We also calculate a return on investment by examining resource inputs and long-term outcomes across the two sectors in each city. In order to calculate ROI, we use the following formula:

Return on Investment = Income Returns to Investment
Cost of Investment

The income return to investment is the net present value of additional lifetime earnings accrued through an improved educational experience.[*] Stanford University economist Eric Hanushek estimated that a one standard deviation increase in academic achievement scores leads to a 13 percent increase in lifetime earnings.[14] In addition, only 70 percent of gains in learning persist each year. If we multiply these two estimates together, we find the learning gains relative to the average worker in the state of Michigan. For example, if a child attends a charter school that produces one standard deviation of higher academic achievement scores each year, and learning fadeout does not occur, that child is estimated to experience a 13 percent increase in lifetime earnings relative to the average child in Michigan. However, we adjust for the fact that about 70 percent of learning gains persist each year by multiplying each year’s learning gains by 0.7.

We use the average income of all employees in the state of Michigan as the closest approximation of what the average child is expected to earn. By comparing test scores relative to the average worker’s income in the state, we estimate the returns to the schooling investment in terms of yearly income. We use data from the United States Bureau of Labor Statistics to find state-level average annual earnings per employee in Michigan and assume that current students will work between the ages of 25 and 70, or 46 years.[15] When calculating the net present value of lifetime earnings, we assume 1 percent yearly growth in average salaries and a 3 percent annual discount rate.[†] The net present value of the average lifetime income in the state of Michigan, using a discount rate of 3 percent and a yearly salary growth rate of 1 percent, is $1,178,223.

[*] Net present value is the current dollar value of expected financial returns after adjusting for the time value of money.

[†] The discount rate is used to estimate inflationary value changes and interest accrued over time.