@Mar Liu
I at one point, in the 1980's started investing in 2 family and 3 family homes. But I spent months searching for each, finding flukes and got them at 25% below market. Many of them are owned by people who had them for 20 or 30 years or more, with tenants paying way below market. So, the question is, what to do?
My best education to this is I bought a duplex in 1984 for $180K when market values for them are $220K. The vacant property needed some work, and I spent a month or two rehabbing it, and patronized a bodega for snacks a few times a day. It turned out the bodega owner owned the 2 story multi use property as well as the 2-family building next to me.
This was in 1984, and the bodega owner bought the building next to me for $72K in 1972, and rented the 2BR units out for $400/month. In 1984, market rents for 2BR's run $650 to $750/month. Surprisingly, he kept the rent for one unit at $400/month, while the other at $600/month as there were some turnover.
Interestingly, I got into a long discussion of why he never raised the rent. So he started telling me stories where landlords kept rents low, rarely raising it, to one owner raising it every year to market. He said even with $400/month, he still cash-flowed, as he had a small mortgage, around $30K at 5% at 1972 rates, and he avoided the constant turnover of tenants in the neighborhood where owners charged market rent. On the other extreme, another owner charged market rents from the beginning, increased it every year to market, had constant turnovers, constant renovations, constant vacancies, that he had to sell it after several years of headaches.
The greatest thing was his $400/month tenant maintained the backyard, swept the hallways and stairs, and swept the sidewalk every morning. When I heard that, I spoke to his tenant next door to me, and for the use of my driveway, swept the hallway, stairs and sidewalk, take the garbage cans out for sanitation pickup and retrieval. Better yet, he stayed by his living room window watching the streets every morning for littering where the city issue citations.
In cases like yours, it's probably better you inform tenants that rents will be raised and give them time to move. I know of this in a number of cases, the tenants who lived there moved out to a smaller place and downsized. The $400/month next door tenant was still there when I sold the property in 2004, and when his landlord sold the property, he and his wife moved in with his son.
In another case, I rented a 1BR apt for $800 when market rents went for $850 to $900 and it was rented quick. Three years went by, and market rents went up to over $1,100. I advised the tenant I'll increase the rents to $850. She was shocked and threatened to move. I said "fine, I'll keep the rent at $800 for 3 months so you can find an apartment for $800. She came back a month later and frantically beg to stay for $850. I got a good laugh out of it.