Ch7. Stock Valuation — P/E, P/B, and Dividend Discount Models

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)

Dividend Discount Model (DDM)

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

P_0 = Σ D_t / (1 + r_E)^t

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

Gordon Growth Model (Constant Growth DDM)

P_0 = D_1 / (r_E − g)

D_1: Next year's dividend = D_0 × (1 + g)
r_E: Required return on equity
g:   Constant dividend growth rate  (requires r_E > g)

Example:
D_0 = $2.00  |  g = 5%  |  r_E = 12%
D_1 = $2.00 × 1.05 = $2.10
P_0 = $2.10 / (0.12 − 0.05) = $2.10 / 0.07 = $30.00

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:

Fair Value = EPS × Industry Average P/E

Example: EPS = $3.00  |  Industry avg P/E = 15
Fair Value = $3.00 × 15 = $45.00

P/B Ratio (Price-to-Book)

P/B = Stock Price / Book Value Per Share (BVPS)

BVPS = Total Equity / Shares Outstanding

P/B < 1: Price < Book Value → Potentially deeply undervalued (or distressed)
P/B = 1: Market accepts book value at face value
P/B > 1: Market recognizes value beyond the balance sheet (brand, growth)

EV/EBITDA

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

EV = Market Capitalization + Net Debt (Debt − Cash)

EV/EBITDA = Enterprise Value / EBITDA

EBITDA = Operating Income + Depreciation + Amortization

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

ROE and Growth Rate

ROE = Net Income / Shareholders' Equity

Sustainable Growth Rate g = ROE × Retention Ratio
Retention Ratio = 1 − Dividend Payout Ratio

Example:
ROE = 15%  |  Payout ratio = 40%
g = 15% × (1 − 0.4) = 15% × 0.6 = 9%

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

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.

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