---
id: "framework-cb-calculation"
type: "framework"
source_timestamps: ["Reel 31"]
tags: ["math", "valuation"]
related: ["concept-cagr-benchmark-cb", "action-calculate-cb", "entity-sp500"]
---
# Calculating the CAGR Benchmark (CB)

## Purpose

A mathematical process to determine whether a stock's embedded growth expectations are realistic compared to the [[entity-sp500]] baseline.

Full conceptual frame: [[concept-cagr-benchmark-cb]].

## Steps

1. **Establish the baseline.** The S&P 500 has a historical P/E of **27.4** and a CAGR of **10%**, yielding a **13.8-year payback period**.
2. **Find the target stock's current P/E ratio.**
3. **Set the target stock's payback period equal to 13.8 years.** This is the equivalence condition with the baseline.
4. **Solve algebraically for the required CAGR.** This is the annual growth rate the stock must sustain to justify its P/E.
5. **Assess realism.** Compare the required CAGR to the company's historical growth, industry growth, and TAM. Classify as fairly valued, under-valued, or "delusional."

## Worked Example

- Tesla P/E: 387
- Required CAGR to match 13.8-year payback: **45.3% per year for 13.8 consecutive years**
- Realism check: "delusional" — therefore overvalued by this framework.

## Actionable Use

Run this *before* any growth-stock purchase. See [[action-calculate-cb]].

## Caveats

Assumes constant discount rate, treats S&P P/E and CAGR as fixed, and ignores risk-adjustment. Best used as a *filter*, not a complete valuation.