or negative aspects ) results in this point.

In step costs may be several break-even point. This means that you can reach the profit zone after a certain sales volume. However, a loss zone is again achieved through the influence of the step costs. In practice, it is usually calculated with a linear development in order to simplify the appearance and operation.

## Graphical representation: the break-even chart

The break-even chart shows the relationship of revenues and costs over the piece Quantity graphically dar.

On the abscissa the quantity is plotted on the ordinate axis of the revenue or cost, sometimes the profit.

## Application of break-even information

The question of the break- even point is an economic consideration to balancing the negative or positive influence factors. Negative factors are, for example, various cost dar. positive feature is its realizable value of a product or service.

This method can be applied in a business not only for cost and revenue analysis of production levels, but also for other business issues.

Break-even analysis, also called profit or Nutzschwellenanalysen can be viewed as implementing supportive decision-making tool. The pertinent management process can be divided into the phases of planning and control process.

In the first planning objectives are defined and clarified. Once problems have been identified and structured in a more central task is to identify alternatives. The alternatives are brought by results of a break-even analysis to rank and select the best alternative. At the design stage of the control closes at. Here the selected alternative will be enforced and executed. The phase of the fuse connects to the monitoring of the implementation of controls in which adaptation measures are executed.

Break-even analysis are formal pictures by mathematical calculations, which represent a high degree of complexity reduction. This makes it easy to demonstrate the decision-maker a problem. For example, in a decision problem on the production of a particular product, the question is answered whether the expected sales volume is below or above the BEP. The break-even analysis uses the existing data into key metrics.

As the example given above shows the complexity reduction is possible only if there is standing in the background on the clarity of purpose. Then the break-even analysis provides information on the thresholds, forming the boundary points of favorability.

In the first case it is a to be performed after the process control, in the second case an in-process control. The latter is a plan progress monitoring. It causes a timely control since early adaptation measures can be initiated. Prerequisite for this is well-founded forecasts, from the planning system, and a powerful control system.

## Interpretation of the break-even analysis

The ratio of the minimum revenue is primarily a danger signal indicative of corporate governance that need to be set in the approach to this point measures. Measures, such as, increased sales efforts, reduction of fixed or even variable costs or if these measures are not sufficient, even the shutdown of production. The determination of the BEP is intended that the operation does not fall into difficulties, as it can soon enough recognize the danger and take action.

## Associated with the amortization period

The payback period can be calculated using the break- even point by the expected sales volume

This additionally answer the question, is reached after which time the break-even point. When you " par " gets out or how long it takes until expects an investment.

## A product - viewing

It should be:

- The cost function
- The revenue function

Where:

- : Unit variable costs
- : Total fixed costs
- : Price per unit of product
- : Produktions-/Absatzmenge of the product

This gives the following value for the break:

It is therefore necessary products are sold to cover all costs. The difference between the sales proceeds ( price) and the average variable cost is also referred to as the contribution margin per unit (). Geometrically, the breakeven point the intersection of the cost function with the sales function.

An example: (revenue - variable costs = contribution margin ). The contribution margin is the portion that remains to cover the fixed costs of it.

### Cost example

Sun Studio fixed costs: € 5,000.00 / month net:

Fixed costs: € 5000.00 / € 3.63 = 1377.41 dignity therefore imply that a tanning salon needed after deducting variable costs, 1,377 tanning sessions per month to cover the fixed ( fixed costs). The variable costs arise only when the supply of the service is created.

## More product viewing

If you look at multiple products, the breakeven point can not be given by the quantity of products sold, as the break-even point can be achieved by several different volumes of the individual product types. So here's the revenue to be obtained is used, which must be generated by the products.

This then results in the following formula for the breakeven point:

In which

: Revenue, which must be achieved to reach the breakeven point

: Number of product types

: Retail price of the product

: Variable cost of product

: Produktions-/Absatzmenge of product

: Contribution margin of product

## Colloquial

Colloquially called the break even

- The monetary reach break a company ( ie not the quantity, but a time )
- The rate at which a securities account in consideration of fixed costs to profitability achieved ( breakeven price or breakeven price )

## Premises

The break-even point analysis is based on certain assumptions:

- Allocation of costs into variable and fixed costs
- Production quantity = sales volume, inventory must be calculated additively
- Constant sale prices during the accounting period
- Constant production program during the accounting period
- Juxtaposition of positive and negative effect