Based on an article from WCCO, ‘During a visit to a Newport Elementary classroom,’ The administration estimates the proposal would affect 47,300 students in its first year, eventually growing to roughly 57,000’ children would be enrolled in UPK.’
(http://minnesota.cbslocal.com/2015/03/20/gov-dayton-proposes-free-preschool-for-4-year-olds/)

Average number of births in Minnesota is approximately 69,000, and the average number of students in each grade in school is approximately 68,000. However 57,000 seems to be a reasonable number based on other states that are pushing UPK.

Minnesota Cost per Pupil

The state spends $12,692 per student.
(https://247wallst.com/special-report/2018/01/29/states-with-the-best-and-worst-schools-6/3/)

Cost of UPK
Students 57,000
Average cost of full time student $12,692
Assuming full day $725,000,000
Assuming ½ days, at 60% $7,615 $434,000,000

The total cost of UPK would appear to be $434 Million. However, that may be a very low estimate due to a number of variables including, a closer range would be $500 million to $750 Million because:
• Student-teacher ratios would have to be higher due to the children’s age.
• Available classrooms
• Supplies
• Cost of additional services may be higher due to the age and maturity of these children.