Setting up category feed from single.php with category parents

I am trying to concatenate a category feed url string to put in single.php. I finally got it working but am getting some output that I can’t eliminate. Specifically, the post ID is being output on my page above the link. So I have two questions:

1. How do I get this code to stop outputting the post id above the link?

2. Is there a better way to do this? The code for doing the same thing on cateogry.php was a lot more simple (and is posted at the very bottom of this post), so I have a feeling I may be missing an implementation with a built in function or something.

Thanks for any thoughts.

Code I have put in single.php:

<?php
$cat_from_post_id = get_the_category(the_ID()); //get child category from post id
$slug = $cat_from_post_id[0]->slug; //get slug from array
$cat_parent = $cat_from_post_id[0]->parent; //get parent category id from array
$parent_cat_name = get_cat_name($cat_parent); //get parent category name from id
$base_url = get_bloginfo( url ); //get base url
?>

<a href='<?php echo $base_url . '/category/' . $parent_cat_name . '/' . '/feed';?>'>Subscribe to the category feed.</a>

For reference, this is how I implemented the category feeds from category.php and first tried, to no avail, to implement it on single.php.

<?php
$this_category = get_category($cat);
echo '<a href="'.get_category_feed_link($this_category->cat_ID, '').'">Subscribe</a>';
?>