Page 157 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes Solution:
The intrinsic value of the equity share is 4/.20 = 20. (This model is more appropriate for an
analysis of preference shares because of the constant dividend assumption).

Constant Growth Case

When dividends grow in all future periods at a uniform rate 'g'

D = D – 1 (1 + g) t …(1)
t t
Substituting 'D ' in equation (1) by the value of D , we get
0 1
D (1 g) t
0
v = t …(2)
t 0 (1 K)
For a constant amount 'D ' can be written out of summation to obtain the following equation
0
D (1 g) t
0
v = D 0 t …(3)
t 0 (1 K)
Constant amount, 'D ' can be written out of summation to obtain the following equation
0
(1 g) t 1 g
v = t …(4)
t 0 (1 K) K g
Substituting mathematical properties of infinite series, if K > g, it can then be shown that
D (1 g)
0
V = …(5)
(K g)
which can be re-written as follows:

D (1 g) D 1
0
V = = …(6)
(K g) K g

Example: Dabba Ltd. paid a dividend of 2.00 per share for the year ending March 31,
1991. A constant growth of 10% income has been forecast for an indefinite future period. Investors'
required rate of return has been estimated to 15%. You want to buy the share at a market price
quoted on July 1, 1991 in the stock market at 60.00. What would be your decision?
Solution:
This is a case of constant-growth-rate situation. Let us now find out the intrinsic value of the
equity share as under

D 1 2(1.10) 2.20
V = = = = 44.00
(K - g) .15 - .10 .05
The intrinsic value of 44 is less than the market price of 60.00. Hence, the share is overvalued
and you should not buy.

Example: The company paid its first cash dividend of 2.50 today and dividends are
expected to grow at a rate of 30% per year for the next three years. Thereafter, cash dividends
will grow at a 10% rate per year. Shareholders expect to earn a 15% return on their investments.
Calculate the present value of dividend.

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