Fannie Mae-No Politics (FNMA)

[kthomp19]

Although I disagree with some of your assumptions the post is pretty thorough.

I'm glad you think so, thoroughness was the whole point!

You can plug in whatever numbers you think are reasonable and crank out the answer. I kind of glossed over how you get from the required ownership percentage in #3 to the actual number of shares, so I'll lay it out here.

In the first scenario, I have the new buyers with 40% of the companies, and 1.8B shares exist before the equity raise. To get the number of new shares issued (call it x, and let it be denominated in billions), we have to solve:

x / (x + 1.8) = 0.4

Multiply by (x + 1.8) to get
x = 0.4x + 0.72

Subtract 0.4x to get
0.6x = 0.72

Then divide by 0.6 to get
x = 1.2

Thus the new buyers get 1.2B shares. Double-checking shows that this is correct:
1.2B / (1.2B + 1.8B) = 0.4

The formula can be rearranged to avoid having to do all these steps every time. If x is the number of new shares (in billions), r is the number of shares that exist before the equity raise (1.8 if there is no junior or senior conversion and no warrant exercise), and p is the percentage ownership required, then

x = rp / (1 - p)

This can be used to verify the other share count numbers I got.

What do you do for a living may I ask?

I'm an actuary, math is in my blood.