We bought Dusan Kuciak for a measly amount (only around $1 mil) and in two years, his value was over $7 million. As Seoul, we got Rasmus Falk on a free, and he started straight off at $600k value. After a year, it was $1.3 million. It's all dependent on how they play, their growing reputation, and their growing ability.
In the case of Kuciak, at his old team he was amazing but the league he played in wasn't big at all. Once he came to Villa, and performed outstandingly, his value skyrocketed.
In the case of Falk, he was only 19, and he immediately got a starting place on our team. As his ability grew (very quickly), his value rose, and as he performed better and better, his value got higher.
One thing to note though is that value changes never happen on a match to match or even a week to week basis. A player bought during the first transfer season, will have the fee paid as his value for at least half the year regardless of performance and the other factors.