Agile delivers results earlier than traditional methods, and organizations can manage ROI more effectively by focusing on the most valuable work and doing less [by cutting lower value features and projects]. It seems like funding agile software development should be simple--provide enough money to pay for the team for a given period of time, don't change who is on the team, and prioritize the most valuable work first--but the budgeting practices of most organizations are far more complicated. Capital vs. operational spending, a heavy reliance on contractors rather than full-time employees, and a focus on projects rather than product development make it more difficult to keep teams stable and focused on the highest value work.
Daniel Greening wrote a lengthy article about agile capitalization that I found interesting, although I suspect organizations will likely be unable to get rid of timesheets completely as long as they have contractors on their teams. But in an agile adoption, it may be wise to talk to the organization's CFO or finance department to build support for investing in people and resources that can further enable success. Lisa Crispin has some great tips on how to talk to the CFO about agile.