Stock Valuation — P/E, P/B, and Dividend Discount Models

1. What Is Stock Valuation?

Stock Valuation: Estimating a stock’s intrinsic value and comparing it to the current market price.

Intrinsic Value > Market Price → Undervalued (potential buy)
Intrinsic Value < Market Price → Overvalued (consider selling)

Valuation Approaches:

• Absolute Valuation: Discount future cash flows (DDM, DCF)
• Relative Valuation: Compare with peers (P/E, P/B, EV/EBITDA)
• Liquidation Value: Asset-based (net asset value)

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2. Dividend Discount Model (DDM)

DDM: A stock’s value equals the present value of all future dividends.

$$P_0 = \sum \frac{D_t}{1 + r_E}^t$$

• D_t: Dividend at time t
• r_E: Required return on equity

(1) Gordon Growth Model (Constant Growth DDM)

$$\begin{aligned} P_0 &= \frac{D_1}{r_E − g} \\ D_1: \text{Next year's dividend} &= D_0 \times \quad \text{(1 + g)} \\ &r_E: \text{Required return on equity} \\ &g: \text{Constant dividend growth rate} \quad \text{(requires r\_E > g)} \\ &\text{Example}: \\ D_0 &= \$2.00 | g = 5\% | r_E = 12\% \\ D_1 &= \$2.00 \times 1.05 = \$2.10 \\ P_0 &= \$\frac{2.10}{0.12 − 0.05} = \$\frac{2.10}{0.07} = \$30.00 \end{aligned}$$

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3. P/E Ratio (Price-to-Earnings)

P/E = Stock Price / Earnings Per Share (EPS)

Interpretation

• High P/E → Market is paying a premium for expected growth
• Low P/E → Shares are cheap relative to earnings (low growth or undervalued)

Application:

$$\begin{aligned} \text{Fair Value} &= EPS \times \text{Industry Average} \frac{P}{E} \\ \text{Example}: EPS &= \$3.00 | \text{Industry avg} \frac{P}{E} = 15 \\ \text{Fair Value} &= \$3.00 \times 15 = \$45.00 \end{aligned}$$

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4. P/B Ratio (Price-to-Book)

$$\begin{aligned} \frac{P}{B} &= \frac{\text{Stock Price}}{\text{Book Value Per Share}} (BVPS) \\ BVPS &= \frac{\text{Total Equity}}{\text{Shares Outstanding}} \\ &\frac{P}{B} < 1: \text{Price} < \text{Book Value} \to \text{Potentially deeply undervalued} (\text{or distressed}) \\ \frac{P}{B} &= 1: \text{Market accepts book value at face value} \\ &\frac{P}{B} > 1: \text{Market recognizes value beyond the balance sheet} (\text{brand}, \text{growth}) \end{aligned}$$

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5. EV/EBITDA

Enterprise Value (EV): Total value of the firm (market cap + net debt).

$$\begin{aligned} EV &= \text{Market Capitalization} + \text{Net Debt} (\text{Debt} − \text{Cash}) \\ \frac{EV}{EBITDA} &= \frac{\text{Enterprise Value}}{EBITDA} \\ EBITDA &= \text{Operating Income} + \text{Depreciation} + \text{Amortization} \end{aligned}$$

Advantage: Removes the distorting effects of capital structure, taxes, and depreciation methods — useful for comparing companies across industries.

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6. ROE and Growth Rate

$$\begin{aligned} ROE &= \frac{\text{Net Income}}{\text{Shareholders' Equity}} \\ \text{Sustainable Growth Rate} g &= ROE \times \text{Retention Ratio} \\ \text{Retention Ratio} &= 1 − \text{Dividend Payout Ratio} \\ &\text{Example}: \\ ROE &= 15\% | \text{Payout ratio} = 40\% \\ g &= 15\% \times (1 − 0.4) = 15\% \times 0.6 = 9\% \end{aligned}$$

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7. Key Concept Cards

Gordon Growth Model ★★★★★ : P₀ = D₁ / (r_E − g). Stock value equals next year’s dividend divided by (required return minus growth rate). Memory tip: P₀ = D₁ ÷ (r − g)

P/E Application ★★★★★ : Fair Value = EPS × Industry Average P/E. A quick relative valuation shortcut. Memory tip: Fair Value = EPS × Industry P/E

EV/EBITDA ★★★★☆ : Neutralizes capital structure, taxes, and D&A for clean peer comparison. Widely used in M&A analysis. Memory tip: EV/EBITDA = total firm value ÷ operating cash proxy

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8. Practice Quiz

Q. D₀ = $0.50, growth rate = 4%, required return = 10%. What is the intrinsic value?

D₁ = $0.50 × 1.04 = $0.52 P₀ = $0.52 / (0.10 − 0.04) = $0.52 / 0.06 ≈ $8.67

Q. A stock trades at $24 with EPS of $2. What is the P/E? If the industry average P/E is 15, is the stock over- or undervalued?

P/E = $24 / $2 = 12. Industry average is 15 → stock appears relatively undervalued.