I have noticed that if you can phrase the discussion in terms of time, like you have done, or money, it starts to resonate with managers more.

If you currently have a staff of 3 QA people doing all the testing for your app, and a good portion of what they are testing could have been caught with better unit tests and other automated testing strategies, the ‘cost’ of writing unit tests should be more than offset by the ‘savings’ from a more efficient QA team.

If you can get catch those problems as close to the development process as possible, where its cheaper to fix them, you can reduce the QA resources you need for that project. If writing better unit tests mean you can go from 3 QA people to 1, how much is that worth? Its not just the rate of that person, its also all the other indirect savings of keeping your team smaller and more nimble. Imagine 2 less people going to all those meetings, reviewing requirements, emails, standups, bug priority meetings, etc.

How much more productive could you be, and how much better could your product could be, if you could take those very valuable and knowledgeable QA resources, and put them on to more important problems?