Could this be a good deal even though it has negative cash flow?

[Kay H.]

Hi guys. I'm in the process of purchasing a property, but I just realized it has negative cash flow when I factor in the maintenance and vacancies. However, I think one of the main reasons it has negative cash flow is because I'm going fha and I am putting a small out of money down, which makes the principal and interest payment higher than it would be if i had put down 20% in a conventional loan. I think the deal could improve over time if I refinance into conventional down the line and put more money down.  What do you think? Here are the numbers: 

purchase price is 270,000 

property is a triplex with all 3 units already rented to long term tenants. the bottom tenant is moving out and that is where I will be living for a year. 

Principal and interest is 1300.00

taxes are 2400 a year

insurance is 1800 a year

rents come out to 2100 per month total for all three units.

down payment is 3.5%

Here are a few bonuses

the property is in a really good neighborhood that is up and coming and this is a neighborhood I personally would want to live in for the next year. 

Also, the units are outdated: old kitchens, carpet, etc. With some rehabbing, I could raise the rent so that the total rent for all three units is about 2500 per month. 

So after i move out and get my unit rented. I think I'm looking at about a negative 169 a year or so. but if I refinance, pay down the mortgage and get rid of the PMI, things could look better.

Is this doable? Is this a bad deal? what are your thoughts on this?