Features of common stock Determining common stock values Efficient markets Preferred stock

9 - 1

Copyright © 2002 by Harcourt, Inc. All rights reserved.

Stocks and Their Valuation(Ref: Brigham, E.F., and J.F. Houston. 2001. Fundamentals of

Financial Management, 9th Ed, Harcourt College Publishers, Ch. 9)

Features of common stock Determining common stock values Efficient markets Preferred stock

9 - 2


Represents ownership.

Ownership implies control.

Stockholders elect directors.

Directors elect management.

Management’s goal: Maximize the stock price.

Facts about Common Stock

9 - 3


Social/Ethical Question

Should management be equally concerned about employees, customers, suppliers, and “the public,” or just the stockholders?

In an enterprise economy, management should work for stockholders subject to constraints (environmental, fair hiring, etc.) and competition.

9 - 4


A firm “goes public” through an IPO when the stock is first offered to the public.

When is a stock sale an initial public offering (IPO)?

9 - 5


Issuer Proceeds from sale

AT&T Wireless $9.03 billion

Infineon Technologies $2.72 billion

Metropolitan Life Ins. Co. $2.50 billion

TyCom $2.88 billion

Genuity $1.91 billion

Biggest IPOs of 2000 in the USA

9 - 6


Average Initial Returns on IPOs in Various Countries

Mal

aysi

a

100%

75%

50%

25%

Brazil

Portugal

Japan

Sweden

United

State

sCan

ada

9 - 7


1. Dividend growth model:

- Constant Growth (Gordon) Model

- Supernormal (Non-constant) Growth Stock

- Erratic Growth Stock

2. Free cash flow method

3. Using the multiples of comparable firms

Different Approaches for Valuing Common Stock

9 - 8


When to use the models?

Constant growth model: most appropriate for mature companies w stable history of growth, and stable future dividends.

Free cash flow method: good for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends.

9 - 9


Definitions of TermsDt = Dividend the stockholder expects to

receive at the end of Year t. D0 is the most recent dividend, which has already been paid; D1 is the first dividend expected, and will be paid

at the end of this year; D2 is the dividend expected at the end of two years, and so forth. D1 represents the first cash flow a new purchaser of the stock will receive. Note that D0, the dividend that has been paid, is known with certainty. But all future dividends are expected values, so the estimate of Dt may differ among investors.

P0 = Actual market price of the stock today

9 - 10


P0 = Expected price of the stock at the end of Year t (pronounced “P hat t”). P0 is the intrinsic, or theoretical, value of the

stock today as seen by the particular investor doing the analysis; P1 is the price

expected at the end of one year; and so on. Note that P0 is the intrinsic value of the stock today based on a particular

investor’s estimate of the stock’s expected dividend stream and the riskiness of that stream. Hence, whereas the market price P0 is fixed and is identical for all investors, P0 could differ among investors depending on how optimistic they are about the company. The caret, or “hat” is used to indicate that Pt is an estimated value.

cont…

9 - 11


cont…

P0, the individual investor’s estimate of the intrinsic value today, could be above or below P0, the current stock price, but an investor would buy the stock only if his/her estimate of P0 were equal or greater than P0. Since they are many investors in the market, there can be many values for P0. However, we can think of an “average” or “marginal” investors whose actions actually determine the market price. For these marginal investors, P0 must = P0; otherwise a disequilibrium would exist, and buying and selling in the market would change P0, until P0 = P0 for the marginal investor.

9 - 12


Market Price, P0 = the price at which the stock sell in the market

Intrinsic Value, P0 = the value of an asset that, in the mind of a particular investor, is justified by the facts; P0 may be different from the asset’s current market price.

Growth Rate, g = The expected rate of growth in dividends per share.

9 - 13


g = expected growth rate in dividends as predicted by a marginal investor. If dividends are expected to grow at a constant rate, g is also equal to the expected rate of growth in earnings and in the stock’s price. Different investors may use different g’s to evaluate a firm’s stock, but the market price, P0, is set on the basis of the g estimated by marginal investors.

9 - 14


Required Rate of Return, ks = The minimum rate of return on a common stock that a stockholder considers acceptable.

ks = minimum acceptable, or required, rate of return on the stock, considering both its riskiness and the returns available on other investments. Again, this term generally relates to marginal investors. The determinants of ks include the real rate of return, expected inflation, and risk.

9 - 15


Expected Rate of Return, ks = The rate of return on a common stock that a stockholder expects to receive in the future.

ks = Expected rate of return that an investor who buys the stock expects to receive in the future. Ks (pronounced “k hat s”) could be above or below ks, but one would buy the stock only if ks were equal or greater than ks.

9 - 16


Actual, Realized Rate of Return, ks = The rate of return on a common stock actually received by stockholders in some past period. Ks may be greater, or less than, and/or ks.

ks = actual, or realized, after-the fact rate of return (pronounce “k bar s”). You may expect to obtain a return of ks= 15% if you buy Exxon today, but if the market goes down, you may end up next year with an actual realized return that is much lower, perhaps even negative.

9 - 17


Dividend Yield = The expected dividend divided by the current price of a share of stock.

D1/P0 = Expected dividend yield on the stock during the coming year. If the stock is expected to pay a dividend of D1 = $1 during the next 12 months, and its current price is P0 = $10, then the expected dividend yield is $1/$10 = 0.10 = 10%

9 - 18


Capital Gains Yield = The capital gain during a given year divided by the beginning price.

(P1-P0)/P0 = Expected capital gains yield on the stock during the coming year. If the stock sells for $10 today, and if it is expected to rise to $10.50 at the end of one year, the expected capital gain is P1- P0 = $0.50. Expected capital gain yield = $0.50/$10 = 5%

9 - 19


Expected Total Return = The sum of the dividend yield and the expected capital gains yield.

Expected total return = ks = Expected dividend yield (D1/P0) + expected capital gains yield (P1-P0)/P0. In our example, the expected total return is 10% + 5% = 15%

9 - 20


P

D

k

D

k

D

k

D

ks s s s

01

12

23

31 1 1 1

. . .

A stock whose dividends are expected togrow forever at a constant rate, g.

Stock Value = PV of Dividends

What is a constant growth stock?

.

9 - 21


For a Constant Growth Stock

D1 = D0(1 + g)1

D2 = D0(1 + g)2 = D1(1+g)1

Dt = D0(1 + g)t

P0 = =

If g is constant, then:

D0(1 + g)ks – g

D1

ks – g^

9 - 22


t

0t g1DD

tt

tk1

DPVD

!P k,>g If 0 t0 PVDP

$

0.25

Years (t)0

9 - 23


What happens if g > ks?

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

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

0P̂ = requires ks > gD1

ks – g

9 - 24


Assume beta = 1.2, kRF = 7%, and kM = 12%. What is the required rate of

return (ks) on the firm’s stock?

ks= kRF + (kM – kRF) βFirm

= 7% + (12% – 7%) (1.2) = 13%

Use the SML to calculate ks:

9 - 25


D0 was $2.00 and g is a constant 6%. Find the expected dividends for the

next 3 years, and their PVs (ks = 13%)

0 1

2.247

2

2.382

3g = 6%

$1.8761$1.7599

D0 = 2.00

$1.6509

13%2.12

9 - 26


= =

What’s the stock’s market value? D0 = 2.00, ks = 13%, g = 6%

Constant growth model:

P0 = = D1

ks – g 0.13 – 0.06

$2.12

$2.12

0.07$30.29

9 - 27


D1 will have been paid, so expected dividends are D2, D3, D4 and so on. With P0= $30.29, D2=D1(1+g)=$2.12(1.06)=$2.247;

Could also find P1 as follows:

ks – g 0.13 – 0.06 P1 = =

What is the stock’s market value one year from now, P1?

^

^

D2 $2.247^

= $32.10

P1= P0(1.06)=30.29(1.06)=$32.10

9 - 28


Find the expected dividend yield, capital gains yield, and total return

during the first year.

Dividend yld = = =

Cap gains yld = =

Total return = 7.0% + 6.0% = 13.0%

D1

P0

P1 – P0

P0

^$30.29$2.12

7.0%

$32.10 – $30.29$30.29

= 6.0%

9 - 29


Rearrange model to rate of return form:

PD

k g

D

Pg

s0

1 1

0

to k s

Then, ks = $2.12/$30.29 + 0.06= 0.07 + 0.06 = 13%

^

–

9 - 30


P0 = = = $15.38

What would P0 be if g = 0?

The dividend stream would be a perpetuity.

2.00 2.002.00

0 1 2 313% ...

^ PMTk

$2.000.13

^

9 - 31


Can no longer use constant growth model.

However, growth becomes constant after 3 years.

If we have supernormal growth of 30% for 3 years, then a long-run constant

g = 6%, what is P0? ks is still 13%.^

9 - 32


Valuing a Supernormal/Non-constant Growth Stock

Supernormal/non-constant growth is that

part of the firm’s life cycle in which it grows

faster than the economy as a whole.

Steps to Value Supernormal Growth Stock:

1. Compute the expected future cash

dividends

cont….

9 - 33


2. Compute the stock’s price at a future point in time, using constant growth model Pt = Dt+1/(r-g). (You must pick a point after the dividend growth rate has become constant)

3. Compute the PV of the expected future sale price and add that to the PV of all the expected cash dividends between now and then.

(Source: Emery, D.R., J.D. Finnerty and J.D. Stowe.1998. Principles of Financial Management. Prentice Hall, pp 172-173)

9 - 34


Nonconstant growth followed by constant growth:

0

2.301

2.647

3.045

46.114

1 2 3 4ks = 13%

54.107 = P0

g = 30% g = 30% g = 30% g = 6%...

D0 = 2.00 2.600 3.380 4.394 4.658

.. .

$66.54P34.65813 0 06

0

...

^

9 - 35


What is the expected dividend yield and capital gains yield at t = 0? At t = 4? (Div yield0=Div1/Price)

Div. yield0 = = 4.81%.

Cap. gain0 = (ks- div yield)

=13.00% – 4.81% = 8.19%.

$2.60$54.11

9 - 36


During nonconstant growth, dividend yield (D/P) and capital gains yield are not constant, and capital gains yield is not equal to g.

After t = 3, g = constant = 6% = capital gains yield; ks = 13%; so D/P

= 13% – 6% = 7%.

9 - 37


25.72

Suppose g = 0% for t = 1 to 3, and then g is a constant 6%. What is P0?

0

1.771.571.39

20.99

1 2 3 4ks=13%

g = 0% g = 0% g = 0% g = 6%

2.00 2.00 2.00 2.00 2.12

.P3

2.12

0 0730.29.

^

...

9 - 38


t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%. (CGY=capital gain yield)

$2.00$25.72

What is D/P and capital gains yield at t = 0 and at t = 3?

t = 0:D1

P0

= = 7.78% (D/P=div yield)

CGY = 13% – 7.78% = 5.22%.

9 - 39


What is the annual dividend yield (D/P) and capital gains yield?

Capital gains yield = g = -6.0%,

Dividend yield= 13.0% – (-6.0%) = 19%.

D/P and cap. gains yield are constant,with high dividend yield (19%) offsettingnegative capital gains yield.

9 - 40


If g = -6%, would anyone buy the stock? If so, at what price?

Firm still has earnings and still paysdividends, so P0 > 0:

PD

k g

D g

k gs s0

1 0 1=

=

$2.00(0.94) $1.880.13 – (-0.06) 0.19

= = = $9.89.

– –+

9 - 41


Further Example of Supernormal Growth Stock

Netscape is operating in a new industry that has recently caught on with the public. Sales are growing at 80% per year. This high sales growth is expected to translate into a 25% growth rate in cash dividends for each of the next 4 years. After that, the dividend growth rate is expected to be 5% forever. Annual dividend paid yesterday is $0.75. The stock’s required return is 22%. What is Netscape’s stock’s price?

(Source: Emery et al, Principles of Financial Management. 1998.

pp 172-173)

cont….

9 - 42


i) Compute the expected future cash dividends:

Time 0 1 2 3 4 5 6 ...

Div($) 0.75 0.938 1.172 1.465 1.831 1.923 2.019 …

g(%) 25% 25% 25% 25% 5% 5% 5% …

ii) Find the stock price at a future time, a point after which the dividend growth rate has

become constant forever. That point is at year 5, thus:

P5 = D6/(r-g) = $2.019/(0.22-0.05) = $11.876

iii) Compute the PVs of all the future expected cash dividends found in step (i)

and add to the PV of the expected future sale price (P5) calculated in step (ii):

P0 = 0.938/1.221 + 1.172/1.222 + 1.465/1.223

+ 1.831/1.224 + 1.923/1.225 + 11.876/1.225

= $(0.768 + 0.787 + 0.807 + 0.827 + 0.711 + 4.394)

= $8.295

9 - 43


Valuing An Erratic-Growth Stock (EGS)Definition: An EGS is a stock which is

expected to have an erratic dividend growth for some finite time, followed by a normal rate forever into the future.

P0=D1/( 1+r)1 + D2/(1+r)2 +…Dn/(1+r)n + {(1+g)Dn)/[(1+r)n(r-g)]}

(Source: Emery et al., Principles of Financial Management. 1998.

pp 173-174)

cont…..

9 - 44


Example:

Novell’s dividend was $1 last year and is to be $1 for each of the next 3 years. After its projects have been developed, earnings are expected to grow at a high rate for 2 years as sales resulting from new projects are realized. The higher earnings are expected to result in 40% increase in dividends for 2 years. After these 2 extraordinary increases in dividends, the dividend growth rate is expected to be 3% per year forever. Novell’s required rate of return is 12%. What is the worth of its share today?

(i) First compute the expected future dividends: Time 0 1 2 3 4 5 6 7 …..

Div($) 1.00 1.00 1.00 1.00 1.40 1.96 2.019 2.079 …

Growth 0% 0% 0% 40% 40% 3% 3% 3% ….

cont…

9 - 45


(ii) D5 is where the growth rate in dividends is expected to become constant forever and is the earliest point that satisfies the constant-growth assumption. With D5 =$1.96, g=3%, and r = 12%,

P0 = D1/( 1+r)1 + D2/(1+r)2 +…Dn/(1+r)n + (1+g)Dn/{(1+r)n(r-g)}

P0 = 1.00/1.121

+ 1.00/1.122

+ 1.00/1.123

+1.40/1.124

+ 1.96/1.125

+ (1+0.03)1.96/{(1.12)5(0.12-0.03)}

= $17.13

9 - 46


Free Cash Flow Method/Total Company or Corporate Valuation Model

The free cash flow method suggests that the value of the entire firm equals the present value of the firm’s free cash flows (calculated on an after-tax basis).

Recall that the free cash flow in any given year can be calculated as:

NOPAT – Net capital investment(NOPAT= Net operating profit after taxes)

9 - 47


The Corporate Valuation Model (Text,pg 306)

Market Value=Vcompany= PV of expected future Free cash flows of company

= FCF1/(1+r)1 +FCF2/(1+r)2+…FCFn/(1+r)n

FCF = (EBIT(1-T) + Dep + Amort)

- (Cap Exp + Change in NOWC);

or

FCF = NOPAT – New Investment in Operating Cap

9 - 48


Once the value of the firm is estimated, an estimate of the stock price can be found as follows:

MV of common stock (market capitalization) = MV of firm – MV of debt and preferred stock.

P = MV of common stock/# of shares.

Using the Free Cash Flow Method

^

9 - 49


Free cash flow method is often preferred to the dividend growth model -- particularly for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends.

Issues Regarding the Free Cash Flow Method

Cont..

9 - 50


Similar to the dividend growth model, the free cash flow method generally assumes that at some point in time, the growth rate in free cash flow will become constant.

Terminal value represents the value of the firm at the point in which growth becomes constant.

FCF Method Issues (continued)

9 - 51


$416.942

FCF estimates for the next 3 years are -$5, $10, and $20 million, after which the FCF is

expected to grow at 6%. The overall firm cost of capital is 10%.

(r-g = 0.10-0.06 = 0.04)

0

-4.5458.264

15.026398.197

1 2 3 4k = 10%

g = 6%

-5 10 20 21.20

21.200.04

...

*TV3 represents the terminal value of the firm, at t = 3

$530 = = *TV3

9 - 52


If the firm has $40 million in debt and has 10 million shares of stock, what is

the price per share?

Value of equity = Total value – Value of debt

= $416.94 – $40

= $376.94 million

Price per share = Value of equity/# of shares

= $376.94/10

= $37.69

9 - 53


Analysts often use the following multiples to value stocks:P/EP/CFP/SalesP/Customer

Example: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price.

Using the Multiples of Comparable Firms to Estimate Stock Price

9 - 54


What is market equilibrium?(Text,pg310-312)

ks = (D1/P0) + g = ks = kRF + (kM – kRF)βfirm^

In equilibrium, stock prices are stable.There is no general tendency for people to buy versus to sell.

In equilibrium, expected returns mustequal required returns:

9 - 55


Expected returns are obtained by estimating dividends and expected capital gains (which can be found using any of the three common stock valuation approaches).^Ks = (D1/P0) + g

Required returns are obtained from the CAPM: ks = kRF + (kM – kRF)βfirm

9 - 56


How is equilibrium established?

If ks = + g > ks (CAPM) then

P0 is “too low” (a bargain).

Buy orders > sell orders;

P0 bid up; D1/P0 falls until

(D1/P0) + g = ks = ks

^

^

D1

P0

9 - 57


Why do stock prices change?

1. ki could change: ki = kRF + (kM – kRF )bi. kRF = k* + IP.

2. g could change due to economic or firm situation.

P0 = . ^ D1

ki – g

9 - 58


What’s the Efficient Market Hypothesis (EMH)?

EMH: Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or better information.

9 - 59


1. Weak-form EMH:

Can’t profit by looking at past trends. A recent decline is no reason to think stocks will go up (or down) in the future.

Evidence supports weak-form EMH, but “technical analysis” is still used.

9 - 60


2. Semistrong-form EMH:

All publicly available information is reflected in stock prices, so doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true, but superior analysts can still profit by finding and using new information.

9 - 61


3. Strong-form EMH:All information, even inside information, is embedded in stock prices. Not true--insiders can gain by trading on the basis of insider information, but that’s illegal.

9 - 62


1. 15,000 or so trained analysts; MBAs, CFAs, Technical PhDs.

2. Work for firms like Merrill, Morgan, Prudential, which have a lot of money.

3. Have similar access to data.

4. Thus, news is reflected in P0 almost instantaneously.

Markets are generally efficient because:

9 - 63


Preferred Stock

Hybrid security.Similar to bonds in that preferred

stockholders receive a fixed dividend that must be paid before dividends can be paid on common stock.

However, unlike interest payments on bonds, companies can omit dividend payments on preferred stock without fear of pushing the firm into bankruptcy.

9 - 64


What’s the expected return of preferred stock with Vp = $50 and

annual dividend = $5?

.k

5$50$V

pp

%.0.1010.050$

5$k̂p

Documents

Features of common stock Determining common stock values Efficient markets Preferred stock