APEX // MILP v2.6 UK Statutory Tax-Trap, Childcare Cliff & Salary Sacrifice Optimizer
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Deterministic Piecewise-Linear & MILP Solver // 2025/26–2026/27 Tax Year

Escape the £100,000–£125,140 62% / 69.5% Marginal Tax Trap & £100k Childcare Cliff

Standard UK salary calculators only compute forward deductions. This solver computes the exact Karush–Kuhn–Tucker (KKT) & Mixed-Integer Linear Programming (MILP) allocation across Employer Salary Sacrifice, Personal SIPP (with 20% HMRC top-up + Self-Assessment rebate), and 3% BiK EV Leasing to maximize total household net wealth.

ITA 2007 s.35 & s.58 (£100k PA Taper) SI 2015/522 (£100,000.00 Childcare Cliff) ITEPA 2003 s.308 (Salary Sacrifice) NIC Act 2025 (15% Employer NI Pass-Back) ITA 2007 s.192 (SIPP Relief at Source)
OPTIMAL TRAP-ESCAPE WEALTH GAIN
+£20,128 / yr
Sacrificing £4,500 gross (£1,710 net cash cost) brings ANI to £100,000, adding +£4,838 to your pension and restoring +£17,000 in childcare (**1,177.0% instant ROI**).
LOAD SCENARIO:
Unoptimized ANI & Marginal Rate
£104,500
Current Marginal Rate: 62.0%
Optimal Extra Sacrifice / SIPP
£4,500 / yr
Net Cash Cost: £1,710/yr (£143/mo)
Pension Gain + Childcare Saved
+£21,838
Pension: +£4,838 | Childcare: +£17,000
Instant Risk-Free Return on Cash
+1,177.0%
Target ANI: £100,000 (Full £12,570 PA)
2A. Statutory Marginal Tax Rate (METR %) Curve 62% / 69.5% Trap Zone

Red dashed line = Your Unoptimized Adjusted Net Income (ANI). Emerald line = Your MILP-Optimized Target ANI clearing the £100k–£125,140 taper & nursery cliff.

2B. Household Net Wealth Frontier vs. Extra Sacrifice Piecewise-Linear KKT Optimum

Plots Total Household Net Wealth (Take-Home Cash + Pension Pot + Childcare + Child Benefit) across extra pension contribution (£0 to Annual Allowance cap).

3. Statutory Execution Comparison Matrix (Annual GBP) Remaining Annual Allowance: £49,000
Metric / Statutory Line Item 1. Unoptimized Baseline 2. Targeted Salary Sacrifice (s.308) 3. Lump-Sum Personal SIPP (s.192) 4. Global Max Wealth (MILP Cap)
4. Parameterized Execution & Regulated Provider Routing FCA FSMA 2000 s.21 Generic Math Tool
5. Automated Payroll Salary Sacrifice Instruction (ITEPA 2003 s.308)