The rate problem
The budget Lunenburg is running on right now cut $1.17M and 9.2 positions, and next year the hole is bigger than the one that bought. That sounds like somebody failed. It is not — it is what happens when you answer a rate problem with an amount. This page lets you do both and watch the difference.
Start here
The increase for next year
$859k
The town gave the schools $26,572,288 this year. Town revenue rises 3.23%, so next year it can give $858,909 more than it did. That is the entire increase.
What standing still costs
$1.40M
What the same staff, the same buses and the same buildings cost next year, one year older. Nobody is hired and nothing is added.
Next year’s gap
$930k
$538,009 of it is costs outrunning the increase — standing still takes 163% of it. The other $392,266 is what the district was already behind before anything grew.
The full width is what next year costs if nothing changes. The top band is who wants the money; the band underneath is the same span colored only by whether there is money for it. The mark is where it runs out. Everything past the mark has to come from somewhere else, and no rearranging of the segments makes it fit. This bar is about the increase only — next year’s full gap is $930,273, because the district also starts $392,266 behind.
| Line | Grows | Costs more | Share of the increase | Running |
|---|---|---|---|---|
| Salaries | 4.0% | +$533,929 | 62% | 62% |
| Health insurance | 9.0% | +$361,716 | 42% | 104% |
| Special education, in district | 6.5% | +$354,633 | 41% | 146% |
| Transportation | 6.0% | +$63,202 | 7% | 153% |
| Everything else | 3.0% | +$53,162 | 6% | 159% |
| Utilities | 5.0% | +$30,276 | 4% | 163% |
| Out-of-district special education | 0.0% | +$0 | 0% | 163% |
| All six | +$1,396,918 | 163% |
Health insurance alone takes 42% of the increase while being 15% of the budget. Salaries take 62% on their own. By the third line the money has run out, and there are three more lines. Nothing in this table is new spending — it is the same staff, the same buses and the same buildings, a year older.
The bar above shows the money runs out, but a large line takes a large share of any increase and looks guilty simply for being large. So here is each line on its own, drawn the same way.
■ Green is growth the increase pays for — up to 3.19%, the rate every line could grow at if the $859k were exactly used up. ■ Red is what the line takes above that, which has to come from somewhere else. The tick is where the money for that line runs out.
Salaries have the longest bar and health insurance has the reddest one. That is the difference between costing a lot and being the problem: salaries take 1.26× their share because of their share of the budget, while health insurance takes 2.83× theirs and is 43% of the whole shortfall on its own.
One line out of six fits, and it fits by $22,302. It is “everything else” — supplies, materials, technology, athletics, clubs — the only line the School Committee fully controls, the only one it has actually been cutting, and the only one that was never the problem. The red segments add up to $538,009 — exactly the part of next year’s $930,273 gap that comes from costs outrunning the increase.
Proposition 2½ is the largest piece but not the whole of it. The schools take their share of whatever the town collects.
What Proposition 2½ allows on the existing base
New construction added to the levy, at the assumed rate
Chapter 70 and the rest, at 2.8%
Fees, excise, permits
Before anything grows, the district is already spending $392,266 more than it was appropriated this year — the special town meeting add-backs cost more than the special town meeting funded.
The same $930,273 the rest of this site starts from, rebuilt from the increase rather than from the total.
The whole thing in two numbers
Costs grow at
5.18%
Weighted across salaries, insurance, transport, special education, utilities and supplies
Revenue grows at
3.23%
Proposition 2½ caps the levy at 2.5%; new growth adds the rest
The gap by FY33
$4.66M
Starting from $930k next year, with nothing going wrong
Every year
| Year | Cost of today’s services | Revenue available | Revenue rose by | Gap, running total= an override passed that year | Grew by |
|---|---|---|---|---|---|
| FY27 today | $26,964,554 | $26,572,288 | — | $392,266 | — |
| FY28 | $28,361,470 | $27,431,197 | +$858,909 | $930,273 | $538,007 |
| FY29 | $29,842,207 | $28,311,734 | +$880,537 | $1,530,474 | $600,201 |
| FY30 | $31,412,392 | $29,214,447 | +$902,713 | $2,197,945 | $667,471 |
| FY31 | $33,078,066 | $30,139,901 | +$925,454 | $2,938,165 | $740,220 |
| FY32 | $34,845,718 | $31,088,674 | +$948,773 | $3,757,043 | $818,878 |
| FY33 | $36,722,314 | $32,061,359 | +$972,685 | $4,660,955 | $903,912 |
| FY34 | $38,715,344 | $33,058,565 | +$997,206 | $5,656,780 | $995,825 |
| FY35 | $40,832,856 | $34,080,914 | +$1,022,349 | $6,751,941 | $1,095,161 |
| FY36 | $43,083,500 | $35,129,048 | +$1,048,134 | $7,954,453 | $1,202,512 |
| FY37 | $45,476,584 | $36,203,621 | +$1,074,573 | $9,272,963 | $1,318,510 |
An override passed in a given year has to match that year’s running total exactly, which is what makes the running total the figure an override is sized against. Passed earlier it can be smaller, because it compounds at 2.5% in the meantime: covering FY30’s $2,197,945 costs $2,092,036 if the vote happens in FY28 instead.
Read the last column. The running total looks explosive because it is cumulative — FY29’s $1.53M includes FY28’s $930k rather than sitting on top of it. What is actually happening is steadier and worse: the hole gets $538,007 bigger next year and more every year after — $888,070 a year on average across the decade, and never once smaller.
The experiment
Still widening — $600,201 bigger in FY29 than in FY28
Costs grow 5.18%. Revenue grows 3.23% today, but that decays to 3.03% by FY39 as a flat new-growth figure becomes a smaller share of a bigger town — so 3.03% is the rate that actually has to be beaten. While it is not, the hole grows every year no matter what you take out of it, and every one-time fix buys about twelve months.
One-time fixes
These change the amount. Take all of them and watch the number at the bottom of this column stay exactly where it is.
Each notch is the smallest override that funds through one more year, given everything else set on this page. Cut something first and they all get smaller.
A school-only question, so the schools keep every dollar. The townwide ask that failed covered every department, which is why it had to be so much larger to do the same work here.
Within the 5–7% the Town measures itself against. $3,354,370 retained, out of the $3,354,370 certified this year.
About 24% — $794,872 a year — can be redirected while staying inside the guideline. Assumes the town keeps certifying at this year's level, which was a record: an ordinary year produces $2,026,212, or 3.96% — already below the floor, with nothing to redirect at all.
Found once: $0
Cost growth rate: 5.18% — unchanged by anything in this column
Growth rates
These change the direction. The number beside each line is how much of the budget it is — that, not the rate, decides how much moving it is worth.
Holding it to 2.5% moves the blend 0.74 pts · Bargained with the unions, three years at a time
Holding it to 2.5% moves the blend 0.97 pts · The Town buys the insurance, not the school district
Holding it to 2.5% moves the blend 0.81 pts · Each child’s plan, and the law behind it
Holding it to 2.5% moves the blend 0.14 pts · Contracted, and exposed to fuel
Holding it to 2.5% moves the blend -0.06 pts · Set by state rates and by which children enroll
Holding it to 2.5% moves the blend 0.06 pts · The market, and the weather
Holding it to 2.5% moves the blend 0.03 pts · The School Committee, mostly
The only revenue rate the town owns. The levy itself is locked at 2.5% by Proposition 2½ and no vote here changes that.
Cost growth rate: 5.18% vs revenue at 3.23% today, 3.03% long-run
Where the leverage actually is
Health insurance
0.97 pts
14.9% of the budget, growing 9.0% · The Town buys the insurance, not the school district
Special education, in district
0.81 pts
20.3% of the budget, growing 6.5% · Each child’s plan, and the law behind it
Salaries
0.74 pts
49.5% of the budget, growing 4.0% · Bargained with the unions, three years at a time
Transportation
0.14 pts
3.9% of the budget, growing 6.0% · Contracted, and exposed to fuel
Utilities
0.06 pts
2.2% of the budget, growing 5.0% · The market, and the weather
Everything else
0.03 pts
6.6% of the budget, growing 3.0% · The School Committee, mostly
Out-of-district special education
-0.06 pts
2.6% of the budget, growing 0.0% · Set by state rates and by which children enroll
Health insurance and Special education, in district are 35% of the budget and worth 1.78 points — 91% of the spread, so those two alone are enough to end it. The other four lines together are worth 0.90 points, or 46% of it: hold transport, special education, utilities and supplies all at the cap, at once, forever, and you have closed under a quarter of the problem.
Note which line the town has actually been cutting. “Everything else” is the only one the School Committee genuinely controls — and it is the smallest on the list, the slowest-growing, and worth -0.06 points. Athletics, clubs, art supplies and devices all live inside it.
The second line on that list
The district's published rate
3.98%
FY26 to FY27 level service — the same staff, the same programs and the same children, one year older.
With one line held flat
6.23%
The same arithmetic with out-of-district tuition left where FY26 had it.
What that line is worth
2.25 pts
The distance between the two. For scale, the whole gap to the levy cap at the published rate is 1.48 points.
Out-of-district tuition is what Lunenburg pays other schools to educate children whose plans it cannot deliver itself. It was budgeted $1,291,293 for FY26 and $700,142 for FY27 — down $591,151, 46%, in one year.
That fall is a level change, not a rate. It drops the cost once and leaves the angle of the curve alone, so the published 3.98% describes a year whose arithmetic does not carry forward. The rate a resident should plan against is 6.23%.
What it is not is unprecedented. An earlier version of this page said there could be no second 46%. Eleven budgets say otherwise: this line fell 45.8% in FY27 and then rose 132% in FY25. It has been as low as $489,918 and as high as $1,291,293, and $700,142 is 12% below its eleven-budget average of $792,857 — an ordinary year for this line rather than a floor. The section below draws the whole series.
Every figure below rests on which budget lines we counted, and that is a judgement rather than a published total. So it is set out first, in full, with the lines listed and the boundary cases named.
There is no account code for special education. The state’s chart of accounts does not have one, and two of the groups the district reports carry both kinds of cost at once — 2330 is paraprofessionals, general education and special education together, and 3300 is transportation, where the special education runs sit beside the yellow buses. So every figure on this page rests on a classification somebody made. This one is ours, and it has two parts:
One. 8 function groups are special education outright, and every line inside them counts — 46 lines. Two. Inside the mixed groups, a line counts when the district’s own label for it says special education — 8 lines, of which one, special education transportation, is most of the money.
They come to $5,466,201, which is the amount every projection on this page starts from. The list is below and it adds up; the underlying file is published as a spreadsheet, with a column marking which lines these are, so the sum can be checked without taking our word for any of it.
And what was deliberately left out. A classification is defined as much by its edges as by its middle.
English Language Learner lines, wherever they appear
FY25 $173,556 · FY26 $193,878 · FY27 $279,342
A different entitlement, serving different children, under a different part of the law — but the district files some of it inside groups that are otherwise special education, so a rule that took those groups at their word counted it. It did, until this was found.
2330 - Paraprofessionals General Education
FY25 $121,233 · FY26 $0 · FY27 $0
General education paras. The group next to the special education one, and the single boundary most likely to be crossed by accident in either direction.
9300 / 9400 — out-of-district tuition
FY25 $1,164,824 · FY26 $1,291,293 · FY27 $700,142
Special education, but escalated on its own because it is set by placement rather than by payroll, and it behaves nothing like staffing.
Split the year into its parts and it is not a general increase. Two entries move in opposite directions and everything else is noise around them.
Out-of-district tuition
−$591,151
$1,291,293 → $700,142 · -45.8%
Paraprofessionals
+$530,038
$1,344,373 → $1,874,411 · +39.4%
Psychologists and testing
−$87,632
$295,355 → $207,723 · -29.7%
Special education transport
+$84,219
$565,734 → $649,953 · +14.9%
Administration, legal, supplies and contracted work
−$39,803
$144,842 → $105,039 · -27.5%
Special education teachers
−$30,336
$1,993,848 → $1,963,512 · -1.5%
Speech, OT and summer services
+$21,568
$567,677 → $589,245 · +3.8%
Substitutes
+$0
$52,500 → $52,500 · +0.0%
What the budget shows. Two lines moved in opposite directions by nearly the same amount in the same year: paraprofessionals $530,038 up, purchased placements $591,151 down. Teachers are flat, therapists are near flat, substitutes are identical to the dollar.
What it does not show. That any child moved, that the two decisions were connected, or that one caused the other. The tuition line may simply have been budgeted too high for years. A budget records dollars against a line; it never records people, and nobody publishes how many children are placed out of district.
What the district said it meant to do. Its own FY27 presentation to the Finance Committee states that “investing in internal staff is significantly more cost-effective than tuition and transportation for OOD placements.” That is evidence of intent. It is not evidence of outcome, and the two are not the same thing.
This is the one rate on the site the district does not publish, so it is ours, and the argument for it is set out in full rather than asserted. It is also an argument against a figure this project published for a day.
Special education apart from the paras, two budgets
1.14%
What the rest of the line did while the paras were being added. Below the levy cap — and it is the paras, not the rest, that make this line a driver.
If every settlement were the whole story
2.53%
The two bargained agreements at their published rates and nothing else — no bus increase, no change in how many people are employed. Published here because it is what this model used to assume, and because the gap between it and the rate above is the part of this line that pay settlements do not explain.
The whole line, two budgets
5.77%
What the in-district line did between the last two budgets. Close to the rate used, and reached a different way.
Each part at its contract, or at what it has measurably doneused
6.49%
Professional staff at the teachers’ agreement; paras and buses at what ten and nine budgets show them doing, because no contract governs how many people are employed. Weighted by each part’s share of the line.
FY27 by itself
9.63%
The single steepest year. One observation, and the top of the range.
A contract sets what one person is paid. It says nothing about how many people are employed — and on this line, that is where the movement is. Both bargained groups here have run away from their agreements, in opposite directions. Special education teachers are on a contract giving 3.5% and their line has grown 2.67% across 8 budgets — headcount drifting down. The paras are on a contract giving 2.0% and their line has grown 12.8%.
Paras, FY{P.firstFy} to FY{P.lastFy}
2.95×
$634,513 to $1,872,411
Compound rate
12.8%
8 of 9 years up. Stays between 11.5% and 17.0% wherever you start it.
Is it a trend?
R² 0.89
Near 1 means the years explain the amount. This is a climb, not a scatter.
This page argued the opposite a day ago, and the correction is worth stating rather than quietly editing. This line was escalated at 2.53% — the settlements alone — on the argument that FY27’s 39% increase in paras was a one-time step whose cost already sat in the amount the model starts from. That argument was sound. Its premise was false.
With two budget years there is no way to tell a step from a climb — they look identical. The archive now reaches back 10 budgets, and it is a climb: the FY27 rise is the steepest year of a trend that has been running since FY18, not a departure from one. The rate went from 2.53% to 6.49%, and the projected gap went up rather than down.
What this rate still assumes. That the climb continues at roughly the rate it has held. That is an assumption and not a measurement, and nothing in a budget column can test it: a budget shows dollars per line and never shows people, and the district does not publish staff counts. What can be said is narrower and firmer — that pricing this line at the pay settlements alone has been wrong in every one of the last 9 budgets.
The buses are the weakest input. There is no published vendor escalator, so the figure is measured, and over 9 budgets it fits far less convincingly than the paras do — R² of 0.33 against 0.89. It is 5.7% because that is the least bad number available, not because the line is well behaved. It is 12% of the total.
There is no special education contract. These staff are paid under the same agreements as everybody else — professional staff on the teachers’ contract, paras on the paraprofessionals’. There is no special education bargaining unit and no special education pay rate, so describing this line with a single number of its own risks implying its staff receive larger increases than other staff. They do not.
Nobody signs an agreement saying how many paras a district will employ. So for these two the rate has to be measured — and drawn, because whether a line has a trend at all is the thing that decides how much weight its number can carry.
Special education teachers
Their contract gives 3.5% a year.
2.7%
a year
0.84
R²
4/7
years up
Below contract, and a good fit. Headcount here has drifted down, so the contract rate would overstate it.
Special education paraprofessionals
Their contract gives 2.0% a year.
12.8%
a year
0.89
R²
8/9
years up
A trend, and a strong one. Escalated at what it has done.
Special education transportation
A vendor contract with no published escalator.
5.7%
a year
0.33
R²
6/8
years up
A weak fit. Used because it is the least bad figure available, and it is the smallest of the three components.
One line does most of the work above, so it is worth asking what it has actually done. The district's budget documents go back to FY17 and carry it, which is far enough to answer.
Budgeted out-of-district tuition, 11 budgets, one budget stage held constant throughout. Average $792,857. The extremes are marked.
The range it has run in
2.64×
$489,918 in FY23 to $1,291,293 in FY26.
Direction
6 up · 4 down
A straight line through the 11 has an R² of 0.10 — for practical purposes, no relationship between the year and the amount.
Where FY27 sits
-12%
Against the 11-budget average of $792,857. Not a floor, and not an outlier — an ordinary year for this line.
So this line is held flat, and the absence of a rate is the point. It used to be escalated at 8% a year, which had no stated basis; the back-test flagged it as the worst-calibrated assumption in the model. The obvious repair is to measure the rate instead — and the measurement will not hold still:
Three ways of asking, three sources, one answer.
The model holding this line flat is its most consequential single decision. It was not arrived at once.
Eleven budgets, FY17 to FY27
The district’s own budget documents
The line runs from $489,918 to $1,291,293 — 2.64 times — with 6 years up and 4 down. A straight line through them has an R² of 0.10, and the compound rate swings from -46% to +12% depending only on which year you start counting.
Five years of budget against actual spending
The district’s budget documents, actual columns
The line missed by +27.0%, +14.3%, +0.4%, −51.5% and −37.8%. Three years over, two under. Not systematically under-provided — unforecastable in both directions.
The two halves of the line, separately
Private and collaborative tuitions, line by line
Private and collaborative miss by 60% to 300% in opposite directions. Pooled they come to −7.9%, not because they cancel but because they happen to be smaller together.
No rate describes this line. The model holds it flat and prices the range instead, because a range is what is actually known.
Since the range is what is known, the range is what gets priced — at every level this line has actually reached.
| If the FY28 line is | Tuition | FY28 gap | Against the model |
|---|---|---|---|
| As the district budgeted it for FY27 | $700,142 | $930,273 | — |
| Midway back | $1,000,000 | $1,230,131 | +$299,858 |
| Back to the FY25 budget | $1,164,824 | $1,394,955 | +$464,682 |
| Back to the FY26 budget | $1,291,293 | $1,521,424 | +$591,151 |
None of these is a forecast. They are the cost of being wrong about one line, and the spread — $591,151 between the budgeted figure and a return to where FY26 had it — is wider than any other single assumption in this model.
There is no slider here on purpose. A control would let a reader pick the number that suits the argument they arrived with, and the honest position is that nobody outside the district can know which of these is right. What would settle it is the FY28 tuition line when the district publishes it, and the count of children placed out of district — which is not published at all, in any year.
Dollars are not children. The state publishes the count, so here it is — all of it.
Students with disabilities as of 1 October, from the state’s own report. All 8 published years. The low point, FY2022, is marked.
Over the whole series the count fell 6.9% — FY2019 277 to FY2026 258 — and the share of enrollment is close to where it started, 16.7% against 16.3%. Measured from the FY2022 low of 227 it is up 13.7%.
Which is why the whole series is drawn. Any three of these years can be chosen to show a rise or a fall, and this project has no business doing that to a reader. What the series does not settle is intensity: the district’s own FY27 presentation shows sub-separate placements — the most intensive end — rising over the same period, on totals that do not reconcile with the state’s. The two count different things and cannot be squared from anything published.
Level against slope
The projection as it stands
Short in every year, starting with $930k next year
Cost growth 5.18% against revenue 3.06% — still widening, back in deficit by FY28
Every sport, the band, clubs, art, 60% of technology and every lawful administrative line — $1.50M at once
Funded for 2 years, then short again from FY30 — $7.06M by FY37
Cost growth 5.18% against revenue 3.06% — still widening, back in deficit by FY30
$1.25M, school-only, so the schools keep all of it — an example size, not a proposal
Funded for 1 year, then short again from FY29 — $7.71M by FY37
An override raises the levy limit; it does not oblige the town to collect it. In a year the schools need less than it raises, the town can levy under the limit — Lunenburg has left as much as $53,706 unlevied — or appropriate the difference elsewhere. The override then compounds at 2½% like the rest of the limit, which is why it falls behind a gap growing faster than that.
Cost growth 5.18% against revenue 3.06% — still widening, back in deficit by FY29
From 9% a year to 4%
Short in every year, starting with $729k next year
Cost growth 4.44% against revenue 3.06% — still widening, back in deficit by FY28
Settle at 2½% and get insurance to 4% — the two lines that are 82% of the budget
Short in every year, starting with $529k next year
Cost growth 3.69% against revenue 3.06% — still widening, back in deficit by FY28
The same two rates, and $400k taken out once
Short in every year, starting with $119k next year
Cost growth 3.69% against revenue 3.06% — still widening, back in deficit by FY28
Notice what the last card does. Fixing the rates first leaves a residue — the gap stops growing but does not vanish, because FY28 already starts behind. A single cut then closes that residue and it stays closed. Done the other way round, the same cut buys twelve months. The order is the whole lesson: a one-time fix only works after the rate is fixed.
The revenue side
The actual question
What “solved” would actually require
12 priced combinations — five years, ten, a generation, and 3 that never reopen — plus why every one of them moves at least two lines, what a moderate result at the State House is worth to each, and the trade table they were drawn from. Any of them loads straight back into the board above.
See what actually holds, and for how long →The other way out
All state aid today
$11.88M
24% of town revenue. Chapter 70 school aid is $9.35M of it — 79% — and covers 35% of the school budget.
It is assumed to grow
2.8%
Below the rate of almost everything it pays for
It would have to grow
9.50%
Every year, forever, with nothing else in this model changing
| Year | All state aid, as assumed | All state aid, required | Extra from the state |
|---|---|---|---|
| FY28 | $12,202,629 | $13,004,332 | $801,703 |
| FY29 | $12,538,201 | $14,239,820 | $1,701,619 |
| FY30 | $12,883,002 | $15,592,687 | $2,709,685 |
| FY31 | $13,237,284 | $17,074,085 | $3,836,800 |
| FY32 | $13,601,310 | $18,696,224 | $5,094,914 |
| FY33 | $13,975,346 | $20,472,476 | $6,497,130 |
| Ten years | $64,067,381 |
The state would have to put in an extra $801,703 next year, $6,497,130 by FY33, and $64,067,381 over the decade — and then keep compounding at 9.50% indefinitely. Chapter 70 has not behaved like that in any recent year, and a town spending $3.48M above its foundation budget is not where the formula sends its money.
These figures are the whole cherry sheet, because the projection carries state aid as one line and grows it as one. Chapter 70 is 79% of it, and the remaining $2.53M — charter reimbursement, transport, lottery — is not money the state would move for this reason. So if the increase had to come from Chapter 70 alone, it would have to grow 11.32% a year rather than 9.50%.
The reason any of these rates is so high is that aid is only 24% of the town’s revenue. Fixing a blended cost rate of nearly 5% by moving a quarter of the revenue means moving that quarter very hard. Worth asking the delegation for; not worth planning around.
Being straight about it
Dragging salaries to 2.5% is a bargaining position, not a decision, and it is a real-terms pay cut for roughly 150 people. Health insurance is bought by the Town, not the district. Out-of-district special education is set by state rates and by which children enroll.
9% health and 4% salaries are this model’s projections, not measured futures. If insurance comes in at 5% much of this eases on its own — which is a reason to watch that number more closely than any cut list.
Every arithmetic here is indifferent to what a school is for. Which cuts are survivable, and which rate is fair to ask of the people who work there, are not questions a curve can answer.
See what each option costs →If this tab makes its point, the rest of the site reads differently: the cut lists are not solutions, they are the price of not having fixed a rate. The static version of this argument is on “Why the gap returns each year” →
Same projection as the rest of the site, opened up at the growth rates. At the default settings it reproduces the main model to the dollar.