PhD funding for only 4 years I'm currently pursuing a master's degree (math) in the US, and I have been accepted to a different PhD program (applied math). I've been offered funding for only four years, though, because I am already pursuing my master's degree. Is this something of a big concern? I'll essentially have to start over at the new program by trying to pass their preliminary examinations, and all other universities seem to provide funding for 5 years, even if students come in with a master's degree because in the US, the PhD process seems to take some time to complete. 

Any ideas and suggestions as to whether this is something of a big concern, and whether students can get funded for an additional year even if they're coming in with a master's degree?

Edit:

Here are some details about the two programs. The program that has offered me 4 year of funding has 2 qualifying exams. I will have to take classes for one of those qualifying exam. In principle, I think I can take the second qualifying exam soon, but I would still need to enroll in one one semester class to cover the last 20-30% of the material. This second exam, however, would require me to take at least some substantial time hitting 3-4 books, and practicing a lot to ensure I can actually solve the exam itself on the day of the exam.The program that has offered 5 years of funding has 3 exams, but I can fulfill the requirement for two of them by taking a sequence of graduate level course. One exam has to be written. The exams at both schools are of comparable difficulty, I suppose, with minor differences, of course.

I have been offered TA support by both schools, but I suppose this takes up a lot of time when it actually comes to getting down to doing research. I also don't know how the research experience, of course, is going to pan out.
I don't think getting 4 years of funding is necessarily a red flag all on its own - the amount of funding you get offered will vary widely both between schools and between fields.  I think there are three things for you to consider:


Non-financial issues.  How good is the school, where is it located, and most importantly, how good of a fit is it for you?
If all else were equal, offering more years of funding is (obviously) better than offering less, since it gives you more time to work.  Even if you don't think you need it now, it's still a benefit in the form of lower pressure, and padding in case something disrupts your work (illness, research setbacks, etc).
Offering you better funding is potentially an indicator of how much the program wants you there.  That is, the program offering you 5 years of funding (with a possibility of 6 even), is signaling their interest in you quite strongly, while the program offering only 4 less so.


The problem is how to compare number 1 to numbers 2 and 3.  What are the merits of the program offering you 4 years of funding?  If there's a strong non-financial argument in their favor, maybe ask the department to put you in touch with some of their current PhDs and recent graduates.  Ask what the program is like, ask if they offer 4 years of funding to everyone, and ask how practical they find that deadline to be.  At least in my field, this was a fairly common occurrence for prospective students.