Before presenting any large project to the management for approval, there needs to be proper supporting proof that such an investment is needed in order for the company to grow. Unfortunately, in most cases, just saying that the system is old and antiquated will garner some nods, but not much action.
Even before the selection of the software and the vendor, you've already identified the major pains in the company, so you can have a meaningful conversation with the Dynamics NAV solution center.
There are a lot of different ways to do business analysis and identify major problems within the organization. Any method is fine as long as you can justify the proper Return on Investment (ROI). There's no one proper way to do an ROI, and the key measures for how you determine an ROI is a science in itself.