Three-Stage DCF: From Philosophy to Algorithm

Most DCF models are a lie.

Not because the math is wrong. The math is fine. Compound growth, present value, discount rates—Finance 101 works just fine.

The lie is this: they pretend the future is one straight line.

You've seen it. Some analyst takes a company growing at 25% CAGR, plugs that into a terminal value formula, and declares: "This company will grow at 25% forever." Or worse: "Perpetual growth rate = 3%"—as if every business eventually becomes a utility.

Here's what I learned after nearly 30 years: The future doesn't move in straight lines. It moves in phases.

High growth → moderation → maturity. Every company that survives long enough goes through this. And if your valuation model doesn't reflect that, you're not forecasting—you're fantasizing.

That's why the Allen Framework uses Three-Stage DCF. Not because it's trendy. Because it's true.

And today, I'm going to show you how it works—not just the philosophy, but the actual Python code we run at IVCO. Because theory without implementation is just noise.

TL;DR: Traditional DCF assumes constant perpetual growth—which is fiction. The Allen Framework splits future cash flows into three realistic stages: (1) high-conviction growth (5 years), (2) mean reversion (years 6-10), and (3) steady-state perpetuity. Combined with a three-tier calibration pipeline (Reality Coefficient → CAGR → Confidence Coefficient), you get an intrinsic value range, not false precision. This article walks through the philosophy, the code, and a full TSMC worked example.

The Problem with Single-Point DCF

Let me tell you what's wrong with most DCF models.

They give you a single number. Not a range. A number. "TSMC is worth NT$5,427 per share."

Really? Not NT$5,426? Not NT$5,428? You're telling me you can predict 10 years of geopolitical shifts, technology disruptions, management changes, competitive dynamics, and macro cycles—and land on a number precise to the ones digit?

That's not analysis. That's astrology.

And here's the second problem: they assume growth is linear.

Most models pick one growth rate—say, 20%—and apply it for 5 years. Then they slap on a "terminal value" using the Gordon Growth Model with some arbitrary perpetual rate like 3%.

But think about what that implies:

• Years 1-5: This company will grow at exactly 20%, every single year, regardless of market conditions.

• Year 6 onward: Growth instantly drops from 20% to 3% and stays there forever.

Does any business actually work that way? Of course not.

Growth moderates. It doesn't cliff-dive. A company expanding capacity aggressively might sustain 25% growth for a few years, slow to 15% as new capacity gets absorbed, and eventually settle into 5-8% mature-phase growth as the market saturates.

That's reality. Your DCF model should reflect it.

Three Stages, Three Realities

Here's how the Allen Framework thinks about the future.

Stage 1 (Years 1-5): High-Conviction Growth

This is where evidence matters most.

If a company is building 10 new fabs (like TSMC), acquiring a competitor (verified, not rumored), launching a new product line (already in production, not PowerPoint), or expanding into a new geography (contracts signed, not "exploring")—you have visibility.

You know what's coming. So you use an adjusted CAGR based on:

1. Historical CAGR (what the company has actually done)

2. Confidence Coefficient (how much conviction you have about the future)

This is the Allen Framework's three-tier calibration pipeline in action:

• Layer 1: Reality Coefficient corrects historical distortions

• Layer 2: CAGR calculation from calibrated data

• Layer 3: Confidence Coefficient adjusts for forward conviction

Formula: Adjusted CAGR = Historical OE CAGR × Confidence Coefficient

For TSMC (detailed in our case study):

• Historical CAGR: 17.66%

• Confidence Coefficient: 1.2x - 1.5x

• Stage 1 Adjusted CAGR: 21.19% - 26.49%

Stage 2 (Years 6-10): Mean Reversion

By year 6, reality starts catching up.

New capacity is absorbed. Competitors respond. Markets mature. The 25% growth story from Stage 1 isn't sustainable forever.

So we apply a moderate, company-specific CAGR—one that reflects "strong but slowing" growth. For TSMC, that's 15%. For a mature consumer goods company, it might be 8%. For a fast-growing SaaS business, maybe 18%.

This is not a guess. It's a parameter you set based on:

• Industry life cycle position

• Competitive moat durability

• Historical behavior of similar companies

• Management guidance (if credible)

The key insight: Stage 2 doesn't cliff-dive. It moderates gracefully.

Stage 3 (Year 11+): Perpetuity

By year 11, we're talking about a mature, steady-state business. Growth is low but sustainable. The company isn't dying—it's just not doubling every few years anymore.

We use the Gordon Growth Model here:

Where:

• CF_11 = cash flow in year 11 (end of Stage 2)

• r = discount rate

• g = perpetual growth rate (e.g., 5% for TSMC, maybe 3% for a utility)

This terminal value is then discounted back to present value by (1 + r)^11.

Why 5% for TSMC? Because semiconductors aren't going away. AI, EVs, IoT, edge computing—demand for leading-edge chips will exist for decades. But TSMC won't be building 10 fabs a year forever. 5% perpetual growth reflects "healthy mature expansion," not stagnation.

The Three-Tier Calibration Pipeline

Before we even get to the three-stage DCF, we need clean data. That's where the Allen Framework's calibration pipeline comes in.

Layer 1: Reality Coefficient

Question: Does this year's reported Owner Earnings reflect true operational capacity?

Method: Assign a percentage to each year's OE.

• 100%: Clean year, use as-is

• >100% (e.g., 125%): One-time loss that year → adjust upward

• <100% (e.g., 80%): One-time gain that year → adjust downward

Example: If 2015's OE was depressed by a lawsuit settlement, you multiply it by 125% to restore the true operational baseline.

Why this matters: If you calculate CAGR from distorted endpoints, your growth rate is garbage. Reality Coefficient ensures you're measuring real operational trajectory, not accounting noise.

Layer 2: CAGR Calculation

Once you have calibrated OE for each year, calculate the growth rate:

For TSMC (2013-2022):

• Start OE (calibrated): NT$286,681,851K

• End OE (calibrated): NT$1,239,030,648K

• Periods: 9 years

• CAGR: 17.66%

This isn't just "revenue growth." It's Owner Earnings growth—the cash actually available to shareholders after maintaining competitive position.

(See our first article for the deep dive on Owner Earnings vs Net Income.)

Layer 3: Confidence Coefficient

Question: How much conviction do I have that the company can sustain (or exceed) this historical CAGR?

Method: Multiply historical CAGR by a confidence multiplier based on evidence.

For TSMC: 1.2x - 1.5x (Steady tier)—because they have 100% management integrity, massive disclosed expansion plans, and technology leadership, but not a 3x moonshot bet.

Adjusted CAGR: 17.66% × 1.2 = 21.19% (lower) / 17.66% × 1.5 = 26.49% (upper)

Show Me the Code

Philosophy is nice. Code is truth.

Here's the actual Python implementation of the three-stage DCF engine from IVCO's open-source CLI tools. This isn't pseudocode—this is production.

The Core DCF Function

What's happening:

1. Stage 1 loop: Compound OE at stage1_cagr for 5 years, discount each year

2. Stage 2 loop: Continue from year 5's ending OE, compound at moderate stage2_cagr for 5 more years

3. Stage 3 (Gordon Growth): Calculate terminal value using year 11's cash flow, discount back to present

4. Sum all stages → total DCF

The Public API

Key design choices:

• Two DCF runs: One for CC lower bound, one for CC upper bound → produces a range

• Long-term debt subtracted: Enterprise value → equity value

• Per-share conversion: Divide by raw shares × par value (10 for Taiwan stocks)

• Returns full breakdown: Not just final IV, but year-by-year DCF contributions

This is the same code that powers ivco calc-iv at the command line. No black boxes.

TSMC: Running the Numbers

Let's run TSMC through the full pipeline. (Full breakdown in our case study—this is the highlight reel.)

Inputs

Output: Full DCF Breakdown (Lower Bound, CC = 1.2x)

Stage 1 CAGR: 17.66% × 1.2 = 21.19%

Stage 2 CAGR: 15% (moderate)

Stage 3 Terminal Value (Gordon Growth: 5% perpetual)

Upper Bound (CC = 1.5x)

Following identical logic with Stage 1 CAGR = 26.49%:

TSMC Intrinsic Value Range: NT$4,565 - NT$5,639

That's the answer. Not a single point. A range of conviction.

If TSMC trades at NT$600? Massive margin of safety—time to load up (assuming nothing fundamentally changed). At NT$5,000? Fair value. At NT$7,000? You're paying for optimism that hasn't been earned yet.

This is how IVCO thinks: Not "what's the price," but "what's the boundary of rational belief."

Why Three Stages, Not Two or Five?

Why not two?

Two-stage DCF (high growth → perpetuity) creates a cliff. Growth drops from 25% to 3% instantly. That's not how businesses work.

Why not five?

Diminishing returns. Adding more stages doesn't improve accuracy—it just adds more parameters to guess. Three stages hit the sweet spot:

1. Near-term (evidence-based)

2. Transition (moderation)

3. Maturity (steady-state)

This matches how companies actually evolve. It's the Goldilocks solution—not too simple, not too complex.