Estimated study time: 60 minutes
Content:
Discounted dividend valuation models estimate intrinsic stock value as the present value of all expected future dividends. The Gordon Growth Model (GGM), also called the Dividend Discount Model (DDM), is the simplest and most widely applied form: P0 = D1 / (r - g), where P0 is the current intrinsic value, D1 is the expected dividend one period from now (D0 * (1+g)), r is the required return on equity, and g is the constant perpetual growth rate. The model requires r > g to produce a finite positive value. At CFA Level 2, the single-stage GGM is extended to multi-stage DDMs for companies with non-constant growth, and candidates must apply these models under realistic scenarios where growth rates, required returns, and payout ratios change over time.
The required return on equity is typically estimated using the Capital Asset Pricing Model (CAPM): r = rf + beta*(rm - rf), where rf is the risk-free rate, beta is the stock's systematic risk, and (rm - rf) is the equity risk premium (ERP). At Level 2, candidates must understand that the ERP is not directly observable and must be estimated — approaches include using historical excess equity returns, a forward-looking implied ERP derived from current market prices and earnings/dividend forecasts, or survey-based estimates. The implied ERP solves: Index Level = Sum of present value of forecast dividends. Mature market equity risk premiums are typically estimated at 4-6%. Country risk premiums are added for emerging markets using sovereign yield spreads or volatility-based adjustments.
The sustainable growth rate is a critical input: g = ROE * b, where b = (1 - payout ratio) is the retention ratio. This formula shows that sustainable long-run dividend growth requires both profitability (ROE) and reinvestment (retention). A firm paying out 100% of earnings has b = 0 and g = 0, regardless of ROE. When using the GGM, the long-run growth rate must be reasonable relative to nominal GDP growth — stock price valuations with growth rates permanently exceeding the economy's nominal growth rate are mathematically unsustainable (the company would eventually become larger than the economy). In practice, long-run g is often assumed to converge to 3-5% for mature companies.
Multi-stage DDMs address companies with non-constant growth. The two-stage DDM projects dividends explicitly for a high-growth period (typically 3-7 years), then calculates a terminal value at the end of the explicit period using the GGM (P_n = D_{n+1} / (r - g_L)), and discounts both components to the present: P0 = Sum[D_t/(1+r)^t] + P_n/(1+r)^n. The H-model is a shortcut for companies with linearly declining growth from a short-term high rate (ga) to a long-term stable rate (gL) over a period 2H: P0 = D0*(1+gL)/(r-gL) + D0*H*(ga-gL)/(r-gL) = [D0/(r-gL)] * [(1+gL) + H*(ga-gL)]. The H-model adds a premium to the GGM price for the above-average growth during the transition period.
At Level 2, dividend model applications include: (1) estimating the implied required return given price and growth assumptions (solving for r in the DDM equation); (2) decomposing equity returns into dividend yield and capital gain components; (3) using spreadsheet models with explicit year-by-year dividend projections; and (4) applying the justified P/E and justified P/B ratios. The justified P/E = (D1/E1) / (r - g) = payout ratio / (r - g); the justified P/B = (ROE - g) / (r - g). These ratios connect fundamental value drivers (ROE, growth, payout) to observable market multiples, providing a framework for determining whether a stock is overvalued or undervalued relative to its justified multiples given current earnings quality.
Key Terms:
Quiz Questions:
Q1. Cascade Utilities pays a dividend of $2.00 per share. Dividends are expected to grow at 4% per year indefinitely. The risk-free rate is 3.5%, the equity risk premium is 5%, and the stock's beta is 0.7. What is the intrinsic value of Cascade Utilities using the Gordon Growth Model?
A) $2.00 / (0.07 - 0.04) = $66.67. B) $2.08 / (0.07 - 0.04) = $69.33. C) $2.08 / (0.035 + 0.05 - 0.04) = $46.22. D) $2.00 / (0.035 - 0.04) = negative (undefined).
Answer: B — Required return: r = rf + beta*(ERP) = 3.5% + 0.7 * 5% = 3.5% + 3.5% = 7.0%. D1 = D0 * (1+g) = $2.00 * 1.04 = $2.08. P0 = D1/(r-g) = $2.08 / (0.07 - 0.04) = $2.08 / 0.03 = $69.33. The model uses next period's dividend (D1), not the current dividend, because dividends are paid at end of period. A beta of 0.7 for a regulated utility reflects its low systematic risk relative to the market.
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Q2. TechVision Corp currently does not pay dividends (all earnings retained for growth). EPS is $5.00, ROE is 20%, required return is 12%, and growth is expected to remain at 15% for 5 years before declining to a stable 5% forever. Which statement best describes the DDM application to TechVision?
A) DDM cannot be applied because TechVision pays no dividends. B) DDM can be applied by modeling when TechVision will begin paying dividends and discounting future expected dividends; or alternatively, using a FCFE or residual income model better suited to non-dividend-paying growth companies. C) TechVision has no equity value because it doesn't pay dividends. D) The DDM gives TechVision an intrinsic value of $5.00 / 0.12 = $41.67.
Answer: B — The DDM technically can be applied to any stock by projecting dividends from the point at which the company begins distributing cash (when g declines to sustainable levels). However, for non-dividend-paying growth companies, this requires forecasting far into the future, amplifying uncertainty. Alternative valuation models — Free Cash Flow to Equity (FCFE) or Residual Income — are typically more tractable for such companies because they don't depend on the timing of dividend initiation. Analysts often use the DDM terminal value (when the company matures and begins paying dividends consistent with stable growth) and discount it back.
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Q3. DuraChem Corp has current EPS of $4.00, a payout ratio of 50%, and ROE of 15%. The required return is 10%. What is the justified trailing P/E ratio (P/E based on current EPS)?
A) Payout ratio / (r - g) = 0.50 / (0.10 - 0.075) = 20.0x (trailing P/E = payout * (1+g) / (r-g) adjustment needed). B) Justified P/E (leading) = Payout / (r - g). g = ROE * retention = 0.15 * 0.50 = 0.075. Justified leading P/E = 0.50 / (0.10 - 0.075) = 20x. Justified trailing P/E = 20x * (1+g) = 20x * 1.075 = 21.5x. C) Justified P/E = 1/r = 1/0.10 = 10x. D) Justified P/E = ROE / r = 0.15/0.10 = 1.5x.
Answer: B — Sustainable growth: g = ROE * (1 - payout) = 15% * 50% = 7.5%. Justified leading P/E (P/E1) = payout / (r - g) = 0.50 / (0.10 - 0.075) = 0.50 / 0.025 = 20x. Justified trailing P/E (P/E0) = justified leading P/E * (1 + g) = 20x * 1.075 = 21.5x (since trailing EPS is divided by (1+g) to get leading EPS, adjusting back gives trailing P/E that's (1+g) times the leading P/E). At the current $4.00 EPS, justified price = $4.00 * 21.5 = $86.00.
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Q4. An analyst applies the H-Model to Beacon Brands, which is expected to have an initial dividend growth rate of 18% that declines linearly to a stable 4% over the next 12 years (H = 6). The most recent dividend was $1.50 and the required return is 10%. What is Beacon's estimated intrinsic value?
A) P0 = $1.50 * (1.04) / (0.10 - 0.04) + $1.50 * 6 * (0.18 - 0.04) / (0.10 - 0.04) = $26.00 + $21.00 = $47.00. B) P0 = $1.50 / (0.10 - 0.18) = undefined (r < g). C) P0 = $1.50 * (1.18) / (0.10 - 0.04) = $29.50. D) P0 = $1.50 * 6 * (0.18 - 0.04) / (0.10 - 0.04) = $21.00 only.
Answer: A — H-Model formula: P0 = [D0 * (1 + gL) / (r - gL)] + [D0 * H * (ga - gL) / (r - gL)]. First component (stable growth value): $1.50 * 1.04 / 0.06 = $1.56 / 0.06 = $26.00. Second component (above-average growth premium): $1.50 * 6 * (0.18 - 0.04) / 0.06 = $1.50 * 6 * 0.14 / 0.06 = $1.26 / 0.06 = $21.00. Total P0 = $26.00 + $21.00 = $47.00. The H-Model captures the additional value from above-average growth during the transition period without requiring year-by-year projections.
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Q5. GlobalBank's stock is trading at $30. The most recent annual dividend was $1.20 and dividends are expected to grow at 6% per year indefinitely. What implied required return does the market appear to be using for this stock?
A) r = D1/P0 + g = (1.20 * 1.06) / 30 + 0.06 = 4.24% + 6% = 10.24%. B) r = D0/P0 + g = 1.20/30 + 0.06 = 4% + 6% = 10%. C) r = D1/P0 = 1.272/30 = 4.24% only (not adding growth). D) r = 6% (the growth rate equals the required return for a zero-value stock).
Answer: A — Solving the GGM for r: P0 = D1/(r-g), so r = D1/P0 + g. D1 = $1.20 * 1.06 = $1.272. r = $1.272/$30.00 + 0.06 = 4.24% + 6.00% = 10.24%. This is the market-implied required return — combining the current dividend yield (based on forward dividend) plus the expected capital gains return (growth rate). This approach is useful for reverse-engineering what return expectations are embedded in the current stock price, which can be compared to the CAPM-estimated required return to assess relative attractiveness.
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