Introduction to Corporate Finance

PARt 2: VALUAtIoN, RISk ANd REtURN

example

Suppose the rapid growth of a telecommunications

company has carried the market for shares in this

firm upwards in a rapid way. Over time, however, as

the relevant technology become more widespread

and copied, the growth rates of the company will

reach a steady state. At that point, the company

may grow at the same rate as the overall economy,

perhaps 5% or less per year. Assume that the

market’s required rate of return on these shares

is 14%.

To value the telecommunication company’s

shares, we split the future stream of cash flows into

two parts. The first part is the rapid-growth period,

and the second is the constant-growth phase.

Suppose that the company’s most recent (Year 0)

dividend was $1 per share. We anticipate that the

company will increase the dividend by 25% per

year for the next three years, and that after that,

dividends will grow at 4% per year indefinitely. The

expected dividend stream for the next seven years

looks like this:

Rapid-growth phase

(g 1 = 25%)

Constant-growth phase

(g 2 = 4%)

Year 0 $1.00 Year 4 $2.03

Year 1 1.25 Year 5 2.11

Year 2 1.56 Year 6 2.197

Year 3 1.95 Year 7 2.28

The value of the dividends during the rapid-

growth phase is calculated as follows:

$3.6 1

()

=

=++

=++=

PV:ofdividends

Initialphase

$1.25

(1.14)

$1.56

(1.14)

$1.95

(1.14)

$1.09 $1.20 $1.32

123

The stable-growth phase begins with the dividend

paid four years from now and continues forever. The

final term of Equation 5.5 is similar to Equation 5.4,

which indicates that the value of a constant-growth

share at time t equals the dividend a year later, at

time t + 1, divided by the difference between the

required rate of return and the constant-growth rate.

Applying that formula here means valuing the share

at the end of Year 3, just before the constant-growth

phase begins:

=

−

=

−

P =

D

rg

$2.03

0.14 0.04

3 4 $20.30

2

Don’t forget that $40.33 is the estimated price

of the share three years from now. To express that

in today’s dollars, we have to discount it for three

additional years as follows:

$20.40

(1.14)

3 =$13.70

This represents the value today of all dividends

that occur in Year 4 and beyond. To estimate the

present value of the entire dividend stream, which

of course represents the price of the share today, we

simply put the two pieces together:

Total value of the share, P 0 = $3.61 + $13.70

= $17.31

The following single algebraic expression shows

the information in a compact form:

P

$1.25

(1.14)

$1.56

(1.14)

$1.95 $20.30

(1.14)

0 =+ 12 + 3 $17.31

+

=

The numerator of the last term contains both the

final dividend payment of the rapid-growth phase,

$1.95, and the present value as of the end of Year 3 of

all future dividends, $20.30. The value of the company’s

shares using the variable growth model is $17.31.

As with most of our valuation models, it is possible to take the share’s market price as given and to

use the model to ‘reverse-engineer’ the growth rate. In other words, a share analyst might use this model

to estimate how much dividend growth investors are expecting given the price they are willing to pay for

the shares.