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CHAPTER 8

Stocks, Stock Valuation, and Stock Market Equilibrium

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Topics in Chapter

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

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Common Stock: Owners, Directors, and Managers

Represents ownership. Ownership implies control. Stockholders elect directors. Directors hire management. Since managers are “agents” of

shareholders, their goal should be: Maximize stock price.

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Classified Stock

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.

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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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Different Approaches for Valuing Common Stock

Dividend growth model Using the multiples of comparable

firms Free cash flow method (covered in

Chapter 15)

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Stock Value = PV of Dividends

What is a constant growth stock?

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

P0 =^

(1+rs)1 (1+rs)2 (1+rs)3 (1+rs)∞

D1 D2 D3 D∞+ + +…+

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For a constant growth stock:

D1 = D0(1+g)1

D2 = D0(1+g)2

Dt = D0(1+g)t

If g is constant and less than rs, then:

P0 = ^ D0(1+g)

rs - g=

D1

rs - g

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Dividend Growth and PV of Dividends: P0 = ∑(PVof Dt)

$

0.25

Years (t)

Dt = D0(1 + g)t

PV of Dt =Dt

(1 + r)t

If g > r, P0 = ∞ !

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What happens if g > rs?

P0 =^

(1+rs)1 (1+rs)2 (1+rs)∞

D0(1+g)1 D0(1+g)2 D0(1+rs)∞ + +…+

(1+g)t

(1+rs)t

If g > rIf g > rss, then, then P0 = ∞.^

> 1, and

So g must be less than rs to use the constant growth model.

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Required rate of return: beta = 1.2, rRF = 7%, and RPM = 5%.

rs = rRF + (RPM)bFirm

= 7% + (5%) (1.2)= 13%.

Use the SML to calculate rs:

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Projected Dividends

D0 = 2 and constant g = 6%

D1 = D0(1+g) = 2(1.06) = 2.12 D2 = D1(1+g) = 2.12(1.06) =

2.2472 D3 = D2(1+g) = 2.2472(1.06) =

2.3820

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Expected Dividends and PVs (rs = 13%, D0 = $2, g = 6%)

0 1

2.2472

2

2.3820

3g=6% 4

1.87611.75991.6508

13%

2.12

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Intrinsic Stock Value: D0 = 2.00, rs = 13%, g = 6%.

Constant growth model:

= = $30.29.0.13 - 0.06

$2.12 $2.12

0.07

P0 = ^ D0(1+g)

rs - g=

D1

rs - g

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Expected value one year from now:

D1 will have been paid, so expected dividends are D2, D3, D4 and so on.

P1 = ^ D2

rs - g=

$2.2427

0.07= $32.10

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Expected Dividend Yield and Capital Gains Yield (Year 1)

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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Total Year-1 Return

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:

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

^

P0 = ^ D1

rs - gto

D1

P0

rs

^= + g.

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If g = 0, the dividend stream is a perpetuity.

2.00 2.002.00

0 1 2 3rs=13%

P0 = = = $15.38.PMT

r

$2.00

0.13^

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Supernormal Growth Stock

Supernormal growth of 30% for 3 years, and then long-run constant g = 6%.

Can no longer use constant growth model.

However, growth becomes constant after 3 years.

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Nonconstant growth followed by constant growth (D0 = $2):

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%

2.60 3.38 4.394 4.6576

^P3 = ^ $4.6576

0.13 – 0.06= $66.5371

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Expected Dividend Yield and Capital Gains Yield (t = 0)

CG Yield = 13.0% - 4.8% = 8.2%.

Dividend yield = = = 4.8%.$2.60

$54.11

D1

P0

At t = 0:

(More…)

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Expected Dividend Yield and Capital Gains Yield (t = 4) 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 =

4 capital gains gains yield = 6%. Because rs = 13%, the t = 4 dividend yield

= 13% - 6% = 7%.

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Is the stock price based onshort-term growth?

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:

= 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?

See next slide.

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Intrinsic Stock Value vs. 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%.

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

2.12P30.07

30.2857

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Dividend Yield and Capital Gains Yield (t = 0)

Dividend Yield = D1 / P0

Dividend Yield = $2.00 / $25.72 Dividend Yield = 7.8%

CGY = 13.0% - 7.8% = 5.2%.

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Dividend Yield and Capital Gains Yield (t = 3)

Now have constant growth, so:

Capital gains yield = g = 6%

Dividend yield = rs – g Dividend yield = 13% - 6% = 7%

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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:^

= = = $9.89.$2.00(0.94)

0.13 - (-0.06)

$1.88

0.19

P0 = ^ D0(1+g)

rs - g=

D1

rs - g

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Annual Dividend and Capital Gains Yields

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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Using Stock Price Multiples to Estimate Stock Price

Analysts often use the P/E multiple (the price per share divided by the earnings per share).

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.

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Using Entity Multiples The entity value (V) 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/EBITDA V/Customers

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Using Entity Multiples (Continued) 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.

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Problems with Market Multiple Methods 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?

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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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Expected return, given Vps = $50 and annual dividend = $5

Vps = $50 =$5

rps

^

rps

$5

$50

^= = 0.10 = 10.0%

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Why are stock prices volatile?

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

g could change.

P0 = ^ D1

rs - g

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Consider the following situation.

D1 = $2, rs = 10%, and g = 5%:

P0 = D1 / (rs-g) = $2 / (0.10 - 0.05) = $40.

What happens if rs or g change?

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Stock Prices vs. Changes in rs and g

g

rs 4% 5% 6%

9% 40.00 50.00 66.67

10% 33.33 40.00 50.00

11% 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.

(More…)

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

In equilibrium, expected returns must equal required returns:

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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 until:

D1/P0 + g = rs = rs.

^

^

D1

P0

^

How is equilibrium established?

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What’s the Efficient MarketHypothesis (EMH)?

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

(More…)

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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.

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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.

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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.

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Markets are generally efficient because:

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

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

Thus, news is reflected in P0 almost instantaneously.

Security Valuation

In general, the In general, the intrinsic valueintrinsic value of of an asset = the an asset = the present valuepresent value of the of the stream of expected cash flows stream of expected cash flows discounted at an appropriate discounted at an appropriate required rate of returnrequired rate of return..

Preferred Stock

A hybrid securityA hybrid security:: it’s like common stock - no fixed it’s like common stock - no fixed maturity.maturity.

technically, it’s part of equity capital.technically, it’s part of equity capital.

it’s like debt - preferred dividends are it’s like debt - preferred dividends are

fixed.fixed. missing a preferred dividend does not missing a preferred dividend does not

constitute default, but preferred dividends are constitute default, but preferred dividends are cumulativecumulative..

Usually sold for $25, $50, or $100 per Usually sold for $25, $50, or $100 per share.share.

Dividends are often quoted as a Dividends are often quoted as a percentage of par.percentage of par. Example:Example: In 1988, Xerox issued $75 In 1988, Xerox issued $75

million of 8.25% preferred stock at $50 million of 8.25% preferred stock at $50 per share.per share.

$4.125 is the fixed, annual dividend per $4.125 is the fixed, annual dividend per share.share.

Preferred StockPreferred Stock

May be May be callablecallable and and convertibleconvertible.. Is usually Is usually non-votingnon-voting.. PriorityPriority: lower than debt, higher than : lower than debt, higher than

common stock.common stock. Usually includes Usually includes protective provisionsprotective provisions.. May include a May include a sinking fundsinking fund provision. provision.

Preferred StockPreferred Stock

Preferred Stock Valuation

A preferred stock can usually be A preferred stock can usually be valued like a perpetuity:valued like a perpetuity:

V =Dk

psps

Example:

Xerox preferred pays an Xerox preferred pays an 8.25%8.25% dividend on a dividend on a $50$50 par value. par value.

Suppose our required rate of Suppose our required rate of return on Xerox preferred is return on Xerox preferred is 9.5%9.5%..

VVpsps ==4.1254.125

.095.095== $43.42$43.42

Expected Rate of Return on Preferred

Just adjust the valuation model:Just adjust the valuation model:

D

Po

kps =

Example

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

D

Po

kps = = = .10314.125

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The Financial Pages:Preferred Stocks

52 weeks 52 weeks Yld Yld Vol Vol

Hi Lo Sym Hi Lo Sym Div % PE 100s Close Div % PE 100s Close

292933//88 25 2511//88 GenMotor pfG 2.28 8.8 … 27 25 GenMotor pfG 2.28 8.8 … 27 25 77//88

Dividend:Dividend: $2.28 on $25 par value $2.28 on $25 par value

= 9.12% dividend rate.= 9.12% dividend rate.

Expected return:Expected return: 2.28 / 25.875 = 2.28 / 25.875 = 8.8%.8.8%.

Common Stock

is a is a variable-incomevariable-income security. security. dividends may be increased or dividends may be increased or

decreased, depending on earnings.decreased, depending on earnings. represents represents equity equity or ownership.or ownership. includes includes voting rightsvoting rights.. PriorityPriority: lower than debt and : lower than debt and

preferred. preferred.

Common Stock Characteristics

Claim on IncomeClaim on Income - a stockholder has a - a stockholder has a claim on the firm’s residual income.claim on the firm’s residual income.

Claim on AssetsClaim on Assets - a stockholder has a - a stockholder has a residual claim on the firm’s assets in case residual claim on the firm’s assets in case of liquidation.of liquidation.

Preemptive RightsPreemptive Rights - stockholders may - stockholders may share proportionally in any new stock share proportionally in any new stock issues. issues.

Voting RightsVoting Rights - right to vote for the firm’s - right to vote for the firm’s board of directors.board of directors.

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

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

Common Stock Valuation(Single Holding Period)

0 1

? 5.50 + 120

Common Stock Valuation(Single Holding Period)

Financial Calculator solution:Financial Calculator solution:

P/Y =1, I = 15, n=1, FV= 125.50P/Y =1, I = 15, n=1, FV= 125.50

solve:solve: PV = -109.13 PV = -109.13

or:or:

P/Y =1, I = 15, n=1, FV= 120, P/Y =1, I = 15, n=1, FV= 120,

PMT = 5.50PMT = 5.50

solve:solve: PV = -109.13 PV = -109.13

The Financial Pages:Common Stocks

52 weeks 52 weeks Yld Yld Vol Vol NetNet

Hi Lo Sym Div % PE 100s Hi Lo Close ChgHi Lo Sym Div % PE 100s Hi Lo Close Chg

139 81 IBM .48 .5 26 56598 108 106 106139 81 IBM .48 .5 26 56598 108 106 10655//88 -2 -2

119 75 MSFT … 60 254888 96 93 95119 75 MSFT … 60 254888 96 93 9533//88 + +11//44

Common Stock Valuation(Multiple Holding Periods)

Constant Growth ModelConstant Growth Model Assumes common stock dividends Assumes common stock dividends

will grow at a constant rate into will grow at a constant rate into the future.the future.

Vcs =D1

kcs - g

Constant Growth ModelConstant Growth Model Assumes common stock dividends will grow Assumes common stock dividends will grow

at a constant rate into the future.at a constant rate into the future.

DD11 = the dividend at the end of period 1. = the dividend at the end of period 1. kkcscs = the required return on the common = the required return on the common

stock.stock. gg = the constant, annual dividend growth = the constant, annual dividend growth

rate.rate.

Vcs =D1

kcs - g

Example

XYZ stock XYZ stock recentlyrecently paid a paid a $5.00$5.00 dividend. The dividend is expected to dividend. The dividend is expected to grow at grow at 10%10% per year indefinitely. What per year indefinitely. What would we be willing to pay if our would we be willing to pay if our required return on XYZ stock is required return on XYZ stock is 15%15%??

D0 = $5, so D1 = 5 (1.10) = $5.50

Example

XYZ stock XYZ stock recentlyrecently paid a paid a $5.00$5.00 dividend. The dividend is expected to dividend. The dividend is expected to grow at grow at 10%10% per year indefinitely. What per year indefinitely. What would we be willing to pay if our would we be willing to pay if our required return on XYZ stock is required return on XYZ stock is 15%15%??

Vcs = = = $110 D1 5.50

kcs - g .15 - .10

Expected Return on Common Stock

Just adjust the valuation modelJust adjust the valuation model

Vcs =D

kcs - g

k = ( ) + gD1

Vcs

Expected Return on Common Stock

Just adjust the valuation modelJust adjust the valuation model

Vcs =D

kcs - g

k = ( ) + gD1

Po

Example We know a stock will pay a We know a stock will pay a $3.00$3.00

dividend at time 1, has a price of dividend at time 1, has a price of $27$27 and an expected growth rate of and an expected growth rate of 5%5%..

kcs = ( ) + gD1

Po

kcs = ( ) + .05 = 16.11%3.00

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