Colin,
Since you are already within PHP brackets, just ditch the extraneous PHP open and close with the echo command that you don't need.
Instead, make your code read:
<?php
$date = "$row_renew_list['date']";
$newdate = strtotime ( '+1 year' , strtotime ( $date ) ) ;
$newdate = date ( 'Y-m-d' , $newdate );
echo $newdate;
?>
Cheers,
Brian