How about just (untested, and also case-sensitive):

sub TestEquity {
  return 
    $_[0] =~ m/private.*equity/ ? 0 :
    $_[0] =~ m/equity/          ? 1 :
                                  0
    ;
    }
[download]

This could be slightly simplified if you can tolerate  "" (empty string) as a false flag in addition to or in place of 0.

BTW: "I can't get it to work" is rarely helpful as a problem description. How about some input strings and actual versus expected output?

Update: Changed  $_[0] =~ m/private.*equity/ to  $_[0] =~ m/private/ because it makes more sense.
Update: ... and then changed it back to  $_[0] =~ m/private.*equity/ because it actually makes even more sense that way! (sigh)