Buy new CDP or just add a newer DAC?


I have a slightly used Pioneer 79Avi DVD player which I am now using for music. I am considering upgrading to a newer player, but was wondering whether I'd be better off just adding a new DAC rather than buying a new CDP.

The transport on the unit seems pretty sturdy and I've never had any problems which makes me think a DAC may be the way to go.

Any suggestions?

Thanks.
sndsrtaud
You've received good arguments for going with a DAC and I would add a couple more.

The area of audio where a lot of the innovative development is happening now seems to be in DACs, quality is going up and prices are dropping relative to the quality. A separate DAC makes for an easier decision if you want to upgrade.

Conversely, the part of a CD or DVD player that's ultimately going to fail is the transport and it's often not possible to get a replacement mechanism. Having it uncoupled from the DAC means not having to give up a perfectly good DAC when you need a new transport.
In past years I never ever would have considered a dac. It was suggested to me in various cdp recommendation threads I started. I did not want an additional box, power cord, interconnects, and the complete randomness of finding system synergy and the randomness of gaining improved sonic performance. Now, I've bought and tried several different dacs. I have to say that compared to a quality cdp, a transport + dac may or may not make a significant SQ difference. It depends on how the dac and transport fits in your system, just like every other component. But a computer + dac combination has really opened up my musical library streaming from the internet and it sounds very good. A dac affords more options and flexibility. I had to be convinced, over time but a dac is better than a new cdp, unless money is no object.
Starting with the right DAC will give biggest bang per buck both short and long term.
Thanks for the input. Now which DACs should I consider? My budget is limited to <$1K since my wife and I are in the process of adopting 2 girls which is going to cost us ~40 large.