[rokhayakebe]

What if it takes more than Y?

No problem there. Educate your clients. Tell them if it takes significantly longer than expected you will come back to them. Tell them it is not likely but you want to be straight from the beginning.

[dkopi]

You still end up taking the financial risk on yourself.

It's one thing if the project is delay because of you. Its another thing if the project is delayed because their backend guy hasn't fixed a few bugs and you're stuck creating ugly workarounds in the client code.