I am going to answer from my personal experience.
It is nearly impossible to turn a horse around for a profit in a 3 month to 1 year window with the board meter running. You would have to find a true diamond in the rough to turn it around in 120 days and make a profit while covering your board and farrier expense.
The big increase in value in a horse is not where most people think it is. Any reasonably competent person can back a young horse and get it to w/t/c both directions. You've added $500 - $1000 to the value of an unbroken horse by doing this, but the catch is, there's no market for that green broke horse.
The real value add is taking that green broke horse and finishing it in a certain discipline. The number of competent people who can do that is much smaller, and it takes some cash outlay to get the horse that experience. That takes a very specific skill set in that discipline, and the ability to put the necessary miles on the horse without paying premium price to get those miles.
Here's the circumstances under which I turned around green horses for a profit:
I was managing a busy lesson/training barn and always had at least one greenie coming along. I could always - 1.) throw the greenie in a lesson or schooling session at will 2.) haul it to a show or schooling session when there was an empty spot in the trailer and make the decision to leave it tied to the trailer, lead it around the show grounds, lunge it, hack it around, or enter it in a schooling class based on how it handled the experience 3.) put a select variety of decent riders on it to see how the greenie reacted under different riders and 4.) could compete it inexpensively.
Here's how I lost money or just broke even:
When I had a nice young horse it a tiny leased facility that was never exposed to anything and I had to pay to haul it off the place to get it any exposure. Took an outrageous amount of time to finish the horse and cost me dearly.
Oh, and that previous personal experience I mentioned? That was when the market was good. I wouldn't attempt it now without the first scenario (busy barn), and no board meter running, and maybe not even then.
There are too many nice finished horses out there with sale prices at way less than what it cost their owners to get them there.