Should I build an application inventory on the CMDB before buying APM?

Yes, build a clean application inventory on the CMDB you already have before you buy Application Portfolio Management or Enterprise Architecture modules. Agree what counts as an application, name a business owner and support group for each one, and put create and retire controls in place before you load hundreds of legacy rows. Treat old trackers as candidate lists, confirm or retire each row, and keep only a short mandatory field set you can actually maintain. Map each confirmed application to the business services it supports, then prove the inventory by requiring major changes and major incidents to name those records. Defer APM licensing until leadership questions are answered by trustworthy data. Empty cost fields and unowned records destroy trust faster than a smaller inventory. John Sansbury argues in The Journey to Service Excellence that without good component information other service management processes stay weak, that relationship mapping is what separates a CMDB from an asset register, and that accuracy controls must come before the big load so you are not chasing a moving target.