CHAPTER 8 Stocks and Their Valuation

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CHAPTER 8Stocks and Their Valuation

Features of common stock Determining common stock

values Efficient markets Preferred stock

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Facts about common stock

Represents ownership Ownership implies control Stockholders elect directors Directors elect management Management’s goal: Maximize the

stock price

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Social/Ethical Question Should management be equally

concerned about employees, customers, suppliers, and “the public,” or just the stockholders?

In an enterprise economy, management should work for stockholders subject to constraints (environmental, fair hiring, etc.) and competition.

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Types of stock market transactions

Secondary market Primary market Initial public offering market

(“going public”)

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Different approaches for valuing common stock

Dividend growth model Corporate value model Using the multiples of

comparable firms

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Dividend growth model Value of a stock is the present value of

the future dividends expected to be generated by the stock.

)k(1D

... )k(1

D

)k(1D

)k(1

D P

s3

s

32

s

21

s

10

^

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Constant growth stock A stock whose dividends are expected

to grow forever at a constant rate, g.

D1 = D0 (1+g)1

D2 = D0 (1+g)2

Dt = D0 (1+g)t

If g is constant, the dividend growth formula converges to:

g -kD

g -kg)(1D

Ps

1

s

00

^

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Future dividends and their present values

t0t ) g 1 ( DD

tt

t ) k 1 (D

PVD

t0 PVDP

$

0.25

Years (t)0

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What happens if g > ks?

If g > ks, the constant growth formula leads to a negative stock price, which does not make sense.

The constant growth model can only be used if: ks > g g is expected to be constant forever

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If kRF = 7%, kM = 12%, and β = 1.2, what is the required rate of return on the firm’s stock?

Use the SML to calculate the required rate of return (ks):

ks = kRF + (kM – kRF)β

= 7% + (12% - 7%)1.2= 13%

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If D0 = $2 and g is a constant 6%, find the expected dividend stream for the next 3 years, and their PVs.

1.8761

1.7599

D0 = 2.00

1.6509

ks = 13%

g = 6%0 1

2.247

2

2.382

3

2.12

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What is the stock’s market value?

Using the constant growth model:

$30.29

0.07$2.12

0.06 - 0.13$2.12

g - k

D P

s0

1

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What is the expected market price of the stock, one year from now?

D1 will have been paid out already. So, P1 is the present value (as of year 1) of D2, D3, D4, etc.

Could also find expected P1 as:

$32.10 0.06 - 0.13

$2.247

g - kD

Ps

2^

1

$32.10 (1.06) P P 0

^

1

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What is the expected dividend yield, capital gains yield, and total return during the first year?

Dividend yield= D1 / P0 = $2.12 / $30.29 = 7.0%

Capital gains yield= (P1 – P0) / P0 = ($32.10 - $30.29) / $30.29 = 6.0%

Total return (ks)= Dividend Yield + Capital Gains Yield

= 7.0% + 6.0% = 13.0%

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What would the expected price today be, if g = 0?

The dividend stream would be a perpetuity.

2.00 2.002.00

0 1 2 3ks = 13% ...

$15.38 0.13$2.00

k

PMT P

^

0

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Supernormal growth:What if g = 30% for 3 years before achieving long-run growth of 6%?

Can no longer use just the constant growth model to find stock value.

However, the growth does become constant after 3 years.

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Valuing common stock with nonconstant growth

ks = 13%

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

P 0.06

$66.543

4.658

0.13

2.301

2.647

3.045

46.114

54.107 = P0

^

0 1 2 3 4

D0 = 2.00 2.600 3.380 4.394

...

4.658

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Find expected dividend and capital gains yields during the first and fourth years.

Dividend yield (first year)= $2.60 / $54.11 = 4.81%

Capital gains yield (first year)= 13.00% - 4.81% = 8.19%

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

After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%.

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Nonconstant growth:What if g = 0% for 3 years before long-run growth of 6%?

ks = 13%

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

0.06 $30.29P3

2.12

0.13

1.77

1.57

1.39

20.99

25.72 = P0

^

0 1 2 3 4

D0 = 2.00 2.00 2.00 2.00

...

2.12

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Find expected dividend and capital gains yields during the first and fourth years.

Dividend yield (first year)= $2.00 / $25.72 = 7.78%

Capital gains yield (first year)= 13.00% - 7.78% = 5.22%

After t = 3, the stock has constant growth and dividend yield = 7%, while capital gains yield = 6%.

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If the stock was expected to have negative growth (g = -6%), would anyone buy the stock, and what is its value?

The firm still has earnings and pays dividends, even though they may be declining, they still have value.

$9.89 0.19$1.88

(-0.06) - 0.13(0.94) $2.00

g - k) g 1 (D

g - k

D P

s

0

s

1^

0

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Find expected annual dividend and capital gains yields.

Capital gains yield= g = -6.00%

Dividend yield= 13.00% - (-6.00%) = 19.00%

Since the stock is experiencing constant growth, dividend yield and capital gains yield are constant. Dividend yield is sufficiently large (19%) to offset a negative capital gains.

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Corporate value model

Also called the free cash flow method. Suggests the value of the entire firm equals the present value of the firm’s free cash flows.

Remember, free cash flow is the firm’s after-tax operating income less the net capital investment FCF = NOPAT – Net capital investment

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Applying the corporate value model

Find the market value (MV) of the firm. Find PV of firm’s future FCFs

Subtract MV of firm’s debt and preferred stock to get MV of common stock. MV of = MV of – MV of debt and

common stock firm preferred Divide MV of common stock by the number

of shares outstanding to get intrinsic stock price (value). P0 = MV of common stock / # of shares

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Issues regarding the corporate value model

Often preferred to the dividend growth model, especially when considering number of firms that don’t pay dividends or when dividends are hard to forecast.

Similar to dividend growth model, assumes at some point free cash flow will grow at a constant rate.

Terminal value (TVn) represents value of firm at the point that growth becomes constant.

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Given the long-run gFCF = 6%, and WACC of 10%, use the corporate value model to find the firm’s intrinsic value.

g = 6%

k = 10%

21.20

0 1 2 3 4

-5 10 20

...

416.942

-4.5458.264

15.026398.197

21.20

530 = = TV30.10 0.06-

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If the firm has $40 million in debt and has 10 million shares of stock, what is the firm’s intrinsic value per share?

MV of equity = MV of firm – MV of debt= $416.94m - $40m= $376.94 million

Value per share = MV of equity / # of shares

= $376.94m / 10m= $37.69

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Firm multiples method Analysts often use the following

multiples to value stocks. P / E P / CF P / Sales

EXAMPLE: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price.

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What is market equilibrium? In equilibrium, stock prices are stable

and there is no general tendency for people to buy versus to sell.

In equilibrium, expected returns must equal required returns.

)k(k k k g PD k RFMRFs

0

1^

s

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Market equilibrium

Expected returns are obtained by estimating dividends and expected capital gains.

Required returns are obtained by estimating risk and applying the CAPM.

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How is market equilibrium established?

If expected return exceeds required return … The current price (P0) is “too low”

and offers a bargain. Buy orders will be greater than sell

orders. P0 will be bid up until expected

return equals required return

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Factors that affect stock price

Required return (ks) could change Changing inflation could cause kRF to

change Market risk premium or exposure to

market risk (β) could change Growth rate (g) could change

Due to economic (market) conditions Due to firm conditions

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What is the Efficient Market Hypothesis (EMH)? Securities are normally in

equilibrium and are “fairly priced.” Investors cannot “beat the

market” except through good luck or better information.

Levels of market efficiency Weak-form efficiency Semistrong-form efficiency Strong-form efficiency

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Weak-form efficiency

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 efficiency

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

Largely true, but superior analysts can still profit by finding and using new information

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Strong-form efficiency

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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Is the stock market efficient?

Empirical studies have been conducted to test the three forms of efficiency. Most of which suggest the stock market was: Highly efficient in the weak form. Reasonably efficient in the semistrong form. Not efficient in the strong form. Insiders

could and did make abnormal (and sometimes illegal) profits.

Behavioral finance – incorporates elements of cognitive psychology to better understand how individuals and markets respond to different situations.

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Preferred stock Hybrid security Like bonds, preferred stockholders

receive a fixed dividend that must be paid before dividends are paid to common stockholders.

However, companies can omit preferred dividend payments without fear of pushing the firm into bankruptcy.

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If preferred stock with an annual dividend of $5 sells for $50, what is the preferred stock’s expected return?

Vp = D / kp

$50 = $5 / kp

kp = $5 / $50

= 0.10 = 10%