my @list = qw(value1 value2);
unless (open (FILE, $filename)){
  die("Error in opening $filename: $!\n");
} # if

else {
  while (<FILE>){
    chomp($_);
    # split up to maximal "two columns" by whitespaces
    my ($str, $val) = split(/\s+/, $_, 2);

    # search @list for $val
    if ( grep { $val eq $_ } @list ){
      print "$val found\n";
    }
  } # while
  close (FILE);
} # else
[download]

If you don't need $str in your code, write something like this:

  ...
  while (<FILE>){
    chomp($_);
    # split up to maximal "two columns" by whitespaces
    my ($val) = ( split(/\s+/, $_, 2) )[1];

    # search @list for $val
    if ( grep { $val eq $_ } @list ){
      print "$val found\n";
    }
  } # while

} # else
[download]

I haven't tested these codes.

Best regards,
perl -le "s==*F=e=>y~\*martinF~stronat~=>s~[^\w]~~g=>chop,print"