Page 159 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes The present value of all dividends forecasts up to and including time 'T' V would be
T(i)
T D
V t
T(i ) t …(i)
t 1 (1 K)
The second phase present value is denoted by V and would based on constant-growth dividend
T(2)
forecast after time 'T'. The position of the investor at time 'T' after which the second phase
commences is viewed as a point in time when he is forecasting a stream of dividends for time
periods T + 1, T+2, T+3 and so on, which grow at a constant rate. The second phase dividends
would be

D = D (1+g)
T+1 T
D = D (1+g) = D (1+g) 2 …(ii)
T+2 T+1 T
D = D (1+g) = D (1+g) 3
T+3 T+2 T
And so on. The present value of the second phase stream of dividends can, therefore, be estimated
using each (i) and at time 'T'

1
V = D …(iii)
T T+1
K g
You may note 'V ' given by equation (iii) is the present value at time 'T' of all future expected
T
dividends. Hence, when this value has to be viewed at time 'zero', it must be discounted to
provide the present value at time for the second phase present value. The latter can also be
viewed at time 'zero' as a series of each dividend that grow at a constant rate as already stated.
The resulting second phase value V will give the following.
T(2)
1
V = V T 1 T …(iv)
T(2) (K g)

D T 1
V = V T 1
T(2) (K g)(1 K)T
Now, the two present values of phases 1 and 2 can be added to estimate the intrinsic value of an
equal that will pass through a multiple growth situation. The following describes the summation
of the two phases.
V = V + V
T(2) T(1) T(2)
T D D
t
T 1
t 1 (1 K)t (K g)(1 K) T

Example: RKV Ltd., paid dividends amounting to 0.75 per share during the last year.
The company is to pay 2.00 per share curing the next year. Investors forecast a dividend of
3.00 per share in that year. At this time, the forecast is that dividends will grow at 10% per year
into an indefinite future. Would you sell the share if the current price is 54.00? The required
rate of return is 15%.
Solution: This is a case of multiple growth. Growth rates for the first phase must be worked out
and the time between the two phases established. It is clear that 'T' = 2 years. Hence, this becomes
the time-partition. Rates before 'T' are:

D - D 2.00 – 0.75
1 g
g = = = 167%
1 D 0.75
0

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