With that being said they are doing more and more deals and cap rates on the purchase side keep going down.

ANALYSIS -Gross Rental Income = $70,200Vacancy (10%) = $7,020CapEx (5%) = $3,510Management (9% of effective gross) = $5,687Taxes = $3,442Insurance = $2,848Repairs (6%) = $4,212Snow = $600Heat = $4,929Electric = $3,343Trash = $652Water/Sewer = $1,500Operating Expenses = $37,743Debt Service = $16,406Net Operating Income = $32,457Cash Flow (after debt service) = $16,051 or $1,338/moPurchase Price = $265,000Cap Rate (of purchase price) = 12.25% Cap Rate (of price + rehab) = 9.55%Total Cash Needed = $66,250 + $75,000 (rehab costs) = $141,250ROI = 11.36%Final analysis - While this property isn't the fantastic homerun deal you hoped, it is still a reasonably good investment assuming your rehab costs (which are just estimates) stay under $75,000 and you can come up with the cash out of pocket to perform all necessary improvements to the property over the next few years. 

they would change the rent cap, or put more restriction on you, after the face that you bought the property.

Mostly 4-5 cap some 6%.

So if you are in a city in demand and get a deal your cap appreciation will grow with the rent roll.

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I'm trying to understand how capex reserves factor into NOI, Cap Rate, Debt Service Ratio, and other metrics.

I was assured by the builder’s sale representative that the association have no leasing cap or rental restriction except it has to be a long term rental.

We do a ton of work to find off-market deals that are cash-flow monsters, and reasonable CAP rates.

So far i have came up with ignoring the list price and finding out what a few other houses near the same neighborhood as a listed house on redfin or similar apps would rent for typically a 3/2 with rents ranging from $1k-$1500 and just googling some common expenses and thinking that taking 30% off the rent to get the NOI and dividing by a 7% cap to get a idea of what i can pay for a property.