Dividend Discount Models: Gordon Growth, Two-Stage, and Three-Stage

Introduction

The dividend discount model is the oldest and most theoretically pure equity valuation methodology: a stock is worth the present value of all future dividends it will pay. While the standard unlevered DCF (which discounts UFCF at WACC to produce enterprise value) dominates most investment banking valuation work, the DDM is the preferred intrinsic method for a specific subset of companies: financial institutions and regulated utilities, where predictable dividends are the primary equity cash flow and where the standard DCF framework does not apply.

The simplest form of the DDM, published by Myron Gordon and Eli Shapiro in 1956, assumes dividends grow at a constant rate forever:

This formula is identical in structure to the perpetuity growth terminal value formula in a DCF, and it carries the same constraint: g must be less than r_e (otherwise the formula produces a negative or infinite value), and g should not exceed long-term GDP growth (2-3%) because no company can pay dividends that grow faster than the economy indefinitely.

Gordon Growth Model

A single-stage dividend discount model that values a stock as the present value of an infinite stream of dividends growing at a constant rate. The formula (V = D1 / (r - g)) is the equity equivalent of the perpetuity growth terminal value formula used in DCF analysis. It is most applicable to mature companies with stable dividend payout ratios and predictable growth, such as large banks and regulated utilities. The model's simplicity is both its strength (easy to apply and interpret) and its limitation (the constant growth assumption is unrealistic for companies whose growth rate is expected to change).

When the Gordon Growth Model Works

The single-stage DDM is appropriate when:

When It Fails

For companies experiencing high growth (which will eventually slow), transitioning between phases, or with irregular dividend histories, the single-stage model produces unreliable results because the constant growth assumption does not match reality.

The two-stage DDM relaxes the constant growth assumption by modeling two distinct phases:

Stage 1 (High Growth): Dividends grow at an above-average rate (g_1) for a specific number of years (n), reflecting a period of elevated growth or recovery.

Stage 2 (Stable Growth): After Stage 1, dividends grow at a sustainable long-term rate (g_2) forever. This is the terminal value phase, calculated using the Gordon Growth formula.

The two-stage model is useful for companies that are currently growing faster than their long-term sustainable rate (a bank that is expanding its loan book aggressively) or recovering from a temporary earnings depression (a utility rebuilding after a rate case reset).

The three-stage DDM adds a transition period between high growth and stable growth, creating a more realistic path:

Stage 1 (High Growth): Dividends grow at an elevated rate (g_1) for n_1 years.

Stage 2 (Transition): Growth gradually declines from g_1 to g_3 over n_2 years, reflecting the company's maturation.

Stage 3 (Stable Growth): Dividends grow at the sustainable long-term rate (g_3) forever.

The three-stage DDM is the most common variant used for bank valuation in investment banking. The three stages typically correspond to:

1. Development/growth stage: Explicit dividend projections for 3-5 years based on the bank's earnings forecast, capital plan, and target payout ratio 2. Maturity/convergence stage: ROE converges toward the cost of equity over 5-10 years as excess returns are competed away 3. Terminal stage: Stable growth at the long-term GDP growth rate, with the terminal value calculated using the Gordon Growth formula

Banks

Commercial banks are uniquely suited to DDM valuation because:

Dividend Payout Ratio

The percentage of net income (or earnings per share) that a company distributes as dividends to shareholders. Calculated as dividends per share / earnings per share. A payout ratio of 50% means the company distributes half its earnings and retains the other half for reinvestment and capital adequacy. For banks, the payout ratio is constrained by regulatory capital requirements: the Federal Reserve's stress tests (CCAR/DFAST) determine the maximum capital that banks can distribute. Banks typically target payout ratios of 35-50% (dividends only) or 60-80% (total capital return including buybacks). The payout ratio is a critical DDM input because it converts the earnings forecast into the dividend forecast: Dividends = Earnings x Payout Ratio.

- Regulatory capital constraints: Banks cannot freely reinvest all earnings; capital adequacy requirements (CET1 ratios, stress test buffers) cap how much capital the bank can retain, making the distributable cash flow (dividends + buybacks) the true equity return.

- Debt is operating: The standard unlevered DCF does not work because separating operating and financing cash flows is impossible when deposits and borrowings fund the core lending business.

Utilities

Regulated utilities are the other natural DDM candidate because:

The DDM is inappropriate for: