Stock Valuation

Stock Valuation

Chapte r 8

8-2

Chapter Outline

• Bond and Stock Differences

• Common Stock Valuation

• Features of Common Stock

• Features of Preferred Stock

• The Stock Markets

Chapter Outline

• Bond and Stock Differences

• Common Stock Valuation

• Features of Common Stock

• Features of Preferred Stock

• The Stock Markets

8-4

Bonds and Stocks:

Similarities

• Both provide long-term

funding for the organization

• Both are future funds that an investor must consider

• Both have future periodic payments

• Both can be purchased in a marketplace at a price

“today”

Bonds and Stocks:

Differences

• From the firm’s perspective: a bond is a long-term debt and stock is equity

• From the firm’s perspective: a bond gets paid off at the

maturity date; stock continues indefinitely.

• We will discuss the mix of bonds

8-6

Bonds and Stocks:

Differences

• A bond has coupon payments and a lump-sum payment;

stock has dividend payments forever

• Coupon payments are fixed;

stock dividends change or

“grow” over time

A visual representation of a bond with a coupon payment (C) and a

maturity value (M)

1 2 3 4 5

$C₁ $C₂ $C₃ $C₄ $C₅

8-8

A visual

representation of a share of common

stock with dividends (D) forever

^{1 2 3 4 5}

$D₁ $D₂ $D₃ $D₄ $D₅ $D_∞

∞

Comparison Valuations

1 Bond 2 3

C C C

P₀ M

0

1 2 3

Common Stock

0

8-10

Notice these differences:

• The “C’s” are constant and equal

• The bond ends (year 5 here)

• There is a lump sum at the end

1 2 3 4 5

$C₁ $C₂ $C₃ $C₄ $C₅

$M

Notice these differences:

• The dividends are different

• The stock never ends

• There is no lump sum

1 2 3 4 5

$D₁ $D₂ $D₃ $D₄ $D₅ $D_∞

∞

8-12

Chapter Outline

• Bond and Stock Differences

• Common Stock Valuation

• Features of Common Stock

• Features of Preferred Stock

• The Stock Markets

Our Task:

To value a share of Common

Stock

8-14

And how will we accomplish

our task?

B A E F E I P

Bring

All Expected Future

Earnings

Into Present

8-16

BAEFEIPVT

Just remember:

Cash Flows for Stockholders

If you buy a share of stock, you can

receive cash in two ways:

1. The company pays dividends 2. You sell your

shares, either to another investor

8-18

One-Period Example

Receiving one future dividend and one

future selling price of a

share of common stock

One-Period Example

Suppose you are thinking of purchasing the stock of

Moore Oil, Inc. 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

8-20

Visually this would look like:

1

D₁ = $2 P₁ = $14 R = 20%

Compute the Present Value

1

D₁ = $2 P₁ = $14 R = 20%

$1.67

$11.67 PV =$13.34

1 year = N

20% = Discount rate

$2 = Payment (PMT)

$14 = FV

PV = ?

-13.34

1st 2nd

TI BA II Plus

8-22 8-22

$14 = FV 1 year = N

$2 = Payment (PMT) 20% = Discount rate

PV = ?

-13.34

HP 12-

C

8-24

Two Period Example

Now, what if you decide to

hold the stock for two years?

In addition to the 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.

Now how much would you be

willing to pay?

Visually this would look like:

2

D₁ = $2

P₂ = $14.70 R = 20% 1

D₂ = $ 2.10

8-26

Compute the Present Value

2

D₁ = $2

P₂ = $14.70 R = 20% 1

D₂ = $ 2.10

$1.67

$1.46

$ 10.21

$ 13.34 = P₀

What is the Observed Pattern?

We value a share of

stock by bring back all expected future

dividends into present

value terms

8-28

Future

Dividends

So the key is to determine the

future dividends when given the growth rate of

those dividends,

whether the growth is zero, constant, or unusual first and

then levels off to a constant growth

rate.

So how do you

compute the future dividends?

Three scenarios:

1.A constant dividend (zero growth)

2.The dividends change by a constant growth rate

8-30

So how do you

compute the future dividends?

Three scenarios:

1. A constant dividend (zero growth)

2. The dividends change by a constant growth rate

3. We have some unusual growth periods and then level off to a constant growth rate

1. Constant Dividend –

Zero Growth

• The firm will pay a constant dividend forever

• This is like preferred stock

• The price is computed using the perpetuity

8-32

So how do you

compute the future dividends?

Three scenarios:

1. A constant dividend (zero growth)

2. The dividends change by a constant growth rate

3. We have some unusual growth periods and then level off to a constant growth rate

2. Constant Growth Rate of Dividends

Dividends are expected to grow at a constant percent per period.

P₀ = D₁ /(1+R) + D₂ /(1+R)² + D₃ /(1+R)³ + …

P₀ = D₀(1+g)/(1+R) + D₀(1+g)²/(1+R)² +

8-34

2. Constant Growth Rate of Dividends

With a little algebra this reduces to:

g -

R D g

- R

g) 1

(

P 0 D 0   1



2. Constant Growth Rate of Dividends

Student caution:

g - R

D g

- R

g) 1

(

P

₀

D

⁰

 

¹



A. What happens if g >

8-36

Dividend Growth Model (DGM)

Assumptions

To use the Dividend Growth Model (aka the Gordon Model), you must meet all three requirements:

1.The growth of all future dividends must be constant,

2.The growth rate must be smaller than the discount rate ( g < R), and

3.The growth rate must not be equal to the discount rate (g ≠ R)

DGM – Example 1

Suppose Big D, Inc., just paid a dividend (D₀) of

$0.50 per share. It is

expected to increase its dividend by 2% per year.

If the market requires a

8-38

DGM – Example 1 Solution

P

₀

= .50 ( 1 + .02) .15 - .02

g - R

D g

- R

g) 1

(

P

₀

D

⁰

 

¹



P

₀

= .51

.13 = $3.92

DGM – Example 2

Suppose Moore Oil 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

8-40

DGM – Example 2 Solution

P

₀

= 2.00

.20 - .05

g - R

D g

- R

g) 1

(

P

₀

D

⁰

 

¹



P

₀

= 2.00

.15 = $13.34

So how do you

compute the future dividends?

Three scenarios:

1.A constant dividend (zero growth)

2.The dividends change by a constant growth rate

8-42

3. Unusual Growth;

Then Constant Growth

Just draw the time line with the unusual growth rates

identified and determine if/when you can use the Dividend Growth Model.

Deal with the unusual growth dividends separately.

Non-constant Growth Problem Statement

Suppose a firm is expected to increase dividends by 20% in one year and by 15% for two years. After that, dividends will increase at a rate of 5%

per year indefinitely.

If the last dividend was $1

8-44

Non-constant Growth Problem Statement

Draw the time line and compute each dividend using the

corresponding growth rate:

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

D₁ D₂ D₃

Non-constant Growth Problem Statement

Draw the time line and compute each dividend using the

corresponding growth rate:

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

8-46

Non-constant Growth Problem Statement

Draw the time line and compute each dividend using the

corresponding growth rate:

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

D₁ D₂ D₃

D₂ = ($1.20) (1 + 15%) = $1.20 x 1.15 = $1.38

=1.38

Non-constant Growth Problem Statement

Draw the time line and compute each dividend using the

corresponding growth rate:

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

8-48

Non-constant Growth Problem Statement

Now we can use the DGM starting with the period of the constant

growth rate at our time frame of year 3:

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

D₁ D₂ D₃

P

₃

= D

₄

/R – g P

₃

= D

₃

(1 + g) / R - g

R = 20%

Non-constant Growth Problem Statement

Now we can use the DGM starting with the period of the constant

growth rate at our time frame of year 3:

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

R = 20%

8-50

Non-constant Growth Problem Statement

We now have all of the dividends

accounted for and we can compute the present value for a share of common stock:

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

D₁ D₂ D₃

R = 20%

1.20 1.38 1.59

P₃ = 11.13

Non-constant Growth Problem Statement

BAEFEIPVT!

g = 20% g = 15% g = 15% g = 5%

D⁰ =

$1.00

1 2 3 4

∞

D D D

R = 20%

8-52

Stock Price Sensitivity to

Dividend Growth, g

D₁ = $2; R = 20%

0 50 100 150 200 250

0 0.05 0.1 0.15 0.2

Growth Rate

Stock Price

Stock Price Sensitivity to

Required Return, R

D₁ = $2; g = 5%

50 100 150 200 250

Stock Price

8-54

Using the DGM to Find R

P g g D

P

g) 1

( R D

g - R

D g

- R

g) 1

( P D

0 1 0

0

1 0

0





 



 



Start with the DGM and then algebraically rearrange the equation to solve for R:

Finding the Required Return - Example

Suppose a firm’s stock is selling for

$10.50. It just paid a $1 dividend, and dividends are expected to grow at 5% per year. What is the required return?

R = [1(1.05)/10.50]

+ .05 = 15%

What is the dividend yield?

1(1.05) / 10.50 =

8-56

Stock Valuation Alternative

But my

company

doesn’t pay dividends!

How can I value

the stock?

Valuation Using Multiples

We can use the PE ratio and/or the price-sales

ratio:

P

_t

= Benchmark PE ratio X EPS

_t

P = Benchmark price-

8-58

Stock Valuation

Summary

Chapter Outline

• Bond and Stock Differences

• Common Stock Valuation

• Features of Common Stock

• Features of Preferred Stock

• The Stock Markets

8-60

Features of Common Stock

• Voting Rights

• Proxy voting

• Classes of

stock

Features of Common Stock

Other Rights

• Share proportionally in declared dividends

• Share proportionally in remaining assets during liquidation

• Preemptive right – first shot

8-62

Dividend

Characteristics

• 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

Dividend

Characteristics

Dividends and Taxes

• Dividend payments are not considered

a business expense; therefore, they are not tax deductible

• The taxation of dividends

received by individuals depends on the holding period

• Dividends received by

8-64

Chapter Outline

• Bond and Stock Differences

• Common Stock Valuation

• Features of Common Stock

• Features of Preferred Stock

• The Stock Markets

Features of Preferred Stock

Dividends

• Stated dividend that must be paid before dividends can be paid to common stockholders

• Dividends are not a

8-66

Features of Preferred Stock

Dividends

• Most preferred dividends are cumulative – any

missed preferred

dividends have to be paid

before common dividends

can be paid

Features of Preferred Stock

• Preferred stock generally does not carry voting rights

8-68

Chapter Outline

• Bond and Stock Differences

• Common Stock Valuation

• Features of Common Stock

• Features of Preferred Stock

• The Stock Markets

Stock Market, Dealers vs.

Brokers

Dealer: trades with inventory for bid and ask prices

Broker: matches buyers and

sellers for a fee

8-70

Stock Market

• New York Stock Exchange (NYSE)

• Largest stock market in the world

• License holders (1,366)

• Commission brokers

• Specialists

• Floor brokers

• Floor traders

• Operations

• Floor activity

NASDAQ

• Not a physical exchange – it is a computer-based quotation

system

• Multiple market makers

• Electronic Communications Networks

8-72

NASDAQ

• Three levels of information:

• Level 1 – median quotes, registered representatives

• Level 2 – view quotes, brokers

& dealers

• Level 3 – view and update quotes, dealers only

• A large portion of technology

stocks are bought and sold each day on NASDAQ

Work the Web

• Electronic Communications Networks provide trading in NASDAQ securities

• Click on the web surfer and visit Instinet

8-74

Reading Stock Quotes

Work the Web

• Click on the web surfer to

go to Bloomberg for current stock quotes.

8-76

Ethics Issues

The status of pension funding (i.e., over- vs. under-funded) depends heavily on

the choice of a discount rate. When

actuaries are choosing the appropriate rate, should they give greater priority to future pension recipients, management, or shareholders?

How has the increasing availability and use of the internet impacted the ability of stock traders to act unethically?

Quick Quiz

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

8-78

Comprehensive Problem

XYZ stock currently sells for $50 per share. The next expected annual

dividend is $2, and the growth rate is 6%. What is the expected rate of return on this stock?

If the required rate of return on this stock were 12%, what would the stock price be, and what would the dividend yield be?

Terminology

Bonds versus Common Stock Cash Dividends

Capital Gain Yield & Dividend Yield

Dividend Growth Model (DGM) Preferred Stock

8-80

Formulas

P g g D

P

g) 1

( R D

g - R

D g

- R

g) 1

( P D

0 1 0

0

1 0 0





 



 



P₀ = D R

Value of a Perpetuity :

Value of a Share of Common Stock using the DGM:

Formulas

Value of a Share of Common Stock using Multiples

P_t = Benchmark PE ratio X EPS_t

P = Benchmark price-sales

8-82

Key Concepts and Skills

• Compute the future dividend stream based on dividend

growth

• Use the Dividend Growth

Model (DGM) to determine the price of stock

• Explain how stock markets work

• Describe the workings of a stock exchange

1. A stock’s value is the present value of all expected future earnings.

2. Computing the future dividends of a stock is the key to understanding its

What are the most important topics of this chapter?

8-84

4. The Dividend Growth Model (DGM) provides us help with infinite dividend streams

5. Stocks are bought and sold each business day with

reporting via stock quotes

What are the most important topics of this chapter?

Questions?