What is "value-based analysis" in an Agile project? When is it done?

There really is only one. Most benefits can be debated depending on the nature of what you are building, the scale of its complexity and the groups of people building it; e.g., imagine building a new OS to compete with windows. Staff level of experience also plays into this as well.

But all of this aside, the effectiveness of Agile is a sliding scale between hardware and the UX. The closer you get to the UX the more powerful its impact. That’s because the one thing that that gives Agile it’s edge is closer integration of the customer with the developer. Since the UX is all about satisfying the customer it is clear why Agile is most effective there.

Rapid prototyping was its pre-cursor which was also effective for this reason. Agile improves on this by adding short predictable periodic cycles that ensure customer feedback is incorporated in a frequent and reliable way. And as any QC analyst will tell you, its all about feedback and response.

Any company should go through it to be successful I gues. But it can be time consuming. especially if you are a newbie. I used to spend a couple of months before I found a really good resource for some useful information. You see, after some research and study I can recommend to read about Discovery stage in more details just to be on the safe side. Good luck