The extra amount I spend on running my led setup for 20/4 for autos is negligible compared to 12/12. I Would rather run my light longer and get those giant tight auto buds that eat up light all day than stress a photo at 12/12. I have also grown autos next to photos in 12/12 and found that it's just plain not worth it to have an auto in 12/12.
Numbers are great, but then you have to factor in how starting a photo on 12/12 stresses it right from the start. The plant thinks that it's sprouting right at the end of the season and rushes itself to finish, causing stress to the plant. I would rather grow an auto for a quick fix and grow a photo proper starting with 18/6 and moving to 12/12. I don't have a link, but I read an article on another site where the did side by side experiments and the 12/12 from the start photos took longer and were smaller than the ones that were vegged proper until sex. Stress led to worse pot as well.
Very informative