I'm doing a little exercise to determine the CoC and cap rate on my most recent purchase.

How do I suggest this with no money down, to not lose my deposit if the option is not exercised?

Not only is this an exercise that will have more effect on your life than any real estate investing, but it will train you to be a better investor, as you will learn to take the same approach with your properties (minimize costs, maximize value). 

But running an intellectual exercise on the numbers, I think you should be able to figure it out.Essentially, you need to make sure your entire expenses/cashflow is covered in 3-4 months. 

Evaluate better, question everything that I legally can, and exercise lease eviction options as soon as necessary.

The exercise we are going through right now is figuring if there's a real pain point for property owners and managers.

This can get complicated because many lenders will exercise the Due on Sale Clause, so to get this type of loan and still get the protection of an LLC, you will need to implement a Land Trust (check out this article for more.)2.

The other methods such as asking the tenant for a rent increase or asking them leave to let you carry out renovation in the apartment may work but it will be a laborious task especially if they want to exercise their right and if it fails i mean if the tenant didn't agree or consent to your rent increase offer or renovation plan, it will ruin your chances of exercising your right as the owner of the property to use owner occupancy. 

Do a morning routine that involves exercising.

Taking a macro-view of real estate is a dangerous exercise for investors - you have to drill down market by market to have things make sense, and to find the real treasures out there today.