Let us examine the city of Detroit as an example, where the annual TPS expenditure is $16,004 per student. The city-level CAP score average for TPS students in Detroit is 92.86. Thus, the average cost effectiveness for TPS in Detroit can be calculated as:

92.86 CAP points
$16.004
= 5.8 CAP points per $1,000

In other words, every $1,000 spent per pupil by a Detroit TPS translates to about 5.8 CAP points, on average.

The average CAP score of 92.86 means that students in Detroit TPS performed 0.476 standard deviations lower than predicted based on how other schools in Michigan performed after controlling for their students’ average poverty rate:

-0.476 SD = 92.86 (actual CAP score) - 100 (expected score)
15 points per SD

Using both Hanushek’s estimates of earning gains based on measurable increases in academic achievement and the net present value determined above, the average lifetime earnings for TPS students in Detroit is:

$1,178,223 * [1 + (-0.476) * (0.13) * (0.70)]13 = $662,549

The city-level ROI for 13 years in a Detroit TPS then equates to:

$662,549
($16,004 * 13)
= $3.18 per dollar spent

In other words, each dollar invested in educating a child in a Detroit TPS results in $3.18 in lifetime earnings for each student, on average. The same calculation can be done for Detroit public charter schools in order to compare the return on investment across sectors.

The average annual per-pupil expenditure in public charters in Detroit is $10,519. The city-level CAP score average for these schools is 99.31. Thus, the average cost effectiveness for charters in Detroit can be calculated as:

99.31 CAP points
$10.519
= 9.44 CAP points per $1,000

The CAP score of 99.31 means that students in Detroit charters performed 0.046 standard deviations lower than predicted based on how other schools in Michigan performed after controlling for their students’ average poverty rate:

-0.046 SD = 99.31 (actual CAP score) - 100 (expected CAP score)
15 points per SD

Using Hanushek’s estimates, the average lifetime earnings for public charter students in Detroit is:

$1,178,223 * [1 + (-0.046) * (0.13) * (0.70)]13 = $1,115,692

The city-level ROI for 13 years in a Detroit public charter school is:

$1,115,692
($10,519 * 13)
= $8.16 per dollar spent

Each dollar spent by a Detroit charter school produces $4.98 ($8.16-$3.18) more in lifetime earnings for the typical student than each dollar spent by a Detroit TPS. This equates to a 157 percent higher return on investment for charter schools in Detroit compared to their TPS counterparts. If these estimates of the correlation between test scores and lifetime earnings are accurate, attending a Detroit charter school leads to substantial extra financial benefits for students, on average. We do identical calculations for the other 70 cities across the state of Michigan where data are available.