Why according to the tanna kama of the mishna we have to wait 30 more days after the year. Why can't we just slaughter it after the year if it develops a mum like the chachamim. What does an extra 30 days going to matter?
The Gemara mentions to wait another 30 days because of Hashavas Aveidah; Rashi explains that if we have to slaughter no later than the end of the year, then if there is no Kohen to take it the meat will spoil, so the Rabanan gave another 30 days. (There is also Rebbi Elazar of the "Ika d'Amri" who learns from "Shanah b'Shanah" an additional 30 days which is considered like a full second year.)
All the best,