In order to determine the relative productivity of public charter schools and TPS, we follow the methodology from the University of Arkansas charter school productivity study and first calculate the cost effectiveness of public charter schools and TPS using the following formula:[13]

Cost Effectiveness = CAP Points
Per Pupil Expenditure

The total cost of the investment is more straightforward. It is the average amount of public expenditures invested on students in TPS and public charter schools for each city multiplied by the average number of years spent in school.[*] We rely on data contained in the Mackinac Center’s “Michigan School District Revenue and Expenditure Report,” the same database used for the analysis of funding disparities between charters and TPS. We use 13 years because the public is investing in each child’s education from kindergarten through 12th grade. The calculations for TPS and public charter school students in each city appear below:

Cost of Investment = Per Pupil Expenditure * 13

We take the average amount of CAP points achieved by students in public charter schools and then divide by the total cost of investment for 13 years of education. This gives us the average amount of CAP points achieved by a student in a public charter school for each $1,000 invested, or spent, over the course of their schooling career. We compare the average cost effectiveness of public charter schools to TPS for 71 cities in Michigan. The result is 142 unique observations of cost effectiveness — CAP score achieved per $1,000 dollars expended — based on city and school type.

[*] We use funding from the most recent year since it is the best estimate of current investment, while multi-year CAP score averages provide the best proxy of general school quality. We use expenditures in this section of the analysis because we are calculating society’s return on the spending decisions made by the schools in each sector.