Hello!!!
I will start providing you a theoretical source:
"Because of the difficulties associated with the estimation of future
dividends, we find it useful to make one of three simplifying
assumptions regarding the pattern of future payments. They are: (1)
zero growth in dividends, or constant dividends; (2) constant rate of
growth in dividends; and (3) a nonconstant rate of growth in
dividends.
A stock with constant dividends is a perpetuity. Previously we noted
that the present value of a perpetuity, PV, equals C/r. Since, for a
zero-growth stock, D = C, the value of a share of stock which pays a
constant dividend is
P0 = PV = D/r.
A growing perpetuity is a series of cash flows, occurring at regular
intervals, which grows perpetually at a constant rate. The series of
dividend payments for a share of common stock can be considered a
growing perpetuity as long as the dividend payment increases at the
same rate each year. Let Dt be the dividend paid in year t, and let g
be the annual growth rate in dividends. The dividend at date (Dt) is:
Dt = D0 × (1 + g)^t .
It can be shown algebraically that, as long as r is greater than g,
the present value of an infinite stream of cash flows which are
changing at constant rate is equal to
P0 = PV = [D0 × (1+g)]/(r - g) = D1/(r - g).
Learning Tip: The constant-growth model is nothing more than a
modified version of the ordinary annuity model described previously.
As such, it assumes that payments occur at the end of each period. In
turn, we can use it to find the price of the stock at any point in
time (t):
Pt = D(t+1)/(r - g).
The assumption of nonconstant growth is realistic for many firms. The
key assumption of this model is the assumption that dividends change
at different rates in different periods, until, at a specified future
date, the growth rate settles at some constant equilibrium rate.
Fortunately, no new formulas are required to value such a stock. To
use the nonconstant or supernormal growth model we simply:
1.Compute the FV of each dividend in the nonconstant growth period,
using the growth rate (g).
2.Compute the PV of the abovementioned dividends discounted at r.
3.Use the constant-growth model to compute the PV of all of the
remaining dividends which, by assumption, are expected to grow at a
constant rate forever.
4.Sum the present values obtained in steps 2 and 4; this is the
present value of all future dividends, which is P0.
Components of the Required Return (p. 225):
Previously we noted that investors buy stock in the hope of earning
returns in the form of dividends and capital gains. Given a constant
growth rate, we can obtain the components of total return by solving
the constant-growth formula for r:
r = D1/P0 + g.
Thus, the rate of return for a constant growth stock consists of two
components: the dividend yield and the capital gains yield. The former
can be thought of as the rate of return for a stock whose dividend is
constant; an investor who purchased a share of common stock for a
price P0, and who received a constant dividend of D1, would be
receiving a perpetuity whose yield is equal to D1/P0. The capital
gains yield represents the expected annual increase in the price of
the stock. Given the assumption that annual cash flows are growing at
a constant rate forever, it is not surprising that the capital gains
yield is the same as the dividend growth rate g."
Taken from "Fundamentals of Corporate Finance 5th Edition - Ross,
Westerfield and Jordan - Online Learning Center ":
http://www.mhhe.com/business/finance/rwj/fund/student/olc/ch08s_sm2.htm
Now we can solve the problem:
r = (D1/P0) + g
g = 0.055 = 5.5%
D0 = $3.86
D1 = D0 * (1+g) = $3.86 *1.055 = $4.0723 .
P0 = $26.75
Then
r = ($4.0723 / $26.75) + 0.055 = 0.20724 = 20.724%
Hope this helps.
Feel free to request for a clarification if it is needed.
Regards.
livioflores-ga |
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