You got some great answers from the vast experience of guys above , like John de Witt and the Long Shot. These guys are knowledgable, and have it down real well.
Unfortunately --- I think the long and short of it is -- it's never really going to ever really "pay back", unless you are going to be "normally" shooting 15 or 20 boxes of ammo a year. It's not meant in any derogatory way --- it is just "to make it pay back" --- you have to shoot a lot of ammo.
If you wouldn't "normally" shoot more than 5 boxes a year ($100/ yr+), then it would probably take you at least 10 years to get your "original investment" back. If you get into reloading, then to justify your "investment", you feel obligated to shoot several hundred rounds. It's kind of like the more shells that I reload and shoot -- then the faster my investment pays off.
But the "potential" reality is --- if you didn't have the reloading equipment -- you probably wouldn't be shooting more than 100 rounds a year ($100 or so).
There are other reasons to reload besides "cost savings":
1) I bought a just bunch of reloading equipment, but a box of my favorite cartridges -- the .300 Weatherby, and .300 Rem Ultramag -- are $60 to $80 a box. The more expensive the round (yours are $1 each, mine cost $4 each) the more rational the decision to reload becomes.
2) The cartridges you reload will likely be better and more accurate that factory ammo. But it is only an real advantage, if your groupings being 1/2" better, actually has a significant usefulness. For the annual deer hunt, and getting shots at 100 yards -- the 1/2" better group will not really be a great advantage.
3) The "real reason" I bought the reloading equipment --- Liberal Politics !! I live in California where they want to get your address and thumbprints and ID when you buy ammo. The Moron in the WhiteHouse (I will likely now get reported to Whitehouse.gov) will likely somehow try to stop ammo purchases buy putting a BIG 500% tax on ammo, or buying up all of the primers for military use, or somehow try to ban ammo sales. I am not letting him get "control" of my guns. If I have brass, bullets and powder, etc. --- he will never control my guns by controlling the ammo. Maybe my reloading investment never pays back --- it doesn't have to. What mattered to me more importantly --- the slickster in the WhiteHouse will never be able to keep ammo out of my hands now. I control my own future now.
There are more advantages to reloading than "cost savings". If you would normally shoot 1000 rounds per year -- you will likely save money. Especially if you ammo/ cartridge is an expensive one -- .300 RUM, 458 Lott, 416 Magnum, etc. If not ........ maybe it doesn't pay back for years.
Your reloaded ammo will be more accurate than factory ammo. You can pick which specific ammo to "self manufacture", and you would never be "restricted" by government intervention in your 2nd Amendment Constitutional Rights.
Sorry, Guys, for the long-winded response.