chapter 8: stocks, stock valuation and stock market equilibrium

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CHAPTER 8Stocks, Stock Valuation and Stock

Market Equilibrium

© Copyright 2005, 2006, 2007 Thomson South-Western, Michael C. Erhardt, John Kevin Doyle and Benedictine University

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Outline of Chapter

Features of common stock

Determining common stock values

Efficient markets

Preferred stock

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Represents ownership.

Ownership implies control.

Stockholders elect directors.

Directors hire management.

Since the managers are “agents” of stake holders, their goal should be to perform as the stake holders wish, e.g., maximize stock price.

Common Stock: Owners, Directors, and Managers

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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.

Classified stock

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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.

Tracking Stock

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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.

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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.

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Dividend growth model

Using multiples of comparable firms

Free cash flow method (covered in Chapter 15)

Valuing Common Stock

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s3

s

32

s

21

s

10

r1

D. . .

r1

D

r1

D

r1

DP̂

Stock Value = PV of Dividends

Where

P0 is the present value of the stock,

Dn is the dividend in year n, and

rs is the required rate of return for the stock.

^

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• A constant growth stock is one whose dividends are expected to grow forever at a constant rate, g.

• This is the CGD model.

Constant Growth Stock

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t0t

202

101

g1DD

...

g1DD

g1DD

gr

D

gr

g1DP̂

s

1

s

00

If g is constant, then*:

For a constant growth stock:

* summing the geometric series

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D D gtt 0 1

ts

tt

r1

DPVD

!P ,r>g If 0s P PVDt0

$

0.25

Years (t)0

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What happens if g > rs?

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

We can’t use model unless g rs and

g is expected to be constant forever.

Because g must be a long-term growth rate, it cannot be rs.

g.r requires gr

DP̂ s

s

10

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Example

Assume β = 1.2, rRF = 7%, and RPM = 5%.

What is the required rate of return on the firm’s stock?.

Use SML to calculate rs:

rs = rRF + RPMβ

= 7% + 5%1.2

= 13%

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Example

Assume D0 = $2.00, g is a constant 6%, and rs = 13%. Find the expected dividends for the next 3 years, and their PVs.

0 1

2.2472

2

2.3820

3g=6% 4

1.87611.75991.6508

D0=2.0013%

2.12

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

Constant growth model:

gr

D

gr

g1DP

s

1

s

00

ˆ

= = = $30.290.13 - 0.06

$2.12 $2.12

0.07

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

D1 will have been paid, so expected dividends are D2, D3, D4, … . Thus,

^

= $2.2427 = $32.100.07

gr

DP

s

21 ˆ

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Find the expected dividend yield and capital gains yield during the first year.

Dividend yield = = = 7.0%$2.12

$30.29

D1

P0

CG Yield = =P1 - P0

^

P0

$32.10 - $30.29

$30.29

= 6.0%

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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.

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Rearrange model to rate of return form:

gP

Dr

gr

DP

0

1s

s

10

toˆ

Then, rs = $2.12/$30.29 + 0.06

= 0.07 + 0.06 = 13%

^

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What would P0 be if g = 0?

The dividend stream would be a perpetuity.

2.00 2.00 …2.00

0 1 2 3rs=13%

P0 = = = $15.38PMT

r

$2.00

0.13^

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Assume r is still 13%.

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?

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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

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

Dividend yield = = = 4.8%$2.60

$54.11

D1

P0

CG Yield = 13.0% - 4.8% = 8.2%

At t = 0:

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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 is constant 6%, so the t = 4 capital gains gains yield = 6%.

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

At t = 4?

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The current stock price is $54.11

The PV of dividends beyond year 3 is $46.11 (P3 discounted back to t=0).

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

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Intrinsic Stock Value vs. Quarterly Earnings

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 tied to quarterly earnings.

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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

^

...

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t = 3: Now have constant growth with g = capital gains yield = 6% and dividend yield rs – g = 13% – 6% = 7%

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%

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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

g1DP

s

1

s

00

ˆ

^

= = = $9.89$2.00(0.94)

0.13 - (-0.06)

$1.88

0.19

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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.

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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.

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 Stock Price Multiples to Estimate Stock Price

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

multiplied by the market 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/EBITDA V/Customers

Using Entity Multiples

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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

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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?

Problems with Market Multiple Methods

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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.

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

annual dividend = $5?

10.0%0.10$50

$5r

r

$5$50V

ps

ps

ps

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Why are stock prices volatile?

grDPs

10

rs = rRF + (RPM)β could change.

Inflation expectations

Risk aversion

Company risk

g could change.

^

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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

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Are 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.

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What is market equilibrium?

^

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

The expected price, P, must equal the actual price, P. In other words, the fundamental value must be the same as the price.

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In equilibrium, expected returns mustequal required returns:

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

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How is equilibrium established?

If rs = + g > rs, then P0 is “too low.”

If the price is lower than the fundamental value, then the stock is a “bargain.”

Buy orders will exceed sell orders, the

price will be bid up, and D1/P0 falls until

D1/P0 + g = rs = rs.

^

^

D1

P0

^

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

Efficient Market Hypothesis (EMH)

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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.

Efficient Market Hypothesis (EMH)

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2. Semistrong-form EMH:

All publicly available information is reflected in stock prices, so it doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true.

Efficient Market Hypothesis (EMH)

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3. Strong-form EMH:

All information, even inside information, is embedded in stock prices. This is false, since insiders can gain by trading on the basis of insider information (although, remember this is illegal).

Efficient Market Hypothesis (EMH)

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Markets are generally efficient because:

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

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

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