Chapter 7
The Valuation and Characteristics of Stocks
COMMON STOCK OWNERSHIP
Stockholder Rights:
Dividend
Asset-ownership (Little role as "owner" in large public companies
Stock is just an investment)
Voting
Preemptive right- Allow stockholders to maintain their proportionate ownership
Common-stock classes
Nonvoting stock
Voting stock
Voting Rights
Majority Voting--(Statutory Voting)
One share = One Vote
In this case, often have no minority viewpoint representation on the Board of
Directors
If own 100 shares have 100 votes for each issue voted upon.
Cumulative Voting
Cumulative voting ensures some minority group representation on the board.
Minority stockholders can cast all votes for a single seat.
-
-
Each share of stock represents as many votes as there are directors to be elected.
If you have 7 directors to be elected (7 issues) and you own 100 shares then you
have 700 votes which you can cast. Can cast all votes for one director (on one
issue).
Stock splits
if management feels stock should sell at lower price to attract more purchasers it
can effect a stock split
seems that optimum price rage is $15-$60
accounting treatment: par value is adjusted accordingly
( ie. 2-1 split: par value is reduced by one half and the # of shares doubled)
Reverse Stock Split
used to bring low-priced shares up to more desirable level
Stock Dividends
dividend to stockholders that consists of additional shares of stock instead of cash
Stock-Repurchases
company repurchase own stock (known as treasury stock)
Advantages:
(1) no fixed-dividend obligation
(2) decreased debt ratio
Disadvantages:
(1)
(2)
high-cost of financing
dilution of original owner's claim
RETURN ON AN INVESTMENT IN STOCK
One year holding period:
Stock Valuation
Ke=
D1 + P1 - P o
Po
Po
Po 
D1  P1
1 k
where
Ke: Market Capitalization Rate
D1: Expected dividend for t=1
P1: Expected price for t=1
Po: Current price
The return on any stock investment is the rate that makes the present value of future cash
flows equal to the price paid today
Common Stock
(1) Cash flows:
dividends
capital gains
K 
P  P0
D1
 1
Po
P0
Dividend
Yield
(2)
Capital
Gain
Growth
Retained
E t+1 = E t + [
Et
Et
Earnings
Et
* R]
Retained
Earnings Earnings
Return
=
+[ Earnings *
]
next year this year
on R.E.
this year
E t+1 = E t + [
Retained
*R]
Earnings
1+ g = 1+ [Retention rate * R]
g = (Retention rate)* (Return on earnings)
Sources to find expected growth rates:
Value Line Investment Survey
Institutional Brokers Estimate System
Zacks Earning Estimate
CASH FLOWS FROM COMMON STOCK OWNERSHIP
Analogous to bonds
A regular series followed by a return of invested funds
however
Far less precise and regular
Not contractually guaranteed
0
1
2
3
Years
n-1
n
D1
D2
D3
Dn-1
Dn
Pn
THE BASIS OF VALUE
Make some assumption about the behavior of future dividends and the
eventual selling price. Then take the present value of future cash flows
P0 = D1[PVFk,1] + D2[PVFk,2] + . . . + Dn[PVFk,n] + Pn[PVFk,n]
Example: Joe Simmons is interested in the stock of Teltex Corp. He feels it will pay
dividends of $2 and $3.50 in the next two years, after which its price will be $75.
Similar stocks return 12%. What should Joe be willing to pay for Teltex?
Solution:
P0 = D1[PVFk,1] + D2[PVFk,2] + P2[PVFk,2]
= $2.00[PVF12,1] + $3.50[PVF12,2] + $75.00[PVF12,2]
= $2.00[.8929] + $3.50[.7972] + $75.00[.7972]
= $64.37
Buy if the price is below about $64
Fundamental Analysis
The Intrinsic (Calculated) Value and Market Price
Joe's research led to a forecast of future dividends and prices which led to a
value of about $64.
If other investors don't agree their intrinsic values will be different.
Market price is a consensus of everyone's intrinsic values.
If Joe is right, he can make money.
GROWTH BASED MODELS OF STOCK VALUATION
We generally don't have the detailed information to forecast exact dividends and prices.
However, we can usually forecast a growth rate.
Develop a model based on today and an assumed growth into the future.
Need to change focus:
Thinking from a Finite Number of Dividends and a Price,
to an Infinite Stream of Dividends
P0 = D1[PVFk,1] + D2[PVFk,2] + . . . + Dn[PVFk,n] + Pn[PVFk,n]
or
Po =
D1 + D 2 + ...+ D n +
Pn
2
n
(1 + K e ) (1 + K e )
(1 + K e ) (1 + K e )n
Imagine the buyer in period n as having a model in mind for Pn stretching farther into the
future to period m and ending with Pm
Pn =
Dn1 + ...+
Dm +
Pm
m
(1 + K e )
(1 + K e ) (1 + K e )m
Replace Pn with that model pushing the selling price farther into the future.
Keep doing this until sale is infinitely distant and its PV = 0
Result is value based on only the PV of an infinite stream of dividends

Dt
Po = 
(1 + K e )t
t +1
A Market Based Argument
The only thing a company can return to equity investors is all of its dividends.
The investing community as a whole has nothing else on which to base value.
Working With Growth Rates
Growth rates work just like interest rates. If g = 6% $100 grows at rate g:
$100 x .06 = $6,
$100(1+g) = $100 x 1.06 = $106
Growing dividends beginning with the last one, D0:
D1 = D0 + gD0
= D0 (1+g)
D2 = D1 (1+g)
D2 = D0 (1+g)2 GROWTH MODEL
THE CONSTANT
inf
In general:
P  
0
D (1  g )i
0
i
i
Di = D0 (1 +i  g)
1 (1  k )
An infinite series of fractions
P0 
Multiply by (1+g) repeatedly for successive values
D0(1 g) D0(1 g)2 ofDa0(growing
1 g)3
dividend
(1 k)

(1 k)2

(1 k)3
 . . . infinity
 (1  g) (1  g)2 (1  g)3

P0  D0 


 . . . inf 
2
3
(1  k) (1  k) (1  k)

If k is larger than g (normal growth), the fractions in the brackets
get smaller as the exponents get larger and the expression is finite
TM 7-5 Slide 1 of 2
The Constant (Normal) Growth Model
The Gordon Model
 Assume a constant growth in dividends
–
Dividends expected to grow at a constant rate, g, over time
Po =
D1
Ke - g
D1 = Do (1 + g)
- g: growth rate
- ke: required return
- Keee >> gg
–D1 is the expected dividend at end of the first period
–D1 =D0 (1+g)
 Implications of constant growth
–
Stock prices grow at the same rate as the dividends
–
Stock total returns grow at the required rate of return
» Growth rate in price plus growth rate in dividends equals k, the required rate of return
–
A lower required return or a higher expected growth in dividends raises prices
Example 7-3: Atlas Motors will grow at 6% indefinitely. It recently paid a dividend of
$2.25 a share. Similar stocks return about 11%. What should Atlas sell for?
Solution:
D0 = $2.25, k = .11, g = .06
Po 
2.25(1.06)
.11  .06
The Zero Growth Case - A Constant Dividend
A perpetuity
P0 
D0
K
THE EXPECTED RETURN
Solve the Gordon model for k
D
K  1 g
P0
An estimate of the return at price P0 assuming the growth rate is g
Compare with one year return
Ke=
D1 + P1 - P o
Po
Po
g = capital gains yield
TWO STAGE GROWTH
We can sometimes forecast a temporary "super normal" growth rate
followed by a long term normal rate. E.g., firm grows at super normal rate g1
for two years then grows indefinitely at normal rate g2
0
g1
1
2
3
g2
4
. . . .
D0
D1
D2
D3
D4
. . . .
D
3
P2 = k  g 2
P0
PVs
Figure 7-2 Two Stage Growth Model
Use the Gordon model at the beginning of the infinite period of constant
D3
normal growth
P 
2
k  g2
TM 7-7
Example 7-5
Zylon stock is selling for $48. A new product will support a growth
rate of 20% for two years, after which growth will slow to 6%. The
annual dividend of $2.00 will grow with the company. Similar stocks
return 10%. Is Zylon a good buy at $48?
D 1  D 0 ( 1  g 1 )  $2.00 ( 1. 20 )  $2.40
Solution:
D 2  D 1 ( 1  g 1 )  $2.40 ( 1. 20 )  $2.88
D 3  D 2 ( 1  g 2 )  $2.88 ( 1.06 )  $3.05
g1=20%
1
0
g2=6%
2
. . .
3
. . .
D0 = $2.00
D1 = $2.40
D2 = $2.88
D3 = $3.05
P2 = $76.25
TM 7-8 Slide 1 of 2
Use the Gordon model at the point in time where the growth rate
changes and constant growth begins, year 2 in this case.
P2 
D3
$3.05

 $76.25
k  g 2 .10  .06
Add present values of everything a buyer at time zero gets: D1, D2,
and P2.
P0  D1 PVFk ,1   D 2  PVFk , 2   P2  PVFk , 2 
P0  $2.40 PVF10 ,1   $2.88 PVF10 , 2   $76.25 PVF10 , 2 
P0  $2.40 .9091  $2.88 .8264  $76.25 .8264
P0  $67.57
Compare $67.57 to the market price of $48.00.
If assumptions are correct we've found a bargain!
TM 7-8 Slide 2 of 2
TWO STAGE GROWTH
 Multiple growth rates: two or more expected growth rates in dividends
–
Ultimately, growth rate must equal that of the economy as a whole
–
Assume growth at a rapid rate for n periods followed by steady growth
 Multiple growth rates
–
First present value covers the period of super-normal (or sub-normal) growth
–
Second present value covers the period of stable growth
» Expected price uses constant-growth model as of the end of super- (sub-) normal period
» Value at n must be discounted to time period zero
Two Period Growth Model:
m
t
1
Do (1 + g 1 )
=

+
( Dm+1 )
Po
t
m
(1 + K e )
(1 + K e ) K e - g 2
t=1
m = length of time firm grows at g1
g2 < k
g1: growth rate for period 1
g2 : growth rate for period 2
ke: required return
Example: required rate of return =18% Current dividend is 2.00 dividends are expected to grow
at 12% for first 6 years then at 6%
Present value of First 6-Years' Dividends:
6
 [ D0 (1 + g 1 )t /(1 + k e )t ]
t=1
Year
t
Dividend
Dt
P.V. Interest Factor
PVIF18.t = 1/(1 + .18)t
Present Value
Dt x PVIF18.t
1
$ 2.240
.874
$ 1.897
2
2.509
.718
1.801
3
2.810
.609
1.711
4
3.147
.516
1.624
5
3.525
.437
1.540
6
3.948
.370
1.461
PV (First 6-Years' Dividends
Value of Stock at End of Year 6:
P6 = D7/(Ke - g2) where g2 = .06
D7 = D6(1 + g2) = 3.948(1 + .06) = $4.185
P6 = 4.185/(.18 - .06) = $34.875
Present Value of P6
PV(P6) = P6/(1 + ke)6 = $34.875/(1 + .18)6
= $34.875 x .370 = $12.904
Value of Common Stock (Po)
Po = PV(First 6-Year's Dividends) + PV(P6)
= 10.034 + 12.904 = $22.94
$10.034
Two period growth model:
1+ g 1 N
N -1
) ]
D (1 + g 1 ) (1 - g 2 )
1+ k
+[ 1
]
k - g1
(1 + k )N (k - g 2 )
D1 [1 - (
Po =
N = No. of years growing at g1
1.12 6
) ]
2.24(1.12 )5 (1.06)
1.18
+
.18 - .12
(.18 - .06)(1.18 )6
2.24[1 - (
P=
2.24[1 - .7312] 2.24(1.76)(1.06)
+
.06
(.12)(2.69 96)
10.04 +
4.18
=
.3239
10.04 + 12.90 = $22.94
PRACTICAL LIMITATIONS OF PRICING MODELS
Although problems solve to the penny, our answers are not that accurate.
Results can never be any more accurate than the inputs.
Projected growth rates and the interest rate can both be off by a lot.
An additional problem arises because of the difference in estimates in the
denominator. Result blows up when the difference is small.
Bond valuation is exact because cash flows are contractually specified and very
likely to occur. Market yields are also precise.
Stock valuation is comparatively fuzzy.
Stocks That Don't Pay Dividends
Have value because they are expected to pay them someday
(Even if management says it won't)
No Dividend Model
CAPM = r j = r f + B j ( r m - r f )
CORPORATE ORGANIZATION AND CONTROL
Corporations are controlled by Boards of Directors whose members are elected by
stockholders.
The board appoints senior management which runs the company.
Major strategic decisions are considered by the board.
A few really big issues, like mergers, are voted on by the stockholders.
Boards generally are made up of top managers and outside directors.
Board members may be major stockholders, but don't have to be.
If stock ownership is widely distributed with no single party having a large share,
top managers have control with little accountability to stockholders.
7-12
PREFERRED STOCK
• Has a mix of the characteristics of common stock and bonds
•Referred to as a hybrid
Features
Par price
Preferred is generally issued at prices of $25, $50, and $100
Pays a constant dividend forever (norm)
Adjustable rate-preferred stock
Cumulative feature
Preferred dividends can be passed but must be caught up before common
dividends can be paid. Designed to enhance safety for investors
Participation in “extra” dividends
Maturity
Call feature
Convertible
Voting rights-none
Advantages of Preferred Stock Financing
(1) Preferred dividend payments are potentially flexible.
(2) Increase a firm's degree of financial leverage.
(3) 70% exclusion of dividend received from other companies from federal
income.
Disadvantages
(1) High after-tax cost as compared with L-T debt.
E.g.: If the interest rate is 10%, preferred shares sold at $100 would offer a
dividend of $10. Refer to as a $10 preferred issue rather than as a 10% preferred
issue. Think of the 10% rate as similar to the coupon rate on a bond, and the
$100 initial selling price as similar to a bond's face value
VALUATION OF PREFERRED STOCK
Valued as a perpetuity
Po =
Dp
Kp
7-13
Example 7-6:
Roman Industries' $6 preferred originally sold for $50. The rate on similar issues is
now 9%. For what should Roman's preferred sell?
Solution:
P=6/.09 = 66.67
Notice current price is above the original issue price because interest rates have
fallen from ($6/$50=) 12% to 9%.
•
•
•
•
•
•
•
Comparing Preferred Stock with Common Stock and Bonds
Payments to investors - Constant, like bonds
Maturity and return of principal - No maturity, like stock
Assurance of Payment - Cumulative feature - Between
Priority in bankruptcy - Between
Voting rights - None, like stock
Tax deductibility of payments - Not deductible, like stock
The Order of Risk - Between
7-14
SECURITIES ANALYSIS
Valuation is a part of Securities Analysis
Fundamental Analysis
Discover as much as possible about a firm and its industry
Use that knowledge to project future cash flows
Calculate intrinsic value
Compare with market price
Invest if market price is below intrinsic value
Technical Analysis
Historical patterns of price and volume repeat over time
Chart prices and volumes to predict changes
Technicians are also called chartists
The Efficient Market Hypothesis (EMH)
Financial markets are efficient in that new information is
disseminated very quickly and prices adjust immediately.
Hence technical analysis is useless
because all available information is already in the price of stocks.
Fundamental analysis also won't help an investor consistently beat the
market because an army of professional analysts will have figured everything
out first.
STOCK MARKET EFFICIENCY
Weak-form: security prices reflect all market-related data from past.
Semistrong: security prices reflect all past information but also all public
information.
Strong:
prices reflect all information including private or insider info.
Tests
Weak-form: look for non-random patterns in sec. prices.
Semistrong: Event studies benchmark to test for abnormal returns
7-15
^
CAPM: rj = rf + β(rm - rf)
abnormal return:
^
rj - rj = e
^
rj: actual rj: estimated
e: is difference
Question: is e significantly different from zero
7-16