In particular, the /root directory is not generally even readable by any user other than root, so adding it to that user's PATH is not enough. Move /root/abin to something like /usr/local/afnibin, for example. Then have users put that directory in their PATHs.
At that point, you might need to be sure that the abin (or /usr/local/afnibin) directories still have world read/execute access, too.
- rick