valuation-model

# Valuation Methodology

## Overview

Systematic corporate valuation framework covering absolute valuation (`DCF / DDM / SOTP`) and relative valuation (`PE / PB / EV-EBITDA`), including sensitivity-analysis methods and a checklist for identifying valuation traps.

## Absolute Valuation Methods

### 1. DCF (Discounted Cash Flow)

**Core formulas**:

```
Enterprise value = Σ FCF_t / (1+WACC)^t + TV / (1+WACC)^n
Equity value = enterprise value - net debt
Per-share value = equity value / total shares outstanding
```

**Detailed steps**:

#### Step 1: Forecast free cash flow (usually 5 years)

```
FCFF = EBIT × (1-tax rate) + depreciation & amortization - capex - increase in working capital

Simplified version:
FCFF ≈ operating cash flow - capex
```

| Year | Revenue (100m RMB) | EBIT (100m RMB) | FCFF (100m RMB) | Growth |
|------|---------|---------|---------|------|
| 2026E | 120 | 24 | 18 | +15% |
| 2027E | 138 | 28 | 21 | +15% |
| 2028E | 155 | 31 | 24 | +12% |
| 2029E | 170 | 34 | 26 | +10% |
| 2030E | 182 | 36 | 28 | +7% |

#### Step 2: Calculate WACC

```
WACC = E/(D+E) × Ke + D/(D+E) × Kd × (1-T)

Ke (cost of equity) = Rf + β × (Rm - Rf)
  - Rf: 10-year government bond yield (about 2.5% for China A-shares)
  - β: industry average or company beta (1.0-1.5)
  - Rm-Rf: equity risk premium (about 5-7% for China A-shares)

Kd: cost of debt (loan rate, about 4-5%)
T: income tax rate (25%)
```

**Reference WACC ranges for China A-shares**:

| Industry | WACC Range | Reference β |
|------|---------|------|
| Consumer | 8-10% | 0.8-1.0 |
| Technology | 10-13% | 1.2-1.5 |
| Financials | 7-9% | 1.0-1.2 |
| Cyclicals | 9-12% | 1.0-1.4 |
| Utilities | 6-8% | 0.5-0.8 |

#### Step 3: Terminal Value

```
Perpetual-growth method: TV = FCF_n × (1+g) / (WACC - g)
  - g: perpetual growth rate (usually 2-3%, should not exceed GDP growth)

Exit-multiple method: TV = EBITDA_n × EV/EBITDA multiple
  - Reference the industry average or historical median
```

#### Step 4: Sensitivity Analysis

```markdown
### DCF Sensitivity Analysis (per-share value, RMB)

| WACC \ g | 2.0% | 2.5% | 3.0% |
|----------|------|------|------|
| 9.0% | 32.5 | 35.8 | 40.2 |
| 9.5% | 28.3 | 30.8 | 34.0 |
| 10.0% | 24.8 | 26.7 | 29.1 |
| 10.5% | 22.0 | 23.5 | 25.3 |
| 11.0% | 19.6 | 20.8 | 22.2 |
```

### 2. DDM (Dividend Discount Model)

**Applicable to**: high-dividend stocks (banks, utilities, mature consumer companies).

```
Two-stage DDM:
P = Σ D_t / (1+Ke)^t + D_n × (1+g) / [(Ke-g) × (1+Ke)^n]

Gordon model (single stage):
P = D_1 / (Ke - g)
```

**Applicability checklist**:
- [x] Has paid dividends continuously for more than 3 years
- [x] Stable payout ratio (>30%)
- [x] Strong earnings predictability
- [ ] Usually not suitable for high-growth stocks (no dividends / low payout)

### 3. SOTP (Sum of the Parts)

**Applicable to**: diversified conglomerates.

```
Group value = Σ valuation of each business segment + net cash - holding-company discount

Example (a group company):
| Segment | Revenue (100m RMB) | Valuation Method | Valuation (100m RMB) |
|------|---------|---------|---------|
| Baijiu | 80 | 30x PE | 600 |
| Real estate | 50 | 0.6x PB | 120 |
| Financials | 30 | 1.0x PB | 200 |
| Total | | | 920 |
| Holding-company discount | | -15% | -138 |
| Group valuation | | | 782 |
```

## Relative Valuation Methods

### 1. PE Band

```
Historical PE percentile analysis:
- Take the past 5 years of PE_TTM time series
- Compute the 10% / 25% / 50% / 75% / 90% percentiles
- Judge overvaluation / undervaluation from the current PE percentile

| Percentile | PE | Implied Price | Interpretation |
|------|-----|---------|------|
| 90% | 35x | 52.5 | Severely overvalued |
| 75% | 28x | 42.0 | Rich |
| 50% | 22x | 33.0 | Fair |
| 25% | 16x | 24.0 | Cheap |
| 10% | 12x | 18.0 | Severely undervalued |
| Current | 18x | 27.0 | Cheap (30th percentile) |
```

### 2. PB-ROE Matrix

```
Theoretical relationship: PB = (ROE - g) / (Ke - g)
Practical use: plot companies in the industry on a PB vs ROE scatter chart

| Quadrant | PB | ROE | Interpretation |
|------|-----|-----|------|
| Lower right | Low PB | High ROE | Undervalued (best buy zone) |
| Upper right | High PB | High ROE | Fair (quality premium) |
| Lower left | Low PB | Low ROE | Value trap or distressed turnaround |
| Upper left | High PB | Low ROE | Overvalued (avoid) |
```

### 3. EV/EBITDA

```
EV = market cap + net debt (interest-bearing debt - cash)
EBITDA = operating profit + depreciation + amortization

Advantages:
- Removes capital-structure differences (vs PE)
- Removes depreciation-policy differences
- Suitable for asset-heavy industries (telecom / energy / infrastructure)

Reference EV/EBITDA ranges by China A-share industry:
| Industry | Median | Undervalued | Overvalued |
|------|--------|------|------|
| Consumer | 15-20x | <12x | >25x |
| Technology | 12-18x | <10x | >22x |
| Energy | 6-10x | <5x | >12x |
| Utilities | 8-12x | <6x | >15x |
```

## Valuation-Trap Detection

### Top 10 Valuation Traps

| # | Trap | Detection Method | Typical Example |
|---|------|---------|---------|
| 1 | Low-PE cyclical at the peak | PE is lowest when earnings are highest and about to fall | Coal at 5x PE in 2021 was the top |
| 2 | High-PE growth can be justified | `PEG < 1` means the growth rate supports the valuation | 30x PE + 40% growth = PEG 0.75 |
| 3 | Low-PB value destruction | Sustained `ROE < Ke` means shareholder value is being destroyed | Long-term loss-making asset-heavy company |
| 4 | Goodwill bomb | Goodwill / net assets >30% implies impairment risk | Underperforming acquisition after paying a high premium |
| 5 | Accounts-receivable trap | Rising receivables / revenue ratio = poor revenue quality | Government receivables + high customer concentration |
| 6 | Capitalization trap | Capitalizing R&D / interest flatters profit | PE doubles after true expensing |
| 7 | One-off gains | Large gap between recurring net profit and reported net profit | Asset sales / govern