How to justify the budget for self-service BI tools?

Calculating ROI on any BI system intended for internal decision making is always tricky. A self-service solution does give you some options though. You can estimate the total hours saved from easy and reliable access to data via the self-service solution versus the current channels (manual extracts, manipulation in Excel, etc.). Start by assessing how many users the self-service solution would have (these could include analysts, controllers, managers, etc. throughout the organization) and ask them to estimate how much time they currently spend retrieving the same data that the self-service solution would provide. Multiply the estimated monthly hours saved by the average hourly salary cost and you have a quantified estimate. Other benefits of BI systems are less quantifiable. A big one is that you will provide a single source of truth which avoid teams arguing whether a specific KPI value is this or that because they each calculated it slightly differently.

Don't.

Get the stakeholders who use a BI tool to defend the investment.