FHA loan/rehab/refi strategy? Does this make sense?

[Joshua Goldberg]

I just had a bid accepted for a 2 unit (zoned for 3) detached home in the Bronx, NY. There is a significant amount of work that needs to be done, including the conversion to 3 units. I'm looking for a good strategy to buy with a relatively low cash outlay, do the renovations and increase equity, and then refinance so that I'm not stuck with paying MIP.

The purchase price is around $850k, and I'm looking to put around $200k into the renovation. If I were able to put 3% instead of 20-25% down on the $850, that would obviously be a big benefit, especially if I planned to refi immediately after the renovation, so as not to pay MIP for an extended period of time. An added benefit to the FHA mortgage is that one bank offered to essentially cover all of closing costs, around 60k.

Is this a solid strategy?  Am I missing anything here?  Thanks in advance for your responses!