DOL

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Kirbskirby

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Hi Guys,
Hope you can help me with this. There seems to be a gap in my knowledge when it comes to DOF.
1) DOL = %change in EBIT / %change in sales.
However, i cannot reconcile it with the other formula.
2) DOL= Q(P-VC) / Q(P-VC)-FC. [For a fixed Q]
According to 2), DOL is a ratio of the earnings before the deduction of fixed cost / Earnings after the deduction of fixed cost.
Earnings after deduction of fixed cost = EBIT
My question is if my understanding of 2) is correct, how does the two formulas equate. Other than EBIT, i do not see anything that will link the two formulas.
I hope someone can help me.
Thanks in advance!
 
I wrote an article on DOL that includes the derivation: http://www.financialexamhelp123.com/degree-of-operating-leverage-dol/
(Note: as of 4/25/16 there is a charge to read the articles on my website.)
In a nutshell:
DOL = %ΔEBIT / %ΔSales
= (ΔEBIT/EBIT) / (ΔSales/Sales)
= (ΔQ(P − VC) / [Q(P − VC) − TFC]) / [(ΔQ × P) / (Q × P)]
= (ΔQ(P − VC) / [Q(P − VC) − TFC]) × [(Q × P) / (ΔQ × P)]
= Q(P − VC) / [Q(P − VC) − TFC]
= [(Q × P) − (Q × VC)] / [(Q × P) − (Q × VC) − TFC]
= (Sales − TVC) / (Sales − TVC − TFC)
 
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