I would probably make an estimation as # of hours spent for doc control without software currently and convert it into $ cost. Then, compare it to # of hours that you would have spent for doc control with software. Plus, you can list them other advantages that cannot be measure with $, i.e.: improve customer satisfaction.
Being a devil's advocate here...since you mentioned that you are in a start-up company, I would probably lean to agree with some of your executives in terms of not purchasing a doc control software in this early stage. Plus, you can probably do it yourself with just a simple excel spreadsheet that has hyperlink to the latest documents. I'm guessing you probably have a server already that you can use to centrally store all your documents. That's all you need to start with. Just a thought...