Let's say there is a project which does not have an exact set of requirements. And then the clients ask for an "tentative" quote.
There is no way to decide that, for example, an iPad app for a hotel can be made in a range of $500 - $5000, since it depends on the quality of design, look, UX, features, etc.
So if the client asks us for the budget, what is to be done?
Well you already answered to the first part of your question by yourself. There is no real way to tell the budget.
Besides that, in my experience I always tell the client without any requirements which should be at least a small scope statement.
In addition you could provide your customer with examples or "price ranges" from your existing portfolio.
However without any requirements it is impossible to set up a correct budget.
If a customer really want one, I prefer giving him examples by (making up) sample requirements or portfolio items and their approx. costs.
I just went through this with a client. I had to think about what was said in the discovery meeting and then also think about how the client conducts business and where their revenue comes from. I went through a few bullet point lists that gave me some priorities for the business and a few options for how a customer might go through a process of paying for the services being offered.
Instead of mocking up working prototypes, I spent a little bit of time in Illustrator making a few static options and pairing the static options with a bullet point of what each example will do. Each example was another increase in complexity, and I tried to make each jump significant enough that it wouldn't allow them to merge the options or allow feature creep.
As far as a specific dollar amount quote, double whatever you think the quote will be. If you come in under the budget, your client will feel like they got a good deal when your final invoice is less that originally estimated. And if the vaugue-ness continues through-out the project, you won't feel gipped. I would recommend setting the project with very specific milestones that the client has to sign-off on before you proceed to the next milestone. It'll, again, prevent the client from backtracking on you within the project. Your milestones can be something like achieving each bullet point that you made earlier.
Good luck!
As with any project, you separate it to simple units (tasks, features). Then you estimate time in work hours needed for any of the small unit. Then you sum all and get a total of work hours needed to finish the project. You can add certain percentage (10%, 50%, 100%, etc.) to QA and bug fixing and research. In the end you multiply the TOTAL with your hourly rate and you will get how much you should charge the project so that your every work hours is paid.
However, deciding on your final price is up to you. You can decrease or increase it as long as you feel you are not losing anything in the project and as long as your are competitive.
