Fixed price for the project

I was talking with a client some years ago and he wanted to create a web application. He had a specific budget and he needed to know exactly from the beginning the cost. Is it possible?

I am going to write down here, the criteria that I needed to have for a fixed price project.
  • The application is small and straightforward
  • The contract has clear objectives (sorry no agile here)
  • You have already done something very similar and the client is willing to cut corners if there is a need
  • It needs the exact designs, wireframes, information flows and use case scenarios
  • The client knows what he is talking about. He has some experience with the software process. He knows how to explain or drive the whole process

Even after the above criteria, there can be a misunderstanding.
If you are a software developer you may have the above already and you may be able to recommend a price range. But what happens when you are a research UX designer? How do you create the interview process and the wireframes in the beginning?

Still I understand the side of the client who cannot spend a fortune without knowing. That's the main advantage of agile, but you still need to give an estimation, try to give a range per epic task. But in the end you may need to play the guestimation game. You may have to raise your price to be sure about your effort gets the right price.

Nowadays I don't get this kind of jobs, but in the beginning you may have to face them. What do you do with inexperienced clients with a strict budget? How do you handle if they insist for a fixed price and they don't have clear requirements?