Chapter

7Equity Markets and Stock Valuation

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 electedUnderstand how stock markets workUnderstand how stock prices are quoted

Feature of Common Stock

Voting RightsProxy votingOther Rights

Share proportionally in declared dividendsShare proportionally in remaining assets during

liquidationPreemptive right – first shot at new stock issue to

maintain proportional ownership if desired

Dividend Characteristics

Firm cannot go bankrupt for not declaring dividendsDividends and Taxes

Dividend payments are not considered a business expense, therefore, they are not tax deductible

Dividends received by individuals are taxed as ordinary income

Dividends received by corporations have a minimum 70% exclusion from taxable income

Features of Preferred Stock

DividendsStated dividend that must be paid before dividends

can be paid to common stockholdersDividends are not a liability of the firm and preferred

dividends can be deferred indefinitelyMost preferred dividends are cumulative – any

missed preferred dividends have to be paid before common dividends can be paid

Preferred stock generally does not carry voting rights

Stock Markets

New York Stock Exchange (NYSE)Huge room with electronic “trading posts”Each stock assigned to single “specialist”Specialists = Employed by exchange to be “market

makers”Hold inventory of stocks, advertise prices to buy

(bid) and sell (ask) at:

Stock Bid Ask

YWEE $28.65 $28.75

Specialists

Bid Ask

YWEE $28.65 $28.75 Specialist buys low, sells high Specialists buys at $28.65, so you sell at

$28.65. Specialist sells at $28.75, so you buy at $28.75 $28.75 - $28.65 = $0.10 = “spread”

Stock Markets

NASDAQNot a physical exchange – computer based

quotation systemNational Association of Securities Dealers

Automated QuotationMultiple dealers acting as “market makers” – Hold

inventory of stock, post bid & ask pricesLarge portion of technology stocks

NASDAQ

DULL Computers: three dealers

Joe Bob Englebert

Bid Ask Bid Ask Bid Ask

8.00 8.50 7.75 8.25 7.50 8.50

NASDAQ reports:Bid Ask8.00 8.25

Cash Flows to Stockholders

If you buy a share of stock, you can receive cash in two waysThe company pays dividendsYou sell your shares, either to another investor in

the market or back to the companyValue = PV of expected future CF’s

Estimating Dividends: Special Cases

Constant dividend The firm will pay a constant dividend forever, like

preferred stock Perpetuity formula

Constant dividend growth The firm will increase the dividend by a constant percent

every periodNonconstant growth

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

Zero Growth

If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity

P0 = D / RSuppose stock is expected to pay a $2 dividend

every year and the required return is 10%. What is the price?P0 = 2 / .1 = $20

Dividend Growth Model

Dividends grow at a constant rate g…

D1 = D0 * (1 + g)

D2 = D1 * (1 + g)

D2 = D0 * (1 + g) * (1 + g) = D0 * (1 + g)2

Dt = D0 * (1 + g)t

D43 = D0 * (1 + g)43

Dividend Growth Model (DGM)

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 + D0(1+g)3/(1+R)3 + …

With a little algebra, this reduces to:

g-R

D

g-R

g)1(DP 10

0

DGM – 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?

What variable is $.50?P0 = .50*(1+.02) / (.15 - .02) = $3.92

DGM – 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?P0 = 2 / (.2 - .05) = $13.33Why isn’t the $2 in the numerator multiplied by

(1.05) in this example?

Example

Gordon Growth Company is expected to pay a dividend of $2 next year and dividends are expected to grow at 6% per year. The required return is 15%.

What is the current price?

Using the DGM to Find R

Start with the DGM:

gP

D g

P

g)1(D R

Rfor solve and rearrange

g-R

D

g - R

g)1(DP

0

1

0

0

100

Components of R

You can get your R in two forms:Dividend yield = D1/P0

Capital gains yield = g

R = D1/P0 + g

Example

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 = $1*(1.05)/$10.50 + .05 = 15%

What is the dividend yield?$1*(1.05)/$10.50 = 10%

What is the capital gains yield?g =5%

Criticisms of P0 = D1 (R – g)

1. Constant g2. g > R P < 0 3. D1 = 0 P = 04. Sensitive to R & g:

1,2,&3 can be fixed (young firms)

Stock Price Sensitivity to Dividend Growth

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

Growth Rate

Stoc

k P

rice

D1 = $2; R = 20%

Stock Price Sensitivity to Required Return

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2 0.25 0.3

Growth Rate

Stoc

k P

rice

D1 = $2; g = 5%

Firms with D1 = $0

Firm expects to pay no divds until year 5

That divd expected = $1

g = 12%, R = 15% P=?

Solution: Throw D, R , & g into equation

Firms with D1 = $0

P = $1 (.15 - .12) = $33.33?

Formula D1 (R – g) = P0

What we did D5 (R – g) = ????

D = always one period ahead of P

(D5 P4)Stock Value = PV (expected divd payments)

Firms with D1 = $0

P4 = $33.33 P0 = ???

P4 = FV P0 = PV

P0 = PV(P4) @ R%

4 N, 15 I/YR, 33.33 FV, PV=???P0 = $19.06

Nonconstant Growth

1. Compute PV(dividends that experience nonconstant growth)

2. Find the P stock the end of the nonconstant growth period, and discount P back to the present

3. Add these two components to find the value of the stock.

Nonconstant Growth

TannerHater.com recently paid a dividend of $1.00. Analysts expect that dividend to grow at 20% annually for 3 years, then grow at 10% indefinitely. If R = 15%, what is the stock’s intrinsic value?

Nonconstant Growth

1. Compute PV(dividends that experience nonconstant growth)

D1 = D0 * (1 + g) = $1.00*1.2 = $1.20

D2 = D1 * (1 + g) = $1.20*1.2 = $1.44

D3 = D2 * (1 + g) = $1.44*1.2 = $1.73

Need PV of D1 D3?

Nonconstant Growth

Use CFj button on calculator:0 CFj (CF in year 0)

1.2 CFj (CF in year 1)1.44 CFj (CF in year 2)1.73 CFj (CF in year 3)

15 I/YR<color> NPV

$3.27 = PV (D1 D3)

Nonconstant Growth

2. Find the P stock the end of the nonconstant growth period, and discount P back to the present.

D4 = D3 * (1 + g) = $1.73 * 1.10 = $1.90

$1.90 (R – g) = $1.90 (.15 - .10) = $38 = P????

Nonconstant Growth

$38.06 = D4 (r– g) = P3 = FV3

3 N15 I/YR38 FVPV = ?

PV = $24.99 = PV(D4 D)

Nonconstant Growth

P0 = PV(D1 D)

PV(D1 D3) = $3.27

+ PV(D4 D) = $24.99

PV(D1 D) = $28.26 = P0

Nonconstant Growth Problem

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 stock?

Remember that we have to find the PV of all expected future dividends.