PDF Features of Common Stock Valuation of Securities: Stocks

Valuation of Securities: Stocks

Econ 422: Investment, Capital & Finance University of Washington Eric Zivot Fall 2007 January 31, 2007

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Features of Preferred Stock

? Dividends

? Stated dividend must be paid before dividends can be paid to common stockholders.

? Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely.

? Most preferred dividends are cumulative ? any missed preferred dividends have to be paid before common dividends can be paid.

? Preferred stock generally does not carry

voting rights.

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Features of Common Stock

? Voting rights (Cumulative vs. Straight) ? Proxy voting ? Classes of stock ? Other rights

? Share proportionally in declared dividends ? Share proportionally in remaining assets during

liquidation ? Preemptive right ? first shot at new stock issue

to maintain proportional E.Zivot2006 ownership if desired R.W. Parks/L.F. Davis 2004

The Stock Markets

? Dealers vs. Brokers

? New York Stock Exchange (NYSE)

? Largest stock market in the world

? Members

? Own seats on the exchange ? Commission brokers ? Specialists ? Floor brokers ? Floor traders

? Operations

? Floor activity

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

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NASDAQ

? Not a physical exchange ? computer-based quotation system

? Multiple market makers ? Electronic Communications Networks ? Three levels of information

? Level 1 ? median quotes, registered representatives

? Level 2 ? view quotes, brokers & dealers ? Level 3 ? view and update quotes, dealers only

? Large portion of technology stocks E.Zivot2006 R.W. Parks/L.F. Davis 2004

Valuing Stock

? Valuing a firm's equity involves the same ideas introduced for valuing a firm's debt instruments

? To value a firm's stock 1. Determine the expected cash flows 2. Calculate the present value of the cash flows

? Valuing stock, however, is more complicated than valuing bonds because the cash flows are not contractually specified or fixed.

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Stock Market Reporting

52 WEEKS

YLD VOL

NET

HI LO STOCK SYM DIV % PE 100s CLOSE CHG

25.72 18.12 Gap Inc GPS 0.18 0.8 18 39961 21.35 ...

Gap has been as high as $25.72 in the last year.

Gap pays a dividend of 18 cents/share.

Given the current price, the dividend yield is .8%.

Gap ended trading at $21.35, which is unchanged from yesterday.

Gap has been as low as $18.12 in the last year.

Given the current

price, the PE ratio is

18 times earnings.

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

3,996,100 shares traded hands in the last day's trading.

Cash Flow

A stock's cash flow consists of: ? Stream of dividend payments received during

ownership of stock ? The sale price for the stock upon deciding to sell

Note: ? The dividend stream may continue indefinitely ? The dividend stream may be finite ? The dividend stream may change over time ? There may be no dividend stream

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

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Valuation of Stocks

Let's calculate the rate of return for holding a stock for one

period (holding period return). Define:

P0 = today's price of the stock P1 = next year's price D1 = next year's dividend

HPR = r = [P1 + D1 - P0]/P0 = [P1- P0]/P0 +

D1/P0

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Valuation of Stocks

r = [P1- P0]/P0 + D1/P0

Rewrite in terms of P0:

P0 = D1/(1+r) + P1/(1+r)

Today's price equals the present value of next year's dividend plus the present value of next year's price.

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Example

? P0 = 100, P1 = 110, D1 = 5. Solve for r:

r = 110 - 100 + 5

100

100

= 0 .1 0 + 0 .0 5 = 0 .1 5

Given r, P1, and D1 = 5 now solve for P0

P0

=

5 1.15

+

110 1.15

= 100

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Valuation of Stocks continued

P0 = D1/(1+r) + P1/(1+r) Similarly, we can write next year's price as a function of the dividend in year 2 and the year 2 price of the stock:

P1 = D2/(1+r) + P2/(1+r) Substituting for P1:

P0 = D1/(1+r) + [D2/(1+r) + P2/(1+r)]/(1+r) P0 = D1/(1+r) + D2/(1+r)2 + P2/(1+r)2

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

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Example

? r = 0.15, P0 = 100, P2 = 121, D1 = 5, D2 = 5.5

P0

=5+ 1.15

5.5

(1.15)2

+

121

(1.15)2

= 100

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Dividend Growth Models

? For a given discount rate r, stock prices will differ based on the firm dividends.

? The stock price is determined by how the firm dividends evolve.

? Typical assumptions are ? No growth in dividends ? Constant dividend growth

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Valuation of Stocks, continued

P0 = D1/(1+r) + D2/(1+r)2 + P2/(1+r)2

This equation is recursive, upon further substitution we can eventually arrive at the following expression:

P0 = D1/(1+r) + D2/(1+r)2 + ... + DT/(1+r)T + ...

P0 = Dt/(1+r)t

for t = 1 to

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Dividend Growth Models

? No growth in dividends: D1 = D2 = ...=D

P0 = D/(1+r)t

for t = 1 to

Note the right hand side is a perpetuity, such that:

P0 = D/r

? Constant dividend growth: D1 = D; D2 = D(1+g); D3 = D(1+g)2; ...

P0 = D(1+g)t-1/(1+r)t for t = 1 to Note the right hand side is a growing perpetuity, such that:

P0 = D/(r-g) (for r > g)

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

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Numerical Examples

? D1 = 5, g = 0.10, r = 0.15

No

growth:

P0

=

D1 r

=

5 0.15

=

33.33

Constant

growth:

P0

=

D1 (r - g)

=

5 0.05

=100

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Numerical Example

? D1 = 5, r = 0.15, g0 = 0.10, g1 = 0.11

dP (r - g)-1dg P

= 0.01 = 0.01 = 0.2 (0.15 - 0.10) 0.05

= 20%

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Comparative Statics

? What happens to the stock price when the dividend growth rate changes?

P = D1 r-g

dP dg

=

-(r

-

g )-2 D1

(-1)

= (r - g)-1 P

dP (r - g)-1dg P

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

Determining the Dividend Growth Rate

Q: What determines whether a firm will grow or issue increased dividends?

? A firm can either retain or payout earnings. ? Dividends represent earnings that are paid out. ? Retained earnings are those earnings not paid out

as dividends that the firm plows back into the business. ? Investing retained earnings may provide growth opportunities for the firm.

E. Zivot 2006 R.W. Parks/L.F. Davis 2004

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