# Modigliani–Miller (MM) Approach — Dividend Irrelevance
Proposed by Franco Modigliani and Merton Miller in 1961, the MM hypothesis argues that dividend policy is irrelevant — it affects neither the price of a firm's stock nor its cost of capital.
## Core propositions
- The market value of a firm's equity depends solely on its earning power, not on how earnings are split between dividends and retained earnings.
- Market value is not affected by dividend size.
- There is no meaningful distinction between dividends and share repurchases — both simply return cash to shareholders.
## Assumptions
1. Perfect capital markets exist and investors are rational.
2. No taxes.
3. All investments are financed through equity only.
4. No floatation or transaction costs.
5. Investors forecast future prices and dividends with certainty.
## Formulas
### Value of the firm
The value of the firm is unchanged by the dividend decision:
$$V_f = nP_0 = \frac{(n + \Delta n)P_1 + E - I}{1 + K_e}$$
| Symbol | Meaning |
|---|---|
| $V_f$ | Value of the firm at the beginning of the period |
| $n$ | Number of shares at the beginning of the period |
| $\Delta n$ | Number of new shares issued to raise required funds |
| $P_1$ | Price at the end of the period |
| $E$ | Total earnings during the period |
| $I$ | Total investment during the period |
| $K_e$ | Cost of equity |
### Market price of a share
$$P_0 = \frac{P_1 + D_1}{1 + K_e}$$
| Symbol | Meaning |
|---|---|
| $P_0$ | Price at the beginning of the period |
| $P_1$ | Price at the end of the period |
| $D_1$ | Dividend at the end of the period |
| $K_e$ | Cost of equity / rate of capitalization / discount rate |
## Mechanism
If a firm pays a dividend, it must issue new shares to fund its investment. The value gained from the dividend is exactly offset by the dilution from new shares — leaving total shareholder wealth unchanged. This 'homemade dividend' logic is the heart of MM's irrelevance argument.