© 2003 The McGraw-Hill Companies, Inc. All rights reserved.

8.1
Key Concepts and Skills

Understand how stock prices depend on future dividends and dividend growth

Be able to compute stock prices using the dividend growth model
 Understand how corporate directors are elected

Understand how stock markets work

Understand how stock prices are quoted

8.2
Chapter Outline

Common Stock Valuation

Common Stock Features

Preferred Stock Features

Stock Market Reporting

8.3
Cash Flows for Shareholders 8.1

If you buy a share of stock, you can receive cash in two ways

Dividends

Selling your shares

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

8.4
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
PV
Stock

Div
1

2

14
1 .
20

$ 13 .
33


1
Sale
 r

Price
0
1
Calculator Approach
16 FV
PMT
N
20
PV
I
$13.33

8.5
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?
PV
Stock

Div
1

1
 r


Div
2


1
Sale
 r

2
Price

2

1 .
20

$ 13 .
33
2 .
10

14 .
70
1 .
20
2
Calculator Approach
0
2
16.80
CF
CF j j
CFj
20
2 nd NPV
I
$13.33

8.6
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?
PV
Stock

Div r
1
Div

1

 
1
 r
2

2

2
1 .
20

$ 13

.
33
2 .
10
1 .
20
2


Div
3


1
Sale
 r

3
Pr ice
2 .
205

15 .
435
1 .
20
3
Calculator Approach
0
2
2.10
CF
CF j
CFj j
17.64
20
2 nd NPV
I
CFj
$13.33

8.7
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?

8.8
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

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

Supernormal growth

Dividend growth is high initially, but later settles down to a long-run constant growth rate

8.9
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?
PV
Preferred
Stock

Div
1 r

0 .
50
0 .
10
4

$ 20 .
00

8.10
Constant Growth Rate
 To value a common stock, we usually assume the dividend stream will grow at some constant growth rate over time
P
0


Div
1
1 r 1
Div
1
0


1 r
 g

Div r

2
2
Div
3
3
1 r
Div
1
0


1 r

2 g

2

.

.
.

Div
 


Div
1
0

1 r

3 g

3

.
.
.

Div
1
0

1 r

 g



With a little algebra, this reduces to:
P
0

Div
0
( 1
 g) r g

Div
1 r g

8.11
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?
P
0

Div
0
( 1
 g) r g
0 .
50 ( 1 .
02 )

0.15
$ 3
-
.
92
0.02

8.12
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?
P
0

Div
1 r g
2 .
00

0.20
$ 1
0.05
3.33

8.13
Stock Price Sensitivity to Dividend Growth, g
250
200
150
100
50
0
0
Div
1
= $2; r = 20%
0.05
0.1
Growth Rate
0.15
0.2

8.14
Stock Price Sensitivity to Required Return, r
250
200
150
100
50
0
0
Div
1
= $2; g = 5%
0.05
0.1
0.15
Required Return
0.2
0.25
0.3

8.15
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?
P
0

Div
1 r g
4 .
00

0.16
$ 4
0.06
0.00

8.16
Gordon Growth Company – Example 2

What is the price expected to be in year 4?
P
4

Div
5 r g

Div r
1

1
 g

4
g
4 .
00

1 .
06

4

0.16
$ 5
0.06
0.50

8.17
Gordon Growth Company - Continued
 What is the holding period return due to the capital gain over the four year period?
HPR

P
1

P
0
P
0
50 .
50

40 .
00

40 .
00

26 .
25 %

What is the annually compounded rate of return due to the capital gain?
r


1

HPR
 1 n


1 .
2625
 1
4

6 %
Note that the price of the stock grows at the same rate as the growth rate in the dividend stream!

8.18
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
20%
1
15%
2
5%
3
5%
4
5% ∞
$1.00

8.19
Non-constant Dividend Growth - Continued

Compute the dividends until growth levels off
0
$1.00
20%
1
$1.20
15%
2
$1.38
5%
3
$1.45
5%
 Find the present value of the expected future cash flows
4
5% ∞
P
0

Div
1
 r
1

Div

2
2

Div
3 r
 g

 
1

1 r

2



1 .
20
1 .
20

$ 8 .
67

1 .
38
1 .
20
2

1 .
45
0 .
20

0 .
05
1
1 .
20
2

8.20
Quick Quiz – Part I

What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?

What if the company starts increasing dividends by 3% per year, beginning with the next dividend? Assume that the required return stays at 15%.

8.21
Calculating the Required Rate of Return

Start with the constant dividend growth formula:
P
0

Div
0
(1
 g) r - g

Div
1 r g r
 rearrange and solve for r
Div
0
(1
 g)

P
0 g

Div
1
 g
P
0

The required rate of return on a common stock can always be decomposed into:

Dividend yield

Capital gain or loss

8.22
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
P
0

1.00(1.05)
10.50

15%

0.05
 What is the dividend yield?
Dividend Yield

Div
0
(1
 g)
P
0

1.00(1.05)
10.50

1 0 %
 What is the capital gains yield?
Capital Gain

g

0.05

5%

8.23
Table 8.1 - Summary of Stock Valuation

8.24
Common Stock – Features

Voting Rights

Other Rights

Share proportionally in declared dividends

Share proportionally in remaining assets during liquidation

Preemptive right – the right to purchase new stock to maintain proportional ownership, if desired

Classes of stock
 Dual class shares
 Voting & not-voting
 Allows founders to retain control while raising new equity

Coattail provision
 Protects non-voting shareholders in the event of a take-over bid

8.25
Dividends

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

Dividends received by corporate shareholders are not taxed, thus preventing the double taxation of dividends

8.26
Preferred Stock - Characteristics

Preferreds have priority to common stock upon liquidation

Dividends

Most preferreds have 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

8.27
Preferred Stock & 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

8.28
Example: Preferreds & Taxes
 Assume that there are two firms, Zero Tax and Full Tax. As the name implies, Zero Tax pays no tax but needs to raise $1,000. It can issue debt at 10% or preferreds at 6.7%. Full Tax is a fully taxed firm which will either purchase the preferreds or extend a loan to Zero Tax.
Issuer: Zero Tax
Dividend or interest
Dividend tax @ 40%
Tax deduction on int.
Total cost of financing
After-tax cost
Buyer: Full Tax
Before tax income
Tax
After-tax income
After-tax yield
Preferred
$67.00
$26.80
0.00
$93.80
9.38%
Preferred
$67.00
0.00
$67.00
6.70%
Debt
$100.00
0.00
0.00
$100.00
10%
Debt
$100.00
$45.00
$55.00
5.5%

8.29
Stock Market Reporting 8.4

Stock market quotations are published in the newspapers and are also available on-line (usually with 15-minute delays)

In Canada, large cap stocks trade on the TSX

Quotes and corporate information on stocks that trade on the
TSX can be found at the exchange’s website

Click on the web surfer to go to the site

8.30
Figure 8.1 – Sample Stock Market Quotation

8.31
Work the Web Example

Information on a large number of stocks in several different markets can also be found at the Globe & Mail website

Click on the web surfer to go to the site

Publicly traded companies usually have an investor relations section on their webpage

8.32
Quick Quiz – Part II

You observe a stock price of $18.75. You expect a dividend growth rate of 5% and the most recent dividend was $1.50.
What is the required return?
 What are some of the major characteristics of common stock?
 What are some of the major characteristics of preferred stock?

8.33
Summary 8.5

You should know:

The price of a stock is the present value of all future expected dividends

There are three approaches to valuing the stock price, depending on the growth rate(s) of the dividends

The rights of common and preferred shareholders

How to read a stock market quotation from the newspaper