Arm's length range builder

Paste the margins from your comparable search, type the tested party margin, and this builds the range the way a study shows it: sorted sample, quartiles by interpolation, the interquartile range, and the distance to the nearer edge.

Transfer pricing Updates as you type Nothing is sent anywhere

The comparable set

Percentages, in whatever profit level indicator your study uses. Signs are respected, so a loss-making comparable goes in as a negative.

%

The same indicator, on the same basis, for the entity being tested.

Where the tested margin sits

Comparables in the set

Inside the interquartile range Inside the 35th to 65th percentile band
Minimum
Lower quartile
35th percentile
Median
65th percentile
Upper quartile
Maximum
Interquartile range, in points
Arithmetic mean
Full spread, in points
Distance to the range, in points
Adjustment to the nearer edge, in points
Adjustment to the median, in points

What a range is, and why the quartiles rather than the whole set

A comparable search never produces one number. It produces a scatter, and the arm's length principle accepts that a range of results can all be arm's length. The question is which part of the scatter to accept. Using the full range from minimum to maximum lets a single odd company set the boundary, so the convention is to narrow it — most commonly to the interquartile range, the middle half of the sample.

The quartiles here are computed by linear interpolation on the sorted sample, which is the method a spreadsheet's inclusive percentile function uses and the one most studies show their working in. The 35th to 65th percentile band is printed alongside it because some jurisdictions use that narrower band instead. Which one applies to you is a matter of local rules, not of statistics.

Reading the result, and the adjustment that follows

If the tested margin is inside the range, the range test produces no adjustment. That is not the same as saying the position is safe: the comparables themselves, the profit level indicator and the characterisation of the tested party are all still open, and they are what an audit usually attacks first.

If it is outside, the size of the adjustment depends on the rule. Some regimes adjust to the nearer edge of the range; others adjust to the median regardless of which side you fell out on. Both figures are printed, and the difference between them is often larger than the argument about the comparables.

Worked example

Ten comparables produce net cost plus margins from 2.1% to 8.6%. The tested entity, a captive service provider, returned 3.0%.

  1. Sorted, the sample gives a lower quartile just under 4% and an upper quartile just over 6%, with the median between them.
  2. 3.0% sits below the lower quartile, so the range test bites and the entity is outside.
  3. The adjustment to the nearer edge is under a point. The adjustment to the median is more than double that.

Delete the two lowest comparables and re-run it. The quartiles move, the tested margin may come inside, and you have just demonstrated why the comparable set is the real argument.

What this calculator assumes

  • Quartiles are computed by linear interpolation on the sorted sample — the inclusive percentile method. Some regimes and some software use an exclusive method and will differ slightly on small samples.
  • The 35th to 65th percentile band is shown because some jurisdictions require it rather than the interquartile range. This tool does not decide which applies to you.
  • Nothing here tests comparability. A sample that passes the arithmetic can still fail on functions, contractual terms, markets or accounting basis.
  • Multi-year averaging, working capital adjustments and accounting adjustments should be applied to the figures before they are pasted in.

An estimate, not advice. This is an estimate built from what you typed, not advice on your file. Nothing here reads your documents, checks your treaty article or looks at the year you are actually in. Where the number matters, we agree a fixed fee in writing before any work starts.

Where these figures come from

Any figure prefilled in the panel above is stated with the year it belongs to and can be changed. Rates and thresholds move; a calculator that asks you for the current one stays right, and one that hides a guess does not.

Files that look like this one

Case study 1

Leaving Canada — the Bill You Get for Assets You Still Own

Emigrating triggers a deemed disposition of most holdings, which produces tax on gains never realised in cash. The file values the property, identifies what is excluded, and looks at whether security can be posted rather than the tax paid outright.

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Case study 2

A Secondment Whose Paperwork Decided the Tax

Who employs, who directs and who bears the cost are the facts a treaty article turns on, and an assignment letter is where they are recorded. Drafting it with the tax position in view prevents an argument later.

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Case study 3

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Several jurisdictions require a locally resident director before a company can be registered or keep its filings current. The requirement is structural and is settled at incorporation rather than discovered at the first annual return.

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Case study 4

A Pricing Study That Started With Who Does What

Functions, assets and risks decide which entity should earn the return, and the method follows from that rather than the other way round. Getting the sequence backwards is how a study fails on its first question.

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Case study 5

Trips That Added Up to a Filing Obligation

Short visits are tracked against a treaty threshold that is measured over a moving window rather than a calendar year. Where the threshold is passed, the obligation reaches back over the whole period.

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Case study 6

A Foreign Affiliate Return Filed Years Late

The reporting obligation on a company held abroad runs separately from the corporate return and carries its own exposure. The work is reconstructing the surplus position across the open years before any filing goes in.

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Case study 7

Wintering in the US Long Enough to Become a US Filer

Days in the United States accumulate across three years, and enough of them make you a US resident for tax regardless of immigration status. The file counts the days properly and files the statement that keeps the position closer connection rather than residence.

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Case study 8

A US LLC Owned by a Canadian, Taxed Twice by Design

The two countries classify an LLC differently, so the credit relief that ought to apply frequently does not. The engagement looks at whether the structure can be changed, and where it cannot, at how to make the credit work.

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Frequently asked questions

The interquartile range is the usual convention, because it stops one unusual comparable setting the boundary. Some jurisdictions require a narrower band instead, and both are shown here so you can see the difference on your own set.
By linear interpolation on the sorted sample, which is what a spreadsheet's inclusive percentile function does. On small samples an exclusive method gives slightly different quartiles, so state which method your study used.
It depends on the regime. Some adjust to the nearer edge of the range, some to the median whichever edge you fell out of. Both figures are printed above because the gap between them can be substantial.
There is no universal minimum, but a very small set makes the quartiles unstable and invites an argument about whether a range exists at all. Add or remove one comparable here and watch how much the boundaries move.
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