Deciding whether a new software subscription saves enough admin time to justify it

A subscription promises to automate invoice reminders, reconcile payments and generate reports. It costs enough each month that I want evidence it saves real admin time. Right now a staff member spends a couple of hours weekly doing these tasks manually. I'm thinking of a trial with a stopwatch and a check for errors, not just a demo of the nicest features. How do you evaluate software savings when setup and ongoing maintenance also take time?