There are 4 common ways that investments decisions are made.
1/ Common sense e.g. this is how we justify the use of: Office, Email, Accounting systems etc. no one in their right mind would not use them. And this is in fact probably the soundest way to justify them i.e. connecting to specific ROI, or short term business outcomes is problematic and not that sensible i.e. perhaps the benefits are pervasive and manifold.
2/ Associate the business value to some current initiatives e.g. we want to save $X in IT cost/risk and to that we need to do by: doing some things (run some programmes); having some people (staff, consultants etc.) and using some suitable tooling.
3/ Try and create specific metrics that allow an ROI to calculated. The real challenge is usually that the quality of the current state analysis is so poor, that accurately slicing and dicing the costs is challenging (hence the reason for a better approach). And IT is good at burying the dead and excusing under delivery i.e. within 20% of budget, within 50% of time, and achieving 50% of original scope is regarded as a success.
4/ We have people who do this job - they need solutions that enable them to do it e.g. we write documents - we need a Word processor (not a type writer), we send messages - we need email (not a faster mail trolley), we do strategic IT planning - we need a strategic IT planning solutuin (not more Visio, Excel, Word and Powerpoint documents). See: Providing professional tools of trade.