Because Equation 5-2 requires a constant growth rate, we obviously cannot use it
to value stocks that have nonconstant growth. However, assuming that a company
currently enjoying supernormal growth will eventually slow down and become a con-
stant growth stock, we can combine Equations 5-1 and 5-2 to form a new formula,
Equation 5-5, for valuing it. First, we assume that the dividend will grow at a noncon-
stant rate (generally a relatively high rate) for N periods, after which it will grow at a
constant rate, g. N is often called the terminal date,or horizon date.
We can use the constant growth formula, Equation 5-2, to determine what the
stock’s horizon,or terminal, valuewill be N periods from today:
(5-2a)
The stock’s intrinsic value today,Pˆ 0 , is the present value of the dividends during the
nonconstant growth period plus the present value of the horizon value:
(5-5)
To implement Equation 5-5, we go through the following three steps:
- Find the PV of the dividends during the period of nonconstant growth.
- Find the price of the stock at the end of the nonconstant growth period, at which
point it has become a constant growth stock, and discount this price back to the
present.
- Add these two components to find the intrinsic value of the stock, Pˆ 0.
Figure 5-3 can be used to illustrate the process for valuing nonconstant growth stocks.
Here we assume the following five facts exist:
rsstockholders’ required rate of return 13.4%. This rate is used to discount
the cash flows.
N years of supernormal growth 3.
gsrate of growth in both earnings and dividends during the supernormal
growth period30%. This rate is shown directly on the time line. Note:
The growth rate during the supernormal growth period could vary from
year to year. Also, there could be several different supernormal growth
periods, e.g., 30% for three years, then 20% for three years, and then a
constant 8%.)
gnrate of normal, constant growth after the supernormal period 8%. This
rate is also shown on the time line, between Periods 3 and 4.
D 0 last dividend the company paid $1.15.
PV of horizon
value, PˆN:
[(DN 1 )/(rsg)]
(1rs)N.
PV of dividends during the
nonconstant growth period
t1, N.
PˆN
(1rs)N
Pˆ 0 .
D 1
(1rs)^1
D 2
(1rs)^2
DN
(1rs)N
PV of dividends during the
constant growth period
tN 1, .
PV of dividends during the
nonconstant growth period
t1, N.
Pˆ 0 D^1
(1rs)^1
D 2
(1rs)^2
DN
(1rs)N
DN 1
(1rs)N^1
D
(1rs)
.
Horizon value PˆN
DN 1
rsg
DN(1g)
rsg
Valuing Stocks That Have a Nonconstant Growth Rate 203
Stocks and Their Valuation 199
