I was imprecise: the second question wasn't strictly necessary, and the first should have asked what portion of the total equity the new investors will demand so as to be unambiguous.
I think new investors will want a $30 share price because there is a stigma on low-priced stocks, and big institutional investors who would be forced to sell below $5 don't want the share price anywhere near that.
But I don't think they would pay anywhere close to $30 without a reverse split because it doesn't give them nearly enough equity to make it worthwhile. See below for the calculations.
The offering price won't depend only on P/E, but also the total equity portion demanded from above. What is your estimate of that? Mine is between 2/3 and 4/5 because of the amount they will be asked for relative to the market cap, that new money generally makes the rules in a restructuring, and that Treasury's warrants prevent them from getting more.
If the commons organically rise to $30 then the existing commons are worth $54B. Treasury's warrants will be worth 4 times as much, or $216B. On a market cap of $250B that leaves less than nothing for new investors, so the offering would fail.
That means new investors won't pay anything close to $30 (without a reverse split).
Even on a pure P/E argument, the first in a series of capital raises would be conducted at the lowest P/E of all of them. That could very well be in the mid single digits.