# Chap008

```Chapter
Eight
Stock Valuation
8.1
Chapter Outline




Common Stock Valuation
Common Stock Features
Preferred Stock Features
Stock Market Reporting
8.2
Cash Flows for Shareholders 8.1
 If you buy a share of stock, you can receive cash in two ways
 Dividends
 As with any asset, the market price of common stock is equal
to the present value of the expected future cash flows the stock
will generate
8.3
One Period Example
 Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and
you expect it to pay a \$2 dividend in one year and you believe that you
can sell the stock for \$14 at that time. If you require a return of 20% on
investments of this risk, what is the maximum you would be willing to
pay?
 Compute the PV of the expected cash flows
Div 1  Sale Price
1  r 
2  14

1.20
 \$13.33
PVStock 
Calculator Approach
16
FV
0
PMT
1
N
20
I
PV
\$13.33
8.4
Two Period Example
 Now what if you decide to hold the stock for two years? In addition to
the \$2 dividend in one year, you expect a dividend of \$2.10 in two
years and a stock price of \$14.70 at the end of year 2. Now how much
would you be willing to pay now?
PVStock 
Div 1 Div 2  Sale Price

1  r 
1  r 2
2
2.10  14.70

1.20
1.20 2
 \$13.33

Calculator Approach
0
CFj
2
CFj
16.80
CFj
20
I
2nd NPV
\$13.33
8.5
Three Period Example
 Finally, what if you decide to hold the stock for three periods? In
addition to the dividends at the end of years 1 and 2, you expect to
receive a dividend of \$2.205 at the end of year 3 and a stock price of
\$15.435. Now how much would you be willing to pay?
PVStock 
Div 3  Sale Pr ice
Div 1
Div 2


1  r  1  r 2
1  r 3
2
2.10 2.205  15.435


1.20 1.20 2
1.203
 \$13.33

Calculator Approach
0
CFj
2
CFj
2.10
CFj
17.64
CFj
20
I
2nd NPV
\$13.33
8.6
Developing The Model
 We could continue this process for many time periods
 In fact, the price of the stock is just the present value of all
expected future dividends
 So, how can we estimate all future dividend payments?
8.7
Estimating Dividends: Special Cases
 Constant dividend
 The firm will pay a constant dividend forever
 Market instrument – preferred stock
 Price is computed using the level perpetuity formula [PV = C/r]
 Constant dividend growth
 The firm will increase the dividend by a constant percent every
period
 Market instrument – common stock
 Price is computed using a growing perpetuity formula
[PV = C/(r-g)]
 Supernormal growth
 Dividend growth is high initially, but later settles down to a
long-run constant growth rate
8.8
Zero Growth Rate
 The dividends on most preferred stocks are expressed as a constant
percentage of the share’s face value
 Suppose a preferred share is expected to pay a \$0.50 dividend every
quarter and the required return is 10% with quarterly compounding.
 What is the price?
Div 1
r
0.50

 0.10 


 4 
 \$20.00
PVPreferred 
Stock
8.9
Constant Growth Rate
 To value a common stock, we usually assume the dividend stream will
grow at some constant growth rate over time
P0 
Div 3
Div 1
Div 2
Div 



.
.
.

1  r  1  r 2 1  r 3
1  r 
Div 0 1  g  Div 0 1  g  Div 0 1  g 
Div 0 1  g 




.
.
.

1  r 
1  r 2
1  r 3
1  r 
2
 With a little algebra, this reduces to:
Div 0 (1  g) Div 1
P0 

r -g
r -g
3

8.10
Constant Growth: Example 1
 Suppose Big D, Inc. just paid a dividend of \$.50. It is expected to
increase its dividend by 2% per year. If the market requires a return of
15% on assets of this risk, how much should the stock be selling for?
Div 0 (1  g)
r -g
0.50(1.02)
0.15 - 0.02
 \$3.92
P0 
8.11
Constant Growth: Example 2
 Suppose TB Pirates, Inc. is expected to pay a \$2 dividend in one year. If
the dividend is expected to grow at 5% per year and the required return is
20%, what is the price?
Div 1
r -g
2.00
0.20 - 0.05
 \$13.33
P0 
Stock Price Sensitivity to Dividend Growth, g
250
Div1 = \$2; r = 20%
200
Stock Price
8.12
150
100
50
0
0
0.05
0.1
Growth Rate
0.15
0.2
Stock Price Sensitivity to Required Return, r
250
Div1 = \$2; g = 5%
200
Stock Price
8.13
150
100
50
0
0
0.05
0.1
0.15
Required Return
0.2
0.25
0.3
8.14
Gordon Growth Company – Example 1
 Gordon Growth Company is expected to pay a dividend of \$4 next
period and dividends are expected to grow at 6% per year. The required
return is 16%.
 What is the current price?
Div 1
r -g
4.00
0.16 - 0.06
 \$40.00
P0 
8.15
Gordon Growth Company – Example 2
 What is the price expected to be in year 4?
P4 
Div 5
r -g
Div 1 1  g 

r -g
4
4.001.06
0.16 - 0.06
 \$50.50
4
8.16
Gordon Growth Company - Continued
 What is the holding period return (capital gains yield) due to the
capital gain over the four year period?
HPR 
P1  P0
P0
50.50  40.00
40.00
 26.25%

8.17
Non-constant Dividend Growth
 Suppose a firm is expected to increase dividends by 20% in
one year and by 15% in year 2. After that, dividends will
increase at a rate of 5% per year indefinitely. If the last
dividend that was just paid was \$1 and the required return is
20%, what is the price of the stock?
 Remember that we have to find the PV of all expected future
dividends.
0
\$1.00
20% 1
15%
2
5%
3
5%
4 5%
∞
8.18
Non-constant Dividend Growth - Continued
 Compute the dividends until growth levels off
0
\$1.00
20% 1
\$1.20
15%
2
5%
\$1.38
3
5%
\$1.45
 Find the present value of the expected future cash flows
P0 
Div 1
Div 2 Div 3  1 




2
2 
1  r  1  r  r  g  1  r  
1.20 1.38
1.45  1 





1.20 1.20 2 0.20  0.05  1.20 2 
 \$8.67
4 5%
∞
8.19
Calculating the Required Rate of Return
Div 0(1  g)
r-g
Div 1

r-g
rearrange and solve for r
Div 0(1  g)
r
g
P0
P0 

Div 1
g
P0
 The required rate of return on a common stock can always be
decomposed into:
 Dividend yield
 Capital gain or loss
8.20
Example – Finding the Required Return
 Suppose a firm’s stock is selling for \$10.50. They just paid a \$1 dividend
and dividends are expected to grow at 5% per year. What is the required
return?
r
Div 0(1  g)
g
P0
1.00(1.05)
 0.05
10.50
 15%

 What is the dividend yield?
Dividend Yield 
Div 0(1  g)
P0
1.00(1.05)

10.50
 10%
What is the capital gains yield?
Capital Gain  g
 0.05
 5%
8.21
Table 8.1 - Summary of Stock Valuation
8.22
Common Stock – Features
 Voting Rights
1- Cumulative voting- total number of votes each shareholder may cast =
(# of shares owned) x (# of directors to be elected)
All directors are elected at the same time. Cumulative voting favors minority
stockholders.
2- Straight voting- directors are elected one at a time (i.e., each directors is
voted on one at a time). Straight voting favors majority shareholders.
Staggered elections- only a portion of the board is elected in any one year.
This makes it difficult for minority shareholder to elect a specific director.
8.23
Example- Voting Rights
 A company has two shareholders: “A” (owns 50 shares); “B” (owns 249
shares). There are 5 directors to be elected and 7 candidates running (T, U,
V, W, X, Y, Z). “A” wants candidate Z to be on the board. B wants
candidates T, U, V, W, and Y.
 Using Straight voting- “A” has 50 votes and “B” has 249 votes. Since each
director is voted on one at a time “B” will be able to vote in all his
candidates and “A” will not be able to vote in his candidate.
 Using Cumulative voting“A” has 50 x 5 = 250 votes (all for Z)
“B” has 249 x 5 = 1,245 votes (&divide; 5 = 249 for T, U, V, W, and Y)
Therefore, Z wins the most votes. “B” cannot arrange votes to block Z.
8.24
Common Stock – Features (cont.)
 Other Rights
 Share proportionally in declared dividends
 Share proportionally in remaining assets during liquidation
 Right to vote on major issues – e.g. mergers
 Preemptive right – the right to purchase new stock to
maintain proportional ownership, if desired (i.e., the right
Example
If an investor has 1% of ownership and 1 million new shares are issued.
The investor will have first rights to buy 10,000 of the new shares.
8.25
Common Stock – Features (cont.)
 Classes of stock- one has voting power, one has high
dividends
 Dual class shares
 Voting &amp; not-voting (restricted)
 Allows founders to retain control while raising new equity
e.g. Class A: 1 vote per share, 100% of dividends
Class B: 10 votes per share, zero dividends (usually not publicly
 Coattail provision
 Protects non-voting shareholders in the event of a take-over bid (it
allows the non-voting shareholders either the right to vote or to
convert their shares into voting shares that can be tendered to the
takeover bid)
8.26
Dividends
 Dividend size is determined by the board of directors
 Dividends are not a liability of the firm until a dividend has
been declared by the board
 Consequently, a firm cannot go bankrupt for not declaring
dividends
 Dividends and Taxes
 Dividend payments are not considered a business expense and
are not tax deductible
 Dividends received by individual shareholders are partially
sheltered by the dividend tax credit (13⅓ %)
 Dividends received by corporate shareholders are not taxed, thus
preventing the double taxation of dividends
8.27
Preferred Stock Valuation
 Preferred stock is a hybrid security with features of bonds and
common stock.
 Its bond features is that preferred stockholders have
preference over common stockholders and have no voting
rights.
 Its common stock features is that dividends on preferred stock
do not have to be paid (i.e., dividends go into arrears and don’t
have to be paid on time).
8.28
Preferred Stock - Characteristics
 Preferred stock has priority over common stock upon
liquidation
 Dividends
 Most preferred stock has a stated dividend that must be
paid before common dividends can be paid
 Dividends are not a liability of the firm and preferred
dividends can be deferred indefinitely
 Most preferred dividends are cumulative – any missed
dividends on preferred stock have to be paid before a
dividend can be paid on common stock
 Preferred stock generally does not carry voting rights
8.29
Preferred Stock &amp; Taxes
 Companies with a low tax rate cannot make use of the tax
shield available from interest
 Therefore, they have an incentive to issue preferred shares,
which typically pay a dividend lower than a comparable
interest rate. The dividend is non-taxable in the hands of the
recipient corporation.
 The loophole was partially closed in 1987 by forcing issuers
of preferreds to pay a tax of 40% of the preferred dividend.
 However, it may still be cheaper to use preferreds than debt
for the firm with a zero marginal tax rate
8.30
Stock Market Reporting 8.4
 Stock market quotations are published in the newspapers and
are also available on-line (usually with 15-minute delays)