How much negotiating latitude does a dealer factor in to the price of a CPO Audi A8? Car has approx 55K and listed for $39,900.

How much does the CPO increase the value of the car?

First, the ability to negotiate is simply a function of how it's priced to the marketplace and nothing more. They could leave $8,000 in negotiation, or $800, or $0. How does $39,900 compare to all of the others out there? Is it way high? Or is it the cheapest you've found? Make them a reasonable offer based on this data and take it from there. Negotiating on cars is a dying ploy, but since some dealers still do negotiate, you're stuck playing the game.

Certified Pre-Owned (CPO) programs are simply extended warranties packed into the purchase price. Would you otherwise buy a warranty? If so, then CPO can be a good value. Audi dealers pay about $1800 to buy the CPO warranty. So a CPO car is "worth" $1800 more than a non-CPO car if you see the value in it. If you don't see the value, some Audi dealers have the option of cancelling the CPO status and selling it cheaper.

A few years ago I bought about a 3-4 year old VW from a BMW dealer 3,000 miles away. Beforre buying I went to my local VW dealer and asked him to pull the maintainence records. They were clean, so I bought the car. It reeked of smoke, and the radio didn't work, but it was a good car.

When I was looking I found 2 that I liked. I rented a car and drove down to North Carolina and looked at the vehicles in person. One vehicle had a noticeable main bearing knock. The other (which I bought) had an aftermarket exhaust and the drivers door panel was slightly damaged.
I only went to GM dealers.
I've had no issues with the vehicle since I bought it.
For the amount of money I spent I think it was worth it to spend on a rental and hotel.