Financial Districts actually take quite a while to pay for themselves, as opposed to just using the manufacturing on the economic stimulus package. While ultimately they do pay for themselves, there are scenarios (especially in the mid to late game) when it may be more lucrative to simply take the project over building up a lot of district infrastructure.
So, you have a new core world that has just blossomed, and its time to get that money! You think, well if I want cash, clearly financial districts are the way to spend my manufacturing for best return. Or is it? Another option is the economic stimulus project, which just turns raw manu into credits. Which is better and when? Lets take a look.
Note: I have an excel that documents these numbers if anyone needs to see it for evidence.
So on our theoretical planet, lets give ourselves a beautiful 7 hex circle to work with (aka we could do a full 7 financial districts together, the ultimate in adjacency!). However, there are no wealth bonus on the tiles, at least not for our first few looks.
This planet is going to be a nice one:
Manu: 5 (a nice 3 base with some asteroids, maybe a colony, plus the colony capital and a few manu buildings, a pretty standard number for an early planet)
Income: 5 (again a nice solid little core world)
Tax Rate: 33% (money!)
Crime: 0! (a true paradise!...and it makes the math a lot easier
Our manufacturing is precious, and we can spend it either on Financial Districts or on the Economic Stimulus Project for credits.
So we could build 4 districts for 160 manu (which is just a bit more than 50 credits worth of the project). But we do have to build those districts up, which takes a while at 5 manu a piece. So how long does it take for my financial districts to pay for themselves.
Time to Breakeven: 79 turns
Income Generated at Breakeven: .891 credits/turn
It actually takes quite a while before the cumulative income of the financial district pushes past the raw income of the project.
Ok now lets build our perfect 7 districts, the ultimate in wealth bonuses for basic districts. This has to beat at least 75 credits worth of project to start to break even. How does it look?
Time to Breakeven: 76 turns (3.8% faster)
Income Generated at Breakeven: 1.881 credits/turn (111% increase from 4 districts)
So we can see how the adjacencies ramp up a bit, as only adding 75% more districts gave me a 111% increase in the income from my districts. But it doesn't change the turn times too much, mainly because of how long it takes to ramp up all the districts, and the extra project income I have to overcome.
7 Districts with Supply Ships
How about 7 districts with supply ships? Often our secondary core worlds are helped out with seeding from another world. Would speading up our construction make a big difference?
Time to Breakeven: 49 turns (35.5% faster)
We broke 50 turns! We can see how much faster the supply ships speed up our income gathering, but its still a good chunk of time.
HOWEVER, we sunk over 240 military production into supply ships....what if we had just done treasure hunts instead? Treasure Hunts are a bit random, but that would easily be over 200 credits! If I add that in, suddenly it takes over 115 turns to break even!
So while supply ships will get you there faster, if your goal is credits, blowing manu on supply ships just to ramp up your income faster isn't really helping much, you could have been better off just going treasure hunts and not even worried about building districts.
So far we have assumed no terrain advantage, but that is rarely the case. There are usually a few tiles at least that give wealth bonuses. So lets again have some fun, lets assume our middle hex has a +3 wealth tile, and all of my other hexes are a +1. Its the ultimate money zone! This also roughly simulates a situation where we have upgraded the level of all of our financial districts.
How much does this effect things?
Time to Breakeven: 66 turns
The Encore - The CENTRAL BANK!
So raw financial districts take a while to cover themselves. How about the ultimate in financials...the central bank itself. This building is a massive multiplier to income, providing a full +1 raw income per level, and a +3 level adjacency boost. If there was ever a sector that should pay for itself quickly, it should be this guy.
The tricky thing here is that the raw income would also be affected by existing multipliers on the planet (including policies and other wealth modifiers). So lets go with a bottom number, assuming no other multipliers (aka this is as bad as it gets for the bank in our scenario).
It does have a 1 durantium cost as well, which we could sell for 30 credits at the bazaar (I often sell it for lower than that, but since we are trying to get a "worst case scenario" for the bank, we will give it a high cost).
Time to Breakeven: 82 turns (only 4 financial districts built)
Breakeven Income: 7.2732
Final Completed Income (Turn 96, all 6 financial districts built): 10.527 (5.60x more income than a standard 7 hex financial)
So still pretty slow, in this case its the high cost of the bank that gets us off to a slow start, but with a lot better income at the end. Ok, so lets bring back the supply ships, and see if accelerating our building this time will give us more income.
Time to Breakeven (Supply ship): 81 turns
Our opportunity cost is still very high with those supply ships, and as such it still takes a very long time for our central bank setup to pay for itself, assuming our low end scenario.
As one last check, what would happen if we only used supply ships for the bank, and then let the rest of the districts build themselves?
Time to Breakeven (Supply ships for Central Bank only): 73 turns
Conclusion: Over the course of a game, your financial districts will eventually pay for themselves, but it can be a lot longer than many people realize (I didn't even factor in crime, and many planets can't make a perfect 7 hex setup). Especially in the mid game, when you colonize or take over a new planet, if your goal is credits, you may be better served with just taking the raw project payout, rather than trying to invest in more infrastructure.