Question

Proofs: how to derive Financial break-even quantity with and without taxes

Answer 1

As per the demand of the demand of the question....

Financial break :- it is the level earning before interest and tax at which firm's earning per share is equal zero.

we know that at break even point, cost and revenue are equal. Accordingly EBIT = 0.

Let us consider sales per unit be "$ x". units be "k".

variable cost per unit be "$y". units same i.e "k".

take fixed cost as "c".

A} Sales = (k)(x) $

less :-

B} variable cost = (k)(y) $

C} fixed cost = c $ .

=> A - (B+C) = kx - ky-c .

=> EBIT = kx-ky-c = z ;

=> kx-ky-c = z ;

=> k(x-y) -c = z ;

=> k(x-y) = c +z ;

=> k = (c + z) / (x-y) ;

EBIT = z ;

less :- interest = I ;

EBT = z- I ;

less :- Tax = t% (z-I) ; {with taxes}.

PAT = (1-t%)(z-I) = 0 ; {at financial break even point PAT = 0} { in case no taxes, EBT = EAT = PAT}.

=> Z = I .

HENCE IT IS DERIVED.