Chapter 8 Stock Valuation

Overview Preferred Stock Characteristics and

Valuation Common Stock Characteristics Common Stock as a Financing Tool Common Stock Valuation

Dividend Discount Model

Preferred Stock Characteristics Unlike common stock, no ownership interest Second to debt holders on claim on

company’s assets in the event of bankruptcy.

Annual dividend yield as a percentage of par value

Preferred dividends must be paid before common dividends

If cumulative preferred, all missed past dividends must be paid before common dividends can be paid.

Preferred Stock Valuation Promises to pay the same dividend year

after year forever, never matures. A perpetuity. Vps = D/kps Example: GM preferred stock has a $25

par value with a 8% dividend yield. What price would you pay if your required return is 9%?

D = $25(0.08) = $2 Vps = $2/0.09 = $22.22

Expected Rate of Return on Preferred

Just adjust the valuation model:

D

Po

kps =

Example

If we know the preferred stock price is $40, and the preferred dividend is $4.125, the expected return is:

Example

If we know the preferred stock price is $40, and the preferred dividend is $4.125, the expected return is:

D

Po

kps = = = 4.125

40

Example

If we know the preferred stock price is $40, and the preferred dividend is $4.125, the expected return is:

D

Po

kps = = = .10314.125

40

The Financial Pages:Preferred Stocks

52 weeks Yld VolHi Lo Sym Div % PE 100s Close2788 2506 GM pfG 2.28 8.9 … 86 25 53

Dividend: $2.28 on $25 par value = 9.12% dividend rate.

Expected return: 2.28 / 25.53 = 8.9%.

Facts about Common Stock: Claim on Income after interest and dividend

payments to creditors and preferred stockholders.

Represents ownership. Ownership implies control. Limited liability. Stockholders elect directors. = Voting

Rights Directors elect management. Management’s goal: Maximize stock price.

Advantages of Financing with Stock: No required fixed payments. No maturity. Improves debt ratio, coverage.

Disadvantages of Financing with Stock: Controlling shareholders may lose some

ownership control. Preemptive Right

Future earnings shared with new stockholders. Possible EPS Dilution.

Higher flotation costs vs. debt. Higher component cost of capital. Too little debt may encourage a takeover

bid.

Common Stock Valuation(Single Holding Period)

You expect XYZ stock to pay a $5.50 dividend at the end of the year. The stock price is expected to be $120 at that time.

If you require a 15% rate of return, what would you pay for the stock now?

Common Stock Valuation(Single Holding Period)

You expect XYZ stock to pay a $5.50 dividend at the end of the year. The stock price is expected to be $120 at that time.

If you require a 15% rate of return, what would you pay for the stock now?

0 1

? 5.50 + 120

Common Stock Valuation(Single Holding Period)

Solution:

Vcs = (5.50/1.15) + (120/1.15) = 4.783 + 104.348 = $109.13

Common Stock Valuation(Single Holding Period)

Financial Calculator solution:P/Y =1, I = 15, n=1, FV= 125.50CPT PV = -109.13or:P/Y =1, I = 15, n=1, FV= 120, PMT = 5.50CPT PV = -109.13

The Financial Pages:Common Stocks

52 weeks Yld Vol NetHi Lo Sym Div % PE 100s Close Chg126 87 IBM .56 0.6 23 77995 98.12 +0.29

63 42 WalMart .28 0.5 47 119515 62.01 -0.24

IBMs Dividend Yield = $0.56/$98.12 = 0.6% PE Ratio = Close Price/Earnings Per

Share(EPS) IBMs Latest EPS = Close/PE = $98.12/23 =

$4.27

Stock Valuation

Multiple Holding PeriodsStock Value = PV of Future

Expected Dividends

cscscscs

csk

D

k

D

k

D

k

DV

1. . .

111 33

22

11

Stock Valuation: Dividend PatternsFor Valuation: we will assume stocks fall

into one of the following dividend growth patterns.

Constant growth rate in dividends Zero growth rate in dividends, like

preferred stock “Supernormal” (non-constant) growth

rate in dividends(see Chapter 8 notes in Syllabus book)

Doh! Doughnuts Stock Valuation Example: Basic Information We have found the following

information for Doh! Doughnuts: current dividend = $2, beta of 0.9 T-bill (risk-free) rate = 1.75% the market risk premium is 9.5%

Using the SML equation to find Doh!’s required return = krf +(krp)b =

1.75% +(9.5%)0.9 = 10.3% = kcs

Analysts Estimates for Doh! Doughnuts

NEDFlanders predicts a constant annual growth rate in dividends and earnings of zero percent (0%)

Barton Kruston Simpson predicts a constant annual growth rate in dividends and earnings of 8 percent (8%).

Moe Homer Simpson & Bernard expect a dramatic growth phase of 20% annually for each of the next 3 years followed by a constant 8% growth rate in year 4 and beyond.

Our Task: Valuation Estimates What should be each analyst’s

estimated value of Doh! Doughnuts?

First Analyst: Zero Growth Stock Valuation No growth in dividends, so Doh!

Doughnuts will remain at the current dividend of $2 forever.

Estimated Value (Vcs)= PV(perpetuity) = D0/kcs

Doh! Kcs = 10.3% NEDFlanders Estimate P0 = $2/.103

= $19.42

Constant Growth Stock Valuation Model Dividends are expected to grow at

an annual constant rate, g, forever. D1 = D0(1+g) Dt = D0(1+g)t

Vcs = D0(1+g) = D1

kcs – g kcs – ggg

g

kD

kDV

cscscs -

=-

)+1(= 10

Constant Growth Stock Valuation Model Terms D0 = today’s (or current) dividend D1 = expected dividend at the end

of this year(year 1) kcs = stock’s required rate of return g = the constant growth rate in

dividends

2nd Analyst: Constant Growth in Dividends Current Dividend = $2 Projected Constant Growth Rate = 8%

or 0.08 Kcs = 10.3%

What happens if g > kcs?

.kcs requires 1 ggkcs

DVcs

If kcs< g, get negative stock price, which is nonsense.

We can’t use model unless (1) kcs> g and (2) g is expected to be constant forever.

Doh! A good buy? Assume Doh! Doughnuts current stock

price is $100. Required return = 1.75% + 9.5%(0.9) =

10.3% Let’s assume the 2nd analyst is correct

and Doh! Has a constant growth rate of 8% and its current dividend is $2.

What is the stock’s expected return? Is Doh! Doughnuts’ current stock price

in equilibrium?

Expected Return of Constant Growth Stocks Expected Rate of Return = Expected Dividend Yield +

Expected Capital Gains Yield D1/P0 = D0(1+g)/P0 = Expected Dividend Yield g = Expected Capital Gains Yield From our example, D1=$2(1.08) = 2.16, P0=$100, g =

8% or 0.08

%16.10%8%16.2%8100$

16.2$

0

1^

gP

Dcsk

DOH! Doh! Doughnuts

Stock Market Equilibrium

The stock price when the stock’s expected return = stock’s required return (CAPM)

D1/P0 + g = krf +(km - krf)b

Expected Return = Required Return

The Effect On the Stock Price

Expected Return needs to rise to the required return of 10.3%. This means the stock price must fall to the the equilibrium price which yields the required return of 10.3%

New Price = D1/(kcs- g)=$2.16/(.103 - .08)= $93.91 At the current price of $100, Doh! has NPV of

$93.91 - $100 = -$6.09

Return

Beta

SML

0.9

1.75

“Supernormal” Growth Stock Valuation Framework: Assume Stock has

period of non-constant growth in dividends and earnings and then eventually settles into a normal constant growth pattern(gc).

0 g1 1 g2 2 g3 3 gc 4 gc 5 gc…

D1 D2 D3

“Supernormal” Growth Period Constant Growth

Supernormal Growth Valuation Process

3 Step Process Estimate Dividends during “supernormal”

growth period. Estimate Price, which is the PV of the

constant growth dividends, at the end of “supernormal” growth period which is also the beginning of the constant growth period.

Find the PV of “supernormal” dividends and constant growth price. The total of these PVs = Today’s estimated stock value.

3rd Analyst:“Supernormal” Growth Stock Valuation for Doh!

“supernormal” growth rate g for years 1-3 = 20% or 0.2

After year 3, Doh! Has constant growth rate gc = 8% or 0.08

D0 = $2.00 kcs = 10.3% or .103

Finally, the Answer!0 g = 20%g = 20% 1 g = 20%g = 20% 2 g = 20% g = 20% 3 ggcc = 8% = 8%

$2.40 $2.88 $3.46PV= P0 $162.28 = P3

10.3%,1 $165.74 2.17 10.3%,2 2.37 10.3%,3123.51128.05 = $128.05 $128.05 = P0

PP00 = $2.40(PVIF = $2.40(PVIF10.3%,110.3%,1)+$2.88(PVIF)+$2.88(PVIF10.3%,210.3%,2)+$3.46(PVIF)+$3.46(PVIF10.3%,310.3%,3))

+ $162.28(PVIF+ $162.28(PVIF10.3%,310.3%,3) = $128.05) = $128.05

Fin’l CalculatorSolution:CF0=0,C01= 2.40C02 = 2.88C03 = 165.74I = 10.3NPV=128.05 NPV=128.05 = P= P00

Summary of Doh! Doughnuts Stock Price Estimates NEDFlanders: 0% constant growth:

P0 = $19.42 Barton Kruston Simpson: 8%

constant growth: P0 = $93.91 Moe Homer Simpson & Bernard:

20%, 3-year supernormal growth followed by 8% constant growth: P0 = $128.05

Other Valuation Approaches Our dividend discount models are best for

established dividend paying companies, which makes it difficult to apply to non-dividend paying start-up companies.

PE Multiple Approach: Forecast a company’s earnings per share and multiply this forecast times the company’s PE ratio.

Value entire firm by finding PV of future expected Free Cash Flows available to stockholders, then divide by number of shares. (Chapter 13)