Not only is this not the "only" way, it not even a very good way in this situation. Metrics are great, don't get me wrong, but they are not very well suited to this task. Problem is, in a small IT shop, while it does show the break/fix and crisis support, it isn't very suited to project and routine maintenance work. There is no easy way to gather metrics in a small company for things like "99.8 uptime of email", "backups and disaster recovery", "keeping automated anti-virus updates working/current", "rebooting that flaky server in the corner every Monday", etc.
If you want to justify your existence, I'd suggest a project program (i.e. MS Project) with a nice Gantt Chart. Start by listing everything that you do routinely every week (e.g. check automated backups - 1 hour, check server logs for errors - 1 hour, weekly IT reporting - 2 hours, etc.) and then list the project you have planned (e.g. install and configure ticketing system - 20 hours, deploy client patches - 4 hours, train staff to use SUM in Excel instead of MS Calc while creating spreadsheets - 160 hours, etc.). Add on to that how much time you spend on client support and begin assigning yourself as a resource percentage to each task (a ticketing system can give you a good idea of how much you and where you spend your time on support).
Personally, I would avoid, at all costs, trying to assign a dollar amount to what I do. Instead, list out how your time is spent and what all you do, then let them decide if they can live without those things. If you really are a asset to the company, it should be obvious.