Buy this multi-family, double the rent, get equity quick?

[Brook Decker]

Hello! I am a first-time poster but I've been reading BiggerPockets for a long time. I am working to purchase my first rental property and I need some advice to calm down my newbie fears.

The deal is a 3-unit, multi-family property that is walking distance from a very large university. The surrounding properties are filled with both families and students. Each unit is 3 bedrooms, 1 bath. The property was renovated 8 years ago and is in great shape (of course, the structural stuff will be confirmed during the due diligence phase). Very little cosmetic work needs to be done, the kitchens are updated, the floors are done, there is even new wiring, plumbing, roof, and windows. The current owner owns several properties in the area and wants to move on to their next project.

The problem is that the current owner never raised the rent for any of their units because "the tenants are quality and they didn't want to risk it". The tenants in each unit now have been there for the last few years, not the entire 10 years that the seller has owned. But with every new tenant, the owner never increased rent. The current tenants are paying $700 a month but the rental comps in that area are $1400 conservatively (similar properties on the same street are going for $500 a bedroom). That means if I purchase this property, I will need to double the rent. More than likely, I expect all the tenants will leave. I did meet the tenants and they do seem like great people, but this is business after all. 

My initial thought would be that this would be a great deal. Without raising rent, I would enter the deal with positive cash flow (not a lot of positive cash flow, but enough to make me feel comfortable). I will increase the rent of each unit to market value. In 6-12 months, I want to refinance and leverage the newly-created equity so I can purchase another property. I also plan on working with a property management company to help me with this process. I'm still deciding on whether to have the entire property vacated when I purchase it or wait for each lease to end (the last lease will end in Spring 2018). 

Is this deal a home run that can really kick start my investing career? Or am I missing something? Has anyone else been in this situation? 

Any advice is appreciated!