If you are translating a certain graduate school's 認証評価基準, the passage you have provided would be one of the criteria (基準) for evaluating the infrastructure of the academic institution. A school has to have facilities, libraries, academic advisors, financial aid, funding and resources for all educational activities, administrative functions, etc.

Since a school needs to be financially sound to operate just like any other organization, it is required to prove its financial stability among other things in order to be accredited. 財政的基礎 in this context will be referring to this kind of financial condition. The 基礎 would not need to be translated literally. I would read the term in question as 財源. In other words, 財政的基礎を有している means 財源が確保されている.

財源, 財源確保
http://www.mext.go.jp/a_menu/koutou/kouritsu/detail/1284531....
http://www.shidaikyo.or.jp/apuji/activity/pdf/ugss2013.pdf
http://repo.lib.ryukoku.ac.jp/jspui/bitstream/10519/1210/1/r...

Fundning
http://www.nea.org/home/33074.htm

Financial resources
http://coolcalifornia.org/article/schools-financial-resource...