Page 156 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 5: Equity Valuation Models

The Zero-growth Case Notes

The growth rate of dividend D at time 't' will be known by solving for 'g' in the following
D = D – 1 (1 + g ) …..(1)
t t t
D - 1(1 + g )
t
t
Or, D = …...(2)
t D - 1
1
You can easily see that when g = 0, 3 equation (1) will yield D = D – 1, which means all future
t t t
dividends would equal to be current dividend (i.e., the dividend of the immediately preceding
period available as on date)
Now, the present value of dividends for an infinite future period would be
D 0 D 1 D 2
V = 1+ k + (1+ k) 2 + (1+ k) 3 + …...(3)

Since, D = D = D = D , under the zero-grown assumption, the numerator D in equation (3) is
0 1 2 3 1
replaced D .
0
You will appreciate that discounting cash flows over a very distant long future period would be
meaningless. Mathematics tells us that if K > 0 then the value of an infinite series like the one in
equation (4) is reduced so that the equation (4) results in following

D 0 D 0
V = 1 = …...(4)
0 K K
0
And since D = D , equation 5 can also be written as
0 1
D
V = 1 …...(5)
K
You may recall that the same equation was used for the valuation of preference shares. This is
one case for application of the zero-growth assumption.
The calculation underlying the zero-growth model can be illustrated.

Example: Consider a preference share on which the company expects to pay a cash
dividend of RKV 9 per share for an indefinite future period. The required rate return is 10%
and the current market price is 80.00. Would you buy the share at its current price?
Solution:
This is a zero-growth case because the dividend per share remains 9 for all future time periods.
You find the intrinsic value of the share using equation
V = 9.00/.10 = 90
The intrinsic value of 90 is more than the market price of 80. You would consider buying the
share.

Example: Assume that the dividend per share is estimated to be 4.00 per year
indefinitely and the investor requires a 20% of return.

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