Newbie with 203k loan questions

[Ashby Tyler Cappelmann]

Hello everyone! I have a few questions about the 203k loan. My wife and I have found a duplex in our market that we want to purchase for our 1st rental property. It's older and needs a lot of work but has been on the market for over a year and is a prime candidate for purchase price well below market value. The listing price itself is technically already well below. My question is how does the 203k loan works in terms of value appreciation? The listing price is currently 185 but I believe we could get it for 160ish. I think a 40-50k dollar renovation would make this one of the most attractive duplexes in the area. The only surrounding comp I could find on the MLS is currently listed for 550k but is comparable because it's in almost brand new condition. I know they base the loan off of the after rehab value but that seems like a lose of an investor? We're going to be house hacking once the deal is done but am I correct in saying that if the after repair value of the property is deemed to be a conservative 300-350 and we only have 200k into it (150k purchase price and 50k rehab), are we taking a loan out on 300-350 or the 200k we have into it? Lastly if we would be forced to lose the equity by taking the loan on the ARV, what's a good alternative option for financing the rehab separately from purchasing the house? We have some cash but not enough to cover the entire rehab. Thanks in advance to anyone who replies.