Transform characters; like A to B, B to C,

I want to have a short and easy way to replace the character A to B, B to C, Z to A,... in PHP.

I already have tried this:

$pwd = "Abc";
for($char = ord('A'); $char <= ord('Z'); $char++) {
  $newc = $char+1;
  if($newc > 90)
    $newc = 65;
  $pwd = str_replace(chr($char), chr($newc), $pwd);
  $pwd = str_replace(chr($char+32), chr($newc+32), $pwd);
}
echo $pwd;

But when I use it I only get "Aaa"... :(

I can't find anything on the internet. Could you maybe help me?

Thanks in advance, Luuc