degree of operating leverage and degree of financial leverage

[cnd]

How do they go from DOL = percentage change in EBIT / percentage change in sales
to
DOL = [Q x (P-V)] / [Q x (P-V) - F] ?
Is there a derivation for this? I fail to see algebraically how the two are linked.
Same for going from
DFL = percentage change in EPS / percentage change in EBIT
to
DFL = EBIT / (EBIT - Interest)
Many thanks.

 

[elcfa]

Remember
percentage change in EBIT / percentage change in sales=
(change in EBIT/ EBIT) / (change in sales/sales)
change in EBIT = change in sales - change in variable cost
=change in sales - change in sales*(variable cost/sales)
=change in sales [1- (variable cost/sales)]
=change in sales/sales [sales- variable cost]
= percentage change in sales*[sales- variable cost]
Divide both with EBIT (which is also = sales- variable cost -fixed cost), you have
percentage change in EBIT =percentage change in sales * [sales- variable cost]/[sales- variable cost -fixed cost]
or
percentage change in EBIT/percentage change in sales = [sales- variable cost]/[sales- variable cost -fixed cost]
Depreciation is assumed to be part of fixed cost.
DFL is similar:
percentage change in EPS / percentage change in EBIT=
(change in earnings/earnings) / (change in EBIT/EBIT)
and
tax/(EBIT-interest) = tax rate
change in earnings = change in EBIT - change in tax (since interest is fixed cost in this context)
=change in EBIT - change in EBIT*[tax/(EBIT-interest)]
=change in EBIT [1- tax/(EBIT-interest)]
=change in EBIT* [(EBIT- tax-interest)/(EBIT-interest)]
=change in EBIT* [(Earnings)/(EBIT-interest)]
Just divide both sides with (earnings* EBIT)
% change in earnings/EBIT =%change in EBIT* [1/(EBIT-interest)]
or
% change in earnings/%change in EBIT= [EBIT /(EBIT-interest)]
QED