400 random draws
How sure is the number? Eight in ten of four hundred re-runs land between $3.59M and $4.24M when the uncertain numbers are allowed to move as much as their evidence allows.
Why a range, and how it’s made
Some of your numbers are exact; some are estimates. Rather than pretend every number is exact, the engine reruns the whole valuation 400 times, each time nudging the uncertain numbers a little within how sure we are of them. Where most of the answers land is the range.
Sensitivity says how far the answer moves if an input is wrong. It doesn’t say how likely the input is to be wrong. The random draws do: each uncertain input is drawn from a spread set by how it was evidenced, the state weights shift, the de-listing prior varies, and the engine runs four hundred times with a fixed seed.
How to read it. Each bar counts how many of the 400 re-runs landed in that $100k band. The orange bar holds the concluded value. The dark bars are roughly the middle eight in ten; the pale ones are the tails.
How much each input is allowed to move
The better an input is evidenced, the less it moves. A figure tied to a document moves a little; an industry median moves a lot. That’s why documenting a number narrows the range, not just moves it.
Spread of each draw, one standard deviation, by how the input is evidenced.
| Input drawn | How it’s evidenced | Spread |
|---|---|---|
| Customer churn | Document-verified | ±2% |
| Service gross margin | Document-verified | ±2% |
| Overhead | Document-verified | ±2% |
| Price per seat | Document-verified | ±2% |
| Reported EBITDA | Document-verified | ±2% |
| Seat growth | From the statements | ±5% |
| Net revenue retention | From the statements | ±5% |
| Seat-price trend | Owner-stated | in points, around −1.5% |
What the range is not
The range is measurement error on the numbers you gave plus the states of the world. It is not a list of different beliefs. If you or a buyer believe a different discount rate or a different weight on the downside, that’s a judgment, and the report tests judgments separately, each re-run at three settings.
The draw, exactly
- Inputs drawn. churn, price trend, service gross margin, overhead, seat growth, net revenue retention, price per seat and reported EBITDA, where present
- Spread. one standard deviation of 2% for document- or third-party-verified inputs, 5% for owner-stated, computed or confirmed, 15% for inferences, 25% otherwise; the price trend moves in percentage points
- Generator. a seeded mulberry32 stream with Box–Muller normals; seed 517810
- States. the mid-case / bundle-compression weight shifts with a standard deviation of 5 points; the de-listing prior is drawn log-normal around 3%, between 0.5% and 50%
- Statistic. each run’s concluded value is kept; P10, P50 and P90 are read from the sorted 400
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