Rich Carlstedt:

First, the Federal Government funds a program for youngsters that need help. It is called Headstart. The cry for help for such an age group should be addressed by this program, however the schools have found a cash cow in Wisconsin’s 4 K Budget and can make extra funds this way.
Second, rather than looking to Arkansas, (or Georgia, who admit that the 4K program is a failure), we can look right here in Wisconsin. Three years ago I challenged Dan Nerad, the Green Bay Superintendent at that time, when he said, “early education promotes advancement of learning .”

“We do not need to look at studies from other communities, when we have the information right here in Green Bay! 8 years ago, we went from ½ day kindergarten to full day, and yet subsequent grade test scores failed to reflect the additional education time… in fact, scores are decreasing which is proof that extending hours does nothing.”

The charge went unanswered.
Third, I have to say that you left a very large arrow out of your quiver, as your financial equation is not correct for 4 K.
While I feel that $9,900 is closer, let’s use your $9,000 number, it is fine for expressing costs. To get funding for a student, he is counted as one FTE ( full time education) to get the 9K. 4K students however get a kicker. For 13 ¼ hours per week they are counted as .6 FTE ( .5 if less than 13 ¼). So 4 year olds are given a morning class, followed in the PM with another 4 year old. Those two half day students count as (2 x.6) 1.2 FTE or in cash terms, they bring in $10,800 to the district.

Much more on Madison’s planned 4K program, here.
The article’s comments are worth reading.