This seems like an easy topic but I’m having a hard time grasping this concept.
Degree of financial leverage = [Q(P–V)–F] / [Q(P–V)–F–C]
Operating income is stated as [Q(P–V)–F–C] where C is the fixed financial cost. Is this interest? Net income is stated as [Q(P–V)–F]
Shouldn’t it be the other way around? Net income is income after ALL expenses have been deducted, including C (financial cost)? While operating income is revenue – operating expense, which excludes C?
DFL is % change in net income / % change in operating income for a given change in quantity sold (delta Q)
% change in net income is given as: [delta Q(P-V)] / [Q(P-V) - F - Int]
% change in operating income is: delta [Q(P-V)] / [Q(P-V) - F]
please note that:
% change in net income / % change in operating income, is the same as:
% change in net income x (1 / % change in operating income), we therefore get:
[delta Q(P-V)] / [Q(P -V) - F - Int] x [Q(P - V) - F] / [delta Q(P-V)]
Once you cancel out the first and last term in this chain (wth the deltas), you are left with:
[Q(P-V) - F] / [Q(P-V) - F - Int], which is what you had, except you used C to denote the fixed interest expense.
Q(P–V) denotes contribution margin.
In regards to the second and third line, the formulas read "For every % change in operating/net income, the contribution margin will change by %. So technically, isn’t that % change in contribution margin (due to operating/net income) because that is what is in the numerator?
No matter what you are examining (change in operating income or net income), this change expressed in dollar terms will always equal the incremental revenue less the incremental variable costs incurred.
For a specific change in Q (delta Q), the change is given as: deltaQ x (P-V).
To express this change as a percentage, you divide by either the current level of operating income or net income (there is no delta in the denominator of these fractions).
The 2nd and 3rd lines therefore read: % change in net income and % change in operating income (due to a change in Q of delta). In both cases its the dollar change of deltaQ x (P-V) divided by the current level of income (operating or net).
I don’t understand this point.
% change in net income and % change in operating income (due to a change in Q of delta) is [Q(P-V) - F / Q(P-V)]
change in Q of delta (due to % change in net income and % change in operating income) is [Q(P-V) / Q(P-V) - F]
They are reciprocals of each other. The denominator is the independent variable. The numerator is the dependent. Therefore, it makes a difference which is on top and which is on bottom.
Your formulas are wrong.
Operating profit is most definitely Q(P-V) - F
Net Income is Q(P-V) - F - C , where C is interest expense.
Tell me where you get lost in the following sequence:
A company currently produces and sells Q units of a product:
Operating income = Q(P-V) - F, where P=unit selling price, V=unit variable cost, F=fixed operating costs.
Net income = Q(P-V) - F - Int, where Int=fixed interest costs.
If we change the quantity produced/sold by deltaQ, both operating income and net income will change.
The dollar amount change in operating income (due to the change in Q by delta) is: deltaQ(P-V).
The dollar amount change in net income (due to the change in Q by delta) is also deltaQ(P-V). In both cases, F and Int are constant and as such do not change with the quantity produced/sold.
In order to express the changes in operating and net income (points 5 and 6) as percentages, you need to divide them by the current (starting or pre-change) levels of operating income and net income (from points 1. and 2.). We therefore get:
% change in operating income (following the change in Q of delta): deltaQ(P-V) / [Q(P -V) - F]
% change in net income (following the change in Q of delta): deltaQ(P-V) / [Q(P-V) - F - Int]
To compute DFL, divide the result of point 8 by the result of point 7, which is equivalent to: (result of point 8) x (1/result of point 7) deltaQ(P-V) / [Q(P-V) - F - Int] x [Q(P-V) - F] / deltaQ(P-V), which, after cancelling out deltaQ(P-V), gives:
[Q(P-V) - F] / [Q(P-V) - F - Int] = the standard formula for DFL.
Hi Wojciech,
Point 6 (7-8): I understood your steps in 6 but I don’t understand why that happens.
Why is it deltaQ(P-V) / [Q(P -V) - F] and not the other way around? You’re trying to find the % change in operating income (relative to deltaQ) so operating income, [Q(P -V) - F], should be in the numerator?
deltaQ(P-V) / [Q(P -V) - F] says change in Q is affected by operating income, not operating income affected by change in Q.
I understood your steps perfectly but I guess I’m confused because I always see quantity as the independent variable and price or revenue as the dependent.
Btw, thanks for you time in explaining this to me.
No worries man. I see where the problem is now.
Don’t look at these as cause and effect relationships. That’s not what we are measuring.
We are simply saying, when Q changes, the overall result (operating income or net income) changes by deltaQ(P-V). If we left it at that, we would have the change expressed in dollars.
The additional step is dividing by the current level of operating or net income to get the change expressed as a PERCENTAGE OF THE CURRENT (Pre-change) INCOME LEVEL.
If current operating income [Q(P-V) - F] was, say 6 million USD, and deltaQ(P-V) amounted to 2 million USD, we would say this is a 33% change relative to the current level, i.e. deltaQ(P-V) / [Q(P -V) - F] = 2/6 = 33%