You are a hard-working analyst in the office of financial operations
for a manufacturing firm that produces a single product. You have developed the following cost
structure information for this company. All of it pertains to an output level of 10 million units.
Using this information, find the break-even point in units of output for the firm.

Return on operating assets = 25%
Operating asset turnover = 5 times
Operating assets = $20 million
Degree of operating leverage = 4 times

Here's a very useful formula...

Reading the forum's homework help rules + Showing your work = Receiving assistance

I've seen this problem before. Using the equation I know for degree of operating leverage, it cannot be solved. However, the student I was working with gave a different equation I was not familiar with, and it could be solved with that. I don't know what it was though.

Can you give the equation used for DOL out of your textbook. And then do as ArcSine suggests -- give it a try and show us your work. Set up all your equations, plug in what you know and work to what you don't know.

Hi, Morgaine... just touching on the point you brought up, there's a version of the DOL that can be used to answer OP's question:

DOL = \frac{Q(p-v)}{Q(p-v) - F}

... where Q, p, v, and F are, respectively, Quantity (units); unit price; unit variable cost; and total Fixed costs.

It's just a few algebraic manipulation steps to get there from the familiar "% change in EBIT / % change in units sold" version.

Note that the term (p - v) is the unit contribution margin. Anyway, with that version of DOL, OP's answer can be derived.

Take care,

Well, that wasn't the equation that student gave me but I think I solved it. If OP doesn't come back, I'll eventually tell you what I got.

Not sure why I bothered. Except for time value of money to an extent, never could stand finance. And don't understand leverage stuff. You know how your brain blocks stuff you don't like. :p

Not sure why I bothered.
The irresistible siren song of The Puzzle... I can relate ;)

(Break-even point) you are a hard-working analyst in the office of financial operations
for a manufacturing firm that produces a single product. You have developed the following cost
structure information for this company. All of it pertains to an output level of 10 million units.
Using this information, find the break-even point in units of output for the firm.
Return on operating assets = 25%
Operating asset turnover = 5 times
Operating assets = $20 million
Degree of operating leverage = 4 times