bank-holiday-maths

---
name: bank-holiday-maths
description: Produces one dated decision file for a single bank holiday or peak trading day: the true cost of opening built from your own rota and your own contracts, the break-even number of covers or wet sales, the rest and holiday rules the rota has to satisfy, and a go or no-go trigger with the date you decide by. Use before you commit staff to a bank holiday, when you are being told everyone opens, or when last year's bank holiday felt busy and you still cannot say whether it paid.
---

# Work out whether opening actually pays before you open

You give this the date, your rota with hourly rates, your contracts or staff handbook wording on bank holidays, and your till history for comparable days. You get back one dated file: the fully loaded cost of opening including the rest days the rota forces you to give afterwards, the break-even covers figure, the revenue range your own tills support rather than a hoped-for number, and a written go or no-go trigger with a decision date. It will not tell you how many people will come through the door. It tells you how many need to, and what happens at each end of your own range.

## What it does

1. **Confirm the date is actually a bank holiday where you trade, and get it from the published list.** Bank holidays differ between England and Wales, Scotland and Northern Ireland, and the substitute days move. GOV.UK states the rule: "if a bank holiday is on a weekend, a 'substitute' weekday becomes a bank holiday, normally the following Monday." For England and Wales in 2027 that gives Friday 1 January, Good Friday 26 March, Easter Monday 29 March, Monday 3 May, Monday 31 May, Monday 30 August, then Christmas Day substitute Monday 27 December and Boxing Day substitute Tuesday 28 December. Write the date, the nation and the day of the week at the top of the file. A Friday bank holiday and a Monday bank holiday are different trading events with different neighbouring days, and a plan built on the wrong one is worthless.

2. **Read your own contracts before you assume anything about pay or leave, because the statutory position is the opposite of what most people believe.** GOV.UK is explicit that "Bank or public holidays do not have to be given as paid leave" and that "An employer can choose to include bank holidays as part of a worker's statutory annual leave." There is no automatic right to the day off and no automatic statutory right to extra pay for working it. What creates a right is the contract. So pull the actual wording from every contract and the staff handbook, and record per person whether bank holidays are included in their leave allowance, whether a premium rate applies, and whether a day in lieu is owed. Where the wording promises time and a half, that promise is a debt and it goes in the cost, whatever the statutory position says.

3. **Establish the statutory leave floor so that lieu days are costed rather than assumed.** Regulation 13 of the Working Time Regulations 1998 gives a worker "four weeks' annual leave in each leave year", and regulation 13A adds 1.6 weeks, with regulation 13A(3) capping the two together: "The aggregate entitlement provided for in paragraph (2) and regulation 13(1) is subject to a maximum of 28 days." That is the 5.6 weeks GOV.UK describes, and GOV.UK adds that "Statutory paid holiday entitlement is limited to 28 days". A day in lieu granted for a bank holiday worked either comes out of that entitlement or sits on top of it, and which one it is changes the cost of opening by a full day's wages per person. The contract decides, not custom.

4. **Build the rota twice: once at the statutory wage floor as a sanity check, once at what you actually pay.** From 1 April 2026 the National Minimum Wage and National Living Wage rates are £12.71 for workers aged 21 and over, £10.85 for 18 to 20, £8.00 for under 18 and £8.00 for the apprentice rate, and GOV.UK notes that "The rates change on 1 April every year." The floor run is not a plan, it is a check: if opening only breaks even at the statutory minimum, it does not break even, because your experienced staff are not on the minimum. Add employer National Insurance and pension contributions on top of gross pay before the number means anything, and take the actual rates from your own payroll rather than from a rule of thumb.

5. **Cost the rest the rota forces you to give afterwards, because it is a real cost on a different day.** GOV.UK sets out that "Workers have the right to one uninterrupted 20 minute rest break during their working day, if they work more than 6 hours a day", that "Workers have the right to 11 hours rest between working days", and that workers get either "an uninterrupted 24 hours without any work each week" or "an uninterrupted 48 hours without any work each fortnight". A long bank holiday shift finishing at one in the morning pushes the earliest lawful start on the following day to midday, which can remove a lunch service you were counting on. Cost that lost service on the bank holiday's ledger. It is caused by the decision to open and it is invisible if you only look at one day.

6. **Accrue holiday on every hour worked for irregular hours and part-year staff, at the published rate.** GOV.UK's reform guidance states that for leave years beginning on or after 1 April 2024 "Holiday entitlement for these workers will be calculated as 12.07% of actual hours worked in a pay period", and that the regulations "allow employers to use rolled-up holiday pay as an additional method for calculating holiday pay for irregular hour and part-year workers only". An irregular hours worker is defined as one whose paid hours in each pay period are "wholly or mostly variable" under the contract. Most bank holiday cover in hospitality is exactly this. Twelve extra hours of casual cover creates roughly one and a half hours of paid holiday, and a bank holiday plan that ignores it understates its own wage bill by about a twelfth.

7. **Build the revenue side as a range from your own tills, never as a single hopeful number.** Take at least three comparable days: the same bank holiday last year, the best equivalent weekend day in the last eight weeks, and an ordinary trading day of the same weekday. Record net of VAT, split wet and dry, and record covers and average spend separately so you can see which one moves. Then state a low, a central and a high figure, each traceable to one of those days. Where you have never opened on this day before, say so plainly and use the nearest equivalent with the difference named. A single forecast number is a wish. A range you can point at is a decision.

8. **Total the costs that exist only because you opened, and find the break-even.** Wages including employer on-costs and accrued holiday, lieu days, the lost service from step 5, extra stock ordered for the day and not otherwise needed, extra cleaning, extra waste collection, any door or entertainment cost, card and delivery commission on the incremental sales, and any premium supplier delivery. Then divide the total by your gross margin per cover, or per pound of wet sales if you are a bar, to get the break-even. Write it as one sentence: we need this many covers at this average spend to stand still. That sentence is the whole output and everybody on the team can hold it in their head.

9. **Write the decision as a trigger with a date and a name, then keep the file and mark it up afterwards.** State the go or no-go rule in advance: open if advance bookings reach a stated number by a stated date, otherwise open short hours or close. Name who decides and by when, because a decision left to the week of the holiday is a decision made by inertia. After the day, go back into the same file and write the actual covers, the actual wage cost and the actual take next to the forecast. That mark-up is the only thing that makes next year's version of this file worth more than this year's, and it takes twenty minutes while the numbers are still on the till.

## Then it checks

1. The date, the nation and the day of the week are stated, and the date appears on the published bank holiday list for that nation rather than being asserted.
2. Every person on the rota has a contract position recorded against them on bank holiday pay, lieu and whether bank holidays come out of their leave allowance, with no entry reading "as usual" or "the same as everyone else".
3. The wage cost includes employer National Insurance, pension contributions and accrued holiday, and the file says which rates were used and where they came from.
4. The rota satisfies the 20 minute break, the 11 hour daily rest and the weekly rest rules, and any service lost on the following day because of them is costed onto the bank holiday.
5. The revenue figures are a low, central and high range, each traceable to a named comparable day from the venue's own tills, with no figure sourced from outside the business.
6. The file states one break-even sentence with a number in it, a go or no-go trigger with a date and a named decider, and its own build date.

Any check fails: name it, redo that step once. Failed twice: say what is wrong and stop.

## Rules
- Public information only.
- Never invent a fact, a number or a quote.
- Anything sent in someone's name says whose name it is. A rota or a message to staff about bank holiday working goes out under the owner's or manager's name and goes to them first.
- Never state a typical bank holiday uplift, a sector average spend per head or an industry wage percentage for a single independent venue. No such published figure exists for one site, and an owner who opens on the strength of a borrowed uplift has borrowed somebody else's risk.
- Never tell a worker or an owner what a contract means. Quote the contract wording exactly and put the question to the owner's HR adviser or solicitor. Reading a bank holiday clause wrongly creates an unlawful deduction from wages claim, and it is not a question a document can settle.
- Refuse to produce a rota that breaches the rest rules, however it is asked for, and refuse to price a shift pattern that has not been checked against them. The correct output is the compliant rota plus a written note of the shifts that had to change, not the requested rota with a caveat.
- Never treat a day in lieu as free. It is a day of wages moved to another date and it belongs in the cost of opening.
- Never let the decision date slip past the point where staff can still be told. A go or no-go trigger with no date is not a trigger.
- This output is a working document prepared for the owner to check against their own contracts, payroll and till data before any commitment is made, and for their HR adviser, accountant or solicitor to check where it touches pay, leave or contractual entitlement. It applies published employment and wage rules to a trading decision; it is not employment advice and it does not settle what any contract means.

## Built from
- GOV.UK, "Holiday entitlement", https://www.gov.uk/holiday-entitlement-rights, no publication date shown on the page, read 16 September 2026: the 5.6 weeks entitlement, the 28 day cap, and the two statements in step 2 that bank holidays "do not have to be given as paid leave" and may be included in statutory annual leave.
- The Working Time Regulations 1998, regulation 13, https://www.legislation.gov.uk/uksi/1998/1833/regulation/13, read 16 September 2026: the four weeks' annual leave entitlement in step 3, and the note that the carryover provisions were amended with effect from 1 January 2024.
- The Working Time Regulations 1998, regulation 13A, https://www.legislation.gov.uk/uksi/1998/1833/regulation/13A, inserted with effect from 1 October 2007, read 16 September 2026: the additional 1.6 weeks and the 28 day aggregate cap quoted in step 3.
- GOV.UK, "UK bank holidays", https://www.gov.uk/bank-holidays, last updated 24 November 2025, read 16 September 2026: the 2027 England and Wales dates and the substitute day rule in step 1.
- GOV.UK, "National Minimum Wage and National Living Wage rates", https://www.gov.uk/national-minimum-wage-rates, no publication date shown on the page, read 16 September 2026: the rates applying from April 2026 and the annual 1 April change, used for the floor run in step 4.
- GOV.UK, "Rest breaks at work", https://www.gov.uk/rest-breaks-work, no publication date shown on the page, read 16 September 2026: the 20 minute break, the 11 hours between working days and the weekly rest entitlement that step 5 costs onto the following day.
- GOV.UK, "Holiday pay and entitlement reforms from 1 January 2024", https://www.gov.uk/government/publications/simplifying-holiday-entitlement-and-holiday-pay-calculations/holiday-pay-and-entitlement-reforms-from-1-january-2024, last updated 1 April 2024, read 16 September 2026: the irregular hours worker definition, the 12.07% accrual and rolled-up holiday pay, all in step 6.

# bank-holiday-maths

## You are given
One trading date for a UK hospitality business, with the nation and the day of the week already established from the published bank holiday list. The draft rota for that date and the two days either side, with, per person, their reference, age band, hourly rate, start time, finish time, unpaid break minutes, and their employment pattern already judged as exactly `fixed hours` or `irregular hours`. The contract position already read and judged by Claude for each person, as three fields: whether bank holidays come out of their statutory leave allowance, the premium multiplier that applies if any, and whether a day in lieu is owed. The employer National Insurance rate and pension contribution rate the owner's payroll actually applies. Till data for at least three comparable days, each labelled with its date, what makes it comparable, net of VAT revenue split wet and dry, cover count and average spend. The gross margin percentage the owner uses. A list of the incremental costs of opening with a cash figure and a description against each. And, where the owner has set one, the go or no-go trigger in their own words with its decision date and the named decider. Every judgement about what a contract means has already been made and supplied to you. You do not interpret a contract.

## Produce
Write into a `./bank-holiday-maths-output/` folder:

1. `rota-cost.csv` with these columns in this order: `person_ref`, `age_band`, `employment_pattern`, `shift_date`, `start_time`, `finish_time`, `unpaid_break_minutes`, `paid_hours`, `base_hourly_rate_gbp`, `premium_multiplier`, `gross_pay_gbp`, `employer_ni_gbp`, `employer_pension_gbp`, `accrued_holiday_hours`, `accrued_holiday_cost_gbp`, `total_cost_gbp`, `below_statutory_floor`. `age_band` is exactly one of `21 and over`, `18 to 20`, `under 18`, `apprentice`. `employment_pattern` is exactly one of `fixed hours`, `irregular hours`. `accrued_holiday_hours` is computed at 12.07% of paid hours for `irregular hours` rows only and is `0` for `fixed hours` rows. `below_statutory_floor` is `yes` where `base_hourly_rate_gbp` is below the supplied statutory rate for that age band.
2. `rest-rule-check.csv` with columns: `person_ref`, `shift_date`, `paid_hours`, `break_taken_minutes`, `break_rule_met`, `hours_rest_before_next_shift`, `eleven_hour_rest_met`, `rest_in_rolling_week_hours`, `weekly_rest_met`, `earliest_lawful_next_start`. Every person appears once per shift across the three days. Each `_met` column is `yes` or `no`. Every `no` is listed in `gaps.md`.
3. `knock-on-cost.csv` with columns: `person_ref`, `service_lost`, `service_date`, `reason`, `lost_gross_margin_gbp`, `lieu_day_owed`, `lieu_day_cost_gbp`. One row for every service that cannot run because of the rest rules or a lieu day. `lieu_day_owed` is `yes` or `no` and comes from the supplied contract position, never from inference.
4. `revenue-range.csv` with columns: `scenario`, `source_comparable_date`, `why_comparable`, `covers`, `average_spend_gbp`, `wet_revenue_net_gbp`, `dry_revenue_net_gbp`, `total_revenue_net_gbp`, `gross_margin_gbp`. `scenario` is exactly one of `low`, `central`, `high`. Exactly three rows. Every row names a real supplied comparable date.
5. `break-even.md` containing exactly four lines: the total cost of opening in GBP; the gross margin per cover used and where it came from; the break-even cover count at that margin; and the one sentence break-even statement in the form "we need N covers at £X average spend to stand still". Figures computed from the CSVs only.
6. `decision.md` containing the go or no-go trigger copied verbatim from the owner, the decision date, the named decider, and the three revenue scenarios with the surplus or shortfall against total cost beside each. Written empty apart from a note in `gaps.md` if no trigger was supplied.
7. `actuals.csv` with columns: `metric`, `forecast_value`, `actual_value`, `variance`, `recorded_on`. Created with the forecast column populated and the actual column empty, ready for the owner to complete after the day. Metrics are exactly: `covers`, `average_spend_gbp`, `total_revenue_net_gbp`, `total_wage_cost_gbp`, `total_cost_gbp`, `gross_margin_gbp`.
8. `gaps.md` as a numbered list of: any person with no contract position supplied on any of the three fields; any rest rule marked `no`; any rate below the statutory floor for that age band; any comparable day missing a cover count or an average spend; any incremental cost with no figure; a missing go or no-go trigger or decision date; and any figure that could not be computed because an input was missing.

## Rules
- Codex computes, checks and records. It never interprets a contract, never decides whether a premium or a lieu day is owed, never estimates how busy the day will be, and never writes a rota.
- Never infer a contract position. Where the three supplied contract fields are not all present for a person, leave the derived columns empty and list the person in `gaps.md`. An absent premium is not a premium of one.
- Never compute a revenue figure from anything other than the supplied comparable days. No sector average, no typical bank holiday uplift, no spend per head benchmark. No such figure exists for one independent venue and none is to be written into any file.
- Never mark a rest rule as met by rounding. Compute the gap between finish time and next start time in whole minutes and report it as found.
- Never produce a rota. Where the rest rule check fails, record the `earliest_lawful_next_start` and list the failure. Changing the shift is the owner's decision.
- Accrued holiday is computed at 12.07% of paid hours for irregular hours workers only, and never for fixed hours workers. Where the employment pattern was not supplied, leave it blank and list it in `gaps.md`.
- Employer National Insurance and pension are computed at the supplied rates only. Never substitute a published rate for a missing supplied one.
- Never send a rota, message a member of staff or write to payroll. These files are drafts for the owner.
- Use British English, GBP and DD Month YYYY dates. Times in 24 hour form. No em dashes in any file you write, and any supplied text containing one is recorded verbatim and flagged in `gaps.md`.
- Every file ends with this line: this is a working document prepared for the owner to check against their own contracts, payroll and till data before any commitment is made, and for their HR adviser, accountant or solicitor to check where it touches pay, leave or contractual entitlement. It is not employment advice and it does not settle what any contract means.

## Return
The absolute path of each file written, the row count of each CSV, the total cost of opening in GBP broken into wages, employer on-costs, accrued holiday, lieu days, knock-on lost margin and other incremental costs, the break-even cover count and the break-even sentence exactly as written, the surplus or shortfall under each of the low, central and high scenarios, the number of rest rule failures with the people and dates named, the number of people with an incomplete contract position, the number of rates below the statutory floor, the go or no-go trigger and its decision date exactly as supplied, and the `gaps.md` item count.