I'm not a network admin, but I used to do financial analysis for IT projects like this at our company. You will likely need help from someone in your Finance department to do this with any credibility.
Most of these projects do not MAKE money, they SAVE money, as you said. So you need to look at which costs could be impacted... labor, contractor costs, licensing, etc. and come up with some relevant metrics which can be translated into periodic cost savings. Of course, you also need to take into account the costs to implement (capital) and maintain (expense) the new solution, which offsets the savings.
Continuing the word processing example, you might find out how much time is spent doing word processing in a given period. Then derive some percentage time savings of using Word vs Notepad. By applying that %age to the total cost of word processing, you could show that as the benefit.
I've found that, especially in a large company, the cost savings is often not the ultimate determinant of whether a project is accepted, but rather for some political motive - i.e. makes the customer (internal or external) happier or maintains some relationship with a vendor. This may not apply as much to a "techie" back-office upgrade, however. Most of the time, the assumptions are complete BS and the project managers just come up with something that the execs want to hear to make them feel justified in approving the project.
Nice that you can get out for a round with the CEO - lucky dog.
