The budget is obviously crucial to any digital project and to the agency who wants to win it! Clients tend to approach this in one of two ways.
Either, "here is the requirement tell me what it costs" or "here is the budget and the requirement, do you want the job?"
There is no "right" answer to this one, but on balance the first option tends to cause less problems down the track. The reason for this is on the second option the scenario often arises where the agency comes back and says: "we'd love to work with you, we think it's a really exciting project but you are being too ambitious for the budget you've set. It can't be done for the money."
So, the client either says "fine, we'll find someone who can do it for the budget" or, and this is where it starts to go wrong, they say: "OK, if we leave this element and part of that element to phase two, can you now do it for the money?" The agency says yes and off we go.
The problem is although the client has lowered the apparent requirement; they haven't lowered their ambitions for the project.
Before you know it, the agency ends up having to deliver something pretty close to the original brief, but for the same budget.
The moral of the story therefore, before anything gets sets in stone, line up your ambitions alongside how much money you have and look at the practicalities of the situation. Then write your brief and set your budget parameters.