Here it is:
Lets say Saison 0 is our start. You have got 5 Mio.
First Way: Build Lvl 4
Lvl 4 is built after 30 days - lets say we start building one day before Saison 0, then we get a better sponsor for Saison 1. The difference between Lvl 3 and 4 are about 29.000€ per home game - so 11 times in a season --> 319k€ + the Bonus at the beginning which is about 42k€ --> round about 360 k€ per season (maybe 380k€-400k€ if you are in PO/PD, but I will not handle with things you can hardly calculate...)
Second Way: Save the money...
Then the only question is: What do you earn in one season (I call it money per season - mps) after subtracting all costs?
You can build Lvl 5 after building Lvl 4, if
x * mps + (x - 1) * 360 k€ = 10 Mio€
You can build Lvl 5 without building Lvl 4, if
y * mps + 5Mio€ = 10 Mio€
If you now set x=y then you get the mps for which the both season times are equal --> mps = 336.000€
If you earn more money per Season, Lvl 5 without building Lvl 4 is more efficient, if you earn less, you should build Lvl 4... One example: You get 1 Mio per season, then x = 7,6 seasons but y = 5 seasons...!
I did not consider special events:
PO/PD should tend to save money, because the money from the visitors and gastro should be extremely more than just the additional 29k€ due to the sponsor
Transfers: it belongs to you: get money due to transfers will tend to build no Lvl 4, spend money for transfers will tend to build Lvl 4
--> I think everyone can save more than 336k€ per Season if he/she wants to save it. Therefore I say: Do not build Lvl 4! But it is up to everyone himself/herself!
PS: I am very excited if you varify or deny the calculation 
Ich hab noch DF2 und DF3 frei, falls jemand mag.