Editing Break-even point (section)

==Construction==
In the linear [[Cost-Volume-Profit Analysis]] model (where marginal costs and marginal revenues are constant, among other assumptions), the '''break-even point (BEP)''' (in terms of Unit Sales (X)) can be directly computed in terms of Total Revenue (TR) and Total Costs (TC) as:
:<math>\begin{align}
\text{TR} &=  \text{TC}\\
P\times X &= \text{TFC} + V \times X\\
P\times X - V \times X &= \text{TFC}\\
\left(P - V\right)\times X &= \text{TFC}\\
X &= \frac{\text{TFC}}{P - V}
\end{align}</math>
where:
* '''TFC''' is '''Total [[Fixed Costs]]''',
* '''P''' is '''Unit Sale Price''', and
* '''V''' is '''Unit Variable Cost'''.

[[File:CVP-FC-Contrib-PL-BEP.svg|thumb|right|240px|The Break-Even Point can alternatively be computed as the point where [[Contribution margin|Contribution]] equals [[Fixed Costs]].]]

The quantity, <math>\left(P - V\right)</math>, is of interest in its own right, and is called the [[Contribution margin|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:
:<math>\begin{align}
\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}</math>

To calculate the break-even point in terms of revenue (a.k.a. currency units, a.k.a. sales proceeds) instead of Unit Sales (X), the above calculation can be multiplied by Price, or, equivalently, the Contribution Margin Ratio (Unit Contribution Margin over Price) can be calculated:
:<math>\text{Break-even(in Sales)}  = \frac{\text{Fixed Costs}}{C/P}.</math>

:R=C,
Where R is revenue generated,
C is cost incurred i.e. 
Fixed costs + Variable Costs
or
:<math>\begin{align}
Q \times P &= \mathrm{TFC} + Q \times VC &\text{(Price per unit)}\\
Q \times P - Q \times \mathrm{VC} &= \mathrm{TFC}\\
Q \times (P - \mathrm{VC}) &= \mathrm{TFC}\\
\end{align}</math>
or,
Break Even Analysis
:Q = TFC/c/s ratio = Break Even

===Margin of safety===
Margin of safety represents the strength of the business. It enables a business to know what is the exact amount it has gained or lost and whether they are over or below the break-even point.<ref>[http://maaw.info/Chapter11.htm#The%20Margin%20of%20Safety ''The Margin of Safety in MAAW,'' Chapter 11].</ref> In break-even analysis, margin of safety is the extent by which actual or projected sales exceed the break-even sales.<ref>[http://accountingexplained.com/managerial/cvp-analysis/margin-of-safety Margin of Safety Definition | Formula | Calculation | Example]</ref>

:Margin of safety = (current output - breakeven output)

:Margin of safety% = (current output - breakeven output)/current output × 100

When dealing with budgets you would instead replace "Current output" with "Budgeted output."
If P/V ratio is given then profit/PV ratio.

===Break-even analysis===
By inserting different prices into the formula, you will obtain a number of break-even points, one for each possible price charged. If the firm changes the selling price for its product, from $2 to $2.30, in the example above, then it would have to sell only 1000/(2.3 - 0.6)= 589 units to break even, rather than 715.

[[File:breakeven small.png|right]]

To make the results clearer, they can be graphed. To do this, draw the total cost curve (TC in the diagram), which shows the total cost associated with each possible level of output, the fixed cost curve (FC) which shows the costs that do not vary with output level, and finally the various total revenue lines (R1, R2, and R3), which show the total amount of revenue received at each output level, given the price you will be charging.

The break-even points (A,B,C) are the points of intersection between the total cost curve (TC) and a total revenue curve (R1, R2, or R3). The break-even quantity at each selling price can be read off the horizontal axis and the break-even price at each selling price can be read off the vertical axis. The total cost, total revenue, and fixed cost curves can each be constructed with simple formula. For example, the total revenue curve is simply the product of selling price times quantity for each output quantity. The data used in these formula come either from accounting records or from various estimation techniques such as [[regression analysis]].