Fundamentals of Financial Management (Concise 6th Edition)

284 Part 3 Financial Assets

assumed average for the economy. The value of this! rm’s stock, like any other asset,

is the present value of its expected future dividends as determined by Equation 9-1.

When Dt is growing at a constant rate, we can simplify Equation 9-1 to Equation 9-2,

Pˆ 0 " D 1 /(rs # g). In the supernormal case, however, the expected growth rate is not a

constant. In our example, there are two distinctly different rates.

Because Equation 9-2 requires a constant growth rate, we obviously cannot

use it to value stocks that are not growing at a constant rate. However, assuming

that a company currently enjoying supernormal growth will eventually slow down

and become a constant growth stock, we can combine Equations 9-1 and 9-2 to

construct a new formula, Equation 9-6, for valuing the stock.

First, we assume that the dividend will grow at a nonconstant 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, or horizon, date. Second, we can use the constant

growth formula, Equation 9-2, to determine what the stock’s horizon, or terminal,

value will be N periods from today:

Horizon Value! PˆN!

DN" 1

_____r

s^ $ g

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:

Pˆ 0!

D 1

_______(1 " r

s)

1 "^

D 2

_______(1 " r

s)

2 "^...^ "^

DN

_______(1 " r

s)

N^ "^

DN" 1

_________(1 " r

s)

N" 1 "^...^ "^

_______D#

(1" rs)#^

PV of dividends during the Horizon value! PV of dividends

nonconstant growth during the constant growth

period, t! 1,... N period, t! N " 1,... #

Terminal (Horizon)

Date

The date when the growth

rate becomes constant. At

this date, it is no longer

necessary to forecast the

individual dividends.

Terminal (Horizon)

Date

The date when the growth

rate becomes constant. At

this date, it is no longer

necessary to forecast the

individual dividends.

Horizon (Terminal)

Value

The value at the horizon

date of all dividends

expected thereafter.

Horizon (Terminal)

Value

The value at the horizon

date of all dividends

expected thereafter.

Illustrative Dividend Growth Rates

F I G U R E 9! 3

Dividend

($)

1.15

Declining Growth, –8%

Zero Growth, 0%

Normal Growth, 8%

Normal Growth, 8%

End of Supernormal

Growth Period

Supernormal Growth, 30%

0 1 2 3 4 5

Years