Dividend Models: Walter and Gordon’s Model

Walter’s Model

Professor James E. Walterargues that the choice of dividend policies almost always affects the value of the enterprise. His model shows clearly the importance of the relationship between the firm’s internal rate of return (r) and its cost of capital (k) in determining the dividend policy that will maximize the wealth of shareholders.

Walter’s model is based on the following assumptions:-

  1. The firm finances all investment through retained earnings; that is debt or new equity is not issued;
  2. The firm’s internal rate of return (r), and its cost of capital (k) are constant;
  3. All earnings are either distributed as dividend or reinvested internally immediately.
  4. Beginning earnings and dividends never change. The values of the earnings pershare (E), and the divided per share (D) may be changed in the model to determine results, but any given values of E and D are assumed to remain constant forever in determining a given value.
  5. The firm has a very long or infinite life.

Walter’s formula to determine the market price per share (P) is as follows:

P = D/K +r(E-D)/K/K

The above equation clearly reveals that the market price per share is the sum of the present value of two sources of income-

(i) The present value of an infinite stream of constant dividends, (D/K) and

(ii) The present value of the infinite stream of stream gains.

[r (E-D)/K/K]

Criticism

Walter’s model is quite useful to show the effects of dividend policy on an all equity firm under different assumptions about the rate of return. However, the simplified nature of the model can lead to conclusions which are net true in general, though true for Walter’s model.

The criticisms on the model are as follows:

  1. Walter’s model of share valuation mixes dividend policy with investment policy of the firm. The model assumes that the investment opportunities of the firm are financed by retained earnings only and no external financing debt or equity is used for the purpose when such a situation exists either the firm’s investment or its dividend policy or both will be sub-optimum. The wealth of the owners will maximize only when this optimum investment in made.
  2. Walter’s model is based on the assumption that r is constant. In fact decreases as more investment occurs. This reflects the assumption that the most profitable investments are made first and then the poorer investments are made.

The firm should step at a point where r = k. This is clearly an erroneous policy and fall to optimize the wealth of the owners.

  1. A firm’s cost of capital or discount rate, K, does not remain constant; it changes directly with the firm’s risk. Thus, the present value of the firm’s income moves inversely with the cost of capital. By assuming that the discount rate, K is constant, Walter’s model abstracts from the effect of risk on the value of the firm.

Gordon’s Model

One very popular model explicitly relating the market value of the firm to dividend policy is developed by Myron Gordon.

Assumptions of Gordon’s model

Gordon’s model is based on the following assumptions.

  1. The firm is an all Equity firm
  2. No external financing is available
  3. The internal rate of return (r) of the firm is constant.
  4. The appropriate discount rate (K) of the firm remains constant.
  5. The firm and its stream of earnings are perpetual
  6. The corporate taxes do not exist.
  7. The retention ratio (b), once decided upon, is constant. Thus, the growth rate (g) = br is constant forever.
  8. K > br = g if this condition is not fulfilled, we cannot get a meaningful value for the share.

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