Economics of scale will define how much attention you get, and rightly so. Here's what I mean.
A good PM knows that each land lord will be a 100% new ball of yarn to untangle. You will have different goals, motives, and expectations to satisfy. Some of your style will mesh perfectly with their policies and procedures...some of it won't. The PM will not know where you fit in that grand scheme until you've been in business for awhile. So....the PM will decide how much is it worthwhile to get into business with you?
Let's say you have 5 units that rent on average for $1000/month each. At 10% per month of rent plus one leasing fee per year at 1/2 month's rent, the PM company will earn $6000 from rent fees and $2,500 from leasing fees for a grand total of $8,500. Take out taxes, overhead, etc, and they will net somewhere around $6,000 - $6,500. Will that be worthwhile to a manager to be on call (or hire someone to be one call) 24/7? Maybe....
Same scneario but with 50 units. Ah, now we're talking $60,000 per year in net profit. Will the PM pay more or less attention to you?
PMs are like the rest of us: they want to maximize profit and minimize hassle. Also, getting a new client "on board" requires time and effort. Will the PM be happy to take you on as a new client as you are downsizing and trying to exit the business, which means their income from you will be shrinking? I don't know. Maybe yes, maybe no.
The best PMs I know look for "whales"...people with 50+ units and growing bigger. The mid-range PMs will do between 20-50 unit customers all day long as they grow toward being the best. The shoddy, half-butt PMs will take anyone because that's all they can get.
Keep this in mind while shopping. They will evaluate you at least as much if not more than you evaluate them.
Good luck!
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P.S. Jeffrey suggested at a Convention a couple years ago hiring someone and training them to be a PM. Have you thought about that? Maybe find a retired police man or other kind of admin person who is bored banging around the house would be excited to make an extra $500-$600 a month an be back involved with people again vs. watching day time TV.... They couldn't be a full-service PM in my state since Missouri requires that a person has a broker's license to manage someone elses' property, but your part-time "helper" could handle 80-90% of the work such as answering phones, unlocking homes for tours, doing inspections, etc. All you'd have to do is do the ads and leases...not too much effort there!
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