Dividend theories: traditional, Walter, Gordon and Modigliani–Miller
Financial Management · Unit II · Topic 8 of 16 · 5 min read
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Cases checked to exist. Read the judgment before quoting a holding.
Every case cited here has been checked to exist — the citation resolves and names the right parties. The propositions attributed to each case have not been verified line by line against the judgment. Case names link through to the full judgment: read it before quoting a holding in an examination answer, and never carry a proposition from notes into court on trust.
1. Relevance against irrelevance
The question is whether the payout itself affects the market price of the share. Relevance theories (traditional, Walter, Gordon) say it does. The irrelevance theory of Modigliani and Miller says the value of the firm depends on its investment policy and earning power; how earnings are split between dividends and retention does not change it.
2. Traditional approach (Graham and Dodd)
Benjamin Graham and David Dodd (Security Analysis) held that the stock market places much more weight on dividends than on retained earnings: P = m (D + E/3), where m is a multiplier, D the dividend per share and E the earnings per share. A rupee paid as dividend counts three times as much as a rupee retained. The reason is the “bird in the hand” argument: a dividend now is certain, while the gain from retention is uncertain. Criticism: the weights are arbitrary, and the view ignores what the retained earnings earn.
3. Walter’s model
James E. Walter: P = [D + (r/ke)(E − D)] ÷ ke. Assumptions: all financing by retained earnings, constant r and ke, constant EPS and DPS, infinite life.
Example: E = Rs. 10, r = 15%, ke = 10%.
| Payout | D | Working | Price Rs. |
|---|---|---|---|
| 0% | 0 | (0 + 1.5 × 10) ÷ 0.10 | 150 |
| 50% | 5 | (5 + 1.5 × 5) ÷ 0.10 | 125 |
| 100% | 10 | (10 + 0) ÷ 0.10 | 100 |
A growth firm (r > ke) maximises price at zero payout; a declining firm (r < ke) at 100% payout; a normal firm (r = ke) gets Rs. 100 at any payout. Criticism: assumes no external finance and constant r and ke.
4. Gordon’s model
Myron Gordon: P = E(1 − b) ÷ (ke − br), where b is the retention ratio and br the growth rate g (requires ke > br). Example: E = Rs. 10, ke = 10%.
| Case | b | g = br | Price Rs. |
|---|---|---|---|
| r = 12% | 0.0 | 0% | 100.00 |
| r = 12% | 0.4 | 4.8% | 115.38 |
| r = 12% | 0.6 | 7.2% | 142.86 |
| r = 10% | 0.4 | 4.0% | 100.00 |
| r = 8% | 0.4 | 3.2% | 88.24 |
The conclusions match Walter’s. Gordon added a further argument (the bird in the hand again): investors discount distant dividends at a higher rate, so even when r = ke a higher payout may raise the price.
5. Modigliani–Miller irrelevance hypothesis (1961)
Merton Miller and Franco Modigliani, “Dividend Policy, Growth, and the Valuation of Shares” (Journal of Business, 1961). Assumptions: perfect capital markets, rational investors, no taxes (or no difference between tax on dividends and on capital gains), no flotation or transaction costs, a fixed investment policy, and certainty about future profits.
The firm that pays a dividend must raise the same amount by issuing new shares to finance its investment. The shareholder gains the dividend but loses an equal amount through the lower price (ex-dividend) and the dilution. Formulas: P0 = (D1 + P1) ÷ (1 + ke); new shares Δn = (I − (E − nD1)) ÷ P1; value nP0 = [(n + Δn)P1 − I + E] ÷ (1 + ke).
Worked problem (February 2025). ke 10%; 25,000 shares at Rs. 100; proposed dividend Rs. 5; net income Rs. 2,50,000; new investment Rs. 5,00,000.
| Step | Dividend paid | Not paid |
|---|---|---|
| P1 = P0(1 + ke) − D1 | 110 − 5 = 105 | 110 |
| Total dividend | 1,25,000 | 0 |
| Retained = 2,50,000 − dividend | 1,25,000 | 2,50,000 |
| New funds = 5,00,000 − retained | 3,75,000 | 2,50,000 |
| Δn = new funds ÷ P1 | 3,571.43 | 2,272.73 |
| (n + Δn) × P1 | 30,00,000 | 30,00,000 |
| − I + E = −5,00,000 + 2,50,000 | 27,50,000 | 27,50,000 |
| Value nP0 = 27,50,000 ÷ 1.10 | 25,00,000 | 25,00,000 |
The value of the firm is Rs. 25,00,000 (25,000 × Rs. 100) whether or not the dividend is paid: the dividend does not affect value, as MM claim.
6. Criticism and empirical evaluation
- Taxes: dividends and capital gains are taxed differently, so investors are not indifferent; the clientele effect follows.
- Floatation costs: new shares cost more than retained earnings, so paying a dividend and issuing shares is not costless.
- Transaction costs: an investor who wants income must sell shares (home-made dividend) and pay brokerage.
- Information content (signalling): markets react to dividend changes because a rise signals management’s confidence; MM accept this but say it is the information, not the dividend, that moves prices.
- Uncertainty: under uncertainty the bird-in-hand argument revives.
- Lintner (1956) showed firms smooth dividends towards a target payout; Fama, Fisher, Jensen and Roll (1969) found that the market reacts to the information in announcements.
How this is examined
The MM problem is a 10-mark Unit II question (February 2025): lay it out as in the table, both columns, and end with the one-line conclusion. A 6-mark note on the traditional approach is section 2 plus one line on Walter or Gordon. In an essay on dividend theories, do all four with the two small tables.
Now try the real questions: Financial Management past question papers.