How to determine rent price - NYC

[Alex Puleio]

Hey guys! I'm new to BiggerPockets and had a couple of questions. My father currently has some buy and hold properties in the New York City area. I have been following him with his real estate work for a while, and have become skeptical on one of his buildings. 

I have been arguing with him to raise the rent on one of his buildings. It is a 3 family. When he bought the building, it was worth 550k. His return on investment (after mortgage), with the rent rates at the time, was around 9%. The property has since doubled in value, and his return on investment is now only around 5%. 

My question is, should a cap rate remain the same when a property's value goes up? Should he still be making a 9% ROI? Thanks in advance! :)