intrinsic-valuation-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):

Year	After-tax EBIT	Reinvestment	FCFF	PV Factor (9%)	PV of FCFF
1	$420.0M	$210.0M	$210.0M	0.9174	$192.7M
2	$470.4M	$235.2M	$235.2M	0.8417	$198.0M
3	$526.8M	$263.4M	$263.4M	0.7722	$203.4M
4	$590.1M	$295.0M	$295.0M	0.7084	$208.9M
5	$660.9M	$330.4M	$330.4M	0.6499	$214.8M

4. 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

5. Firm value = $1,017.8M + $5,631M = $6,649M

6. 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

7. Sensitivity grid (per-share value):

WACC \ Growth	2.0%	2.5%	3.0%	3.5%	4.0%
7.5%	$62	$68	$76	$86	$99
8.0%	$53	$57	$62	$69	$78
8.5%	$45	$48	$52	$57	$63
9.0%	$39	$41	$44	$48	$52
9.5%	$34	$36	$38	$41	$44

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:

Situation	Model	Discount Rate	Result
Most companies, changing capital structure	FCFF	WACC	Firm value (bridge to equity)
Stable capital structure, predictable debt	FCFE	Cost of equity	Equity value
Mature dividend payers	DDM	Cost of equity	Equity value per share
Financial services	FCFE or DDM	Cost of equity	Equity value
Long growth runway, transition needed	Three-stage	WACC or ke	Depends on variant

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