The idea is to get preferred out of the way so they don’t have to pay the dividend coming out of the restructure AND it increases tangible common equity .
The tangible common equity part is correct, as shown by your link. I didn't see anything in the press release about reduced dividend obligations being a motivator but it certainly didn't hurt.
FnF's equivalent of tangible common equity is CET1 capital. A senior-to-common conversion (or writedown) would increase CET1 capital by $193B for FnF combined, and a junior-to-common conversion would increase CET1 capital by $33B.
It doesn’t really say if they did the conversion at face value, but I’m assuming they must have offered a pretty good ratio to entice investors to make the swap.
It was at a haircut of 5-15%. Considering that those preferred shares traded around 25% of par the day before the offer, they got a really good deal. Three times as good as what they could have gotten by converting in the open market the day before.