I'll try to give my stats without any kind of exaggeration.
I champ farm 2 bots, each of them cost between 5 and 10 million to equip, but I probably could have done it for less if I was more patient. I tried out a new skill build last night that runs Act 1 faster and could do it with less eq, so I would be willing to bet that 5 mil would make a perfectly servicable and fast barb build for Act 1. You could probably spend less, but at the cost of speed. Both bots run with 0 extra MF or GF.
That said, my new fast build is averaging 100k per hour, while my slower build is doing 80k. My Giles settings are only picking up inferno level items, so I don't sell anything and am bringing in about 50 essences per hour per bot (conservative estimate). So, at the current rate of about 1500 per essence, my bots are bringing in at least 150k per hour each in just gold, again with 0 MF or GF. I typically bot an account from 16-18 hours a day just because the tin-foil hat part of me says that its more humanish, so I would estimate my gold income at 2.5 million per day, per bot.
Item drops are harder to quantify. In the past 10 days I've moved about $80 in items on the RMAH, and I have about another $150 or $200 in inventory waiting to sell. I've found 3 or 4 items valued in the $10-20 range, quite a few in the sub-$10 range, a Natalya's something that sold for $25, and a shield that I can't even appraise because there's nothing comparable on either auction house (1550 armor, lvl 63, 12% block, 172 vit, 82 dex, 49 res all, +10 crit%, and more), so I'm holding out for more RMAH activity before I list for $100+.
There are better ways to get rid of gold than to sell it for 50 cents per million, even if gold sales on RMAH are crap. Invest it in equipment you can resell on RMAH if need be, but I would personally just hang on to it, move it to a safer account, and use it to gear more bots.
So... take all that as you will. I would value my bots at between $6 and $10 per day each.
As far as initial investment...
I buy my keys at Walmart because I'm lazy, and I had this silly idea of selling the guest passes for a dollar each before Blizzard screwed that up the other day. Oh well. Maybe next time I'll try to find somewhere to buy these 40 or 50 dollar keys.
I have a set of leveling gear that cost 2 or 3 million, and it speeds things up a lot. It is transferrable! No need to reinvest the time and gold on the auction house for every new bot, just make a mule character to hold 30 pieces of useful gear, give the whole mess to a new bot at level 1, and use Giles auto equipper to handle looking at it. If you're spending keyboard time leveling bots then you're doing it wrong.
As I said above, my level 60 equipment investment is less than 10 million, and I think my next bots will be 5 million or less. The gold should be coming from other bots, so no Blizzard fees there.
Anything else? Electricity? 400 watt system running 10 bots, double that for AC consumption. Maybe say 0.1 kilowatt hour per bot, that's about 1 cent per hour.
Overall, I would estimate my investment in a bot at $63 (with tax) + 5 million + 32 hours, and leveling offsets the cost by 1 million at least, so a maximum of about $70 for a level 60 character with equipment, ready to farm act 1. Buy him a demonbuddy license and you're still under $100. Averaging $8 per day, I would recover a new bot and be making profit in 16-17 days.