intrinsic-valuation-dcf（内在估值 DCF）

Intrinsic Valuation (DCF)

Table of Contents

• Example
• Workflow
• Common Patterns
• Guardrails
• Quick Reference

Example

Scenario: Two-stage FCFF model for a mature growth company

Inputs:

• Base year EBIT: $500M, Tax rate: 25%, CapEx: $200M, Depreciation: $150M, WC change: $20M
• High-growth period: 5 years, revenue growth 12%, reinvestment rate 50%, WACC 9%
• Stable period: perpetual growth 3%, reinvestment rate 30%, WACC 8.5%

Step-by-step:

1. Base year after-tax operating income: $500M x (1 - 0.25) = $375M
2. Base year FCFF: $375M - ($200M - $150M) - $20M = $305M
3. Year-by-year projections (high-growth, 12% growth, 50% reinvestment):

1. Terminal value (end of year 5):

- Stable FCFF = $660.9M x (1.03) x (1 - 0.30) = $476.5M - Terminal value = $476.5M / (0.085 - 0.03) = $8,663M - PV of terminal value = $8,663M x 0.6499 = $5,631M

1. Firm value = $1,017.8M + $5,631M = $6,649M
2. Equity bridge:

- Firm value: $6,649M - Minus debt: -$2,000M - Plus cash: +$500M - Minus employee options: -$200M - Equity value: $4,949M - Per share (100M shares): $49.49

1. Sensitivity grid (per-share value):

Workflow

Copy this checklist and track your progress:

DCF Valuation Progress:
- [ ] Step 1: Select DCF model variant
- [ ] Step 2: Establish base year cash flows
- [ ] Step 3: Estimate growth rate and high-growth period length
- [ ] Step 4: Project year-by-year cash flows
- [ ] Step 5: Compute terminal value
- [ ] Step 6: Discount, bridge to equity, compute per-share value
- [ ] Step 7: Build sensitivity analysis

Step 1: Select DCF model variant

Choose the model that matches the company and context. See resources/methodology.md for the full decision tree.

Quick selection guide:

• FCFF: Default for most companies. Values the entire firm, discounts at WACC, subtracts debt for equity. Use when capital structure is expected to change or when the company has significant debt.
• FCFE: Values equity directly, discounts at cost of equity. Use when capital structure is stable and debt ratio is predictable.
• DDM: Values equity via dividends, discounts at cost of equity. Use for mature, stable dividend-paying companies (utilities, REITs, mature banks).

Step 2: Establish base year cash flows

Start from cleaned financials (ideally from financial-statement-analyzer output). See resources/template.md for the base year input template.

For FCFF:

• After-tax operating income = EBIT x (1 - tax rate)
• FCFF = After-tax EBIT - (CapEx - Depreciation) - Change in non-cash working capital

For FCFE:

• FCFE = Net Income - (CapEx - Depreciation) - Change in WC + (New debt issued - Debt repaid)

For DDM:

• Current dividends per share, payout ratio, earnings per share

Step 3: Estimate growth rate and high-growth period length

See resources/methodology.md for growth estimation methods.

Three approaches to estimating growth:

• Fundamental: g = Reinvestment rate x Return on capital (for FCFF) or g = Retention ratio x ROE (for FCFE/DDM)
• Historical: Extrapolate recent growth with judgment about sustainability
• Analyst consensus: Use as cross-check, not primary source

High-growth period length depends on competitive advantage magnitude and sustainability (typically 5-10 years).

Step 4: Project year-by-year cash flows

Build the projection table for each year of the high-growth period. See resources/template.md for the projection template.

For each year, compute:

• Revenue (or operating income) based on growth rate
• Reinvestment (based on reinvestment rate or sales-to-capital ratio)
• Free cash flow = Income after tax - Reinvestment
• Present value factor = 1 / (1 + discount rate)^year
• Present value of cash flow

Step 5: Compute terminal value

See resources/methodology.md for terminal value approaches and constraints.

Growing perpetuity (preferred):

• Terminal value = CF in year n+1 / (discount rate - stable growth rate)
• Stable growth rate should not exceed the risk-free rate or nominal GDP growth
• Reinvestment rate in stable period: g / ROC (so growth is consistent with reinvestment)
• Cost of capital should converge toward mature company levels

Exit multiple cross-check (secondary):

• Apply industry EV/EBITDA or PE multiple to terminal year financials
• Compare to perpetuity-based terminal value for reasonableness

Step 6: Discount, bridge to equity, compute per-share value

See resources/template.md for the equity bridge template.

1. Sum PV of high-growth cash flows + PV of terminal value = Operating asset value
2. Add: Value of cash and non-operating assets
3. Subtract: Market value of debt (all debt included in WACC calculation)
4. Subtract: Value of employee stock options (use treasury stock method or Black-Scholes)
5. Subtract: Minority interests (at market value if available)
6. Divide by diluted share count = Per-share intrinsic value

Step 7: Build sensitivity analysis

See resources/template.md for the sensitivity grid template.

At minimum, vary:

• Stable growth rate (rows)
• Discount rate / WACC (columns)

Additional sensitivity dimensions to consider:

• Revenue growth rate in high-growth period
• Target operating margin
• Length of high-growth period
• Reinvestment rate

Validate using resources/evaluators/rubric_intrinsic_valuation_dcf.json. Minimum standard: Average score of 3.5 or higher.

Common Patterns

Pattern 1: FCFF Two-Stage (Most Common)

• When: Company with identifiable high-growth period followed by stable growth. Changing or uncertain capital structure. Most non-financial companies.
• Structure: Project FCFF for 5-10 years at above-normal growth, then terminal value at stable growth. Discount at WACC.
• Equity bridge: Firm value - Debt + Cash - Options = Equity value
• Key risk: Terminal value dominance. If terminal value exceeds 85% of total value, consider whether the high-growth period is too short or growth too low.

Pattern 2: FCFE Two-Stage

• When: Stable, predictable capital structure. Company manages to a target debt ratio. Financial services firms where FCFF is not meaningful.
• Structure: Project FCFE for high-growth period, then terminal value. Discount at cost of equity.
• Equity bridge: Not needed -- result is equity value directly. Subtract option value, divide by shares.
• Key risk: Debt ratio assumption. If actual debt policy deviates from assumption, value will be wrong.

Pattern 3: Dividend Discount Model (DDM)

• When: Mature, stable companies with long dividend track records. Utilities, REITs, mature banks, consumer staples.
• Structure: Project dividends per share, discount at cost of equity. Terminal value uses stable dividend growth.
• Equity bridge: Not needed -- result is per-share equity value.
• Key risk: Dividends may not reflect capacity to pay. If payout ratio is very low, DDM underestimates value. Consider augmented DDM (dividends + buybacks).

Pattern 4: Three-Stage Model

• When: Companies with long growth runways needing a transition period (young growth transitioning through mature growth to stable).
• Structure: Stage 1 (high growth, 5 years), Stage 2 (transition, growth declining linearly, 5 years), Stage 3 (stable perpetuity).
• Key risk: More parameters to estimate. Transition assumptions (how fast growth declines, when margins stabilize) add uncertainty.

Guardrails

1. Discounting consistency: Match cash flows to discount rates. FCFF at WACC, FCFE at cost of equity, dividends at cost of equity. Mixing them produces meaningless numbers.
2. Stable growth rate ceiling: The stable growth rate should not exceed the risk-free rate (for real cash flows) or nominal GDP growth (for nominal cash flows). A company cannot grow faster than the economy in perpetuity.
3. Terminal value proportion: Terminal value typically represents 50-80% of total value for growth firms. Flag if it exceeds 90% -- this may indicate that the high-growth assumptions are too conservative or the growth period too short.
4. Reinvestment-growth consistency: In the stable period, reinvestment rate should equal g / ROC. If stable growth is 3% and ROC is 10%, reinvestment rate should be 30%. Disconnect between growth and reinvestment implies value creation from thin air.
5. Equity bridge completeness: When using FCFF, bridge from firm value to equity by subtracting the market value of debt that was included in the cost of capital, adding cash and non-operating assets, and subtracting employee option value and minority interests.
6. Diluted share count: Use the diluted share count (treasury stock method for in-the-money options) rather than basic shares outstanding. For companies with large option grants, the difference is material.
7. Cost of capital convergence: In the stable period, beta should converge toward 1.0, debt ratio toward industry average, and WACC toward the weighted average of the market. A company cannot maintain an extremely high or low cost of capital in perpetuity.
8. Sensitivity analysis breadth: Vary at least the growth rate and discount rate. The interaction between these two drivers accounts for most of the valuation range. Report the value as a range, not a point estimate.

Common pitfalls:

• Projecting high growth for too long (10+ years is rare outside pharmaceutical or platform businesses)
• Using book value of debt instead of market value in the equity bridge
• Forgetting to subtract employee stock option value (material for tech companies)
• Double-counting growth: applying a high growth rate to income that already reflects growth spending
• Assuming current margins are sustainable without checking industry convergence
• Using the same WACC for both the high-growth and stable periods when capital structure is expected to change

Quick Reference

Key formulas:

FCFF = After-tax EBIT - (CapEx - Depreciation) - Change in Non-cash WC
     = After-tax EBIT x (1 - Reinvestment Rate)

FCFE = Net Income - (CapEx - Depreciation) - Change in WC + Net Debt Issued
     = Net Income x (1 - Equity Reinvestment Rate)

DDM = Dividends per Share (growing at g, discounted at ke)

Terminal Value (perpetuity) = CF(n+1) / (r - g_stable)

Growth (fundamental):
  g_operating_income = Reinvestment Rate x Return on Capital
  g_net_income = Retention Ratio x Return on Equity

Reinvestment Rate = (CapEx - Depreciation + Change in WC) / After-tax EBIT

Equity Bridge:
  Equity Value = Firm Value - Debt + Cash - Options - Minority Interests
  Per Share = Equity Value / Diluted Shares

Model selection quick guide:

Key resources:

• resources/template.md: Base year inputs, year-by-year projection table, terminal value template, equity bridge, sensitivity grid, value decomposition
• resources/methodology.md: Model selection decision tree, growth estimation methods, terminal value approaches, option adjustment, three-stage mechanics, mid-year convention
• resources/evaluators/rubric_intrinsic_valuation_dcf.json: Quality criteria for model selection, projections, terminal value, equity bridge, sensitivity analysis

Inputs required:

• Current after-tax operating income (FCFF) or net income (FCFE/DDM)
• Current CapEx, depreciation, and working capital change
• Revenue growth rate for high-growth period
• Target operating margin and reinvestment rate (or sales-to-capital ratio)
• Length of high-growth period (years)
• Stable growth rate
• WACC and/or cost of equity (from cost-of-capital-estimator)
• Current debt, cash, minority interests
• Shares outstanding and employee options (number, strike, maturity)

Outputs produced:

• dcf-valuation.md: Complete DCF model with year-by-year projections, terminal value, equity bridge, per-share value, sensitivity grid, value decomposition