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Bennie Waller
[email protected]
434-395-2046
Longwood University
201 High Street
Farmville, VA 23901
Bennie D Waller, Longwood University
Stocks
Bennie D Waller, Longwood University
Stocks
Shares of Stock Represent Pieces of a Business
Owning stock in a company in essence indicates that you are
part-owner in the company. Generally each share of stock
entitles the stockholder to be have one vote toward the election
of the Board of Director (typically charged with the oversight
of management).
When organizations need to raise capital (money), they
typically have two broad options. One they can borrow the
money (either from a bank or issue debt (bonds) or they can
give up ownership in the firm and sell stock.
Bennie D Waller, Longwood University
Stocks
Shares of Stock Represent Pieces of a Business
Imagine you start you own landscaping business. You decide
that you need $1,000 to get the business started. You divide the
company into 10 pieces, or "shares" of stock. You price each
new share of stock at $100. If you sell all of the shares, you
should have the $1,000 you need. If the business earns $500
after taxes during its first year, each share of stock would be
entitled to 1/10th of the profit. You'd take $500 and divide it by
10, resulting in $50.00 earnings per share (EPS).
Source: http://beginnersinvest.about.com/od/stocksoptionswarrants/a/what-is-stock.htm
Bennie D Waller, Longwood University
Stocks
 Stock investors expect to earn a return (no guarantee).
 Capital Appreciation –
 Income - dividends
 Firm’s that pay dividends?
 Why firms may not pay a dividend
 Types of investors that invest in these firms
 Firm’s that don’t pay dividends, and why?
 Types of investors that invest in these firms and why
 Many/most firms pay some dividends as well as enjoy price
appreciation.
Bennie D Waller, Longwood University
Stocks
 Stocks are liquid
 Limited liability (unlimited potential)
 Claim on income (declaration and ex-dividend dates)
 Stock splits / reverse splits
 Stock repurchases
 Bear market – falling prices
 Bull market – rising prices
Bennie D Waller, Longwood University
Buy and Hold Stratgey
 Involves buying stock and holding it for a period of years.
 Avoids timing the market.
 Minimizes brokerage fees, transaction costs.
 Postpones capital gains taxes.
 Gains taxed as long-term capital gains.
Bennie D Waller, Longwood University
Stocks
Bennie D Waller, Longwood University
Stocks
 Stock market indices – groups of stocks performance that
represent the market or segment of market
 DJIA
 S&P 500
 NASDAQ
 Classification of stocks
 Blue-chip – large well known firms
 Growth – firms with growth above industry average (many
times these are new firms)
 Income –
 Speculative Bennie D Waller, Longwood University
Stocks
 Classification of stocks
 Blue-chip – large well known firms
 Growth – firms with growth above industry average
(many times these are new firms)
 Income –
 Speculative –
 Defensive – stocks that tend not to be affected in
economic swings
 Large caps - >$5 billion
 Small caps - <$1 billion
Bennie D Waller, Longwood University
Stock Valuation
 Technical Analysis – charts/graphs/ models used to predict
prices and trends
 Price/Earnings Ratio – is an earnings multiple.
 Discounted Dividends Model – stock price is based on present
value of future dividends.
Bennie D Waller, Longwood University
STOCKS
Dividend Per Share (DPS) - represents the dollar amount of
dividends that is paid to stockholders.
Dividend per share  EPS x PO  .60x5  $3/share
Price Earnings (PE)- is an earnings multiple. The P/E is
sometimes referred to as the "multiple", because it shows
how much investors are willing to pay per dollar of earnings.
If a company were currently trading at a multiple (P/E) of 10,
the interpretation is that an investor is willing to pay $10 for
$1 of current earnings.
Price Earning (PE) 
Price 50

 10
EPS
5
Bennie D Waller, Longwood University
STOCKS
Earnings Per Share (EPS) - measures the earnings of the firm on a per
share basis.
NI
50,000
Earnings Per Share (EPS) 

 $5
shares outstanding 10,000
Payout ratio (PO) - dictates what percent of earnings the firm will
payout to stockholders in the form of dividend. Conversely 1-PO
indicates what percent of net income the firm plans to retain. A
payout ratio of 60% illustrates that the firm is planning on paying
out 60% of the firm's net income and retaining 40 percent.
Payout (PO) 
DPS 3
  .60
EPS 5
Bennie D Waller, Longwood University
Stock valuation
 Dividend Growth Model – used to value stocks that pay
dividends
 In essence, taking present value of future cash flows
 As you go further out into the future, the impact of the cash
flows decrease
𝐷1
𝐷2
𝐷3
𝐷𝑛
𝑃0 =
+
+
+⋯
2
3
(1 + 𝑘) (1 + 𝑘)
(1 + 𝑘)
(1 + 𝑘)𝑛
Bennie D Waller, Longwood University
Stock Valuation
Stock Valuation assuming constant growth - Constant Growth
(Gordon Dividend) Model – used to determine the intrinsic value of
a stock, based on a future series of dividends that grow at a constant
rate. Given a dividend per share that is payable in one year,
and the assumption that the dividend grows at a constant rate in
perpetuity, the model solves for the present value of the infinite
series of future dividends.
Stock Value = 𝑷𝟎 =
𝑫𝟏
𝒌−𝒈
Because the model assumes a constant growth rate, it is generally
only used for mature companies (or broad market indices) with low
to moderate growth rates.
Bennie D Waller, Longwood University
Stock valuation
Stock Valuation assuming abnormal growth – firms with high
growth or emerging areas such as technology or pharmaceutical
are likely to experience periods of abnormal or super-abnormal
growth.
 Assume that a biotech firm discovers a cure for a terminal
disease. The firm is expected to have growth rates of 30%, 25%
and 20% over the next three years at which time, growth is
expected to level off and remain constant at 10% for the
foreseeable future. The current required rate of return is 12%
for investors (k=.12) and the last dividend paid was $2.00
(D0=2.00).
• Since the growth will become constant in year 4, we can then
apply the constant growth formula.
Bennie D Waller, Longwood University
Stock Valuation
•
•
•
•
•
•
g1=.30 – expected growth in year 1
g2 =.25 – expected growth in year 2
g3 =.20 – expected growth in year 3
G4+=.10 – expected growth in year 4 and thereafter
D0=2.00 – last dividend paid
k=.12 –required rate of return (rate firm must pay to encourage investment in firm)
•
Since the growth will become constant in year 4, we can then apply the constant
growth formula using the formula below.
𝐷4
𝐷1
𝐷2
𝐷3
(𝑘 − 𝑔)
𝑃0 =
+
+
+
2
3
(1 + 𝑘) (1 + 𝑘)
(1 + 𝑘)
(1 + 𝑘)3
We need to calculate the dividends for each of the next 4 years
D1=D0(1+g1) = 2(1.30) =2.60
D2=D1(1+g2) = 2.60(1.25) =3.25
D3=D2(1+g3) = 3.25(1.20) = 3.90
D4=D3(1+g4) = 3.90(1.10) = 4.29
Bennie D Waller, Longwood University
Stock Valuation
We need to calculate the dividends for each of the next 4 years
D1=D0(1+g1) = 2(1.30) =2.60
D2=D1(1+g2) = 2.60(1.25) =3.25
D3=D2(1+g3) = 3.25(1.20) = 3.90
D4=D3(1+g4) = 3.90(1.10) = 4.29
𝐷4
𝐷1
𝐷2
𝐷3
(𝑘 − 𝑔)
𝑃0 =
+
+
+
2
3
(1 + 𝑘) (1 + 𝑘)
(1 + 𝑘)
(1 + 𝑘)3
4.29
2.60
3.25
3.90
(.12 − .10)
𝑃0 =
+
+
+
2
3
(1 + .12) (1 + .12)
(1 + .12)
(1 + .12)3
Bennie D Waller, Longwood University
Stock Valuation
We need to calculate the dividends for each of the next 4 years
D1=D0(1+g1) = 2(1.30) =2.60
D2=D1(1+g2) = 2.60(1.25) =3.25
D3=D2(1+g3) = 3.25(1.20) = 3.90
D4=D3(1+g4) = 3.90(1.10) = 4.29
𝑃0 =2.32 + 2.59 + 2.78 +
214.50
(1+.12)3
= $160.37
So how do we interpret this estimated price?
Bennie D Waller, Longwood University
STOCKS
The last dividend paid by Klein Company was $1.00. Klein’s
growth rate is expected to be a constant 5 percent for 2 years, after
which dividends are expected to grow at a rate of 10 percent
forever. Klein’s required rate of return on equity (ks) is 12 percent.
How much should a prudent investor be willing to pay for this
stock based on the above assumptions?
𝐷3
𝐷1
𝐷2
(𝑘 − 𝑔)
𝑃0 =
+
+
2
(1 + 𝑘) (1 + 𝑘)
(1 + 𝑘)2
Bennie D Waller, Longwood University
STOCKS
•
•
•
•
•
g1=.05 – expected growth in year 1
g2 =.05 – expected growth in year 2
g3+ =.10 – expected growth in year 3 and thereafter
D0=1.00 – last dividend paid
k=.12 –required rate of return (rate firm must pay to encourage
investment in firm)
𝐷3
𝐷1
𝐷2
(𝑘 − 𝑔)
𝑃0 =
+
+
2
(1 + 𝑘) (1 + 𝑘)
(1 + 𝑘)2
This problem has been set up, calculate the expected stock price
Bennie D Waller, Longwood University
STOCKS
Another example
Assume that you plan to buy a share of XYZ stock today and to hold it for 2
years. Your expectations are that you will not receive a dividend at the end
of Year 1, but you will receive a dividend of $9.25 at the end of Year 2. In
addition, you expect to sell the stock for $150 at the end of Year 2. If your
expected rate of return is 16 percent, how much should you be willing to
pay for this stock today?
Bennie D Waller, Longwood University
STOCKS
Another example
Womack Toy Company’s stock is currently trading at $25 per
share. The stock’s dividend is projected to increase at a
constant rate of 7 percent per year. The required rate of return
on the stock, ks, is 10 percent. What is the expected price of
the stock 4 years from today?
Bennie D Waller, Longwood University
STOCKS
Capital Asset Pricing Model or CAPM –describes the relationship
between risk and expected return and is commonly used in the pricing of risky
securities.
The idea behind CAPM is that investors need to be compensated in two ways:
time value of money and risk. The time value of money is represented by the
risk-free (𝑅𝑓 ) rate in the formula and compensates the investors for placing
money in any investment over a period of time. The other half of the formula
represents risk and calculates the amount of compensation the investor needs for
taking on additional risk. This risk measure (β) that compares the returns of the
asset to the market over a period of time and to the market premium (𝑅𝑚 − 𝑅𝑓 ).
Beta measure the systematic or business risk.
𝐶𝐴𝑃𝑀: 𝑅𝑎 = 𝑅𝑓 + 𝛽𝑎 (𝑅𝑚 − 𝑅𝑓 )
Source: investopdia.com
Bennie D Waller, Longwood University
Stock Valuation
 Researchers have shown that the best measure of the risk of a
security in a large portfolio is the beta (b)of the security.
 Beta measures the responsiveness of a security to movements
in the market portfolio (i.e., systematic risk).
i 
Cov( Ri , RM )
 ( RM )
2
Bennie D Waller, Longwood University
STOCKS
The CAPM says that the expected return of a security or a portfolio equals the
rate on a risk-free security plus a risk premium. If this expected return does not
meet or beat the required return, then the investment should not be undertaken.
Using the CAPM model and the following assumptions, we can compute the
expected return of a stock in this CAPM example: if the risk-free rate is 3%, the
beta (risk measure) of the stock is 2 and the expected market return over the
period is 10%, the stock is expected to return 17% (3%+2(10%-3%)).
𝐶𝐴𝑃𝑀: 𝑅𝑎 = 𝑅𝑓 + 𝛽𝑎 (𝑅𝑚 − 𝑅𝑓 )
𝐶𝐴𝑃𝑀: 𝑅𝑎 = .03 + 2 .10 − .03 = .17
The security market line plots the results of the CAPM for all
different risks (betas).
SML illustrated
Source: investopdia.com
Bennie D Waller, Longwood University
STOCKS
Security Market Line (SML)
Return
Rm
Rf
β=0
β=1
Bennie D Waller, Longwood University
β
STOCKS
EXAMPLE
The common stock of Anthony Steel has a beta of 1.20. The
risk-free rate is 5 percent and the market risk premium (kM kRF) is 6 percent. Assume the firm will be able to use retained
earnings to fund the equity portion of its capital budget. What
is the company’s cost of retained earnings, ks?
𝐶𝐴𝑃𝑀: 𝑅𝑎 = .05 + 1.2 .06 = .122
𝐻𝑃𝑅 =
𝑃1 −𝑃0
𝑃0
=
10−8.91
8.91
= .122
Bennie D Waller, Longwood University
STOCKS
Security Market Line (SML)
Return
.122
Rm
Overpriced stocks will fall below the
SML In the previous example, if the
stock was currently trading at
$9.00/share, the expected return
would only be 11%, which is well
below the required return of 12.2%
Rf
β=0
β=1
β=1.2
Bennie D Waller, Longwood University
β
Thank You
Bennie D Waller, Longwood University