Tools

Turnover Past a Registration Threshold

Crossing a registration threshold applies a charge to the whole of turnover rather than to the part above it. What does that first unit of turnover cost, and how far does the range run over which earning more leaves you with less?

A tax band charges you on the part above the line. A registration threshold charges you on everything, from the moment you cross it — so the unit of turnover that takes you over does not cost you the charge on that unit, it costs you the charge on the whole year. This page takes your own threshold and charge and says two things: how large that jump is, and how much further you would have to earn before you were back where you started.

What this tool does not decide

  • Whether to stay below the line. A business that stops growing to avoid a boundary has decided about customers it will not take and staff it will not hire, and none of that is in five numbers. Registration can also be worth something this page does not model.
  • What your threshold or charge is. This tool publishes neither, names no country, scheme, authority or adviser, fetches nothing and has no field to name one with. They are yours to enter, and that is why nothing on this page can go out of date.
  • How much you can really pass on or recover. Both are estimates with no answer to look up, and between them they decide the size of everything here. Run the page at both ends rather than guessing at the middle.
  • Whether the business works. Everything here is turnover retained: sales after the charge. It is not profit and not income, and no cost, wage, purchase or margin appears in it anywhere.
  • Anything about tax, in any jurisdiction.

Your figures

Your figures, in five numbers

The threshold and the charge are yours to enter and this page publishes neither. Registration schemes differ between countries, the thresholds move, and what can be recovered depends on what a business buys — a figure published here would be out of date before it was read and would only ever be right for one reader. Take the threshold and the charge from the authority or the adviser you are actually dealing with. Nothing you type is sent anywhere.

Sales over whatever window your threshold is measured on. There is no period in this arithmetic — a rolling twelve months and a tax year are the same calculation, as long as the turnover and the threshold are measured over the same one. Enter 0 if you have none yet.

The figure at which registration becomes compulsory. This page publishes none: take it from the authority or the adviser you are dealing with, because thresholds differ between countries and they move.

The rate registration applies to your turnover — 20 for twenty per cent. Enter it as the rate on the whole of turnover, not on the part above the threshold: the second is what a tax band does, and this is not one.

An estimate, and there is no right answer to look up. Enter 100 if your customers are themselves registered and will not care what your prices do, and 0 if you sell to consumers at a price the market fixes. Most businesses are somewhere between, and running this page at both ends brackets where you actually are.

What you can set against the charge you were yourself charged on what you buy. A business that buys very little relative to what it sells recovers very little; one that buys heavily recovers more. Enter 0 if none of it is recoverable. This share and the one above cannot add up to more than the whole charge.

Result

A registration threshold is not a tax band and it does not behave like one. A band applies its rate to the part above the line; a registration threshold applies its charge to the whole of your turnover the moment you cross it. So the unit of turnover that takes you over does not cost you the charge on that unit — it costs you the charge on everything you have already earned. That is why no marginal-rate reasoning gets the right answer here, and why there is a range above the threshold over which more work leaves you with less. This page publishes the size of that jump and the width of that range together, because either one on its own is half the story.

Enter your five figures above and select Calculate. Nothing is sent anywhere: the calculation runs in this browser, and no value is stored, shared or placed in the address bar.

The share of turnover you actually lose, after passing on and recovering
Not yet calculated
The liability the first unit over the threshold triggers
Not yet calculated
How wide the range is where earning more leaves you with less
Not yet calculated
The turnover at which you keep the threshold again
Not yet calculated
How much more turnover would take you out of it
Not yet calculated
What you keep at your own turnover
Not yet calculated
What you would have kept by stopping at the threshold
Not yet calculated
What the next unit of turnover keeps, away from the boundary
Not yet calculated

Every figure here is turnover retained: what is left of your sales after the charge, once what you can pass on to customers and what you can recover on your inputs are taken out of it. It is not profit and it is not income. Costs, wages, stock and everything else you spend are not in this arithmetic at all — the question it answers is what the boundary does to your top line, and that is a different question from whether the business works.

This is arithmetic on five numbers you supplied. It assumes the charge falls on the whole of turnover at a single point rather than phasing in over a band — some schemes taper instead, and a taper has no dead zone and is not this model with a different rate. It assumes the share you can pass on and the share you can recover both stay where you put them, which they will not: the price a market will bear changes with the price you ask, and what you can recover changes with what you buy.

A dead zone is not advice to stay out of it. A business that stops growing to stay below a boundary has made a decision about far more than one window of retained turnover — about customers it will not take, staff it will not hire, and a ceiling it has agreed to. None of that is in this arithmetic, and registration itself can carry advantages this page does not model. What is published here is the size of the step and the width of the range. What to do about them is not a question five numbers can answer.

How this is worked out

Why a threshold is not a tax band

Nearly everyone reasons about a registration threshold the way they reason about an income tax band, and the two behave completely differently. A band applies its rate to the partabove the line, so the first pound over costs you the rate on that pound.A registration threshold applies its charge to the whole of your turnover the moment you cross it. So the pound that takes you over does not cost you the charge on a pound. It costs you the charge on everything you had already earned.

Two boundaries, and one difference between them that everything else follows from: what the charge is applied to.
BoundaryCharge applies toThe first unit overShapeRange where more earns less
A tax bandTo the part above the line onlyCosts the rate on itself, and nothing moreThe slope changes; the value does not jumpNone. More is always more
A registration thresholdTo the whole of turnover, from the first unit overTriggers the charge on everything already earnedThe value jumps; the slope does not changeA range above the line where more leaves you with less

The three quantities that follow

The notch
The threshold multiplied by the share you actually bear. It is what the first unit over the line triggers, and it is charged on turnover you had already earned before you crossed
Break-even
The turnover at which what you keep is back to the threshold itself. Below it you are behind a business that stopped at the line; above it you are ahead
The dead zone
Break-even less the threshold. The width of the range over which the answer to "what does more work earn" is negative — and the only place on this site where that is true

The arithmetic

Write S for turnover, T for the threshold, c for the charge,p for the share you can pass on and k for the share you can recover. What you actually bear is e = c × (1 − p − k), and everything on this page is built from it:

R(S) = S                    for S < T
R(S) = S × (1 − e)          for S ≥ T

notch      = T × e          break-even = T ÷ (1 − e)          dead zone = T ÷ (1 − e) − T

Note where e is and is not. It multiplies S and notS − T, and that single difference is the whole mechanism. At a fifth of turnover borne in full, the dead zone is a quarter as wide as the threshold itself — which is a long way from an edge case.

The two shares are estimates, and they matter more than anything else here

Neither how much you can add to your prices nor how much you can recover has an answer you can look up, and between them they decide the size of everything on this page. A business selling to registered customers who will not notice a price change bears almost none of the charge; a business selling to consumers at a price the market fixes bears nearly all of it.Run this page at both ends rather than guessing at the middle: the two answers bracket where you actually are, and the width of that bracket is itself informative.

What you enter, and what this page will never enter for you

A turnover, a threshold, a charge and the two shares.This page publishes no threshold and names no jurisdiction. Registration schemes differ between countries, the thresholds move, and what is recoverable depends on what a business buys — a figure published here would be stale before it was read and would only ever be right for one reader. Because it holds no such fact, there is nothing on this page that can go out of date.

The limits this calculation imposes on itself

  • Turning over exactly the threshold counts as registered. That is a convention rather than a fact about any scheme, and it is why the dead zone starts at the threshold rather than just above it.
  • The share you can pass on and the share you can recover are held constant across every turnover on the page. Neither really is: the price a market bears changes with the price you ask, and what you can recover changes with what you buy.
  • Break-even is reported on exact equality rather than within a tolerance. Reporting a business as level while it is measurably behind is the one reading arithmetic about a shortfall must not produce.
  • Everything here is turnover retained. It is not profit and not income — no cost, wage, purchase or margin appears anywhere in it.
  • Nothing here is conditional on any jurisdiction, scheme, authority or adviser, and no figure below describes anybody’s actual rules.

What is not modelled

  • a scheme that phases the charge in over a band rather than applying it at a point
  • any flat-rate, cash-accounting or simplified alternative to the ordinary calculation
  • the cost of registering and complying — filings, software, advice and the time they take
  • anything a registration is worth: recovering charges on past purchases, or credibility with larger customers
  • your costs, wages, stock or margins, none of which appear in turnover retained
  • what happens if you register voluntarily before you reach the threshold
  • the window the threshold is measured over, whether it rolls or resets
  • penalties, interest or anything that follows registering late
  • the identity of any jurisdiction, scheme, authority or adviser
  • tax, in any jurisdiction

The mechanism behind the share you can pass on — what a margin contains, and how a price relates to a cost — is taught in the explainer:markup, gross margin and contribution margin.

Go deeper

  • The nearest published mechanism

    Markup, Gross Margin and Contribution Margin Explained

    Why the same price can be a 40% markup, a 28.57% gross margin and a lower contribution margin again — and why two reputable sources can report different margins for identical figures without either doing the arithmetic wrongly.

    The share of the charge you can add to your prices is the figure that decides most of what this page reports, and it is a statement about your own margins. The explainer is about what a margin contains and what it does not.

    Read the explainer: Markup, Gross Margin and Contribution Margin Explained

Calculation model and corrections

Calculation model
Registration Threshold Notch v1.0
Last reviewed
What the charge falls on
The whole of turnover, and not the part above the threshold. That is the mechanism, and it is why the first unit over the line carries a liability many times its own size
What you actually bear
The charge, less the share you can add to your prices and the share you can recover on your inputs. Every figure here is built from that one number rather than from the headline charge
The notch
The threshold multiplied by what you actually bear. It is a jump in the level rather than a change in a rate, which is why it has no equivalent as a percentage
The dead zone
From the threshold to the turnover at which you keep the threshold again. Over that range a business retains less than one that stopped at the line
Registered at exactly the threshold
Turning over exactly the threshold counts as registered. It is a convention rather than a fact about any scheme, and it is why the dead zone starts at the threshold rather than just above it
Break-even reported exactly
Reported on exact equality rather than on a tolerance. Reporting a business as level while it is measurably behind is the one reading arithmetic about a shortfall must not produce
The marginal rate and the notch
Two separate figures on purpose. Away from the boundary each extra unit keeps a constant share; at the boundary the value jumps, and a rate that tried to carry both would be a derivative of a function that has none there
Turnover retained
Sales after the charge. Not profit and not income: no cost, wage, purchase or margin appears anywhere in this arithmetic
The threshold and the charge
Yours. This page publishes neither, names no jurisdiction and has nowhere to put one. It therefore holds nothing that can go out of date
The unit
Unspecified, and the answer does not depend on it. Every amount is in the same unit and every share is invariant in it. There is no period either: turnover is over whatever window your threshold is measured on
Excluded
Tapered schemes, flat-rate and simplified alternatives, the cost of complying, anything registration is worth, and voluntary registration below the line
Rounding
Display only; intermediate values remain unrounded

Correction history

  • Generating the vector in which the charge is entirely neutralised produced an effective charge of minus one part in ten thousand million million, a notch of minus a trillionth, no break-even at all for the wrong reason, and a marginal retention rate fractionally above one. The cause is that one minus eight tenths minus two tenths is not zero in binary floating point. The share borne is now clamped at zero, and the clamp is recorded as a correction to representation rather than to arithmetic: the domain already guarantees the mathematical quantity cannot be negative.
  • Break-even was specified to be reported on exact equality rather than within a tolerance, and the two absences of a break-even were kept as one value rather than split into a fifth state. A charge that is entirely borne away leaves no notch to climb out of; a charge that takes everything leaves no turnover that ever retains the threshold again. Both report nothing, and which case a reader is in is a fact about the charge rather than about their position, so the share actually borne is what says so.