Gordon’s growth model

What is Gordon’s growth model ?

Gordon’s model of calculation of price of a share is based on the Dividend relevance theory. As per the Dividend relevance theory, Dividends are relevant and Dividend policy of the firm is relevant to the price of the firm’s stock. As per Gordon’s model the market value of a share is the sum of the present value of stream of dividends.

What are the assumptions of Gordon’s growth Model ?

The Gordon model is based on the following assumptions :

1.Retained earnings are the only source of finance available for financing investment plans. No external financing i.e., Debt is used by the firm. The firm is an all equity firm.

2.There are no corporate taxes.

3.The firm is assumed to be a going – concern i.e., expected to continue for an indefinite period in the future.

4.The cost of capital of the firm is greater than the growth rate ( g = br )

5.The retention ratio of the firm once fixed, shall remain constant.

6. The firm’s rate of return on investment (r) and cost of capital (ke) is constant. Else, a change in the cost of capital will affect the present value calculation of dividends.

7.The dividend’s are expected to grow at a constant rate. ( g = br )

8.The firm’s firm uses all its free cash flows to pay dividends at periodic intervals.

As per the Gordon growth model, the market price of a share is calculated using the follows :

P = [ E * ( 1 – b ) ] / ( K– br )

P = Price per share ;     E = Earnings per share    ;    b = Retention ratio ;

1 – b = Payout ratio ;     Ke = Cost of capital  ;    br = growth rate ;

Example :

Cash Rich Co. makes the following details available

 10 % Preference shares outstanding \$ 50,000,000 5 % Debentures \$ 25,000,000 Number of Equity shares 200,000 Net profit \$ 20,000,000 Return on Investment 15 % Cost of capital ( Ke ) 10 %

Calculate the price per share as per Gordon’s model if the retention ratio is 40 %

Solution :

(a) Statement showing Calculation of Earnings per share

 Particulars Amount Net Profit \$ 20,000,000 Less : Debenture Interest ( \$ 25,000,000 * 5 % ) \$ 1,250,000 Less : Preference dividend ( \$ 50,000,000 * 10 % ) \$ 5,000,000 Earnings available to Equity share holders \$ 13,750,000 No. of Equity shares 2,500,000 Earnings per share = \$ 13,750,000 / 200,000 \$ 5.50

(b) Calculation of Price per share as per Gordon growth model

As per the information available

E = \$ 5.50 ;  b = 40 % = 0.40  ;  Ke = 10 % = 0.10  ; r = 15 % = 0.15 ;

Thus the price of the share is

= [ ( \$ 5.50 * ( 1 – 0.40 ) ]

[ ( 0.10 – ( 0.4 * 0.15 ) ]

=  [ ( \$ 5.50 * 0.60 ]

[ ( 0.10 – 0.06 ]

\$ 3.30

0.04

= \$ 82.50

Thus the Price per share as per Gordon growth model = \$ 82.50

Criticism of the Gordon’s model :

1.The model assumes that there are no corporate taxes. This is highly unlikely in a real world situation.

2.The firm’s rate of return on investment (r) and cost of capital (ke) is constant. This is practically not possible.

3.The firm is financed entirely by equity and there is no debt component in the capital structure of the firm.

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