# Gordon's Dividend Capitalization Model

Gordon's theory contends that dividends are relevant. This model is of the view that dividend policy of a firm affects its value.

Assumptions of this model:
• The firm is an all equity firm. No external financing is used and investment programmes are financed exclusively by retained earnings.
• Return on investment( r ) and Cost of equity(Ke) are constant.
• The firm has perpetual life.
• The retention ratio, once decided upon, is constant. Thus, the growth rate, (g = br) is also constant.
• Ke > br

Arguments of this model:
• Dividend policy of the firm is relevant and that investors put a positive premium on current incomes/dividends.
• This model assumes that investors are risk averse and they put a premium on a certain return and discount uncertain returns.
• Investors are rational and want to avoid risk.
• The rational investors can reasonably be expected to prefer current dividend. They would discount future dividends. The retained earnings are evaluated by the investors as a risky promise. In case the earnings are retained, the market price of the shares would be adversely affected. In case the earnings are retained, the market price of the shares would be adversely affected.
• Investors would be inclined to pay a higher price for shares on which current dividends are paid and they would discount the value of shares of a firm which postpones dividends.
• The omission of dividends or payment of low dividends would lower the value of the shares.

Dividend Capitalization model:

According to Gordon, the market value of a share is equal to the present value of the future streams of dividends.

 P = E(1 - b) Ke - br

Where:
 P = Price of a share E = Earnings per share b = Retention ratio 1 - b = Dividend payout ratio Ke = Cost of capital or the capitalization rate br - g = Growth rate (rate or return on investment of an all-equity firm)

Example:  Determination of value of shares, given the following data:

 Case A Case B D/P Ratio 40 30 Retention Ratio 60 70 Cost of capital 17% 18% r 12% 12% EPS \$20 \$20

 P = \$20 (1 - 0.60)      0.17 – (0.60 x 0.12) => \$81.63 (Case A) P = \$20 (1 - 0.70)       0.18 – (0.70 x 0.12) => \$62.50 (Case B)

Gordon's model thus asserts that the dividend decision has a bearing on the market price of the shares and that the market price of the share is favorably affected with more dividends.

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