No-Growth DDM (Preferred Stock)
Special case of the dividend discount model with zero growth: a perpetual fixed dividend discounted at the required return. The right framework for preferred stock and any fixed-perpetuity income stream.
When to use: Use to value preferred stock with a fixed dividend, or as a sanity-check valuation for a stable common stock with effectively no growth in dividends. Equivalent to a perpetuity formula on the dividend.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| V0 | Intrinsic Value | Per-share intrinsic value implied by the model | $ |
| D0 | Current Dividend | Most recent annual dividend per share | $ |
| r | Required Return | Annual required rate of return as a decimal | % |
Real-Life Examples
Example 1: $5 Perpetual Preferred at 7%
A preferred stock pays $5 annually in perpetuity. Required return is 7%.
Given
Step-by-Step
Intrinsic value $71.43 — the present value of an infinite stream of $5 payments at a 7% discount rate. As discount rates rise, preferred-stock prices fall sharply because the perpetuity has no maturity to anchor the value.
Frequently Asked Questions
Yes — exactly. Gordon's formula V = D₁ / (r − g) reduces to D / r when g = 0. The no-growth case is so common (preferred stock, fixed-coupon perpetuities) that it earns its own treatment.
Identical math. The standard TVM perpetuity formula PV = PMT / k is the same as V = D / r — only the labels differ. Any perpetual constant cash flow uses this form.
Real preferred stock often has callable, cumulative, or convertible features that affect value beyond pure perpetuity math. This formula gives the baseline intrinsic value; option-adjusted models refine it for the embedded features.