Fundamentals of Financial Management (Concise 6th Edition)

Chapter 9 Stocks and Their Valuation 285

Pˆ 0!

D 1

_______

(1 " rs)^1

"

D 2

_______

(1 " rs)^2

"... "

DN

_______

(1 " rs)N

"

PˆN

_______

(1 " rs)N

9-6

PV of dividends during the PV of horizon

nonconstant growth period value, PˆN:

t = 1,... N

[(DN" 1 )/(rs $ g)]

_____________

(1 " rs)N

To implement Equation 9-6, we go through the following three steps:

1. Find the PV of each dividend during the period of nonconstant growth and
   sum them.


2. Find the expected stock price at the end of the nonconstant growth period, at
   which point it has become a constant growth stock so it can be valued with the
   constant growth model, and discount this price back to the present.


3. Add these two components to! nd the stock’s intrinsic value, Pˆ 0.

Figure 9-4 illustrates the process for valuing nonconstant growth stocks. Here
we use a new company, Firm M, and we assume that the following! ve facts exist:

rs " stockholders’ required rate of return " 13.4%. This rate is used to discount
the cash " ows.
N " years of nonconstant growth " 3.
gs " rate of growth in both earnings and dividends during the nonconstant
growth period " 30%. This rate is shown directly on the time line. (Note:
The growth rate during the nonconstant growth period could vary from
year to year. Also, there could be several different nonconstant growth
periods—for example, 30% for three years, 20% for the next three years,
and a constant 8% thereafter).
gn " rate of normal, constant growth after the nonconstant period " 8.0%. This
rate is also shown on the time line, after Period 3, when it is in effect.
D 0 " last dividend the company paid " $1.15.

The valuation process diagrammed in Figure 9-4 is explained in the steps set
forth below the time line. The value of the nonconstant growth stock is calculated
to be $39.21.
Note that in this example, we assumed a relatively short 3-year horizon to
keep things simple. When evaluating stocks, most analysts use a longer horizon
(for example, 5 years) to estimate intrinsic values. This requires a few more calcu-
lations; but because analysts use spreadsheets, the arithmetic is not a problem. In
practice, the real limitation is obtaining reliable forecasts for future growth.

Explain how one would " nd the value of a nonconstant growth stock.

Explain what is meant by terminal (horizon) date and horizon (terminal)

value.

SEL

F^ TEST (^)