Gordon’s Model

Gordon proposed a model of stock valuation using the dividend capitalization approach. His model is based on the following assumptions:

1. All-equity firm: The firm is an all-equity firm, and it has no debt

2. No external financing: Retained earnings would be used to finance any expansion.

3. Constant return: The internal rate of return, r, of the firm’s investment is constant.

4. Constant cost of capital: The appropriate discount rate k for the firm remains       

constant and is greater than the growth rate.

5. No taxes: Corporate taxes do not exist.

6. Constant retention: The retention ratio, b, once decided upon, is constant.

Valuation Formula: Based on the above assumptions, Gordon put forward the following formula:

P₀ = EPS₁ (1-b) / K-br

P₀ = price per share at the end of year 0

EPS₁= earnings per share at the end of year 1

(1-b) = fraction of earnings the firm distributes by way of earnings

b= fraction of earnings the firms ploughs back

k= rate of return required by the shareholders

r = rate of return earned on investments made by the firm

br = growth rate of earnings and dividends

Let’s apply the Gordon’s formula to a practical illustration to be clearer. We will again take an example of three firms; growth, normal and the declining one. The financial highlights of all these firms is given as follows:

Growth firm                 (r>k)	Normal firm (r = k)		Declining firm (r<k)
r	15%	10%	8%
k	10%	10%	10%
EPS	Rs 10	Rs 10	Rs 10
b	0.6	0.6	0.6
1-b	0.4	0.4	0.4

As, we have all the elements of the formula. Lets compute the share price for the growth firm first.

We know that:

P₀ = E₁ (1-b)

k-br

Lets substitute the data in the formula:

0 P₀ = 10 (0.4)

0.10-(0.6)(0.15)

By solving the equation, you will get the share price equal to Rs 400.In the same way, you can get the share price of the other two firms also. i.e. the price of the share for Normal firm is Rs 100 and declining firm also it is Rs 77

Now, suppose that I change the value of b from 0.4 to 0.6. Can you compute the new share price for all the firms other things remaining the same. Are you getting the following?

Growth firm: Rs150

Normal firm: Rs 100

Declining firm: Rs 88

Lets make a small analysis from the above:

• The marker value of the share, P0, increases with the retention ratio, b,for firms with growth opportunities .i.e. when r >k.

• The marker value of the share, P0, increases with the payout ratio, (1-b), for declining firms. i.e. when r < k.

• The market value of the share is not affected by dividend policy when r = k

You must have noticed that Gordon’s model’s conclusions are similar to that of Walter’s model. This similarity is due to the similarities of assumptions, which underlie both the models. Thus the Gordon model suffers from the same limitations as the Walter model.

Till now, we have been discussing the theories, which believe in the relevance of paying dividends. Now we will turn attention to the other side where Miller & Modigliani (MM) who advanced their view that the value of the firm depends solely on its earnings power and is not influenced by the manner in which they are split.