However you decide to work out things financially,
I'd be careful not to undervalue his effort. You say he contributed nothing to your current product, but I find it unlikely that was the case. Even if you are working on a new product, surely you learned something from the previous one. Also, if it wasn't for his efforts, perhaps you wouldn't have got so far with your previous product, and would still be working on it. A business is a fluid beast, and what you set out to create usually isn't what actually makes you succeed.
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You say he contributed nothing to your current product
Actually, I said
A's contribution to our current efforts is zero
It's an important difference and I chose the word carefully. Our early efforts with him did not succeed, but based on my experience it is almost impossible to succeed without making mistakes first and learning from them. We value his contribution, which is why I am trying to determine a fair way to compensate him for this efforts.
Edit: Let me expand on what I said. It is hard to talk about separation while sounding entirely positive, because separation is not a positive event. I wouldn't even have met my other cofounder if it were not for A. So, rest assured, however this separation is structured, in my mind he will have earned his keep.
I agree with this to an extent. However, I think it's equally important not to over-value his effort.
[Edit: This is coming from someone who's gone through this and later had many people tell me I was far too generous with the buy-out]
If only the world were fair enough that we could all be compensated every time we exert effort. Unfortunately, the world often does not reward us for effort, but rather for outcome.
I'll illustrate my point with a slightly exaggerated example: You could say that if it weren't for my tenth-grade English teacher, I would never have gained the insight to question things widely believed to be true. Then I would have never grown to question my own unhappiness in a white-collar job. Then I never would have never quit and started my own companies. In a very real way, if it weren't for the things I learned from my tenth-grade English teacher, I would have never seen the success I have. Should I track my teacher down and give here X% of every one of my companies?
Of course, in this example, I've almost convinced myself that I should. But my point is that every person in your life contributes in some way. If you go out trying to compensate every person who helped get you to where you are, there will be nothing left for yourself.
Now, this co-founder may deserve to be well-compensated. But don't do it based purely on the idea that they helped contribute in some intangible way to your product's current success. Do it if it was tangible and significant.