Build addition to rent out or buy new (Ladue)

[Mike Han]

So my house is on the east side of Ladue (good schools, nice neighborhood, etc.) with a per sq ft value of $240. I have enough room in the back to build a three-story addition. The addition will be 1,700 sq ft with three bedrooms, 3.5 baths, and a two-car garage. The building cost will be $175 per sq ft, for a total of ~$300k. The addition will essentially be built as a townhouse, sharing a solid brick wall with the existing house (i.e., good privacy). Stylistically the addition will be built in a way that incorporates well with the existing house. After the build, I will still have a decent back yard (0.2 acre-ish). I hope to price the rent for the addition to >$2,500, for a family wanting to get into the Ladue schools or college students wanting to share a large apt with individual baths (I am within 15min driving distance from WashU).

The alternative is to spend the $300k on another house somewhere in STL and rent it out. My sense is that while the rental market is healthy in STL, the real estate price has increased in recent years, so I may not be getting a great deal valuation-wise. I am not too interested in buying multiple cheaper units, as I do not want to deal with too many tenants. I have another rental in NYC that was my former residence. I am renting that one out for $3,500 a month to one family and like the experience so far.

I am capable of managing the rental and doing small time repairs -- I can paint, refinish floors/walls, and fix electrical issues (being an electrical engineer myself). I like the addition idea because it will be a new build (fewer issues) that I can customize. I can probably get at least $200 per sq ft on the addition part if I decide to sell -- my house is among the smaller ones in a neighborhood of $1m plus, 4,000 sq ft houses. My thinking is that as I already paid for the land, why not monetize it to the max. 

What do you think? Does STL have a healthy $2,500-plus rental market? Any gating issues with building and renting out your own addition (my subdivision allows it)? I have never rented here, so am really not sure. 

I likely will get a construction-to-perm loan to finance the build.