One flaw here is that you assume that the juniors would convert at a price that is calculated with no conversion. However, the conversion happens at the beginning, even before warrant exercise.
Right now, the FNMAS:FNMA ratio is around 5.5:1. Let's say half of the juniors convert at 6:1 (needs to be higher than the market ratio to get them to agree). Remember that this actually helps the companies recap because issuing new juniors (at a lower, market-based interest rate) adds directly to capital.
Fannie has $19B of juniors, so half convert. $19B / 2 / 25 * 6 = 2.28B shares. That's roughly twice the number of current outstanding common shares, so that alone cuts 2/3 off of your price.
Going through your same math, but with $9.5B in prefs instead of $19B and with 17.19B shares pre-equity raise (1.158B + 2.28B, then multiply by 5 after warrant exercise), gives a final price of $6.22. Quite a difference!
The other flaw, however, is more glaring. You calculate $16.89 as the secondary offering price, but what incentive would the new buyers have to pay anywhere near that much? In fact, they would push for the lowest price possible so that they own a bigger share of the companies. They certainly wouldn't pay more than $16.89, so that represents a ceiling. As in, that's the most optimistic it's possible to be.
I also think your $200B market cap for Fannie alone is rather high: the updated Moelis plan has a market cap of $235-267B, but that's for both companies combined. It's also possible the administration moves faster, meaning that even less than two years' of retained earnings go towards the recap. Another factor that could push the valuation lower is fear of reduced earnings due to Calabria and Mnuchin wanting a reduced company footprint. That would manifest itself in a lower P/E multiple.
All that together means that I find it very easy for your numbers to be lower, and nearly impossible for them to be higher.
