CHAPTER 8

STOCKS AND THEIR STOCKS AND THEIR VALUATIONVALUATION

Represents ownership.

Ownership implies control.

Stockholders elect directors.

Directors elect management.

Management’s goal: Maximize the stock

price.

2SITI AISHAH BINTI KASSIM (FM2)

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

the public.

SITI AISHAH BINTI KASSIM (FM2) 3

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


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.



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.


D1 = D0(1 + g)1

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

Dt = D0(1 + g)t

If g is constant, then:

P0 = = D0(1 + g)

ks – g

D1

ks – g

^


0P̂ = requires ks > gD1

ks – g

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.

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:


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

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

0.07$30.29

$2.12

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

SITI AISHAH BINTI KASSIM (FM2)12

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 = =

^

D2 $2.247^

= $32.10

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

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

year.


Dividend yield = = =

Cap gains yield = =

Total return = 7.0% + 6.0% = 13.0%

P0

P1 – P0

P0

^$30.29

$2.12 7.0%

$30.29

= 6.0%

D1

$32.10 – $30.29


^

P0 = = =$15.38

The dividend stream would be a perpetuity.

2.00 2.002.00

0 1 2 313% ...

^ PMTk

$2.000.13

Can no longer use constant growth model.

However, growth becomes constant after 3 years.


^

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 dividends2. 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)



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

.

. .$66.54P

3

4.658

13 0 06

0

...

^


Div. yield0 = = 4.81%.

Cap. gain0 = (ks- div yield)

=13.00% – 4.81% = 8.19%.

$2.60$54.11

During non-constant 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%.


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)



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

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)


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


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.


^

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.

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.



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 millionPrice per share = Value of equity/# of shares

= $376.94/10

= $37.69

Analysts often use the following multiples to value stocks:◦P/E◦P/CF◦P/Sales◦P/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.


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

In equilibrium, expected returns must equal required returns:


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

^

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


^


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


P0 = ^ D1

ki – g

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

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

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



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.

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.


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.


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.


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.


What is the expected return of preferred stock with Vp = $50 and annual dividend =

$5?


.k

5$50$V

pp

%.0.1010.050$

5$k̂p

THE ENDTHE END


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CHAPTER 8