Read More on Excerpt

Is there any way of getting a Read More link to show up on an excerpt? I’ve tried the following code in my functions file…

function new_excerpt_more( $more ) {
	return ' <a class="read-more" href="'. get_permalink( get_the_ID() ) . '">Read More</a>';
}
add_filter( 'excerpt_more', 'new_excerpt_more' );

but this only appears when no Excerpt has been added to a post and therefore it’s just taking the first part of the post.

I would like to add an excerpt to each post but then for the Read More link to also show up inline. I also tried this…

function excerpt_read_more_link($output) {
 global $post;
 return $output . '<a href="'. get_permalink($post->ID) . '"> Read More...</a>';
}
add_filter('the_excerpt', 'excerpt_read_more_link');

But that just adds a Read More link to the line after the excerpt and not inline.

Any ideas or help would be much appreciated.