The first film made enough money (especially when not just measured by sales in the US) that New Line Cinema probably doesn't mind putting more money into the second and third films.
I wonder if the same news story will pop-up again between the second and third installments.
If you are referring to New Line Cinema investing more money for the re-shoots, then yeah, because Peter Jackson have shot all THREE films in an 18-month period (1999-2001?).
IOW, New Line Cinema have already invested in the entire LOTR film series.
They've already been doing the reshoots for awhile. During the MTV Movie Awards, they showed a piece on the reshoots in New Zealand.
Reshoots are a part of almost any movie. They did reshoots for the first LOTR movie. They will do reshoots for the third LOTR movie. The reshoots are already figured into the budgets of the movies.