Worked example: Builder, 38, £45,000 of turnover
Picture a builder aged 38 for the 2026/27 tax year, trading as a sole trader with £45,000 of turnover. The optimisation goal for this profile is a balance of cash and pension contribution (modest pension preference, treating £1 of pension as £0.50 of cash for the search).
Running the engine for this exact profile:
- Taxable profits after the trading-allowance choice: £42,750
- Income tax: £6,036
- Class 4 NI: £1,811
- Class 2 (voluntary): £179
- Net cash: £34,724 (17.8% effective on turnover)
- Same turnover as a Ltd Co (no pension): £34,081 — a gap of £643 in favour of staying a sole trader
The vignette is hypothetical but the numbers are not — every figure above was produced by the same engine code that powers the live BracketMath calculators, run at build time on inputs drawn from a single CSV row.