There have been a number of studies published that portray Windows as less expensive than Linux, so I think you should frame this discussion as what costs in your company will be. Come up with hard costs of what it takes to administer a Windows box vs. a Linux box. Create a spreadsheet with the costs documented in black and white. That's the kind of ammunition you need.
Keep in mind that your CIO is probably going to be concerned with human switching costs (i.e., the costs to get less technically-sophisticated users up to speed on Linux/Open Office/Evolution -- and don't forget e-mail! Do a small study with a willing end user about how much effort it was to switch. Emphasize that OpenOffice supports Office file formats, so the content of the organization can be retained.
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