💰 DCF Valuation (Discounted Cash Flow)

Definition: DCF is a valuation method that estimates the value of an investment by discounting future free cash flows back to the present using an appropriate discount rate (WACC).

Heavily covered at: Wharton · Booth · Columbia · HBS Finance II

🔑 The Core Idea

A company is worth the present value of all future free cash flows it will ever generate.

$Enterprise Value = \sum_{t = 1}^{n} \frac{FCF F _{t}}{( 1 + W A CC ) ^{t}} + \frac{T V}{( 1 + W A CC ) ^{n}}$

Where:

FCFF = Free Cash Flow to the Firm
WACC = Weighted Average Cost of Capital
TV = Terminal Value
n = explicit forecast period (typically 5–10 years)

📐 Step-by-Step DCF Process

Step 1: Project Free Cash Flows

$FCFF = EB I T (1 - T) + D & A - C a pE x - Δ N W C$

Component	Meaning
EBIT(1-T)	NOPAT — operating profit after tax
+ D&A	Add back non-cash charges
− CapEx	Capital expenditure (maintenance + growth)
− ΔNWC	Change in Net Working Capital

Forecast period: Typically 5–10 years; beyond that, use a Terminal Value.

Step 2: Calculate WACC

→ See WACC for full calculation

$W A CC = \frac{E}{V} \cdot r_{e} + \frac{D}{V} \cdot r_{d} (1 - T)$

Step 3: Calculate Terminal Value

Gordon Growth Model (most common): $T V = \frac{FCF F _{n} \times ( 1 + g )}{W A CC - g}$

Exit Multiple Method: $T V = EB I T D A_{n} \times Exit Multiple$

💡 A common mistake: TV often represents 60–80% of total value in growth companies. Your terminal value assumption matters enormously.

Step 4: Discount Everything Back

$E V = \sum \frac{FCF F _{t}}{( 1 + W A CC ) ^{t}} + \frac{T V}{( 1 + W A CC ) ^{n}}$

Step 5: Bridge to Equity Value

$Equity Value = E V - Net Debt$ $Share Price = \frac{Equity Value}{Shares Outstanding}$

🎯 DCF Sensitivity Analysis

Never present a single DCF number. Always run a sensitivity table:

	WACC 8%	WACC 10%	WACC 12%
g = 2%	$120	$95	$78
g = 3%	$145	$110	$88
g = 4%	$185	$132	$102

⚠️ DCF Pitfalls & Limitations

Pitfall	Why It Matters
Garbage in, garbage out	Revenue assumptions drive everything
Terminal value dominance	60-80% of value may sit in TV
WACC precision illusion	Small changes in WACC = huge EV swings
Ignores real options	Flexibility has value not captured
Circular reference risk	Debt affects WACC which affects value

Damodaran’s wisdom: “A DCF is only as good as the story behind it.”

🔄 DCF vs. Other Valuation Methods

Method	Pros	Cons
DCF	Intrinsic value, not market-dependent	Highly sensitive to assumptions
Comparable Companies	Market-grounded	Requires truly comparable peers
Precedent Transactions	Includes control premium	Historical data may be stale
LBO	Sets a price floor	Only relevant if buyable

In practice, bankers use all three and triangulate.

📊 Real Example: Simple DCF

Assume a company with:

Year 1-5 FCFF growing from $100 Mt o$ 146M (8%/year)
WACC = 10%
Terminal growth = 3%

Year	FCFF	Discount Factor	PV
1	100	0.909	90.9
2	108	0.826	89.2
3	116.6	0.751	87.6
4	125.9	0.683	86.0
5	136.0	0.621	84.1
TV	1,997	0.621	1,240
EV			$1,677.8M

💻 Practitioner Python Implementation

import numpy as np
 
def run_dcf(fcff_list, wacc, terminal_growth):
    """Runs a standard 5-year DCF using the Gordon Growth Model"""
    # 1. Discount explicit cash flows
    discount_factors = [(1 + wacc)**t for t in range(1, len(fcff_list) + 1)]
    pv_fcff = sum(fcff / df for fcff, df in zip(fcff_list, discount_factors))
    
    # 2. Calculate Terminal Value
    final_fcff = fcff_list[-1]
    terminal_value = (final_fcff * (1 + terminal_growth)) / (wacc - terminal_growth)
    
    # 3. Discount Terminal Value
    pv_tv = terminal_value / discount_factors[-1]
    
    # 4. Enterprise Value
    enterprise_value = pv_fcff + pv_tv
    return enterprise_value, pv_fcff, pv_tv
 
# Scenario: $100M base FCF growing at 8% for 5 years
fcf = [100.0, 108.0, 116.6, 125.9, 136.0]
wacc = 0.10
g = 0.03
 
ev, pv_fcf, pv_tv = run_dcf(fcf, wacc, g)
print(f"PV of Cash Flows: ${pv_fcf:.1f}M")
print(f"PV of Terminal Value: ${pv_tv:.1f}M ({(pv_tv/ev):.1%} of Total)")
print(f"Total Enterprise Value: ${ev:.1f}M")

🎯 When Would I Use This?

Investment Banking Pitch Book: “We need to present a rigorous intrinsic valuation of the target company to prove to the board that $50/share is a fair takeover premium.”
Internal Project Finance: “Should we build a new $500M factory? I will run a DCF on the projected cash flows to ensure the NPV is positive.”
Value Investing Buy-Side: “The market has panicked and dumped this stock. My DCF model indicates the intrinsic value is 40% higher than the current trading price.”

🔗 Connected Concepts

Time Value of Money — the mathematical foundation
WACC — the discount rate input
CAPM — how to compute cost of equity for WACC
Comparable Company Analysis — market-based alternative
LBO Model — PE-specific valuation
Terminal Value — the most sensitive assumption

🏫 School Context

Wharton (FNCE 236): Extremely rigorous DCF with full sensitivity frameworks
Columbia: Value Investing program uses DCF with heavy margin of safety cushions (Graham tradition)
HBS: Taught via cases; emphasis on judgment in assumptions, not mechanics
Booth: DCF linked to efficient market debate — when does intrinsic value diverge from price?

← 📊 Finance MOC | Related: WACC · Comparable Company Analysis · LBO Model

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