Lecture Essentials of corporate finance (2/e) – Chapter 7: Equity markets and stock valuation

The topics discussed in this chapter are equity markets and stock valuation. After completing this unit, you should be able to: Understand how share prices depend on future dividends and dividend growth, be able to compute share prices using the dividend growth model, understand how share markets work, understand how share prices are quoted.

Equity markets and share

valuation

Chapter 7

Key concepts and skills

• Understand how stock prices depend

on future dividends and dividend

• Understand how stock markets work

• Understand how stock prices are

Chapter outline

• Ordinary share valuation

• Some features of ordinary and

preference shares

• The share markets

Cash flows for stockholders

• If you own 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 in the market or back to the company.

• As with bonds, the price of the stock is the present value of these expected cash

flows.

– Dividends → cash income

– Selling → capital gains

– You require a return of 20% on

investments of this risk

– What is the maximum you would be willing

One-period example (cont.)

• D1 = $2 dividend expected in one year

13

$ 20

1

) 14 2

(

P 0

Two-period example

• Now, what if you decide to hold the share for two years?

• In addition to the dividend in one year, you expect a

dividend of $2.10 and a share price of $14.70 at the end of

year 2 Now how much would you be willing to pay?

• Calculator:

• CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1;

• [NPV]; I = 20; [CPT][NPV] = $13.33

33 13

$ )

20 1 (

) 70 14 10

2

( 20

1 2

Three-period example

• What if you decide to hold the stock for three years?

• 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 share price of $15.435

• Now how much would you be willing to pay?

• Calculator:

• CF 0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64; F03 = 1;

• [NPV]; I = 20; [CPT] [NPV] = $13.33

33 13

$ )

20 1 (

) 435

15 205

2

( )

20 1 (

10

2 20

1 2

Developing the model

• You could continue to push back when you would sell the share.

• You would find that the price of the

share is really just the present value of

all expected future dividends.

Stock value = PV of

dividends

P 0 =

(1+R) 1 (1+R) 2 (1+R) 3 (1+R) ∞

How can we estimate all future dividend

payments?

Estimating dividends:

Special cases

• Constant dividend

– The firm will pay a constant dividend forever

– This is like a preference share

– The price is computed using the perpetuity

formula

• Constant dividend growth

– The firm will increase the dividend by a

constant percentage every period

• Supernormal growth

– Dividend growth is not consistent initially, but settles down to constant growth eventually

Zero growth

• If dividends are expected at regular

intervals forever, this is like a

preference share and is valued as a

perpetuity

– P 0 = D/R

• Suppose a share is expected to pay a

$0.50 dividend every half-year and the required return is 10% with half-yearly compounding What is the price?

– P = 50 / (0.1 / 2) = $10

Constant growth stock

• Dividends are expected to grow at a

constant percentage per period.

Dividend growth model

) 1

(

) 1

P

g

­ R

D g

­ R

g) 1

(

D

0

DGM—Example 1

• Suppose Outback Ltd just paid a dividend

of $0.50 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 share be selling for?

• D 0 = $0.50

• g = 2%

• R = 15%

92 3

$ 02

15

) 02 1 ( 50

0 P

g R

) g 1

(

D P

0

0 0

DGM—Example 2

• Suppose Deep Pirates Ltd 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

$ 05

20

00

2 P

g R

D P

0

1 0

Share price sensitivity to

Share price sensitivity to

Example 7.3—Gordon Growth

Company I

• 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?

• Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g.

40

$ 06

16

00

4 P

g R

D P

0

1 0

Example 7.3—Gordon Growth

• What is the implied return given the

change in price during the 4-year

Constant  growth model

conditions

1 Dividend expected to grow at g forever.

2 Stock price expected to grow at g

forever.

3 Expected dividend yield is constant.

4 Expected capital gains yield is constant

and equal to g.

5 Expected total return, R, must be > g.

6 Expected total return (R):

= expected dividend yield (DY) + expected growth rate (g)

Non-constant growth problem

statement

• Suppose a firm is expected to increase dividends by 20% in one year and by

15% in two years After that dividends

will increase at a rate of 5% per year

indefinitely If the last dividend was $1

and the required return is 20%, what is the price of the share?

• Remember that we have to find the PV

of all expected future dividends.

Non-constant growth problem

D R

D R

D P

1

. .

  1

1

3 2

2 1

1 0

Dividend growth model

g R

D

Non-constant + Constant

growth (cont.)

2

2 2

2 1

1 0

) 1

( 1

P R

D R

D P

g R

D P

then 2,

t after constant

g If

) R 1

(

D P

Because

3 2

3

t 2

Non-constant growth followed by constant

growth 0

Quick quiz: Part 1

• 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? The required return remains at 15%.

33 13

$ 15

.

00

2

0

P

17 17

$ 03

15

) 03 1 ( 00 2

P 0

Using the DGM to find R

• Start with the DGM:

g P

D g

P

g) 1

(

D R

g - R

D g

R

-g) 1

(

D P

0

1 0

0

1

0 0

Rearrange and solve for R:

Finding the required return

— Example

• Suppose a firm’s shares are selling for

$10.50 They just paid a $1 dividend

and dividends are expected to grow at 5% per year What is the required

Summary of share valuation

Table 7.1

Features of ordinary shares

• Voting rights

– Stockholders elect directors

– Cumulative voting vs straight voting

– Proxy voting

• Classes of share

– ‘One share, one vote’

Features of ordinary shares

(cont.)

• Other rights

– Share proportionally in declared

dividends

– Share proportionally in remaining

assets during liquidation

– Pre-emptive right

• Right of first refusal to buy new stock issue to maintain proportional

ownership if desired

Dividend characteristics

• Dividends are not a liability of the firm

until declared by the Board of Directors

– A firm cannot go bankrupt for not declaring dividends

• Dividends and taxes

– Dividends are not tax deductible for a firm

– Taxed as ordinary income for individuals

– Dividends received by corporations have a minimum 100% exclusion from taxable

Features of preference

shares

• Dividends

– Stated dividend must be paid before

dividends can be paid to ordinary

shareholders

– Dividends are not a liability of the firm and preference dividends can be deferred

indefinitely

– Most preference dividends are cumulative

— any missed preference dividends have

to be paid before ordinary dividends can

be paid

• Preference shares generally do not

The share markets

• Primary vs secondary markets

– Primary = new-issue market

– Secondary = existing shares traded

among investors

• Dealers vs brokers

– Dealer: Maintains an inventory

Ready to buy or sell at any time Think ‘Used car dealer’

– Broker: Brings buyers and sellers

together

Australian Stock Exchange

(ASX)

• Australian Stock Exchange (ASX)—1987

– Result of amalgamation of state-based

exchanges

• 1987—Introduction of Stock Exchange

Automated Trading System (SEATS)

ASX and NZX operations

• Operational goal = Attract order flow

• Both ASX and NZX are auction markets

– Agency trading—Brokers buying and selling

for clients

– Principal trading—Brokers buying and selling their own accounts

• Orders

– Limit order—specified sell/buy price

– Market order—at best market price

• Trading in both ASX and NZX takes place

on computer network

Share market reporting

Figure 7.2

Work the Web

• Click on the information icon to go to <

Quick quiz: Part 2

• You observe a share 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 ordinary shares?

• What are some of the major

characteristics of preference shares?

Chapter 7 END