Interesting question but hard to answer. It depends totally on your choosen route to the finished build. I guess if you use a modified old surfboard and go with the outrunner option (without gearbox) cheap ESC (like the HEP120) and Lipo- batteies you could get away with as little as 1500 EUR. This of course impiles that you already have all the tools needed for manufacturing of the essential parts. A decent 3d printer foremost.
However if you are a little more ambitious the cost could rise considerably. I have spent about 4000 eur on my buld so far. But that involves some iterations, different foils, remotes, ESCs etc.
The most expensive part is the homemade board (money and hours) but also one of the most fun to build
Consider looking at some of the DOM (documents of material) that some of the builders post here. Maybe the original pacficmeister build is the most comprehensive.