Two-Borough Settlement: Does the Protection Clause Bind?
A regional fund of £4.20 million is split between two boroughs by a fixed formula: 60% weight on population share and 40% on deprivation share. Borough X has 182,000 residents and a deprivation score of 34; Borough Y has 118,000 residents and a score of 61. A protection clause guarantees each borough at least 90% of last year's allocation: X received £2.35 million, Y £1.85 million. The deprivation scores come from a survey with a stated margin of error of ±3 points, and one ward's return is still outstanding. The finance lead must sign the settlement letter today. Officers disagree about whether the protection clause will bind for X.
1. Calculate both formula allocations and test the protection clause.
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Population shares: X 182/300 = 0.60667; Y 118/300 = 0.39333.
Deprivation shares (total 34 + 61 = 95): X 34/95 = 0.35789; Y 61/95 = 0.64211.
Weighted: X = 0.6(0.60667) + 0.4(0.35789) = 0.36400 + 0.14316 = 0.50716 → £2.130m. Y = 0.6(0.39333) + 0.4(0.64211) = 0.23600 + 0.25684 = 0.49284 → £2.070m. Check: 2.130 + 2.070 = 4.200.
Floors: X 0.9 × £2.35m = £2.115m; Y 0.9 × £1.85m = £1.665m.
X clears its floor by £15,000 (0.7%); Y clears by £405,000. The officers who say the clause binds for X are wrong on current data - but only just.
2. Find the deprivation score at which the clause would bind for X, holding Y at 61.
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Set X's allocation equal to its floor: £2.115m ÷ £4.20m = 0.50357.
Population term: 0.6 × 0.60667 = 0.36400. So the deprivation term must be at least (0.50357 − 0.36400) ÷ 0.4 = 0.34893.
Solve d/(d + 61) = 0.34893: d = 0.34893d + 21.285, so 0.65107d = 21.285 and d = 32.69.
Any score of 32.7 or below triggers the floor. The stated margin is ±3 points around 34, so the floor outcome sits inside the error band.
Worth flagging: if the floor binds at £2.115m for X, Y takes the residual £4.20m − £2.115m = £2.085m, which is more than the formula gave it. The clause can help the borough it was not designed for.
3. Should the finance lead sign today? Support the answer with the size of the data risk.
Read the worked answer
Test the error band. At score 37: X share = 0.364 + 0.4(37/98) = 0.51502 → £2.163m. At score 31: 0.364 + 0.4(31/92) = 0.49878 → £2.095m, below the floor, so the clause binds.
So the plausible range for X is roughly £2.095m–£2.163m, a swing of about ±£34,000 - more than twice the £15,000 margin that currently separates X from its floor.
The settlement letter would lock in a figure the data cannot yet support. Judgement: sign only with a written reservation making the amount provisional pending the outstanding ward return, re-run the formula within 30 days, and adjust next cycle; if the letter can wait 48 hours, wait. Do not present £2.130m to either borough as final.