One of the biggest controversies surrounding the whole voucher program is cost. Depending on who you talk to, the program with either save a ton or cost a ton with little room left in the middle. One of the big questions for me has centered around the impartial analysis and whether the numbers were net or gross. This should have been answered when the updated document got posted by Green Jello, but it only provided insight as to the assumptions being made about the program. I'm going to break down the numbers as I know them to give a clear picture of how we make our assumptions.
What we know is that the voucher amount will be between $500 and $3000 with the average being around $2000 per enrolled student. We know that about 3% of Utah's students current attend private schools. We also know that the national average for private school attendance is around 12%, about four times what we have in our own state. The education fund is about 45% income taxes, 45% property and general fund taxes and about 10% miscellaneous (if memory serves me correctly). State per-pupil expenditures are $7500. These are the facts that we can all agree on.
We also know that the projections show just over
13,700 17,400 non-switcher private school students in FY 2008 and just over 18,900 26,000 total private school enrollment in FY2020. Now we're starting to get into assumption territory which can be tricky to navigate. This comes to about 5200 8600 new private school students over the course of 12 years or around 435 720 new private school students per year. Getting this baseline is important for establishing base costs of the program and determining overall student growth (about 3% per year in this case).
From this, we can figure the base costs of the program for each year it's in effect. In Years 1-5, there's
no direct cost from current enrollees only a cost from new enrollees, about 1/13 of the student population per year. In Year 6 and beyond, we phase in 1/13 of the private school student population (K-12) as voucher eligible. Because of the "hold harmless" provisions of Years 1-5, all vouchers are considered to be a cost since the money is slated to come from non-education monies in the general fund. Since we don't know the switcher rate, I'll go with the LFA estimate of about 3700 students. This comes to a cost of $7.6M per year (with $200K per year in administrative costs) or $40M during the course of the first five years. The education fund, meanwhile, gets to keep the $7500 per student in education spending without the overhead associated with said student. Update: The cost of new students is about $18.5M. That comes to a $27.75M windfall for schools each of the first five years or of $92.5M in total. In other words, schools do pretty well on the funding end of things during the first five years should the projections prove true.
So what happens when the
private school students start becoming eligible mitigation funds go away? In Year 6, 1/13 6/13 of the private school population of non-switchers become eligible. Based on the projections above, that's about 1300 9800 students which will cost about $2.6M $19.5M that year. Figuring that the switcher numbers grow at a similar rate, we have about 4300 4500 switchers costing about $8.6M $9M for a total cost (with administration) of $11.2M $28.5M. The 4300 4500 switchers will leave behind $5500 per student in the education fund or $23.7M $24.8M. Given that the switchers vouchers are already paid for, we can exclude them we calculating net cost or savings. So far, this looks like a pretty good deal for the state at a $21.1M $5.3M windfall and we haven't even factored in new construction at all.
By Year 13, we have
over half all of the non-switchers eligible or about 10,700 27,900 students. This has a cost of $21.4M $55.7M. Switchers will now number about 5500 5900 for a cost of $11.2M $12M. The total voucher cost is now $32.6M $67.7M. The money left behind by the switchers is about $30.3M $32.5M, so we still have a windfall to the state loss of $8.9M $23.2M. It's not the billions of dollars exclaimed by legislators, but it's nothing to sneeze at either. Now let's take a hard look at Year 18, when all students are eligible. We now should have around 21,800 non-switchers costing $43.6M. Switchers are up to 6300 students for a cost of $12.6M. The switchers now leave behind around $34.7M, a loss to the state. Update: Given how off my projections were, Year 18 doesn't really figure anything anymore.
Over the life of the program, we're looking at a total cost of $335.9M and a total savings of $338.4M for a net savings of $2.5M. This doesn't factor in the building costs saved by not having all of those switchers in private school campuses. Using numbers from the Senate Site, we can expect to save somewhere in the neighborhood of an additional $118.5M in building costs.
The problem with this scenario, however, is that we presume the switchers never surpass
1% 0.65% of the total student population and that we never exceed more than 4% 3.65% of the total student population in private schools. Given the national average of 12%, this seems like a very low-ball figure. Consider that most of our student growth is coming from out-of-state and that these new residents are, on average, four times as likely to opt for a private school as native Utahns.
Let's work backwards: let's figure out how many switchers we need in Year
18 13 to achieve a break even. We've already established our baseline cost of $43.6M $55.7M. We also know that each switcher saves about $5500. This means we need about 7900 10,100 switchers to hit the break even in Year 18 13 compared to an estimate of 6300 5900. In other words, instead of 1% of the student population being comprised of switchers, we'd need 1.25% 1.7% of them to be switchers, still well within the national average.
As you can see, the estimates are little more than best guesses; they could be higher, they could be lower. But we will never know without the five-year pilot. Think of the pilot as a research project of sorts to gather data. You might not like the process, but I would hope we can all agree that the data itself is very valuable.
BIG UPDATE: Jeremy kindly pointed out a flaw in my figures regarding when private school students start becoming eligible. This is why we should leave match to Excel and not our four-function calculators. I've stuck-though all of the old text and updated as appropriate as well as putting new content in italics. You all get to see my mistakes.
UPDATE 2: I made some additional corrections to the percentage of students who are switchers.
UPDATE 3: Here's a handy Excel spreadsheet you can use to see the calculations on a year-by-year basis.
UPDATE 4: I made a new copy of the spreadsheet with a graph to show costs versus savings. I also made the switchers a ratio of current private school enrollments so you can play with the
numbers. Just adjust the value in cell G2 from 0.65 to the new percentage of switchers. It'll auto-update the graph as well so you can get visuals on the changes and where the break-even point lies. Based on these adjustments, the break-even is around 0.96% switchers with building costs factored in and 1.09% with building costs excluded, a pretty reasonable figure to be met. I'm hoping this is the end of my updates.
While we're on the topic of math, I also want to take a moment to address the criticisms of The Sutherland Institutes's figures on private school tuition. A lot of folks have been howling over the "average" that has been calculated, but it belies a lack of understanding of proper statistical analysis. One of the biggest points of contention is that they shouldn't have excluded the highest end schools when calculating the arithmetic mean (which is what we really mean when we say average). That, however, flies in the face of statistical analysis.
For an arithmetic mean to be worth anything, you have to exclude aberrations in the numbers that would skew it too heavily in one direction. Many hosting companies do this for billing: they lop off the top 5% of traffic spikes when calculating your peak bandwidth. This is standard practice. (See Wikipedia for more.) Granted, it would have been more meaningful to get the mode or median either instead of or in addition to an arithmetic mean, but that's water under the bridge at this point. Remember, kids: math doesn't like to be abused.