1.
Equity Markets Common Stock
l Stockholders are owners of the firm.
Investments: F303 l Stockholders are “residual” claimants.
l Stockholders have the right to:
Kelley School of Business, Indiana » vote at company meetings
University » dividends and other distributions
» sell their shares
l Stockholders benefit in two ways:
» Dividends – periodic payments
Professor Christian Lundblad
» capital gains – appreciation in value
l Stock is typically issued by public corporations to finance
investments
Copyright Campbell Harvey and Christian Lundblad. All rights reserved.
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Transactions Involving Stocks Stock Market Indices
l Buy l Short Sell
l Stock Market Indices: Average Return
Savings motive Sell stock without first owning it.
» of equities in particular regions (geographical)
Expect stock to Borrow stock from your broker
appreciate in value with the promise to repay it at » Of market segments (i.e. small companies, value stocks,
some later date. technology, etc.)
Long position
Sell the borrowed stock. Construction:
l Sell
∑
j= N
Liquidity needs Repurchase it at a later date to R Index = j =1
w jR jt
Expect stock to decline repay your broker.
in value Responsible for all dividends and » Equally weighted: w1=w2=…=wN=1/N
other distributions while short the – Return on a portfolio with $1 in each stock
stock. » Value weighted: wj= Proportion of market capitalization
– Return on a portfolio where more is invested in larger
companies
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2.
U. S. Stock Markets World Stock Markets
Major U. S. Stock Exchanges
l New York Stock Exchange (NYSE)
l American Stock Exchange (AMEX)
l Over-The-Counter (OTC) l Johannesburg
l New York l Mexico
» National Association of Securities Dealers (NASDAQ) l Sydney
l Tokyo l Canada
U. S. Stock Market Indices (August 27, 2002) l London l Brussels l Stockholm
Value Net Chg Pct Chg l Amsterdam
l Frankfurt l Hong Kong
INDU DOW JONES INDUS. AVG 8919.01 46.05 0.52
l Paris l Singapore l Switzerland
SPX S&P 500 INDEX 947.95 7.09 0.75
CCMP NASDAQ COMB COMPOSITE IX 1391.74 11.12 0.81
Other Indices
l NYSE Composite
l Russell 2000
l Wilshire 5000
l Value Line 5 6
Stock Valuation
Why short-termists are long-termists
Shareholders require a rate of return k for buying a share. They buy for
P0 and sell after one year for P1 and receive dividends D1: l The price an investor is willing to pay for a share of stock
depends upon:
D1 + P1 » Magnitude and timing of expected future dividends.
P0 =
1+ k » Risk of the stock.
The next buyer also sells after one year:
D 2 + P2 D D + P2 The stock’s discount rate, k, is the rate of return investors can
P1 = ⇒ P0 = 1 + 2 l
1+ k 1 + k (1 + k )2 expect to earn on securities with similar risk.
The same holds for P2. Continuing gives:
l Where are the capital gains?
D1 D2 D3
P0 = + + + ...
1 + k (1 + k )2 (1 + k )3
Share price = PV of dividends
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3.
Payouts The “Constant Growth” Formula
Assumption: Dividends grow at a constant rate g for ever:
l Holders of stock receive payouts in two forms:
D2 = D1 (1 + g ) , Dt = Dt −1 (1 + g ) = ... = D1 (1 + g ) t −1 = D0 (1 + g ) t
» Dividend payouts
» Capital gains (stock appreciation P1-P0) Then:
D (1 + g )
t −1
D1 D1 (1 + g ) D1
D 1 P1 − P 0 P0 = + + ... + 1 + ... =
k =
P0
+
P0 1 + k (1 + k ) 2 (1 + k )t k−g
Prospective Dividend per Share
» Capital Gain reflects expected growth in future dividend Share Price =
Required return - growth rate
l Issues:
» constant growth
» g<k
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Simplifying the Dividend Discount
Constant Dividends: An Example
Model
l Constant Dividends l Consider a company that pays a dividend of:
g = 0 ⇒ D1 = D2 = ... = D $3 per share in bad years (Probability = 50%)
$15 per share in good years (Probability = 50%)
Then the pricing relation simplifies to: » Required rate of return is 18%
» What is the share price?
D D
P0 = ⇒k = E( Div ) = 0.5 * $3 + 0.5 * $15 = $9
k P0 $9
P0 = = $50
» Stock similar to perpetuity 0.18
l If dividends are constant, then we have:
Required return on equity = Dividend yield
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4.
Constant Dividends: Constant Growth:
RJR Nabisco Preferred Stock Duke Power Common Stock
l RJR Nabisco has stock outstanding l Duke Power currently pays a dividend of $2.04 per share.
» annual dividend of $2.50 per share. » Duke Power expects its profits and dividends to grow at about
» Securities with similar risk are expected to return 9.6% 7% per year.
– what is the price of the preferred stock? » Stockholders require a 12% rate of return
– what is the market price of Duke Power’s common stock?
D $2.50
P0 = = = $26.04 P0 = (1 + g )
D0
k 0.096 k−g
2.04(1.07)
P0 = = $43.66
0.12 − 0.07
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Valuation with Growing Dividends Valuation of GM
An Example: Valuation of GM
l Generally, companies have growing dividends on stocks, hence l Alternative valuations:
apply general formula: Return/Growth 3% 4% 4.50% 5% 6% 7%
D 1 7% 34.23 45.64 54.77 68.47 136.93 -
P0 = 8% 27.39 34.23 39.12 45.64 68.47 136.93
k − g 9% 22.82 27.39 30.43 34.23 45.64 68.47
l Consider data for GM: 10% 19.56 22.82 24.90 27.39 34.23 45.64
» Number of shares: 855,820 11% 17.12 19.56 21.07 22.82 27.39 34.23
12% 15.21 17.12 18.26 19.56 22.82 27.39
» Market capitalization $42.051bn
» Historic dividend $1.50 per share Example:
» Your forecast: $1.60 855,820,000*$1.60=$1.37bn
– What valuation do you obtain for GM, depending on g
and k? D1997 $1.37bn
MCAPGM = = $34 .23bn
k GM − g GM 0.09 − 0.05
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