# DOL

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.

1. 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.

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)

That was very helpful. Thank you very much!

You’re welcome.