relative-valuation-multiples

What this skill does

# Relative Valuation Multiples

## Table of Contents
- [Example](#example)
- [Workflow](#workflow)
- [Common Patterns](#common-patterns)
- [Guardrails](#guardrails)
- [Quick Reference](#quick-reference)

## Example

**Scenario**: Technology company trading at PE 35x vs. sector median 25x. Is the premium justified?

**Step 1 -- Define**: PE = Market Price per Share / Earnings per Share (trailing twelve months, diluted). Equity multiple: numerator (equity market value) and denominator (net income to equity) go to the same claimholders.

**Step 2 -- Describe**: Sector distribution of 45 software firms: mean 28x, median 25x, 25th percentile 18x, 75th percentile 33x, standard deviation 12x. Target sits at approximately the 75th percentile.

**Step 3 -- Analyze**: The fundamental driver equation for PE is:

```
PE = Payout Ratio x (1 + g) / (ke - g)
```

Target has expected earnings growth of 20% vs. sector median 12%, and beta of 0.95 vs. sector 1.1 (lower risk). Higher growth and lower risk both justify a higher PE.

**Step 4 -- Apply via sector regression**:

```
Regression (n=45, R-squared=0.62):
  PE = 8.2 + 1.5 x (Expected Growth %) - 0.3 x (Beta)

Target predicted PE:
  = 8.2 + 1.5 x (20) - 0.3 x (0.95)
  = 8.2 + 30.0 - 0.285
  = 37.9x (call it ~38x)

Actual PE = 35x
Under/overvaluation = (35 - 38) / 38 = -7.9%
```

**Conclusion**: The regression predicts a PE of ~38x given the company's growth and risk profile. At 35x, the stock appears approximately 8% undervalued relative to sector peers after controlling for fundamentals. Relative valuation suggests it is cheap relative to peers, though this does not address whether the entire sector is fairly priced.

## Workflow

Copy this checklist and track your progress:

```
Relative Valuation Analysis Progress:
- [ ] Step 1: Select appropriate multiples for company type
- [ ] Step 2: Define multiples precisely (numerator, denominator, consistency)
- [ ] Step 3: Build comparable universe and describe distributions
- [ ] Step 4: Analyze fundamental drivers of each multiple
- [ ] Step 5: Apply via simple comparison and sector regression
- [ ] Step 6: Synthesize implied values and assess relative pricing
```

**Step 1: Select appropriate multiples for company type**

Choose multiples based on company characteristics: earnings-positive companies (PE, EV/EBITDA), capital-intensive or financial firms (PBV), negative-earnings or early-stage firms (EV/Sales). Use at least two multiples for triangulation. See [resources/methodology.md](resources/methodology.md#multiple-selection-guide) for the selection decision tree.

**Step 2: Define multiples precisely**

For each selected multiple, specify: numerator (equity value or enterprise value), denominator (which earnings/book measure, what time period), and verify consistency (equity multiples use equity-level metrics; firm multiples use firm-level metrics). See [resources/methodology.md](resources/methodology.md#step-1-define-the-multiple) for definitional tests.

**Step 3: Build comparable universe and describe distributions**

Identify peer companies sharing similar risk, growth, and cash flow characteristics. Compute the multiple for each peer. Report distribution statistics: mean, median, 25th and 75th percentiles, standard deviation, count. See [resources/template.md](resources/template.md#peer-comparison-table) for the comparison table and [resources/template.md](resources/template.md#distribution-analysis-template) for distribution analysis.

**Step 4: Analyze fundamental drivers**

Every multiple has a fundamental driver derived from DCF. PE is driven by growth, risk, and payout. PBV is driven by ROE, growth, and risk. EV/EBITDA is driven by tax rate, reinvestment, growth, and WACC. Connect the company's fundamentals to its multiple. See [resources/methodology.md](resources/methodology.md#step-3-analyze-the-multiple) for driver equations and derivations.

**Step 5: Apply via simple comparison and sector regression**

Two approaches: (a) Simple comparison -- compare target's multiple to peer median, adjust qualitatively for fundamental differences. (b) Sector regression -- regress the multiple against its fundamental drivers across the peer universe, plug in the target's values, and compute predicted multiple. See [resources/template.md](resources/template.md#sector-regression-template) for the regression template.

**Step 6: Synthesize implied values**

Convert predicted multiples to implied share prices or enterprise values. Compute under/overvaluation percentage. Compare results across multiples for consistency. Validate using [resources/evaluators/rubric_relative_valuation_multiples.json](resources/evaluators/rubric_relative_valuation_multiples.json). **Minimum standard**: Average score of 3.5 or above.

## Common Patterns

**Pattern 1: PE Ratio Analysis**
- **When**: Earnings-positive companies, cross-sector comparisons where earnings quality is comparable
- **Multiple**: PE = Price / EPS (use diluted, trailing twelve months for consistency)
- **Fundamental driver**: PE = Payout x (1+g) / (ke - g). Higher growth and lower risk justify higher PE
- **Regression variables**: Expected earnings growth rate, beta (or other risk proxy), payout ratio
- **Pitfall**: PE is undefined for negative-earnings firms. Cyclical earnings distort trailing PE; use normalized earnings

**Pattern 2: EV/EBITDA Analysis**
- **When**: Comparing firms with different capital structures or across tax jurisdictions. Good for capital-intensive industries
- **Multiple**: EV/EBITDA = (Market Cap + Debt - Cash) / EBITDA
- **Fundamental driver**: Driven by tax rate, depreciation-to-EBITDA ratio, reinvestment rate, WACC, and growth
- **Regression variables**: Expected revenue or EBITDA growth, tax rate, reinvestment rate, WACC
- **Pitfall**: EBITDA ignores capital expenditure differences. Firms with heavy capex relative to depreciation may look artificially cheap

**Pattern 3: PBV (Price-to-Book) Analysis**
- **When**: Financial services (banks, insurance), capital-intensive industries, or when earnings are volatile
- **Multiple**: PBV = Price / Book Value per Share
- **Fundamental driver**: PBV = (ROE - g) / (ke - g). Higher ROE relative to cost of equity justifies higher PBV
- **Regression variables**: ROE, expected growth in earnings, beta or cost of equity
- **Pitfall**: Book value depends on accounting conventions (historical cost vs. fair value). Cross-country comparisons require consistent accounting standards

**Pattern 4: EV/Sales (Revenue Multiple) Analysis**
- **When**: Early-stage companies, negative-earnings firms, or when comparing firms with very different margin structures
- **Multiple**: EV/Sales = (Market Cap + Debt - Cash) / Revenue
- **Fundamental driver**: EV/Sales = After-tax operating margin x (1 - Reinvestment Rate) x (1+g) / (WACC - g). Margin is the key driver
- **Regression variables**: Expected revenue growth, operating margin (or net margin), WACC
- **Pitfall**: A low EV/Sales multiple may simply reflect low margins, not undervaluation. Control for profitability differences

## Guardrails

1. **Numerator-denominator consistency**: Equity multiples (PE, PBV) use market value of equity in the numerator and equity-level metrics in the denominator. Firm multiples (EV/EBITDA, EV/Sales) use enterprise value in the numerator and firm-level metrics in the denominator. Mixing levels produces meaningless numbers.

2. **Comparable universe quality**: Comparable companies should share similar risk, growth, and cash flow characteristics. Same industry is a starting point, not a guarantee of comparability. A fast-growing SaaS firm is not comparable to a mature enterprise software firm just because both are "technology."

3. **Report distribution statistics**: Present mean, median, 25th and 75th percentiles, standard deviation, and count. Median is more robust than mean for skewed distributions (PE ratios are heavily right-skewed). Do not rely on the average alone.

4. **Regr