4.3 Equity Valuation Models

Equity Valuation Models

Quick Summary: Equity valuation seeks to establish the intrinsic value of a company's shares to determine whether market pricing represents an overvaluation or undervaluation. Absolute models, such as the Dividend Discount Model (DDM) and Discounted Cash Flow (DCF), value equity based on the present value of expected future cash flows. Relative valuation employs market multiples such as Price-to-Earnings (P/E), PEG, Price-to-Book (P/B), and Enterprise Value to EBITDA (EV/EBITDA) to benchmark valuations across peers and historical cycles.

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1. Fundamentals of Equity Valuation: Intrinsic Value vs. Market Price

The central premise of fundamental equity analysis is that financial assets possess an intrinsic (fair) value grounded in their economic reality—their capacity to generate cash flows, their growth trajectory, and their risk profile:

• Market Price ($P_M$): The observable clearing price established by the interaction of buyers and sellers in secondary financial markets.
• Intrinsic Value ($P_0^*$): The present value of all future cash flows expected to accrue to the shareholder, discounted at an appropriate risk-adjusted rate of return.
• Investment Decision Framework:
  • If $P_0^* > P_M$: The security is undervalued (Buy / Overweight recommendation).
  • If $P_0^* < P_M$: The security is overvalued (Sell / Underweight recommendation).
  • If $P_0^* = P_M$: The security is fairly priced in accordance with the Efficient Market Hypothesis.
• Margin of Safety: Popularized by Benjamin Graham, wealth managers seek to invest when market price trades at a substantial discount to intrinsic value to provide a buffer against analytical errors or adverse business shocks.

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2. Dividend Discount Models (DDM)

Under the Dividend Discount Model, the fundamental value of an ordinary share equals the sum of all future dividends discounted to present value. From the perspective of a minority shareholder, dividends represent the only direct cash flow ever distributed by the company:

$P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1 + r)^t}$

Where $D_t$ is the dividend paid in year $t$, and $r$ is the investor's required rate of return (cost of equity), typically derived from the Capital Asset Pricing Model (CAPM): $r = R_f + \beta (R_m - R_f)$.

Model 1: The Zero-Growth Dividend Model (Perpetuity)

When a company pays a fixed, unchanging dividend indefinitely ($D_1 = D_2 = D_t$):

$P_0 = \frac{D}{r}$

• Application: Most commonly applied to preference shares with fixed dividends, or mature, highly regulated utilities with flat earnings distributions and near-zero reinvestment.

Model 2: The Gordon Growth Model (Constant Growth DDM)

Developed by Myron J. Gordon, this model assumes that dividends will grow indefinitely at a constant annual compound rate $g$:

$P_0 = \frac{D_1}{r - g} = \frac{D_0 (1 + g)}{r - g}$

Where:

• $P_0$ = Current intrinsic value per share
• $D_0$ = Most recent dividend just paid
• $D_1$ = Expected dividend over the next 12 months ($D_0 \times (1 + g)$)
• $r$ = Required rate of return on equity
• $g$ = Constant perpetual growth rate of dividends

The Non-Negotiable Mathematical Constraint: $r > g$

The Gordon Growth Model requires that the required return strictly exceeds the growth rate ($r > g$):

1. If $r = g$, the denominator is zero, yielding an impossible infinite valuation.
2. If $g > r$, the denominator becomes negative, producing a meaningless negative share price.
3. In economic terms, no corporate enterprise can sustain a growth rate higher than the long-term nominal growth rate of the broader economy indefinitely; if it did, the company would eventually become larger than the world economy.

Sustainable Growth Rate Derivation ($g$)

The fundamental growth rate $g$ is driven by how much profit the firm retains and the return it generates on that retained capital:

$g = b \times \text{ROE}$

Where:

• $b$ = Retention Ratio = $\frac{\text{Retained Earnings}}{\text{Net Income}} = 1 - \text{Dividend Payout Ratio}$
• $\text{ROE}$ = Return on Equity = $\frac{\text{Net Income}}{\text{Shareholders' Equity}}$

Worked Example: Gordon Growth Model

A company just paid an annual dividend of £0.80 per share ($D_0$). Its historical return on equity is 15%, and it retains 40% of its net earnings. The risk-free rate is 4%, the market risk premium is 5%, and the company has a beta of 1.2.

1. Calculate the Sustainable Growth Rate ($g$): $g = b \times \text{ROE} = 0.40 \times 15\% = 6.0\%$

2. Calculate the Required Return ($r$) via CAPM: $r = R_f + \beta (R_m - R_f) = 4\% + 1.2 \times 5\% = 4\% + 6\% = 10.0\%$

3. Calculate Expected Dividend ($D_1$): $D_1 = D_0 \times (1 + g) = £0.80 \times (1 + 0.06) = £0.848$

4. Calculate Intrinsic Share Value ($P_0$): $P_0 = \frac{D_1}{r - g} = \frac{£0.848}{0.10 - 0.06} = \frac{£0.848}{0.04} = £21.20$

Model 3: Multi-Stage Dividend Discount Models

Fast-growing companies rarely exhibit stable perpetual growth. Instead, they progress through lifecycle phases:

1. High-Growth Stage (Supernormal Phase): High dividend or earnings growth rate ($g_{\text{high}}$) sustained for a finite horizon of $n$ years.
2. Terminal Mature Stage (Stable Phase): Growth decelerates to a long-term sustainable rate ($g_{\text{terminal}}$) consistent with GDP expansion.

$\text{Valuation} = \sum_{t=1}^{n} \frac{D_t}{(1 + r)^t} + \frac{P_n}{(1 + r)^n} \quad \text{where } P_n = \frac{D_{n+1}}{r - g_{\text{terminal}}}$

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3. Relative Valuation Multiples

Relative valuation assesses what an asset is worth by comparing its market price against a standardized financial metric (earnings, book value, sales, or cash flow) relative to comparable peer companies.

Price-to-Earnings (P/E) Ratio

The P/E ratio is the most ubiquitous valuation multiple in global equity markets:

$\text{P/E Ratio} = \frac{\text{Market Price per Share}}{\text{Earnings per Share (EPS)}}$

• Trailing (Historic) P/E: Utilizes diluted EPS reported over the trailing 12 months (TTM). It reflects verified, audited financial results but is backward-looking.
• Forward (Prospective) P/E: Utilizes consensus estimated EPS for the upcoming 12-month fiscal period. It is forward-looking but vulnerable to analyst forecasting optimism.
• Analytical Role: P/E indicates how much investors are willing to pay for £1 of current or future corporate earnings. A higher P/E implies that the market expects superior future growth, lower risk, or higher quality earnings.

Price/Earnings-to-Growth (PEG) Ratio

The P/E ratio fails to account for differences in earnings growth rates between companies. The PEG ratio adjusts the P/E multiple by dividing it by the expected percentage annual earnings growth rate:

$\text{PEG Ratio} = \frac{\text{P/E Ratio}}{\text{Annual EPS Growth Rate (as a percentage number)}}$

Convention Note: In the PEG formula, growth is entered as a whole number (e.g., a 15% growth rate is entered as 15, not 0.15).

• PEG = 1.0: The standard benchmark for fair valuation (popularized by legendary fund manager Peter Lynch).
• PEG < 1.0: Suggests the stock may be undervalued relative to its growth potential (Growth at a Reasonable Price, or GARP).
• PEG > 1.0: Suggests the stock may be overvalued or carries a premium for exceptionally high quality or safety.

Price-to-Book (P/B) Ratio

$\text{Price-to-Book Ratio} = \frac{\text{Market Price per Share}}{\text{Book Value (Net Asset Value) per Share}}$

Where Book Value per Share equals $\frac{\text{Total Shareholders' Equity} - \text{Intangibles}}{\text{Total Ordinary Shares Outstanding}}$.

• Application: Essential for evaluating capital-intensive businesses and financial institutions (commercial banks, insurance companies, real estate investment trusts) whose balance sheet assets are marked close to market value.
• Limitations: Meaningless for modern asset-light service and software businesses whose most valuable assets (intellectual property, software code, brand equity) are expensed under accounting rules and omitted from balance sheet book equity.

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4. Enterprise Value (EV) Multiples

While equity multiples (like P/E and P/B) focus strictly on ordinary equity, Enterprise Value (EV) assesses the total operating value of the enterprise across all capital providers.

+-----------------------------------------------------------------------------------------+
|                         ENTERPRISE VALUE (EV) ANATOMY                                   |
+-----------------------------------------------------------------------------------------+
|                                                                                         |
|   ENTERPRISE VALUE (EV)  =  Market Capitalisation (Ordinary Equity)                     |
|                             + Total Debt (Short-Term & Long-Term)                       |
|                             + Preferred Stock                                           |
|                             + Minority / Non-Controlling Interest                       |
|                             - Cash & Cash Equivalents                                   |
|                                                                                         |
+-----------------------------------------------------------------------------------------+

• Economic Rationale: Enterprise Value represents the theoretical total takeover cost of an enterprise: an acquirer must buy all equity, assume all outstanding debt obligations, and can use the company's existing cash balances to offset acquisition costs.

EV/EBITDA Multiple

$\text{EV/EBITDA} = \frac{\text{Enterprise Value}}{\text{Operating Profit (EBIT)} + \text{Depreciation} + \text{Amortization}}$

EBITDA reflects pure pre-tax operating cash flow generated by corporate assets prior to capital structure financing decisions (interest) and capital asset accounting policies (depreciation).

Key Advantages of EV/EBITDA over the P/E Ratio

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5. Discounted Cash Flow Concepts: FCFF vs. FCFE

While accounting earnings are vulnerable to accrual manipulation and revenue recognition choices, cash flows represent hard economic liquidity:

1. Free Cash Flow to Firm (FCFF):

   • The cash flow generated by core business operations available to all providers of capital (both debt lenders and equity investors) after meeting operational expenses, working capital adjustments, and essential capital expenditures (capex).
   • Valued by discounting FCFF at the firm's Weighted Average Cost of Capital (WACC) to arrive at Enterprise Value.

2. Free Cash Flow to Equity (FCFE):

   • The residual cash flow remaining available strictly to ordinary shareholders after paying operating costs, financing capital expenditures, meeting all interest expenses, and accounting for net debt principal repayments.
   • Valued by discounting FCFE at the Cost of Equity ($r$) to arrive directly at Equity Intrinsic Value.