The computer machine is a good as I know that they base cost is 250 days. He started it in July 1937 so about 170 days left of the year.
With 200% penalty each day is only counted for 1/3 of a real research day so we have 194 days left after end of year. Remove 25 days because of 10% tech cost reduction
(194+170-25)/250 = 1.556
Upon inspection I belive my initial statements to be true.
At 6:49 you can see the 1940 battle cruiser has a 510% research penalty on July 10 1937. 3 years is 600%, but it goes by month, so it would be 2 years 5 months early, 29 months early. Taking the penalty as 16.67% per month, the penalty should be 483%. The per month in game calculation must be rounded in some way then. So however it is it seems to not be multiplicative, especially if it's true that Johan has a 25% research bonus like you say.
Now to your other statement on the computing machine. At 8:34 you can see the 1938 computing machine has a 180% research penalty on July 31 1937. It would seem to be only a 4 month ahead of time penalty so it should be 80%, but it's much higher. I can only conclude from both of the above that the tech year doesn't start exactly at the beginning of the year and may be different for each tech. I also believe it must round to the nearest 10% or 5% because I haven't seen anything not be by the 10% except the research bonuses.
We'll find out eventually but it appears to be additive and the ahead of time is based on a month not the first of the year.
Jan 25 1938 there are 44 days left on the computing machine and an 80% research bonus on it. If it was multiplicative that would mean without the bonus there would be 220 days left, nearing the end of the year, which I don't believe is how it works.