Stock Valuation
McGraw-Hill/Irwin Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.

 Understand how stock prices depend on future dividends and dividend growth
 Be able to compute stock prices using the dividend growth model
 Understand how growth opportunities affect stock values
 Understand the PE ratio
 Understand how stock markets work
9-1

9.1
The Present Value of Common Stocks
9.2
Estimates of Parameters in the Dividend Discount
Model
9.3
Growth Opportunities
9.4
Price-Earnings Ratio
9.5
The Stock Markets
9-2

 The value of any asset is the present value of its expected future cash flows.
 Stock ownership produces cash flows from:
 Dividends
 Capital Gains
 Valuation of Different Types of Stocks
 Zero Growth
 Constant Growth
 Differential Growth
9-3

 Assume that dividends will remain at the same level forever
Div
1

Div
2

Div
3
 

Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:
P
0

Div
1
( 1

R )
1

Div
2
( 1

R )
2

Div
3
( 1

R )
3
 
P
0

Div
R
9-4

Assume that dividends will grow at a constant rate, g , forever, i.e.,
Div
1

Div
0
( 1
 g )
Div
2

Div
1
( 1
 g )

Div
0
( 1
 g )
2
Div
3

Div
2
( 1

.
..
g )

Div
0
( 1
 g )
3
Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:
P
0

Div
R

1 g
9-5

 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 level, how much should the stock be selling for?
 P
0
= .50(1+.02) / (.15 - .02) = $3.92
9-6

 Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter.
 To value a Differential Growth Stock, we need to:
 Estimate future dividends in the foreseeable future.
 Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2).
 Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.
9-7


Assume that dividends will grow at rate g
1 years and grow at rate g
2 thereafter. for N
Div
1

Div
0
(1
 g
1
)
Div
2
Div
N


Div
Div
1
(1
 g
1
)
.
..
N

1
(1

 g
1
)
Div

0
(1
Div
0

(1 g

1
)
2 g
1
)
N
Div
N

1

Div
N
(1

.
..
g
2
)

Div
0
(1
 g
1
)
N
(1
 g
2
)
9-8

Dividends will grow at rate g
1 at rate g
2 thereafter for N years and grow
0
Div
0
(1
 g
1
)
1
…
Div
0
(1
 g )
1
N
N
Div
0
(1

… g
1
)
2
2
Div
N
(1
 g
2
)

Div
0
(1
 g
1
)
N
(1

… g
2
)
N+1
9-9


We can value this as the sum of:
 a T -year annuity growing at rate g
1
P
A

R
C
 g
1

 1

( 1

( 1
 g
1
)
T
R )
T

 plus the discounted value of a perpetuity growing at rate g
2 that starts in year T +1
P
B



Div
R

T

1 g
2
( 1

R )
T


9-10

Consolidating gives:
P

C
R
 g
1


1

( 1

( 1
 g
1
)
T
R )
T





Div
R

T

1 g
2
( 1

R )
T


Or, we can “cash flow” it out.
9-11

A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity.
What is the stock worth? The discount rate is 12%.
9-12

P

$ 2

( 1 .
08 )
.
12

.
08


1

( 1 .
08 )
( 1 .
12 )
3
3





$ 2 ( 1 .
08 )
3
( 1 .
04 )
.
12

.
04


( 1 .
12 )
3
P

$ 54


1

.
8966



$ 32 .
75

( 1 .
12 )
3
P

$ 5 .
58

$ 23 .
31 P

$ 28 .
89
9-13

$ 2(1 .
08) $ 2(1 .
08)
2 $ 2(1 .
08)
3
$ 2(1 .
08)
3
( 1 .
04 )
…
0
P
0
0

$ 2 .
16
1
1
$ 2 .
16

1 .
12
$ 2
$ 2 .
33
( 1 .
12 )
2
2
.
2
33 $ 2 .
52

3
3
$ 2 .
62
.
12

.
04
4
The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3 .

$ 2 .
52

$ 32 .
75
( 1 .
12 )
3
P
3

$ 28 .
89

$ 2 .
62
.
08

$ 32 .
75
9-14

 The value of a firm depends upon its growth rate, g , and its discount rate, R .
 Where does g come from?
g = Retention ratio × Return on retained earnings
9-15

R
 The discount rate can be broken into two parts.
 The dividend yield
 The growth rate (in dividends)
 In practice, there is a great deal of estimation error involved in estimating R .
9-16

 Start with the DGM:
P
0

D
0
( 1
 g)
R g

D
1
R g
Rearrange and solve for R:
R

D
0
( 1

P
0 g)
 g

D
1
P
0
 g
9-17

 Growth opportunities are opportunities to invest in positive NPV projects.
 The value of a firm can be conceptualized as the sum of the value of a firm that pays out
100% of its earnings as dividends plus the net present value of the growth opportunities.
P

EPS

NPVGO
R
9-18

Consider a firm that has forecasted EPS of $5, a discount rate of 16%, and is currently priced at $75 per share.
 We can calculate the value of the firm as a cash cow.
P
0

EPS
R

$ 5
.
16

$ 31 .
25
 So, NPVGO must be: $75 - $31.25 = $43.75
9-19

 An increase in the retention rate will:


Reduce the dividend paid to shareholders
Increase the firm’s growth rate
 These have offsetting influences on stock price
 Which one dominates?
 If ROE> R , then increased retention increases firm value since reinvested capital earns more than the cost of capital.
9-20

 Many analysts frequently relate earnings per share to price.
 The price-earnings ratio is calculated as the current stock price divided by annual EPS.
 The Wall Street Journal uses last 4 quarter’s earnings
P/E ratio

Price per share
EPS
9-21

 Recall, P

EPS

NPVGO
R
 Dividing every term by EPS provides the following description of the PE ratio:
PE

1
R

NPVGO
EPS

So, a firm’s PE ratio is positively related to growth opportunities and negatively related to risk ( R )
9-22

 Dealers vs. Brokers
 New York Stock Exchange (NYSE)


Largest stock market in the world
License Holders (formerly “Members”)
 Entitled to buy or sell on the exchange floor
 Commission brokers
 Specialists
 Floor brokers
 Floor traders
 Operations
 Floor activity
9-23

 Not a physical exchange – computer-based quotation system
 Multiple market makers
 Electronic Communications Networks
 Three levels of information
 Level 1 – median quotes, registered representatives
 Level 2 – view quotes, brokers & dealers
 Level 3 – view and update quotes, dealers only
 Large portion of technology stocks
9-24

52 WEEKS YLD VOL NET
HI LO STOCK SYM DIV % PE 100s CLOSE CHG
21.89
9.41 Gap Inc GPS 0.34 3.1
8 88298 11.06 0.45
Gap has been as high as $21.89 in the last year.
Gap pays a dividend of 34 cents/share.
Given the current price, the dividend yield is 3.1%.
Gap ended trading at
$11.06, which is up 45 cents from yesterday.
Gap has been as low as $9.41 in the last year.
Given the current price, the PE ratio is
8 times earnings.
8,829,800 shares traded hands in the last day’s trading.
9-25

 What determines the price of a share of stock?
 What determines g and R in the DGM?

Decompose a stock’s price into constant growth and NPVGO values.
 Discuss the importance of the PE ratio.
 What are some of the major characteristics of
NYSE and Nasdaq?
9-26