Learning Module 8
Equity Valuation: Concepts and Basic Tools
Key Outcomes Summary & Practice Problems
What you must be able to do
Curriculum Year: 2026
Evaluate whether a security is overvalued, fairly valued, or undervalued by comparing estimated value and market price.
Describe major categories of equity valuation models.
Describe regular cash dividends, extra dividends, stock dividends, stock splits, reverse stock splits, and share repurchases.
Describe dividend payment chronology.
Explain the rationale for present value models; describe the dividend discount and FCFE models.
Explain advantages and disadvantages of each category of valuation model.
Calculate intrinsic value of a non-callable, non-convertible preferred stock.
Calculate and interpret intrinsic value using the Gordon growth model or a two-stage DDM.
Identify characteristics of companies for which the Gordon growth or multistage DDM is appropriate.
Explain rationale for price multiples, how P/E relates to fundamentals, and use of comparables.
Calculate and interpret P/E, P/CF, P/S, and P/B multiples.
Describe enterprise value multiples and their use in estimating equity value.
Describe asset-based valuation models and their use in estimating equity value.
1 · Estimated Value vs Market Price
By comparing estimated intrinsic value with market price, an analyst concludes whether a security is undervalued, overvalued, or fairly valued.
Estimated Value > Market Price
Estimated Value ≈ Market Price
Estimated Value < Market Price
Confidence intervals: Analysts require a meaningful divergence before acting on an apparent mispricing.
Convergence: Ability to profit depends on market price converging to intrinsic value within the investment horizon.
Multiple models: Using several models and inputs increases confidence and reveals sensitivity of value estimates.
2 · Categories of Equity Valuation Models
Category | Description | Key Models / Multiples | Advantages | Disadvantages |
|---|---|---|---|---|
Present Value (DCF) | Value = PV of expected future benefits | DDM, FCFE, DCF | Intuitive, grounded in fundamentals | Requires forecasts; sensitive to inputs |
Multiplier (Market Multiple) | Value = multiple × fundamental variable | P/E, P/S, P/CF, P/B, EV/EBITDA | Easy to calculate, widely available | May not capture future; comparability issues |
Asset‑Based | Value = market value of assets − liabilities | Adjusted book value, liquidation value | Good for tangible‑asset companies | Difficult for intangibles; often a floor value |
Analyst best practice: Use more than one model type to increase confidence. The choice depends on data availability and the analyst's confidence in the inputs and model appropriateness.
3 · Dividends & Dividend Chronology
Regular cash dividend — paid at known intervals.
Extra / special dividend — non‑recurring supplement.
Stock dividend — additional shares instead of cash (no economic effect).
Stock split — increases shares, lowers price (no economic effect).
Reverse stock split — reduces shares, increases price (no economic effect).
Share repurchase — alternative to dividends; signals undervaluation, tax‑efficient.
Declaration date — board announces dividend.
Ex‑dividend date — first day shares trade without the dividend; price drops by dividend amount (all else equal).
Holder‑of‑record date — shareholder listed on company books receives dividend.
Payment date — dividend is actually paid.
4 · Dividend Discount Model (DDM) & FCFE
The DDM values a share as the present value of all expected future dividends. FCFE models use dividend‑paying capacity rather than actual dividends.
V₀ = Σ Dₜ / (1 + r)ᵗ (for t = 1 to ∞)
Dₜ = expected dividend in year t; r = required rate of return
FCFE = CFO − FCInv + Net borrowing
V₀ = Σ FCFEₜ / (1 + r)ᵗ
DDM advantages: Intuitive, based on cash flows to shareholders.
DDM disadvantages: Requires dividend forecasts; difficult for non‑dividend‑paying stocks.
FCFE advantages: Can value non‑dividend‑paying stocks; reflects dividend‑paying capacity.
FCFE disadvantages: Requires more detailed cash flow forecasting.
Required rate of return estimated using CAPM: r = Rf + β(Rm − Rf).
5 · Preferred Stock Valuation
V₀ = D₀ / r
Example: $5.50 dividend, 6% required return → $5.50 / 0.06 = $91.67
V₀ = Σ Dₜ / (1 + r)ᵗ + F / (1 + r)ⁿ
F = par value, n = years to maturity
Callable preferred: Lower value for investor (issuer can call when beneficial).
Putable/retractable preferred: Higher value for investor (floor on price).
Embedded options require more complex valuation; the curriculum covers only non‑callable, non‑convertible preferred.
6 · Gordon (Constant) Growth Model
V₀ = D₀ / r
Example: $5.50 dividend, 6% required return → $5.50 / 0.06 = $91.67
V₀ = D₀ / r
Example: $5.50 dividend, 6% required return → $5.50 / 0.06 = $91.67
D₀ = €3.70, g = 5.4%, r = 7.5% → V₀ = €3.70(1.054) / (0.075 − 0.054) = €185.70
Sensitivity table shows extreme sensitivity to r and g changes.
Gordon model is appropriate for: Dividend‑paying companies in mature growth phases, relatively insensitive to business cycles, with stable dividend growth (e.g., utilities, staple food producers).
Limitations: Cannot be used if g > r; assumes perpetual constant growth; not appropriate for non‑dividend stocks or high‑growth companies.
Alternatives: Multistage DDMs, FCFE models, or multiplier approaches.
7 · Multistage Dividend Discount Models
Used when a company has a period of non‑constant growth before settling into stable growth.
V₀ = Σ D₀(1+gS)ᵗ / (1+r)ᵗ + Vn / (1+r)ⁿ (for t=1 to n)
Vn = Dn+1 / (r − gL)
Dn+1 = D₀(1+gS)ⁿ(1+gL)
gS = short‑term high growth rate; gL = long‑term sustainable growth rate
D₀ = $6.21, gS = 5% (1 year), gL = 2.33%, r = 6.75%
D₂₀₁₉ = $6.5205, V₂₀₂₀ = $154.48 → V₂₀₁₈ = $147.52
Value Line report suggests IBM was fairly valued at ~$148.56.
Two‑stage DDM appropriate for: Companies transitioning from high growth to mature growth (e.g., IBM).
Three‑stage DDM appropriate for: Younger companies just entering the growth phase.
Growth rates can be estimated from historical dividend growth, industry medians, or the sustainable growth formula (g = b × ROE).
8 · Price Multiples & Comparables
Multiple | Formula | Key Considerations |
|---|---|---|
P/E | Price / EPS | Most common; justified P/E = payout ratio / (r − g) |
P/B | Price / Book Value per share | Useful for companies with tangible assets; value tilt |
P/S | Price / Sales per share | Useful for companies with negative earnings; stable |
P/CF | Price / Cash Flow per share | Less affected by accounting; uses operating or free cash flow |
P₀/E₁ = Dividend Payout Ratio / (r − g)
Derived from the Gordon growth model.
P/E ↑ with ↑ payout ratio, ↑ g; P/E ↓ with ↑ r
Method of Comparables: Assumes similar companies should trade at similar multiples. Benchmark multiple can be from an individual stock, industry average, or time‑series average. Must consider differences in growth, risk, and profitability.
Nestlé example: Justified forward P/E = 32.38 using p=68%, r=9%, g=6.9%. Highly sensitive to inputs — analysts must use sensitivity analysis.
Telefónica vs Deutsche Telekom: P/E, P/CF, P/S all suggest Telefónica is more attractively valued, but P/B is higher — investigating EBITDA multiples (EV/EBITDA) helps resolve contradictions.
Caution: Multiples may not be comparable across countries (different accounting standards) or across cyclical companies (earnings distorted by business cycle).
9 · Enterprise Value Multiples
EV = Market cap + Market value of preferred stock + Market value of debt − Cash & investments
EV represents the cost of a takeover — acquirer assumes debt but receives cash.
EV/EBITDA — proxy for operating cash flow; widely used in Europe.
EV/Operating Income — alternative when EBITDA is not available.
EV/Sales — for companies with negative earnings.
Advantages: EBITDA is usually positive even when earnings are negative; EV multiples are useful for comparing companies with different capital structures.
Disadvantages: Market value of debt may be difficult to obtain; book value of debt is a rough proxy.
Cameco example: Estimated market value of debt using yield curves and risk premiums; EV/EBITDA = 12.4.
Mining companies example: Norilsk Nickel and Barrick Gold had the lowest EV/OI, suggesting they were undervalued.
10 · Asset‑Based Valuation
Estimates equity value as the market value of assets minus the market value of liabilities.
Companies with high proportion of tangible assets (e.g., natural resources, financial institutions).
Private companies (where market prices are unavailable).
Companies being liquidated.
Provides a floor value for companies with significant intangibles.
Intangible assets are hard to value (brands, R&D, human capital).
Book values often differ significantly from market values.
Hyper‑inflation can distort asset values.
May give a "floor" but not capture going‑concern value.
Adjusted assets = Cash 5,000 + AR 15,000 + Inventory 30,000 + 1.1 × Net fixed assets 50,000 = 105,000
Liabilities = 3,000 + 17,000 + 25,000 = 45,000
Equity value = 105,000 − 45,000 = 60,000 (or $60/share for 1,000 shares)
Warren Buffett on book value vs intrinsic value: Book value is historical input; intrinsic value is the discounted value of future cash flows. A company with low book value can have high intrinsic value (e.g., a college education). Market value attempts to capture intrinsic value but may be inaccurate.