Break-Even Analysis:
It refers to a technique of determining the level of operations where total revenues equal total expenses i.e. the point of no profit no less.
Computation of Break-Even Point
$$Sales\;revenue\;at\;B.E.\;P.\;=\;F\;+\;V$$
a) Break-even Point in Units:
$$B.E.P.(UNITS)\;=\frac{\;(Fixed\;\cos t)}{(Selling\;Price\;per\;unit\;-\;Variable\;\cos t\;per\;unit)}$$
$$or,\;B.E.P.(UNITS)\;=\;\frac F{(Contribution\;per\;unit)}$$
BEP in terms of Money
$$S\;=\;F\;+\;V$$
$$or,\;S\;-\;V=F$$
$$or,\;\frac{(S-V)}V\;\;=\;\;\frac F{(S-V)}$$
$$or,\;1\;=\;\frac F{(S-V)}$$
$$or,\;S\;=\;\frac{(F\times S)}{(S-V)}$$
$$Therefore,\;B.E.P.\;=\;\frac{(Fixed\;Cost)}{(Sales\;-\;Variable\;Cost)}\times\;Sales$$
$$or,\;B.E.P.\;=\;\frac FC\times\;S$$
$$With\;\frac PV\;-\;Ratio\;B.E.P.\;=\;\frac F{(P/V\;-\;Ratio)}$$