Finance Assignment Help With Dividend Gordon's Model

9.2.2. Gordon’s Model

Myron Gordon has also proposed a model suggesting that the dividend is relevant and can affect the value of the share and that of the firm. This model is also based on the assumptions similar to that Walter’s model. However, two additional assumptions made by this model are as follows:

  • The growth rate of firm ‘g’ is the product of retention ratio, b, and its rate of return, r, i.e., r= br, and
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  • The cost of capital besides being constant is more than the growth rate i.e., ke>g

Gordon argues that the investors do have a preference for current dividends and this is a direct relationship between the dividend policy and the market value of the share. The basic premise of the model is that the investors are basically risk averse and they evaluate the future dividends/ capital gains as a risky and uncertain proposition. Dividends are more predictable than capital gains; management can control dividends but it cannot dictate the market price of the share. Investors are certain of receiving incomes than from future capital gains. The incremental risk associated with capital gains implies a higher required rate of return for discounting the capital gains than for discounting the current dividends. In other words, an investor values, current dividend more highly than an expected future capital gain.

So, the “bird in the hand” argument of this model suggests that the dividend policy is relevant as the investors prefer current dividends as against the future uncertain capital gains. When the investors are certain about their returns, they discount the firms earning at a lower rate and therefore, placing a higher value for the share and that of the firm. So, the investors require a higher rate of return as retention rate increases and this would adversely affect the share price.

Thus, Gordon’s Model is a share valuation model. Under this model, the market price of a share can be calculated as follows:

P =   E (1-b)

ke- br

Where,

P = Market price of equity share

E = Earnings per share of the firm

B = Retention ratio (1- payout ratio)

R = Rate of return on investment of the firm

Ke = Cost of Equity share capital, and

Br = g i.e., Growth rate of the firm

This model shows that there is a relationship between payout ratio (i.e., 1-b), cost of capital ke, rate of return, r, and the market value of the share. This can be explained with the help of the following example:

The following information is available in respect of Axis Ltd.

Earning per share (EPS or E) $ 10

Cost of Capital, ke, 10%

Find out the market price of the share under different rate of return, r, of 8%, 10%, and 15% for different payouts of 0%, 40%, 80% and 100%.

ANSWER:

The market price of the share as per Gorden’s model may be calculated as follows:

If r=15% and payout ratio is 40%, then the retention ratio, b, is .6 (i.e. 1-.4) and the growth rate, g= br= .09 (i.e., .6*.15) and the market price of the share is

P = E (1-b)

ke- br

P = 10(1-.6)/.10-.09

P = $ 400

If r= 8% and payout ratio is 80%, then the retention ratio, b, .2 (i.e., 1-.8) and the growth rate, g=br=.016 (i.e., .2*.08) and the market price of the share is

P = 10(1-.2)//10-.016

P = $ 95

Similarly the expected market price under different combinations of ‘r’ and dividend payout ratio have been calculated and shown below:

r = 15% 10% 8%

D/P Ratio 0%0               0                   0

40% $400 $100 $77

                                    80%                            114.3              100                 95

                                    100%                         100                  100                 100

On the basis of figures given in the table above, it can be seen that if the firm adopts a zero payout then the investor may not be willing to offer any price. For a growth firm (i.e., r>ke>br), the market price decreases when the payout is increased. For a firm having r<ke, the market price increases when the payout is increased.

If r=ke, the dividend policy is irrelevant and the market price remains constant at $100 only. Gordon had also argued that even if r=ke, the dividend payout ratio matters and the investors being risk averse prefer current dividends which are certain to future capital gains which are uncertain. The investors will apply a higher capitalization rate i.e., ke to discount the future capital gains. This will compensate them for the future uncertain capital gain and thus, the market price of the share of a firm which retains profit will be adversely affected.

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