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# Break-even

[breyk-ee-vuhn]

In economics, specifically cost accounting, the break-even point (BEP) is the point at which cost or expenses and revenue are equal: there is no net loss or gain, and one has "broken even". Therefore has not made a profit or a loss.

## Computation

In the linear Cost-Volume-Profit Analysis model, the break-even point (in terms of Unit Sales (X)) can be directly computed in terms of Total Revenue (TR) and Total Costs (TC) as:
begin\left\{align\right\}
text{TR} &= text{TC} text{P}times text{X} &= text{TFC} + text{V} times text{X} text{P}times text{X} - text{V} times text{X} &= text{TFC} left(text{P} - text{V}right)times text{X} &= text{TFC} text{X} &= frac{text{TFC}}{text{P} - text{V}} end{align} where:

• TFC is Total Fixed Costs,
• P is Unit Sale Price, and
• V is Unit Variable Cost.

The quantity $left\left(text\left\{P\right\} - text\left\{V\right\}right\right)$ is of interest in its own right, and is called the Unit Contribution Margin (C): it is the marginal profit per unit, or alternatively the portion of each sale that contributes to Fixed Costs. Thus the break-even point can be more simply computed as the point where Total Contribution = Total Fixed Cost:

begin\left\{align\right\}
text{Total Contribution} &= text{Total Fixed Costs} text{Unit Contribution}times text{Number of Units} &= text{Total Fixed Costs} text{Number of Units} &= frac{text{Total Fixed Costs}}{text{Unit Contribution}} end{align}

In currency units (sales proceeds) to reach break-even, one can use the above calculation and multiply by Price, or equivalently use the Contribution Margin Ratio (Unit Contribution Margin over Price) to compute it as: $text\left\{Break-even Point \left(in Sales\right)\right\} = frac\left\{text\left\{Fixed Costs\right\}\right\}\left\{text\left\{C\right\}/text\left\{P\right\}\right\}.$

R=C Where R is revenue generated C is cost incurred i.e. Fixed costs + Variable Costs or Q X P(Price per unit)=FC + Q X VC(Price per unit) Q X P - Q X VC=FC Q (P-VC)=FC or Q=FC/P-VC=Break Even Point

## Application

The break-even point is one of the simplest yet least used analytical tools in management. It helps to provide a dynamic view of the relationships between sales, costs and profits. A better understanding of break-even—for example, expressing break-even sales as a percentage of actual sales—can give managers a chance to understand when to expect to break even (by linking the percent to when in the week/month this percent of sales might occur).

The break-even point is a special case of Target Income Sales, where Target Income is 0 (breaking even).

There is a myth that Black Friday is the annual break-even point in American retail sales, but in fact retailers generally break-even (and indeed profit) nearly every quarter. lololo

## Other uses of the term

The break even point is also the point on a chart indicating the time when something has broken even, and is a general term for not having gained or lost something in a process.

In nuclear fusion research, the term breakeven refers to a fusion energy gain factor equal to unity, this is also known as the Lawson criterion.

The notion can also be found in more general phenomena, such as percolation, and is rather similar to the critical threshold. In energy, the breakeven point is the point where usable energy gotten from a process exceeds the input energy.

In computer science, the term refers to a point in the life cycle of a programming language where the language can be used to code its own compiler or interpreter. This is also called self-hosting. This usually marks a transition from a "toy" language to a language usable in the real world.

In medicine, it is a postulated state when the advances of medicine permit every year an increase of one year or more of the life expectancy of the living, therefore leading to medical immortality(barring accidental death).