# Gordon's Model (Dividend Growth Model)
Gordon's Model is another relevance theory. It values a share as the present value of an infinite, constantly growing stream of dividends.
## A. Assumptions
- Growth rate g (= b × r) is constant.
- Ke remains constant.
- Ke > g (essential — otherwise the formula breaks down).
- Retention ratio (b) remains constant.
- r remains constant.
- The firm is an all-equity firm (no debt).
- All investment proposals are financed through retained earnings only.
## B. Gordon's Formula
$$P_0 = \frac{D_1}{K_e - g} \quad=\quad \frac{D_0(1 + g)}{K_e - g} \quad=\quad \frac{E_1(1 - b)}{K_e - br}$$
Where:
- P₀ = Price per share
- D₀ = Current year dividend
- D₁ = Expected dividend per share = D₀(1 + g)
- E₁ = Earnings per share
- b = Retention ratio; (1 − b) = Payout ratio
- Ke = Cost of capital
- r = IRR
- br = g = Growth rate
## C. Optimum Dividend Payout under Gordon's Model
| Type of Firm | Condition | Optimum Dividend Payout Ratio |
|---|---|---|
| Growth | r > Ke | 0% |
| Constant | r = Ke | No optimum ratio |
| Declining | r < Ke | 100% |
This is identical to Walter's conclusion.
## Doubt Busters
1. Walter's and Gordon's models prescribe the same optimum dividend payout criteria.
2. D₁ vs D₀ confusion:
- If the question says 'Dividend Expected' → treat it as D₁.
- If the question says 'Dividend Paid' → treat it as D₀.
- If the question is silent, you may assume the figure is either D₁ or D₀ — just write a clear note stating your assumption.