PJ,
Here's my take on it. The how many per acre is much like stocking ponds...it all depends. How much rainfall, the chemistry of your pastures (you really are growing grass not cows), and what level of risk you are willing to take, among other things.
Let's take your example... 20 cows will reasonably produce 16 to 18 calves per year, more if you have top genetics and manage closely less, if not. A calf raised from spring till fall can reach 500 pounds, again more under good conditions and less if not. 500 pounds at $1.20 per pound times 17 = about $10k.
How much hay do you need? I figure about 4 round bales per head (depending on severity of winter, first frost date, etc.) and for 20 cows that would be minimum of 80 bales. Minimum cost is probably about $2000 maybe more, maybe less. Add to that about 5 tons of meal for another $1000. Then you have the other costs...fencing, equipment, fertilizers, lime, and the cost of the cows themselves and the herd bull depreciated against the revenue. Throw in the tax deductions, including ag. exemptions to offset costs.
Bottom line, yes you can probably make more by running 20 yourself, but what is your time and freedom from the obligation worth? In the end, if you enjoy having cows and working with them, then it's worth it, but if not, it isn't. You are not going to get rich on 20 cows...but then again, the lifestyle may offer much more than just money.
Looking at it longer term, over a period of several years, say 20 or 30 years, and including tax benefits, which can be very significant, you can add up to some substantial money vs just letting the land go idle. The cows can help pay for the land, the improvements (e.g. ponds), and generate some cash flow...all the while the property is appreciating in value.
