There are several factors that go into what number makes sense to buyout a stabilized tenant. Mostly, what is the current stabilized rent and what is the market rent you could obtain for that apartment. Also, how much money do you need to put into the apartment to get it above the $2,000 threshold? What are your motives - are you interested in increasing your cash flow, increasing the value of your proerpty or a combination of the two?

If you have a unit that is currently rented at $750/month and the market rate for that apartment is $3,000, I would consider paying upto $40,000 to buyout the tenant. Once the tenant leaves you can automatically increase the rent by 20% (on a two-year lease). That means the new rent will be $900/month. To get the rent up to $2,000, you will need to increase the rent by $1,100 and therefore will need to put $44,000 into the unit ($44,000 x 1/40 = $1,100). So now you are out $84,000. but you increase your rent by $2,250/month or $27,000 for the year. That is a 32% cash on cash return, which is very good. Not to mention, you increased the value of your property by at least $450,000 ($27,000/6% = $450,000), assuming a 6% cap rate, which is about what properties in Manhattan are going for now that have a mix of market rate and rent stabilized units.

The above example is what I try to achieve, of course you can use this example to figure out what works for you.