Practical financial managment 7e LASHER chapter 8

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

A capital gain (loss) occurs if you sell the stock

or
k=

D1
P
{0

dividend yield

+

( P1-P0 )

for a price greater (lower) than you paid for it.

P
14 2043

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
When selling, investor receives money from
another investor

–

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

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, D 0, 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

k must be greater than

D1
P0 =
k −g

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:

Year

Expected 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