Johanna writes about how you should fund project in an incremental manner especially when it comes to the most risky ones:

incrementally, in some sort of a timebox. (Gotcha!) But here’s why it make sense to do that:

• If you show value to someone, preferably your customer, you are much more likely to get more funding.
• If you’re not showing value early and often, you get feedback early enough to change before you start a death march for something your customers don’t want.
• You can start highly risky projects, because you’re not committing a ton of money and time to that much risk. You’re just committing 2, 3, or 4 weeks.

I have to say I agree 100%. One nice anecdote in this regard, happened to me a few years ago. I was working for a rather bureaucratic, waterfallish organization. I wanted to outsource part of a project I was running and I found an agile sub-contractor for the job. I somehow managed to convince both my management and the methods and practices group that this project should be using SCRUM (the only "cost" for me was that I had to write a Software Development Plan , proving that SCRUM can be ISO 90003 compliant, but that's another story).
We set up a rough plan (release plan) with timeboxed releases every three months (every 3 iterations) and we were all set. Almost, that is - when I approached the procurement group they told me to hold my horses. They were not willing to go through the procurment process every three month. They also weren't very keen on the cost plus nature of the plan (the deliverables weren't prefixed as we were going to evolve the solution). To went over this hurdle I had to prepare a pseudo plan were they had "real" mile stones (basically based on the release planning mentioned above). We ended up budgeting the whole thing in advance, however I did convince them to establish sort of a blanket purchase order, so that we were able to release funds incrementally as we progressed.