Nearly everyone in the usability field is challenged at one time or another to justify their contribution to a project. UX practitioners hear this statement as a request for some sort of ROI study that presents data showing the unique contribution of usability to, for example, money saved or revenue generated. Since it's pretty hard to separate out the contributions of various players on a project, this usually is very hard to do.
Nevertheless, I was able, one time, to directly quantify UX contribution to cost savings for a call center I did some consulting work for. Callers were unable to correctly enter a policy number in the IVR to obtain automated information on an insurance policy. The problem was that the policy number had four fields, three of which were variable length, and some fields contained letters the A - F. Nearly all callers errored out and wound up in the call center. I and a developer wrote an algorithm that correctly parsed the callers' keypad input, I re-wrote the prompting and usability tested it, and we implemented it. Correct policy number input went from 10% to 90% immediately. Since call centers know their average handle time and the amount they spend per call, it was easy to show how much money was saved by our fix. We knew how much time we spent on the effort. We estimated savings to be $300,000/year due to our one-time fix. We even wrote a paper showing our calculations, and recommended that we be allowed to make similar fixes to the company's 40 other call centers.
This is a well and good, and should have led to an enormous cost savings across the entire company. Unfortunately, there was simply no one to execute this excellent recommendation. The 40 call centers all operated independently, so there was no single person, or even committee, to push for improvements to all call centers. The opportunity was lost because the developer and I simply didn't have enough standing within the company to push for changes.
Bottom line, ROI studies are great, but even if you have them they don't automatically lead to changes. Managers with a mandate to lower costs by some means other than layoffs are the ones who drive change. Sometimes they're harder to find than you might expect.