Fuller-Hsia H-Model Dividend Discount Lab
Simulate two-stage equity valuation with linear growth fade, terminal value, implied cost of equity, and discrete DCF cash flow schedules.
Model Parameters & Assumptions
Fuller-Hsia Mathematical Foundation
The Fuller-Hsia (1984) closed-form valuation equation decomposes equity value into a mature perpetual annuity plus a linear growth premium:
- Stable Value: V_stable = [D₀·(1 + gₙ)] / (r - gₙ)
- Growth Premium: V_growth = [D₀·H·(gₐ - gₙ)] / (r - gₙ)
- Implied Return: r_implied = (D₀ / P_mkt)·[(1 + gₙ) + H·(gₐ - gₙ)] + gₙ
- Implied Initial Growth: gₐ = gₙ + {[P_mkt·(r - gₙ) / D₀] - (1 + gₙ)} / H
Valuation Decomposition & Metrics
Fuller-Hsia Closed Form| Component | Value per Share ($) | % of Total Value | Analytical Explanation |
|---|---|---|---|
| Stable Perpetuity Base Value | $0.00 | 0.0% | Value if firm grew at perpetual rate gₙ immediately: D₀(1+gₙ)/(r-gₙ) |
| Competitive Advantage Growth Premium | $0.00 | 0.0% | Added value from temporary supernormal growth over 2H years: D₀·H·(gₐ-gₙ)/(r-gₙ) |
| Intrinsic Share Price (P₀) | $0.00 | 100.0% | Total intrinsic equity value under Fuller-Hsia theorem |
| Discrete Step-by-Step DCF Sum | $0.00 | 0.0% delta | Exact discounted sum of year-by-year decaying dividends + terminal value |
| Justified Trailing P/E (P₀ / EPS₀) | 0.0x | - | Based on user dividend payout ratio |
| Forward Dividend Yield (D₁ / P₀) | 0.0% | - | Expected cash yield in Year 1 at intrinsic valuation |
Growth Rate Fade & Dividend Trajectory (Glidepath)
The blue curve indicates linear growth decay from gₐ to gₙ across 2H years; bars depict nominal projected dividends ($/share).
Discrete Year-by-Year Dividend Cash Flow Schedule
Explicit DCF Table| Year (t) | Growth Rate (g_t) | Dividend (D_t) | Discount Factor | PV of Dividend | Cumulative PV |
|---|
Institutional Sensitivity Matrices
Matrix 1: Initial Growth (gₐ) vs. Long-Term Growth (gₙ) on P₀ ($)
Shows how intrinsic share price responds to differing initial fade rates and terminal growth expectations.
Matrix 2: Cost of Equity (r) vs. Transition Half-Life (H) on P₀ ($)
Evaluates valuation impact across discount rate hurdles and durability of competitive advantage.
H-Model & Equity Valuation Mastery Quiz
Understanding the Fuller-Hsia Framework
The Fuller-Hsia H-Model was published in 1984 by Russell J. Fuller and Chi-Cheng Hsia in the Financial Analysts Journal to resolve a major flaw in classical dividend discount modeling. Standard two-stage models assume that a company’s high-growth phase ends abruptly—growing at 20% in Year 5, then instantaneously collapsing to 4% in Year 6. In real-world competitive business environments, return on invested capital (ROIC) and growth rates fade gradually as patents expire, competitors replicate products, and industry capacity increases.
By parameterizing the growth transition through the half-life $H = ext{Duration} / 2$, the H-Model establishes a smooth, linear descent from the supernormal rate $g_a$ to the sustainable rate $g_n$. This yields an elegant, closed-form valuation formula that avoids multi-page DCF spreadsheets while maintaining high empirical accuracy.
Strategic Insights for Equity Research & Corporate Treasurers
- Decomposition of Value: Every stock's value can be separated into its baseline "boring" perpetuity value ($V_{ ext{stable}}$) and its temporary competitive moat ($V_{ ext{premium}}$). If growth premium accounts for >50% of share price, the equity is highly sensitive to competitive disruption.
- Reverse Engineering Market Expectations: Rather than arguing over what a stock is worth, analysts can invert the H-Model to determine what required return ($r$) or supernormal duration ($2H$) the market is currently pricing in.
- Gordon Growth Model Equivalence: When initial growth equals mature growth ($g_a = g_n$), the growth premium collapses to zero ($D_0 cdot H cdot 0 = 0$), reducing the H-Model perfectly back to the standard Gordon Growth Model $P_0 = D_1 / (r - g)$.