Why a separate DAC?

An upgrade is only worthwhile if it actually is an improvement. Problem is that the medium itself is intrinsically flawed. Garbage in gives garbage out as the old saying puts it. 

An external DAC might be an upgrade or it might not. I'd recommend choosing an external DAC with a multibit (sometimes called R2R) chip and substantial power supplies, preferably one free of opamps in the audio chain.

What model of Burr Brown chip does it have? There are tons of really good DACs on the market in the $1000 range. But if your Yamaha's existing BB chip is good, then you may not notice too much a difference.

Wow, a lot of sincere advice given. I would agree with some but find that I think differently from several points in the previous responses. In my opinion,

• There is nothing wrong with digital (at least nothing worse than is wrong with analog). The medium is fine for listening to music.
  
• The brand or type of chip in the device doesn't matter as much as the overall quality of engineering.
  

One thing I do agree with is that you can't know if a given DAC will be an improvement until you try it.  This is an area where auditions count for a lot.

In your price range, the Audiolab MDAC+ has gotten good reviews and (if you are in the USA) is available by mail order with return privileges. I have not heard it myself.

Plain and simple; one box CD players are becoming obsolete as streamers are taking over. I have both a decent digital and analog setup and in my opinion digital has caught up or passed up most analog setups unless you have a lot of money to invest in it and even then is it really worth the effort? I feel that most people that quickly toss out digital is crap don’t know what they are talking about because they haven’t spent the time or money on digital recently or are just grumpy old men. The fact is, stand alone DACs have advanced a lot recently and I’d say it’s because of streaming and not CD sales. If you’re Yamaha has digital out then experiment and listen for yourself but apparently something is going on because DAC sales and streamers are probably the main components that are keeping this hobby alive at the moment.

$1500 to spend? Room treatment if you haven’t already. If you must buy a DAC then visit your local brick and mortar shop to try in your own home or if that’s not an option then buy used so if you don’t like you can resale and not lose much if any. If neither is an option then look for a company or store that will offer a trial return if you don’t like.

Plenty of flavors of the months here so read old post and hopefully something will catch your interest. Denafrips, MHDT, Border Patrol, Schitt and others seem to be popular. Will any of these $1500 DACs be better than your three year old Yamaha? Maybe if you’re system is capable of revealing the difference. I’d recommend try something half your budget used to see if you hear the difference if you don’t have any local shops. No one here knows your system, room or what your reference is so be cautious of recommendations. Best advise is trial and error. 

If you’re looking to get into streaming and your Yamaha does not have digital in then a DAC definitely makes sense. Hot affordable DACs right now are the Denafrips Ares then a little more, the MHDT Orchard.

Good luck.