7 - 1

CHAPTER 7Valuation Models: Stocks

Features of common stockDetermining common stock valuesSecurity market equilibriumEfficient marketsPreferred stock

S05

7 - 2

Represents ownership?Ownership implies control?

Agency problemStockholders elect directors?Directors elect management?Management’s goal: Maximize

stock price.

Facts about Common Stock?

7 - 3

Classified stock has special provisions.Could classify existing stock as

founders’ shares, with voting rights but dividend restrictions.

New shares might be called “Class A” shares, with voting restrictions but full dividend rights.

What’s classified stock? How might classified stock be used?

7 - 4

The dividends of tracking stock are tied to a particular division, rather than the company as a whole.Investors can separately value the

divisions.Its easier to compensate division

managers with the tracking stock. But tracking stock usually has no

voting rights, and the financial disclosure for the division is not as regulated as for the company.

What is tracking stock?

7 - 5

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

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

Prior to an IPO, shares are typically owned by the firm’s managers, key employees, and, in many situations, venture capital providers.

7 - 6

What is a seasoned equity offering (SEO)?

A seasoned equity offering occurs when a company with public stock issues additional shares.

After an IPO or SEO, the stock trades in the secondary market, such as the NYSE or Nasdaq.

7 - 7

ANALYZING STOCKS

7 - 8

Dividend growth modelUsing the multiples of comparable

firms

Free cash flow method (covered in Chapter 12)

Different Approaches for Valuing Common Stock

7 - 9

DIVIDEND GROWTH MODEL

7 - 10

P0 = + + . . . . ^ D1

(1 + r)

D2

(1 + r)2

D

(1 + r)

Stock value = PV of dividends

ABSOLUTELY FUNDAMENTAL!

7 - 11

D1 = D0(1 + g1)D2 = D1(1 + g2)

.

.

.

Future Dividend Stream:

7 - 12WHAT IS A CONSTANT GROWTH STOCK? HOW ARE CONSTANT

GROWTH STOCKS VALUED?A stock whose dividends grow at a

constant rate.In application, doesn’t mean that

each year must have precisely a growth rate equal to the constant rate, but rather that our best guess is that that dividends will grow at a constant rate. Slide T7-14.

7 - 13WHAT IS A CONSTANT GROWTH STOCK? HOW ARE CONSTANT

GROWTH STOCKS VALUED?

D1 = D0(1+g)

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

. . .Dn = D0(1+g)n

7 - 14

P0 = = .^ D1

rs - g

D0 (1 + g)

rs - g

If growth of dividends g isconstant, then:

Model requires: rs > g (otherwise results in negative

price).g constant forever.

7 - 15

D D gtt 0 1

tt

tr

DPVD

1

!P k;>g 0 IfP PVD t0

$

0.25

Years (t)0

7 - 16

What happens if g > rs?

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

We can’t use model unless (1) g rs and (2) g is expected to be constant forever. Because g must be a long-term growth rate, it cannot be rs.

.r requires ˆs

10 g

gr

DP

s

7 - 17

PROOF OF GORDON MODEL

7 - 18

= 1.2.rRF = 7%.rM = 12%.

Bon Temps Company: What is the required rate of return?

Use SML equation to calculate rs:

rs = rRF + (rM - rRF)= 7% + (12% - 7%)(1.2)

rs = 13%.

7 - 19

.Hint:

D0 = 2.00 (already paid).

D1 = D0(1.06) = $2.12

D2 = D1(1.06) = $2.247

D3 = D2(1.06) = $2.382 T7-16,7-17.

Last dividend = $2.00; Dividend is expected to grow at 6%, i.e. g = 6%.

What is the value of Bon Temps’ stock, P0, given rs = 13%, D0 = 2.00 ?

7 - 20

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

Constant growth model:

gr

D

gr

gDP

ss

100

1ˆ

= = =$30.29.0.13 - 0.06

$2.12 $2.12

0.07

7 - 21

What is Bon Temps’ value one year from now?

7 - 22

P1 = D2/(rs - g) = 2.247/0.07 = $32.10.

^

What is Bon Temps’ value one year from now?

Note: Could also find P1 as follows:

P1 = D2 /(rs - g) = D1 (1 + g)/(rs - g) = P0 (1 + g) = $30.29(1.06) = $32.10.So, price grows at rate = g.

^

^

7 - 23

P0 = D1/(rs - g)

P1 = D2/(rs - g)

BUT, D2 = D1( 1+g)

So, P1 = D1( 1+g) (rs - g)

OR: P1 = P0( 1+g)

7 - 24

Find the expected dividend yield, capital gains yield, and total return during the 1st, 2nd and 3rd years.

7 - 25

^Dn

Pn - 1

= .

In 1st year:D1

P0

= = 7.00%.^$2.12

$30.29

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

during the first year.

Dividend yield in Year n

7 - 26

^Dn

Pn - 1

= .

In 2nd year: D2

P1 = = 7.00%.^

$2.247$32.10

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

during the first year.

Dividend yield in Year n

7 - 27

So, in CGR models, Dividend and Price both grow at a rate = g; consequently

the dividend yield is:

?

7 - 28

So, in CGR models, Dividend and Price both grow at a rate = g;

consequently the dividend yield is:

CONSTANT!

7 - 29

= 6%.

In CGR models, Capital gains yield = g

Pn - Pn - 1

Pn - 1

^

= .^

^

In 1 year:

$32.10 - $30.29$30.29

Capital gains yield in any Year n:

7 - 30

= 7% + 6% = 13% = rs.

Total yield = Div. yield + Cap. gains yield

7 - 31

Find the total return during thefirst year.

Total return = Dividend yield + Capital gains

yield.Total return = 7% + 6% = 13%.Total return = 13% = rs.

For constant growth stock:

Capital gains yield = 6% = g.

7 - 32

Rearrange model to rate of return form:

.r to ˆ0

1s

10 g

P

D

gr

DP

s

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

^

7 - 33

If a stock is in equilibrium, then:Price = Value.

(P0 = P0)

Required return = Expected return. (rs = rs)

^

^

Points to Remember

7 - 34

For any stock, the expected total return in any year equals dividend yield + capital gains yield.

7 - 35

For constant growth stocks:Dividend yield is constant,

D1/P0 = D2/P1 = D3/P2.Capital gains yield is constant = g.

(P1 - P0)/P0 = (P1/P0) - 1 = (1+g) - 1 = g.Stock price grows at constant

rate = g.

7 - 36

DIGRESSION: PRICE-EARNINGS RATIO

Po = D1/(rs - g)

D1 = E1( 1-b)

Where b = retention ratio, and (1-b) = payout ratio.

7 - 37

PRICE-EARNINGS RATIO

Po = E1(1-b)/(rs - g)

Po = (1-b)

E1 (rs - g)

A greater g implies a larger P/E.

7 - 38

WHAT WOULD THE STOCK PRICE OF BON TEMPS BE IF DIVIDENDS HAVE

ZERO GROWTH?

7 - 39

What would P0 be if g = 0?

The dividend stream would be a perpetuity.

2.00 2.002.00

0 1 2 3rs=13%

P0 = = = $15.38.PMT

r

$2.00

0.13^

7 - 40

What is Subnormal or Supernormal Growth

7 - 41

Subnormal or Supernormal Growth

Non-constant growth followed by constant growth in dividends. (e.g. after some point, best we can do is estimate a constant growth in dividends.)

Cannot use constant growth model alone

Value the nonconstant & constant growth periods separately

7 - 42

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

g = 6%, what is P0?^

0 rs=16% 1 2 3 4

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

D0 =$2.00

7 - 43

Nonconstant growth followed by constantgrowth:

0

2.3009

2.6470

3.0453

46.1135

1 2 3 4rs=13%

54.1067 = P0

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

D0 = 2.00 2.60 3.38 4.394 4.6576

^

5371.66$06.013.0

6576.4$P̂3

n.b. P3= D4/(rs - g)

7 - 44

What is the expected dividend and capital gains yields at t = 0? At t = 4?

7 - 45

What is the expected dividend yield and capital gains yield at t = 0? At t = 4?

Dividend yield = = = 4.81%.$2.60

$54.11

D1

P0

CG Yield = 13.0% - 4.8% = 8.19%.

At t = 0:

(More…)

7 - 46

Check on Capital gains yield:

Capital Gains yield = (P1 - P0)/P0

P1= PV(D2) + PV(D3) + PV(P3)

= 3.38/1.13 + 4.394/(1.13)2 + 66.53/(1.13)2 = $58.53

Capital Gains yield = (P1 - P0)/P0 = (58.53- 54.11)/54.11 = 8.19%

42

7 - 47

During nonconstant growth, dividend yield and capital gains yield are not constant.

If current growth is greater than g, current capital gains yield is greater than g.

After t = 3, g = constant = 6%, so the t t = 4 capital gains gains yield = 6%.

Because rs = 13%, the t = 4 dividend yield = 13% - 6% = 7%.

7 - 48

At Year 4, stock is constant growth, so

CG yield4 = 6% = g.

Div. yield4 = 7%.

7 - 49

The current stock price is $54.11The PV of dividends beyond year 3 is

$66.53/(1.13)^3 (P3 discounted back to t = 0) =46.11.

The percentage of stock price due to “long-term” dividends is:

Is the stock price based onshort-term growth?

= 85.2%.$46.11$54.11

7 - 50

If most of a stock’s value is due to long-term cash flows, why do so many

managers focus on quarterly earnings?

Sometimes changes in quarterly earnings are a signal of future changes in cash flows. This would affect the current stock price.

Sometimes managers have bonuses (or options) tied to quarterly earnings.

7 - 51

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

0

1.76991.56631.3861

20.9895

1 2 3 4rs=13%

25.7118

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

2.00 2.00 2.00 2.12

2.12.

P3 0 0730.2857

^

...

7 - 52

What is dividend yield and capital gains yield at t = 0 and at t = 3?

t = 0:D1

P0

CGY = 13.0% - 7.8% = 5.2%.

2.00$25.72

7.8%.

t = 3: Now have constant growth with g = capital gains yield = 6% and dividend yield = 7%.

7 - 53

If g = -6%, no one buy the stock? Right?

7 - 54

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

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

gr

D

gr

gDP

ss

100

1ˆ

^

= = = $9.89.$2.00(0.94)

0.13 - (-0.06)

$1.88

0.19

7 - 55

What are the annual dividendand capital gains yield?

Capital gains yield = g = -6.0%.

Dividend yield = 13.0% - (-6.0%)= 19.0%.

Both yields are constant over time, with the high dividend yield (19%) offsetting the negative capital gains yield.

7 - 56

Using Free Cash Flows

We will cover this later in Chapter 12.

7 - 57

Suppose this firm decides to expand:

Finance expansion by borrowing $40 million and halting dividends.

How do we value a firm with no dividends?

7 - 58

Projected free cash flows (FCF):Year 1 FCF = -$5 millionYear 2 FCF = $10 millionYear 3 FCF = $20 millionFCF grows at constant rate of 6%

after year 3.

7 - 59

The corporate cost of capital, kc, is 10%.

The company has 10 million shares of stock.

7 - 60

Free Cash Flows

Recall the definition of free cash flows:

FCF=NOPAT - Net Capital InvestmentwhereNet Capital Investment = Net

operating working capital [non-interest bearing CA - CL] - operating capital

7 - 61

Vop at 3

Find the value of operations by discounting the free cash flows at

the cost of capital.0

-4.545

8.264

15.026

398.197

1 2 3 4rc=10%

416.942 = Vop

g = 6%

FCF= -5.00 10.00 20.00 21.2

$21.2. .

$530.10 0 06

0

7 - 62

Find the price per share ofcommon stock.

Value of equity = Value of operations - Value of debt = $416.94 - $40

= $376.94 million.

Price per share = $376.94/10 = $37.69.

7 - 63

In equilibrium, expected returns mustequal required returns:

rs = D1/P0 + g = rs = rRF + (rM - rRF)b.^

7 - 64

Using multiples of comparable firms

7 - 65

Analysts often use the following multiples to value stocks:P/EP/CF or P/EBITDAP/SalesP/marginP/Customer

.

Second Method: Using the Multiples of Comparable Firms to Estimate Stock

Price (Price Multiples)

7 - 66

Analysts often use the P/E multiple (the price per share divided by the earnings per share) or the P/CF multiple (price per share divided by cash flow per share, which is the earnings per share plus the dividends per share) to value stocks (or other multiples).

Example:Estimate the average P/E ratio of

comparable firms. This is the P/E multiple.Multiply this average P/E ratio by the

expected earnings of the company to estimate its stock price.

Using the Stock Price Multiples to Estimate Stock Price

7 - 67

Example: BOHEstimate the average P/E ratio of

comparable firms. This is the P/E multiple.The P/E multiple for Pacific Banks is 19.06.Multiply this average P/E ratio by the

expected earnings of the company to estimate its stock price.

The EPS(ttm) is 3.22Consequently, the Implied price is: $61.37This is 16% greater than the current $52.81

price.

Using the Stock Price Multiples to Estimate Stock Price

7 - 68

The entity value (V) of the comparable firm is:the market value of equity (# shares of stock

multiplied by the price per share)plus the value of debt.

Pick a measure, such as EBITDA, Sales, Customers, Eyeballs, etc.

Calculate the average entity ratio for a sample of comparable firms. For example,V/EBITDAV/Customers

Using Entity Multiples

7 - 69

Find the entity value of the firm in question. For example,Multiply the firm’s sales by the V/Sales

multiple.Multiply the firm’s # of customers by the

V/Customers ratio The result is the total value of the firm. Subtract the firm’s debt to get the total value

of equity. Divide by the number of shares to get the

price per share.

Using Entity Multiples (Continued)

7 - 70

It is often hard to find comparable firms. The average ratio for the sample of

comparable firms often has a wide range.For example, the average P/E ratio might

be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?

What factors account for the difference in P/E ratios?

Problems with Market Multiple Methods

7 - 71

Why are stock prices volatile?

grD

0P

s1

rs = rRF + (RPM)βi could change. Inflation expectations Risk aversion Company risk

g could change.

^

7 - 72

Stock value vs. changes in rs and g

D1 = $2, rs = 10%, and g = 5%:P0 = D1 / (rs-g) = $2 / (0.10 - 0.05) = $40.

What if rs or g change?g g g

rs 4% 5% 6%9% 40.00 50.00 66.67

10% 33.33 40.00 50.0011% 28.57 33.33 40.00

7 - 73Are volatile stock prices consistent

with rational pricing?

Small changes in expected g and rs cause large changes in stock prices.

As new information arrives, investors continually update their estimates of g and rs.

If stock prices aren’t volatile, then this means there isn’t a good flow of information.

7 - 74

What is market equilibrium?

7 - 75

What is market equilibrium?

r = D1/P0 + g = r = rRF + (rM - rRF)β.

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

In equilibrium, expected returns mustequal required returns:

^

7 - 76

How is equilibrium established?

^

7 - 77

D1

P0

How is equilibrium established?

If r = + g > r, then

P0 is “too low,” a bargain.

Buy orders > sell orders; P0 bid up;

D1/P0 falls until D1/P0 + g = r = r.

^

^

7 - 78

Why do stock prices change?

10 gr

DP

i

ri = rRF + (rM - rRF )βi could change. Inflation expectations Risk aversion Company risk

g could change.

^

7 - 79

What’s the Efficient Market Hypothesis?

7 - 80

What’s the Efficient Market Hypothesis?

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

7 - 81

What are the three forms of the EMH?

7 - 82

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. Seems empirically true, but “technical analysis” is still used.

7 - 83

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; especially on smaller stocks.

7 - 84

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.

7 - 85

Markets are generally efficient because:

1. 100,000 or so trained analysts--MBAs, CFAs, and PhDs--work for firms like Fidelity, Merrill, Morgan, and Schwab.

2. These analysts have similar access to data and megabucks to invest.

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

7 - 86

Preferred Stock

Hybrid security.Similar to bonds in that preferred

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

However, unlike bonds, preferred stock dividends can be omitted without fear of pushing the firm into bankruptcy.

7 - 87

What’s the expected return on preferred stock with Vps = $50 and

annual dividend = $5?

%.0.1010.050$

5$

5$50$

ps

ps

ps

r

rV

7 - 88

END!