# Gordon's Model of Dividend Relevance
Gordon's model argues that dividend policy is relevant to share value. It values a share as the present value of an infinite stream of growing dividends.
## Core Formula
$$P_0 = \frac{D_1}{K_e - g}$$
This can be expressed in three equivalent ways:
| Form | Formula | When to use |
|---|---|---|
| Using expected dividend | $P_0 = \dfrac{D_1}{K_e - g}$ | $D_1$ given directly |
| Using current dividend | $P_0 = \dfrac{D_0(1+g)}{K_e - g}$ | Only $D_0$ given |
| Using earnings & retention | $P_0 = \dfrac{E_1(1-b)}{K_e - br}$ | EPS and retention ratio given |
## Notation
| Symbol | Meaning |
|---|---|
| $P_0$ | Price per share |
| $D_0$ | Current year dividend |
| $D_1$ | Expected dividend per share = $D_0(1+g)$ |
| $E_1$ | Earnings per share |
| $b$ | Retention ratio |
| $(1-b)$ | Payout ratio |
| $K_e$ | Cost of equity capital |
| $r$ | Internal Rate of Return (IRR) |
| $g = br$ | Growth rate |
Note that growth is generated internally: $g = b \times r$ (retention ratio × rate of return).
## Optimum Dividend Payout under Gordon's Model
The optimum payout depends on the relationship between the firm's return on investment ($r$) and its cost of capital ($K_e$):
| Type of company | Condition | Optimum dividend payout ratio |
|---|---|---|
| Growth firm | $r > K_e$ | 0% (retain everything) |
| Constant / Normal firm | $r = K_e$ | No optimum ratio (payout is irrelevant) |
| Declining firm | $r < K_e$ | 100% (distribute everything) |
Logic: When the firm earns more than shareholders' required return ($r > K_e$), reinvesting maximises value, so it should pay no dividend. When it earns less ($r < K_e$), shareholders are better off receiving cash to invest elsewhere, so it should pay everything out.
## Key takeaway
Gordon's model and Walter's model prescribe the same optimum dividend payout criteria — both link the decision to the comparison of $r$ vs $K_e$.