Get Value of Custom Field

As the $posts are the posts of post_type abschreibungstabelle, you can get the custom field values by using get_post_custom_values

if( ! $posts ) return;

$out="<select id="afa_select"><option>Anlagegut auswählen</option>";
foreach( $posts as $p )
{
  $custom_field_value = get_post_custom_values( 'nutzungsdauer', $p->ID );
  // Now you can use the value the way you want
    $out .= '<option value="' . get_permalink( $p->ID ) . '">' . esc_html( $p->post_title ) . '</option>';  
 }
$out .= '</select>';
return $out;
}