In what way will they pay off?
You will eventually save CIC on imports that equals the cost of the synthetic plants you build.
You figure the cost of the synthetic plants, then compare it to the rubber they give you (not total rubber, but the rubber you get at the current trade law), and compute that against the CIC required to import the rubber over time.
Let me give an example:
Let's take the Soviet Union with 1939 IC techs and synthetic rubber techs.
Okay, so at those techs, in Moscow (a state with 80% infrastructure), 15 CIC generate 189 construction speed, which will take 76.71 days to complete (which, in HOI4, is 77 days) given a construction cost of 14500.
That's 15 CIC per day, though, so we need to break that down to 1 CIC per day for comparison purposes, since 1 CIC will generate 8 rubber per day for imports. So, 1 CIC per day will generate 12.6 construction speed (189 construction speed / 15 CIC). At that speed, it will take 1,151 days to complete (14,500 cost / 12.6 construction speed instead of 189 construction speed).
Okay, so it takes 1 CIC 1151 days to finish the synthetic plant. That 1 CIC could just buy 8 rubber for 1151 days.
But....
... At 1939 techs, you only get 3 rubber. So, even when that 1 CIC finishes the synthetic plant, it's not as efficient as buying 8 rubber.
But...
... Unless your economy is closed, you are also exporting that rubber.
So, in our example, the Soviet Union is sitting on Export focus, so that 3 rubber really equals 1.5 rubber per day. So, we need to multiply that time to build the synthetic plant by 5.3 (due to the difference between 8 rubber for 1 CIC and 1.5 rubber for 1 CIC) to give us the time it would take the synthetic rubber plant to pay for itself.
That's 6,138 days.
So, yes, it will eventually pay for itself. Just not by 1945.
This is also modified again if someone buys your exported rubber. If 100% of your exported rubber is purchased, you don't have to worry about the rubber you "lose" from exports. In that case, we redo the math with 3 rubber (since all rubber is being used or bought). That's a 2.66 increase in the 1151 days due to dividing the 8 rubber you get from purchases by the 3 rubber the plant produces and sells. That gives us 3069 days until it pays itself off. So, that's around 8.4 years.
That's still beyond 1945.
But...
... If you get a boost to rubber output via NF and reduce your exports, it changes the math.
If the Soviets got the same NF that Germany does, and if they stepped down to Limited Exports, they are now producing 5 rubber per day per plant at 1939 techs.
If you use or sell 100% of the rubber in this scenario, you are looking at 8 rubber from purchases divided by 5 rubber used or sold from the synthetic plant. That's 1.6 times the 1151 days for 1 CIC to build a synthetic plant, yielding 1841 days to pay it off. That's 5 years.
If you can't sell it all, you need to dump 25% of the output out of the equation. That gives us 5 rubber modified by the 15% you didn't sell, which gives us 3.75 rubber a day. That's 2.13 times the 1151 days you spent 1 CIC to build a synthetic plant, yielding 2455 days to pay off the plant. That's 6.72 years.
Obviously, if you build the plants at 1941 techs (or higher) and research more rubber output sooner (so that the extra output applies from day 1 of the plant being built), the plants pay for themselves sooner. But unless you can use and sell 100% of the output of those plants (at whatever trade law you have), they won't pay for themselves any time during a typical war.
The irony is that Germany and its boost to rubber output, plus being one of the only trading partners for the European Axis, means that it can get those plants to pay for themselves within a reasonable amount of time. No one else really can unless they build very late and research those rubber techs to high levels.
This discussion should also highlight the power of that boost to rubber output that Germany gets. +2 rubber makes a huge difference when it comes to synthetic plants.
