stocks and their valuation lecture

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CHAPTER 8 Stocks and Their Valuation

8-2

Facts about common stock

• Represents ownership

• Ownership implies control

• Stockholders elect directors

• Directors elect management

• Management’s goal: Maximize the stock price

8-3

Legal Rights and Privileges of Common Shareholders

• Control of the Firm

– Friendly takeover

– Hostile takeover

• Tender Offer

• Proxy Fight

• Preemptive Right

– Prevents management from issuing a large number of additional shares and purchasing those shares itself

– To protect the existing common shareholders from dilution.

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Types of Common Stock

• Classified Stock

– Common stock that is given a special designation such as Class A or Class B to meet the special needs of the company

• Founders’ Shares

• Stock owned by the firm’s founders that has sole voting rights but restricted dividends for a specified number of years.

• Golden Share

– A nominal share which is able to outvote all other shares in certain specified circumstances, often held by a government organization.

8-5

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”)

8-7

Stock Price and Intrinsic Value

• Stock Price

– A “perceived” value determined by investors (through the law of supply and demand)

– Represents perceived investor returns, caused by investors’ perceived risk.

• Intrinsic Value

– A “true” value determined by companies

– Represents true investor returns, caused by true risk.

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Why should investors care about intrinsic value?

• By nature, investors would like to buy low, sell high. Thus, investors would buy the stock when it is undervalued and sell the stock when it is overvalued.

• Overvaluation

– When the stock price > intrinsic value

• Undervaluation

– When stock price < intrinsic value

8-9

Different approaches for valuing common stock

• Dividend growth model

• Corporate value model

• Using the multiples of comparable firms

• EVA Approach

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Dividend growth model or Discounted Dividend Model

• Value of a stock is the present value of the future dividends expected to be generated by the stock.

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D ...

)r(1

D

)r(1

D

)r(1

D P

s

3

s

3

2

s

2

1

s

10

^

8-11

Constant growth stock (Gordon Growth Model)

• 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 -r

D

g -r

g)(1D P

s

1

s

00

^

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What happens if g > rs?

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

• The constant growth model can only be used if:

– rs > g

– g is expected to be constant forever

8-13

Future dividends and their present values

t0t ) g 1 ( DD

t

tt

)r 1 (

DPVD

t0 PVDP

$

0.25

Years (t) 0

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If rRF = 7%, rM = 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 (rs):

rs = kRF + (kM – kRF)β

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

= 13%

Computing for the Required Rate of Return

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G = Retention Ratio x Return on Equity

= RE/NI x NI/Equity or (1 – DPO) x NI/Equity

A firm has $1,000,000 of assets and no debt. The expected net income is $100,000. If the company plans to pay out 40% in dividends, how much is the growth rate?

G = 60/100 x 100/1,000 = 6%

Computing for the growth rate

8-16

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

rs = 13%

g = 6% 0 1

2.247

2

2.382

3

2.12

8-17

What is the stock’s intrinsic value?

• Using the constant growth model:

$30.29

0.07

$2.12

0.06 - 0.13

$2.12

g - r

D P

s

10

8-18

What is the expected value 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 - r

D P

s

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 (rs) = Dividend Yield + Capital Gains Yield

= 7.0% + 6.0% = 13.0%

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• The dividend stream would be a perpetuity.

$15.38 0.13

$2.00

k

PMT P

^

0

2.00 2.00 2.00

0 1 2 3 rs = 13%

...

If D0 = $2, RRR is 13%, and g is a constant 0%, find the expected dividend stream for the next 3 years, and

their PVs.

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Supernormal Growth

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

• However, the growth does become constant after 3 years.

If D0 = $2 and g = 30% for 3 years before achieving long-run growth of 6%, find the intrinsic value of the

stock.

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Valuing common stock with nonconstant growth

ks = 13%

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

$ P 0.06

$66.54 3

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

8-23

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

• 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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Find expected dividend and capital gains yields during the second year.

• Dividend yield (second year)

= $3.38 / $58.54 = 5.77%

• Capital gains yield (second year)

= 13.00% - 5.77% = 7.23%



8-25

Find expected dividend and capital gains yields during the third year.

• Dividend yield (third year)

= $4.394 / $62.77 = 7%

• Capital gains yield (third year)

= 13.00% - 7% = 6%



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ks = 13%

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

0.06

$ $30.29 P 3

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

If D0 = $2 and g is 0% for 3 years before long run growth of 6%, find the intrinsic value of the stock.

8-27

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%


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• 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

If D0 = $2 and g is a constant –6% (negative growth), would anyone buy the stock? What is its intrinsic

value?

8-29

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 (-or-)

– FCF = (EBIT(1-T) + Depreciation and Amortization) – (CAPEX + change in NWC)

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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% after year 3, and WACC of 10%, use the corporate value model to find the firm’s intrinsic value, if the FCF for Years 1, 2, and 3 are -5m, 10m, and

20m, respectively.

g = 6%

k = 10%

21.20

0 1 2 3 4

-5 10 20

...

416.942

-4.545 8.264

15.026 398.197

21.20

530 = = TV3 0.10 0.06 -

8-34

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

8-35

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.

8-36

EVA Approach

• It is an estimate of a firm’s economic profit.

• It is the value created in excess of the required return of the company’s investors.

• EVA = (Equity Capital) x (ROE – Cost of Equity Capital)

• Market value of equity = Book value + PV of all future EVAs

• Intrinsic Value = MV of equity / # of common shares outstanding

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EVA Approach

• Consider the following table below:

• What is the intrinsic value of the stock for the year 2011?

2011 2012 2013

Equity capital 100,000 120,000 150,000

Net income 20,000 25,000 30,000

Cost of equity 12% 12% 12%

Number of shares outstanding

10,000 12,000 10,000

8-38

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.

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D r MRFs

0

1^

s RFr-

8-39

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

8-41

Factors that affect stock price

• Required return (rs) could change

– Changing inflation could cause rRF 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.

8-47

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.

8-48

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

Vp = D / rp

$50 = $5 / kp

kp = $5 / $50

= 0.10 = 10%

8-49

Exercises:

• A stock, which currently does not pay a dividend, is expected to pay its first dividend of $1.00 per share in five years (D5 = $1.00). After the dividend is established, it is expected to grow at an annual rate of 25 percent per year for the following three years (D8 = $1.953125) and then grow at a constant rate of 5 percent per year thereafter. Assume that the risk-free rate is 5.5 percent, the market risk premium is 4 percent, and that the stock’s beta is 1.2. What is the expected price of the stock today?

8-50

Exercises:

• The Textbook Production Company has been hit hard due to increased competition. The company’s analysts predict that earnings (and dividends) will decline at a rate of 5 percent annually forever. Assume that rs = 11 percent and D0 = $2.00. What will be the price of the company’s stock three years from now?

8-51

Exercises:

• A stock is expected to pay a $2.50 dividend at the end of the year. The dividend is expected to grow at a constant rate of 6 percent a year. The stock’s beta is 1.2, the risk-free rate is 4 percent, and the market risk premium is 5 percent. What is the expected stock price eight years from today?

8-52

Exercises:

• Assume an all equity firm has been growing at a 15 percent annual rate and is expected to continue to do so for 3 more years. At that time, growth is expected to slow to a constant 4 percent rate. The firm maintains a 30 percent payout ratio, and this year’s retained earnings net of dividends were $1.4 million. The firm’s beta is 1.25, the risk-free rate is 8 percent, and the market risk premium is 4 percent. If the market is in equilibrium, what is the market value of the firm’s common equity (1 million shares outstanding)?

8-53

Exercises:

• During the past few years, Swanson Company has retained, on the average, 70 percent of its earnings in the business. The future retention rate is expected to remain at 70 percent of earnings, and long-run earnings growth is expected to be 10 percent. If the risk-free rate, rRF, is 8 percent, the expected return on the market, rM, is 12 percent, Swanson’s beta is 2.0, and the most recent dividend was $1.50, what is the most likely market price and P/E ratio (P0/E1) for Swanson’s stock today?

8-54

Exercises:

• Conner Corporation has a stock price of $32.35 per share. The last dividend was $3.42. The long-run growth rate for the company is a constant 7 percent. What is the company’s capital gains yield and dividend yield?