Practical financial manaegment lasher 7th ed chapter 08

Chapter 8 - The Valuation and Characteristics of Stock


Common Stock
Corporations are owned by common
stockholders
Most large companies are “widely held’
– Ownership spread among many investors.
Investors don’t think of their role as owners
2


The Return on an
Investment in Common Stock
Income in a stock investment comes from:
– dividends
– gain or loss on the difference between the purchase and sale
price
If you buy a stock for price P0, hold it for one year, receive a dividend
of D1, then sell it for price P1, you return, k, would be:

k=

D1+ ( P1 -P0 )
P0
or

k=

D1
P

{0

dividend yield

+

( P1-P0 )
P
14 2043

A capital gain (loss) occurs
if you sell the stock for a
price greater (lower) than
you paid for it.

capital gains yield

3


The Return on an
Investment in Common Stock
Solve the previous equation for P0, the stock’s
price today:
kP0 = D1 + ( P1 − P0 )
P0 + kP0 = D1 + P1

( 1 + k ) P0 = D1 + P1

D1 + P1

P0 =
( 1+ k )

4


The Return on an
Investment in Common Stock
The return on a stock investment is the interest
rate that equates the present value of the
investment’s expected future cash flows to the
amount invested today, the price, P0


Figure 8-1 Cash Flow Time Line for
Stock Valuation

6


The Nature of Cash Flows
from Stock Ownership
Comparison of Cash Flows from Stocks and Bonds
– For stockholders:
Expected dividends and future
selling price are not known
with any precision
Similarity to bond cash flows is
superficial – both involve a
stream of small payments

followed by a larger payment

– For bondholders:
Interest payments are
guaranteed, constant
Maturity value is fixed
At maturity, the investor
receives face value from
the issuing company.

When selling, investor receives
money from another investor
7


The Basis of Value
The basis for stock value is the present value
of expected cash inflows even though
dividends and stock prices are difficult to
forecast

P0 = D1 PVFk,1  + D2 PVFk,2  + K + Dn PVFk,n  + Pn PVFk,n 

8


Concept Connection Example 8-1 Valuation of Stock
Based on Projected Cash Flows

Joe Simmons is interested in the stock of Teltex Corp.

He feels it is going to have two very good years because
of a government contract, but may not do well after that.
Joe thinks the stock will pay a dividend of $2 next year
and $3.50 the year after. By then he believes it will be
selling for $75 a share, at which price he'll sell anything
he buys now.
People who have invested in stocks like Teltex are
currently earning returns of 12%. What is the most Joe
should be willing to pay for a share of Teltex?


Concept Connection Example 8-1 Valuation
of Stock Based on Projected Cash Flows

Joe shouldn’t pay more than the present value of the
cash flows he expects: $2 at the end of one year and
$3.50 plus $75 at the end of two years.

P0 = $2 PVF12%,1  + $3.50 PVF12%,2  + $75 PVF12%,2 
= $2[0.8929] + $3.50[0.7972] + $75.00[0.7972]
= $64.37

10


The Intrinsic (Calculated)
Value and Market Price
A stock’s intrinsic value is based on
assumptions about future cash flows made
from fundamental analysis of the firm and its

industry
Different investors with different cash flow
estimates will have different intrinsic values

11


Growth Models of Common
Stock Valuation
Based on predicted growth rates since
forecasting exact future prices and dividends is
difficult
More likely to forecast a growth rate of
earnings rather than cash flows

12


Developing Growth-Based Models
A stock’s value today is the sum of the present values
of the dividends received while the investor holds it
and the price for which it is eventually sold
P0 =

D1
D2
Dn
Pn
+
+

K
+
+
n
n
( 1+ k ) ( 1+ k ) 2
1
+
k
1
+
k
(
) (
)

An Infinite Stream of Dividends
Many investors buy a stock, hold for awhile, then sell, as
represented in the above equation

13


Developing Growth-Based Models
A person who buys stock at time n will hold it until
period m and then sell it
– Their valuation will look like this:
Pn =

Dn + 1

Dm
Pm
+…+
+
m-n
m-n
(1 + k)
(1 + k)
(1 + k)

Repeating this process until infinity results in:
∞

P0 = ∑
i=1

Di

(1 + k)

i

14


The Constant Growth Model
If dividends are assumed to be growing at a constant rate forever
and the last dividend paid is, D0, then the model is:

D 0 (1 + g)i

P0 = ∑
(1 + k )i
i=1
∞

This represents a series of fractions as follows
P0 =

D0 ( 1 + g )

( 1+ k )

+

D0 ( 1 + g )

( 1+ k )

2

2

+

D0 ( 1 + g )

( 1+ k )

3

3

+K∞

If k>g, the fractions get smaller (approach zero) as exponents get larger

15


Constant Normal Growth
The Gordon Model
Constant growth model can be simplified to
D1
P0 =
k −g

k must be
greater than
g.

The Gordon Model is a simple expression for forecasting
the price of a stock that’s expected to grow at a constant,
normal rate

16


Concept Connection Example 8-3 Constant Normal
Growth - The Gordon Model

Atlas Motors is expected to grow at a constant rate of
6% a year into the indefinite future. It recently paid a
dividends of $2.25 a share. The rate of return on
stocks similar to Atlas is about 11%. What should a
share of Atlas Motors sell for today?

D1
P0 =
k-g
$2.25 (1.06)
=
.11 - .06
= $47.70
17


The Zero Growth Rate Case —
A Constant Dividend
If a stock is expected to pay a constant, non-growing
dividend, each dollar dividend is the same
Gordon model simplifies to:

D
P0 =
k
A zero growth stock is a perpetuity to the investor

18

The Expected Return
Recast Gordon model to focus on the return (k)
implied by the constant growth assumption

D1
k=
+g
P0
The expected return reflects investors’ knowledge of a
company
If we know D0 (most recent dividend paid) and P0
(current actual stock price), investors’ expectations
are input via the growth rate assumption
19


Two Stage Growth
At times, a firm’s future growth may not be expected to be
constant
– A new product may lead to temporary high growth

The two-stage growth model values a stock that is expected
to grow at an unusual rate for a limited time
– Use the Gordon model to value the constant portion
– Find the present value of the non-constant growth periods

20


Figure 8-2 Two Stage Growth Model

21


Concept Connection Example 8-5
Valuation Based on Two Stage Growth
Zylon Corporation’s stock is selling for $48 a share.
We’ve heard a rumor that the firm will make an
exciting new product announcement next week.
We’ve concluded that this new product will support an
overall company growth rate of 20% for about two
years.

22


Concept Connection Example 8-5
Valuation Based on Two Stage Growth
We feel growth will slow rapidly and level off at about
6%. The firm currently pays an annual dividend of
$2.00, which can be expected to grow with the
company.
The rate of return on stocks like Zylon is
approximately 10%.
Is Zylon a good buy at $48?


Concept Connection Example 8-5 Valuation
Based on Two Stage Growth
D1 = D0 (1+g1) = $2.00(1.20) = $2.40

D2 = D1 (1+g1) = $2.40(1.20) = $2.88
D3 = D2(1+g2) = $2.88(1.06) = $3.05


Concept Connection Example 8-5
Valuation Based on Two Stage Growth
We’ll develop a schedule of expected dividend
payments:
Expected
Year
Dividend
Growth
1

$2.40

20%

2

$2.88

20%

3

$3.05

6%

Next, we’ll use the Gordon model at the point in time
where the growth rate changes and constant growth
begins. That’s year 2, so:

D3
$3.05
P2 =
=
= $76.25
k - g2
.10 - .06

25