Need help figuring out a Calculated Field to combine custom field choices into one

We have a field called Packaging Project Type and there are 4 options. 3 of the 4 options fall to a one main option. Sometimes we want to report out on the larger options and sometimes we want to report on the sub options. My thought was to have a calculated field that would see the 3 sub options and label them Non-New and the 4th option New would be labeled as New. And then we could report on that calc field as a grouping.

Example

Packaging Project Type

1. New
2. Non-New
   1. CORRECTIONS
   2. DMOD
   3. PROMO

IF({Packaging Project Type}="CORRECTIONS",Non-New,IF({Packaging Project Type}="DMOD",Non-New,IF({Packaging Project Type}="PROMO",Non-New,IF({Packaging Project Type}="NEW",NEW))))