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CHAPTER 7

Stocks, Stock Valuation, and Stock Market Equilibrium

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Topics in Chapter Features of common stock Valuing common stock Preferred stock Stock market equilibrium Efficient markets hypothesis Implications of market efficiency

for financial decisions

ValueStock = + + +D1 D2 D∞(1 + rs )1 (1 + rs)∞(1 + rs)2

Dividends (Dt)

Market interest rates

Firm’s business risk

Market risk aversion

Firm’s debt/equity mixCost of

equity (rs)

Free cash flow(FCF)

The Big Picture:The Intrinsic Value of Common

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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Tracking Stock 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.

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Different Approaches for Valuing Common Stock Dividend growth model

Constant growth stocks Nonconstant growth stocks

Free cash flow method (covered in Chapter 11)

Using the multiples of comparable firms

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Stock Value = PV of Dividends

What is a constant growth stock?

One whose dividends are expected to grow 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 = ∑(PV of 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)tP0 = ∞^> 1,

and

So g must be less than rs for the constant growth model to be applicable!!

If g > rs, then

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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%

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 $2.120.07

P0 = ^ D0(1 + g)

rs – g = D1rs – g

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Expected value one year from now:

P1 = ^ D2

rs – g= $2.2472

0.07= $32.10

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

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Expected Dividend Yield and Capital Gains Yield (Year 1)

Dividend yield = = = 7.0%.

$2.12$30.29

D1P0

CG Yield = =P1 – P0^

P0

$32.10 – $30.29$30.2

9= 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 – g to D1P0

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.PMTr

$2.000.13

^

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Supernormal Growth Stock Supernormal growth of 30% for

Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, 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

2.30092.54522.5903

39.2246

1 2 3 4rs = 13%

46.6610 = P0

g = 30% g = 25% g = 15% g = 6% 2.6000 3.2500 3.7375 3.9618

^P3 = ^ $3.9618

0.13 – 0.06

= $56.5971

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

CG Yield = 13.0% – 5.6% = 7.4%.

Dividend yield = = = 5.6%

$2.60$46.66

D1P0

At t = 0:

(More…)

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Expected Dividend Yield and Capital Gains Yield (after t = 3) 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 capital gains yield = 6%.

Because rs = 13%, after t = 3 dividend yield = 13% – 6% = 7%.

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Is the stock price based onshort-term growth?

The current stock price is $46.66.The PV of dividends beyond Year 3 is:^P3 / (1+rs)3 = $39.22 (see slide 22)

= 84.1%.$39.22$46.66

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

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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

2.12P3 0.07 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 (after 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)

$1.880.19

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 firm’s total value. Subtract the firm’s debt to get the total

value of its equity. Divide by the number of shares to calculate

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 =$5rps^

rps$5

$50^ = = 0.10 =

10.0%

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Why are stock prices volatile?

P0 = ^ D1

rs – g

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

g could change.

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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 changes?

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Stock Prices vs. Changes in rs and g

grs 4% 5% 6%

9% $40.00 $50.00 $66.6710% $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, the intrinisic price must equal the actual price.

If the actual price is lower than the fundamental value, then the stock is a “bargain.” Buy orders will exceed sell orders, the actual price will be bid up. The opposite occurs if the actual price is higher than the fundamental value.

(More…)

Stock’sIntrinsic Value

“True” ExpectedFuture Cash

Flows

“Perceived”

Risk

“True”Risk

“Perceived” Expected

Future Cash Flows

Stock’sMarket Price

Intrinsic Values and Market Stock Prices

Managerial Actions, the EconomicEnvironment, and the Political Climate

Market Equilibrium:Intrinsic Value = Stock Price

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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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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 until:

D1/P0 + g = rs = rs.

D1

^

^P0

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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.

EMH does not assume all investors are rational.

EMH assumes that stock market prices track intrinsic values fairly closely.

(More…)

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EMH (continued) If stock prices deviate from

intrinsic values, investors will quickly take advantage of mispricing.

Prices will be driven to new equilibrium level based on new information.

It is possible to have irrational investors in a rational market.

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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, Morgan, and Prudential.

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

Thus, news is reflected in P0 almost instantaneously.

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Market Efficiency For most stocks, for most of the

time, it is generally safe to assume that the market is reasonably efficient.

However, periodically major shifts can and do occur, causing most stocks to move strongly up or down.

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Implications of Market Efficiency for Financial Decisions

Many investors have given up trying to beat the market. This helps explain the growing popularity of index funds, which try to match overall market returns by buying a basket of stocks that make up a particular index.

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Implications of Market Efficiency for Financial Decisions

Important implications for stock issues, repurchases, and tender offers.

If the market prices stocks fairly, managerial decisions based on over- and undervaluation might not make sense.

Managers have better information but they cannot use for their own advantage and cannot deliberately defraud investors.

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Rational Behavior vs. Animal Spirits, Herding, and Anchoring Bias

Stock market bubbles of 2000 and 2008 suggest that something other than pure rationality in investing is alive and well.

People anchor too closely on recent events when predicting future events. When market is performing better than

average, they tend to think it will continue to perform better than average.

Other investors emulate them, following like a herd of sheep.

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Conclusions Markets are rational to a large extent, but

at time they are also subject to irrational behavior.

One must do careful, rational analyses using the tools and techniques covered in the book.

Recognize that actual prices can differ from intrinsic values, sometimes by large amounts and for long periods.

Good news! Differences between actual prices and intrinsic values provide wonderful opportunities for those able to capitalize on them.