> For the complete documentation index, see [llms.txt](https://matterhorn-doc.mometic.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://matterhorn-doc.mometic.com/understand-the-scores/compounding-and-emergence.md).

# Compounding and emergence

Read Matterhorn compounding-rate calculations, per-share dilution adjustments, emergence scores, durability evidence, and market-size headroom.

**Compounding** asks what could allow a business to become more valuable per share over time. **Emergence** adds the question of how much opportunity might remain from today's starting point.

![Company Compounding tab showing filed growth inputs and the compounding-rate calculation](https://981865776-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FNOJXLd7UJBniObM136Nu%2Fuploads%2Fgit-blob-6acc401fbe99271c306466f3eb407c63346853b7%2Fcompany-compounding.png?alt=media)

## Read the calculation's basis first

The capital-led framework is **return on invested capital × reinvestment rate**, with a per-share adjustment when supported. It connects what the business earns on capital to how much it puts back to work. The application distinguishes capital-led and R\&D-led businesses and can use a discounted multi-year-growth fallback where the preferred capital-return calculation is unavailable or unsuitable.

Check the stated fiscal year, basis, inputs, and fallback wording. A displayed rate is a model calculation over recorded financials. It is not proof that intrinsic value grew at exactly that rate, and it is not a forecast of the share price. A missing input or fallback can materially change the interpretation.

## Dilution matters to the holder

If the business grows 20% while shares increase 8%, the corresponding per-share change is approximately **1.20 / 1.08 − 1 = 11.1%**. Growth and shareholder participation are different questions. Confirm comparable share-count definitions, periods, splits, and business changes.

## Standard Emergence

The standard emergence score combines the compounding-rate assessment, durability, and headroom at **50%, 30%, and 20%**. It can be withheld when necessary inputs are not measurable. This is distinct from the [ML emergence percentile](/understand-the-scores/ml-enhanced.md).

## Headroom is a plausibility check

The application shows market value and the implied size at 10× or 100×. This helps challenge an unrealistic scale assumption. A business with limited 100× headroom can still produce an attractive investment outcome. Do not let a search for extraordinary multiples exclude a well-supported, more modest thesis.

“Years to 10×” is conditional arithmetic: **log(10) / log(1 + rate)**. The rate must persist for that many years for the illustration to hold. It does not incorporate every change in valuation, financing, or business conditions.

## Durability has more than one meaning here

The standard panel describes current evidence that could defend the compounding mechanism. The ML durability axis has a narrower operational definition: persistence of favorable margins and operating income over the next four reported quarters. Neither is a measurement of an invulnerable moat lasting decades.

> **Pro Tip — Give a high rate a mechanism.** Ask whether it is supported by repeat demand, attractive reinvestment, customer economics, and balance-sheet capacity. Extrapolation becomes more useful when you can explain what would sustain it and what would stop it.

Next: [forward-demand interpretation](/investigate-the-business/forward-demand.md), [emergence-to-durability playbook](/investor-playbooks/emergence-to-durability.md).