That would be reasonable. If they negotiate it down to 50,000, you're still ok with that, I'd imagine.
If they ask you to host it, charge plenty for that as well.
(The rather high hourly rate takes into account that you're selling them something you already built before.)
Bill any additional work over the first 14 or so at $1000 a day or quote fixed price to add specific features.
For an organization with 30K employees, $100K is a rounding error.
To be honest that depends very much on how the organization is structured and who the actual client is. Many 30K companies are essentially three hundred 100 person companies that each have their own, very limited, budget. If you're dealing with the CEO who wants to roll this out to the entire company, then $100K is doable. If, on the other hand, you're dealing with the manager of a 12 person groups within a department of a division of that company then $100K is probably his annual budget.
Thanks for all the comments, we are amazed at how high the quotes are coming in at (again becuase it is a university these may now change) - we really appreciate all the help.