Financial Management I

FIN-325

Lecture Seven:
Stocks and Stock Valuation
 Agenda
• Stocks and Stock Valuation
– Common stock characteristics
– Stock markets
– Pricing
• Class Exercise
 Stocks
St. Patrick’s Day –
U.S. Stocks Rally, Push Dow Into Green for 2016
(Wall Street Journal)
– “Wall Street moved higher on Thursday, pushing the Dow
Jones Industrial Average into positive territory for the year”
(Yahoo! Finance)
March 18, 2016 –
U.S. Stocks Notch Fifth Straight Week of Gains
(Wall Street Journal)
– “The S&P 500 erased its losses for the year Friday, joining
the Dow industrials in positive territory”
(Ibid.)
.DJI
.SPX
 Stocks

• When we read or hear in the media that “the market

is up today,” what is generally being referenced is
“the Dow” – i.e., the Dow Jones Industrial Average
• The Dow is an index comprised of the 30 “most
influential” companies in the U.S. – i.e., “blue chips”
– and is the most recognized index in the world
• Other popular indexes include the S&P 500 and the
■ Nasdaq Composite Index
Dow
• 3M
Jones Industrial
• IMB
Average
• American Express • Intel

• Apple • Johnson & Johnson

• Amazon • JP Morgan & Chase

• Boeing • McDonald’s

• Caterpillar • Merck

• Chevron • Microsoft

• Cisco • Nike

• Coca-Cola • Procter & Gamble

• Travelers
• Disney
• Dow • Salesforce

• General Electric • UnitedHealth

• Goldman Sachs • Verizon

• Home Depot • Visa

• Honeywell • Walmart
Dow Jones Industrial Average
• The Dow is effectively a portfolio holding one share of
each component stock, where the investment in each
company in that portfolio is proportional to the
company’s share price – i.e., a price-weighted average
– Higher-priced shares are given more weight in
determining performance of the index
(Bodie, Kane & Marcus, 2011)
Wall Street
 Stocks
• In order to understand the market, we
must first understand the individual
components of the market – i.e., stocks
– and how they are valued
• But before we do that, we need to define
some of the basic terms associated with
stocks…
 What is a stock?

• A stock is a share of ownership in a company

– A claim on that company’s assets and earnings
■ (i.e., profits)
– Stock ownership also confers voting rights
• Shareholders participate in the management of
the company by electing the board of directors,
which ultimately selects the management team
that runs the company’s day-to-day operations
 Why do companies issue stock?
• While a corporation can raise capital from willing
investors by issuing bonds – i.e., debt financing –
another form of corporate funding is the
issuance of stock – i.e., equity financing

While stocks and bonds differ in several ways,

what is perhaps the most significant?
When you own a share of company stock,
you own a share of the company
Characteristics of
Common Stock
Characteristics of Common Stock
• Equities provide investors with an opportunity to
share in the future cash flows of the issuer
• Unlike bonds, holding common stock signifies
ownership in the company, with no maturity
date and variable periodic income
– A good grasp of this material is tantamount to
understanding the valuation models that follow
Characteristics of Common Stock
• Ownership
– As part owners of the company, common shareholders
are entitled to share in the residual profits of the
company, and have a claim to all its assets and cash flow
once the creditors, employees, suppliers and taxes are
paid off
– Ownership via common stock also confers voting rights
to the shareholders – allowing them to participate in the
management of the company by electing the board of
directors, which ultimately selects the management team
that runs the company’s day-to-day operations
• Claim on assets and cash flow (i.e., residual claim)
– Right to share in the residual assets and cash flow
of the issuer, once all the other stakeholders have been
paid off
Characteristics of Common Stock
• No maturity date
– Common stock is considered to have an infinite life
• Unlike bond-holders, shareholders do not have a promised
future date when they will receive their investment back
• Dividends and tax effect
– Companies pay cash dividends, periodically (e.g.,
quarterly, annually) to their shareholders out of net
income
• Unlike coupon interest paid on bonds, dividends cannot be
treated as a tax-deductible expense by the company
• For the recipient, however, dividends are considered to be
taxable income
Stock Markets
Twitter Inc
Alibaba Group Holding Limited
 Initial Public Offering (IPO)
• In November 2013, Twitter Inc (TWTR) raised
$1.8 billion through the sale of 70 million
shares at $26/share
• In September 2014, Alibaba Group Holding
Limited (BABA) – the Chinese e-commerce firm –
raised $25 billion by issuing 368.1 million
shares at $68/share
 Stock Markets
Stocks are traded in two types of markets:
1) Primary
– “first sale” market, where the firm “goes public” –
i.e., initially sells its stock to investors, frequently
with the assistance and expertise of investment
banking firms
• e.g., initial public offering (IPO) – first public equity
issue of the company
2) Secondary
– “after-sale” market, where previously issued
shares are traded among investors, themselves
• e.g., NYSE, NASDAQ
 Secondary Markets
Forum where common stock can be traded among investors,
providing them with liquidity and variety. In the U.S., there
are three well-known secondary stock markets:
• New York Stock Exchange (NYSE)
– “Big Board” founded in 1792
– General Electric, McDonald’s, Citigroup, Coca-Cola, Gillette,
Walmart
• National Association of Securities Dealers
Automated Quotation System (NASDAQ)
– over-the-counter (OTC) market where registered dealers
trade stocks via a telecommunication network (i.e., trading
system)
– Microsoft, Cisco, Intel, Dell, Oracle
• American Stock Exchange (AMEX)
 Secondary Markets

• Ask price

– Price at which the dealer is willing to

sell
• Bid price

– Price at which the dealer is willing to

buy
• Bid-ask spread

– Dealer’s profit, i.e., difference between

bid and ask prices
Stock Valuation
 Stock Valuation
• Theoretically speaking, the value of a share of
stock, like any financial asset, can be estimated
as the present value of its expected future cash
flow, which would include:
– the cash dividends paid by the company (if any)
– the future selling price of the stock, when sold to
another buyer
– the discount rate as the appropriate rate of
return that should be earned given the riskiness
of the company
 Stock Valuation
Thus, valuation is more of an “art”
than a science
• No guaranteed cash flow information
• No maturity date
Differences between Stocks and Bonds
 Pricing stock with known
dividends and sale price
Tara wants to purchase common stock of
New Frontier Inc. and hold it for 3 years.
The company’s directors just announced that
they expect to pay an annual cash dividend
of $4.00 per share for the next 5 years. Tara
believes that she will be able to sell the stock
for $40 at the end of 3 years. In order to earn
12% on this investment, how much should
Tara pay for this stock?
 Pricing stock with known
dividends and sale price
By equation:
1− 1
1 (1 + 𝑟)𝑛
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 = 𝑓𝑢𝑡𝑢𝑟𝑒 𝑠𝑎𝑙𝑒 𝑝𝑟𝑖𝑐𝑒 × + 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑠𝑡𝑟𝑒𝑎𝑚 ×
(1 + 𝑟)𝑛 𝑟

1− 1
1 1 + 0.12 3
= $40.00 × 3
+ $4.00 ×
1 + 0.12 0.12

= $40.00 × 0.7118 + $4.00 × 2.4018

𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 = $28.4712 + $9.6073 = $38.08

 Pricing stock with known
dividends and sale price
Using a financial calculator:
• Set number of payments per year (P/Y) = 1
• Set frequency of compounding (C/Y) = 1

𝒏 = 3; 𝒊 = 12%; 𝑷𝑴𝑻 = $4; 𝑭𝑽 = $40

<CPT> 𝑷𝑽 = −$38.08
Dividend Discount Models

DDM
 Dividend Discount Model
• The dividend discount model
(DDM) is a formula stating that the
intrinsic value of a firm’s common stock
is the present value of all expected
future cash dividends – i.e., payments
of cash to the stockholders of the
company
 Stock Valuation
a) Constant dividend model with an
infinite horizon
b) Constant dividend model with a
finite horizon
c) Constant growth dividend model
with an infinite horizon
d) Constant growth dividend model
with a finite horizon
e) Non-constant growth dividends
 (a) Constant dividend model
with an infinite horizon
• Assumes that the firm is paying the same dividend amount in
perpetuity
– i.e., 𝐷𝑖𝑣1 = 𝐷𝑖𝑣2= 𝐷𝑖𝑣3 = 𝐷𝑖𝑣4 = 𝐷𝑖𝑣∞

• Remember that for perpetuities:

𝑃𝑀𝑇
𝑃𝑉 =
𝑟
– where,
𝑃𝑀𝑇 = 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤
𝑟 = 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛

Thus, for a stock that is expected to pay the same dividend forever,

𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑃𝑟𝑖𝑐𝑒 =
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛
(a) Constant dividend model
with an infinite horizon
Quarterly dividends forever

Let’s say that the Surfside Securities

Corporation is paying a quarterly dividend of
$0.50 and has decided to pay the same
amount forever. If Natalia wants to earn an
annual rate of return of 12% on this
investment, at what price should she offer to
buy the stock today?
(a) Constant dividend model
with an infinite horizon
• Quarterly dividend
= $0.50
• Quarterly rate of return
𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 12%
= = = 3%
4 4
• Price
𝑃𝑀𝑇 $0.50
= = = $16.67
𝑟 .03
(b) Constant dividend model
with a finite horizon
• Assumes that the stock is held for a finite
period of time and then sold to another investor
• Constant dividends received over the
investment horizon
• Price estimated as the sum of the present value
of:
– constant stream of dividends (i.e., an annuity)
– selling price (i.e., single, lump-sum payment)
• Similar to a typical (non-zero) coupon bond
• Need to estimate the future selling price, since
that is not a given value – unlike the par value
of a bond
(b) Constant dividend model
with a finite horizon
Let’s say that the Hawaiian Clothing
Company is paying an annual dividend of
$2.00 and has decided to pay the same
amount forever. If Rita wants to earn an
annual rate of return of 12% on this
investment, and plans to hold the stock for 5
years, with the expectation of selling it for
$20 at the end of 5 years, then at what price
should she offer to buy the stock today?
(b) Constant dividend model
with a finite horizon
• Annual dividend, 𝑃𝑀𝑇 = $2.00
• Selling price, 𝐹𝑉 = $20.00
• Annual rate of return, 𝑟 = 12%
Using TVM formulae:
PV = PV of 5-year dividend stream + PV of price at Year 5
1− 1
(1 + 𝑟)𝑛 + 𝑓𝑢𝑡𝑢𝑟𝑒 𝑠𝑎𝑙𝑒 𝑝𝑟𝑖𝑐𝑒 × 1
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 = 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑠𝑡𝑟𝑒𝑎𝑚 ×
𝑟 (1 + 𝑟)𝑛
1
1− 1
(1 + 0.12)5 + $20.00 ×
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 = $2.00 ×
0.12 (1 + 0.12)5
𝑝𝑟𝑖𝑐𝑒 = $7.21 + $11.35 = $18.56
 (b) Constant dividend model
with a finite horizon
Alternatively, using a financial calculator,
we can solve for the current price
• Set number of payments per year (P/Y) = 1
• Set frequency of compounding (C/Y) = 1

𝒏 = 5; 𝒊 = 12%; 𝑷𝑴𝑻 = $2; 𝑭𝑽 = $20

<CPT> 𝑷𝑽 = −$18.56
(c) Constant growth dividend model
with an infinite horizon
• Gordon growth model
– Developed by Myron Gordon
– Estimates the present value of stock based
on the discounted value of an infinite
stream of future dividends that grow at a
constant rate, g
𝐷𝑖𝑣0 × (1 + g)1 𝐷𝑖𝑣0 × (1 + g)2 𝐷𝑖𝑣0 × (1 + g)3 𝐷𝑖𝑣0 × (1 + g)∞
𝑃𝑟𝑖𝑐𝑒0 = + + + ⋯+
(1 + 𝑟)1 (1 + 𝑟)2 (1 + 𝑟)3 (1 + 𝑟)∞

Where, 𝒓 = 𝑡ℎ𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛

(c) Constant growth dividend model
with an infinite horizon
Simplifying, algebraically:
𝐷𝑖𝑣0 × (1 + g)
𝑃𝑟𝑖𝑐𝑒0 =
(𝑟 − g)
And since 𝐷𝑖𝑣0 × 1 + g = 𝐷𝑖𝑣1 then:
𝐷𝑖𝑣1
𝑃𝑟𝑖𝑐𝑒0 =
(𝑟 − g)
And more generally:
𝐷𝑖𝑣𝑛+1
𝑃𝑟𝑖𝑐𝑒𝑛 =
(𝑟 − g)
Where, 𝑫𝒊𝒗𝒏+𝟏 is the estimated next dividend of the
stock, with the given growth rate, g, at time period, n
(c) Constant growth dividend model
with an infinite horizon
Note: for the Gordon growth model to be
applicable, the required rate of return, r, must
be greater than the growth rate, g. Otherwise,
we will be dividing by zero (i.e., if 𝒓 = 𝐠) or by a
negative value (i.e., if 𝒓 < 𝐠), both of which
would lead to non-meaningful values.
(c) Constant growth dividend model
with an infinite horizon
Growth rate given

Suppose the Organic Candle Company

just paid its shareholders an annual
dividend of $2.00 and announced that the
dividends would grow at an annual rate of
8%, forever. If investors expect to earn an
annual rate of return of 12% on this
investment, then at what price should
they offer to buy the stock today?
(c) Constant growth dividend model
with an infinite horizon
𝑫𝒊𝒗𝟎 = $2.00; 𝐠 = 8%; 𝒓 = 12%
• First, find the estimated value of the next dividend:
𝐷𝑖𝑣1 = 𝐷𝑖𝑣0 × 1 + g
= $2.00 × 1.08
= $2.16
• Then, compute the current price:
𝐷𝑖𝑣1 $2.16
𝑃𝑟𝑖𝑐𝑒0 = = = $54.00
(𝑟 − g) (0.12 − 0.08)
Note that r and g must be in decimals
(c) Constant growth dividend model with an infinite horizon

Growth rate estimated from dividend payout history

Let’s say that you are considering an investment in

the common stock of Red Dragon Enterprises and
are convinced that its last paid dividend of $1.25
will grow at its historical average growth rate going
forward. Using the past 10 years of dividend payout
history (below) and a required rate of return of 14%,
calculate the price of Red Dragon’s stock.

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
$0.50 $0.55 $0.61 $0.67 $0.73 $0.81 $0.89 $0.98 $1.08 $1.25
(c) Constant growth dividend model with an infinite horizon
(and growth rate estimated from dividend payout history)

• First, estimate the historical average growth rate

of dividends, using the following equation:
1/n
𝐹𝑉
𝐠= −1
𝑃𝑉
Where,
𝑭𝑽 = 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑2014 = $1.25
𝑷𝑽 = 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑2005 = $0.50
𝒏 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 = 9

$1.25 1/9
𝐠= − 1 = 0.1072 = 10.72%
$0.50
(c) Constant growth dividend model with an infinite horizon
(and growth rate estimated from dividend payout history)

• Next, find the estimated value of the next dividend:

𝑫𝒊𝒗𝟎 = 𝐷𝑖𝑣2014 = $1.25
𝐷𝑖𝑣1 = 𝐷𝑖𝑣0 × 1 + g = $1.25 × 1.1072 = $1.3840
• Then, use the constant growth, infinite horizon
model to calculate price:
𝐷𝑖𝑣1
𝑃𝑟𝑖𝑐𝑒0 =
(𝑟 − g)
Where, 𝒓 = 14%; 𝐠 = 10.72%
$1.3840
𝑃𝑟𝑖𝑐𝑒0 = = $42.16
(0.14 − 0.1072)
(d) Constant growth dividend model
with a finite horizon
• In cases where an investor expects to hold a stock – i.e.,
with dividends growing at a constant rate – for a limited
number of years, the following adjusted formula can be
used to value the stock:
𝑛
𝐷𝑖𝑣0 × (1 + g) 1+g 𝑃𝑟𝑖𝑐𝑒𝑛
𝑃𝑟𝑖𝑐𝑒0 = × 1− +
(𝑟 − g) 1+𝑟 (1 + 𝑟)𝑛
Where,
𝐠 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒
𝒓 = 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛
n = investor’s holding period
𝑃𝑟𝑖𝑐𝑒𝑛 = 𝑠𝑒𝑙𝑙𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝒏

Note: this formula would lead to the same price estimate as the Gordon
model if it is assumed that the growth rate of dividends and the required
rate of return of the next owner (i.e., after n years) remain the same
(d) Constant growth dividend model
with a finite horizon
Red Dragon Enterprises just paid a dividend of
$1.25 and analysts expect the dividend to grow
at its compound average growth rate of 10.72%,
forever. If Margo plans on holding the stock for
just 7 years, and she has an expected rate of
return of 14%, how much would she pay for the
stock? Assume that the next owner also expects
to earn 14% on her investment.
(d) Constant growth dividend model
• 𝑫𝒊𝒗𝟎 = $1.25
with a finite horizon
• 𝐠 = 10.72%
• 𝒓 = 14%
• 𝒏=7
Method One
– The constant growth, finite horizon formula:
𝑛
𝐷𝑖𝑣0 × (1 + g) 1+g 𝑃𝑟𝑖𝑐𝑒𝑛
𝑃𝑟𝑖𝑐𝑒0 = × 1− +
(𝑟 − g) 1+𝑟 (1 + 𝑟)𝑛
Where,
𝐷𝑖𝑣𝟖
𝑷𝒓𝒊𝒄𝒆𝟕 = (𝑟−g) , and 𝑫𝒊𝒗 𝟖 = 𝐷𝑖𝑣0 × (1 + g)8= $1.25 × 1.10728 = $2.8231
𝐷𝑖𝑣𝟖 $2.8231
𝑷𝒓𝒊𝒄𝒆𝟕 = = = $86.07
(𝑟 − g) (0.14 − 0.1072)
7 $86.07
$1.25 × (1 + 0.1072) 1 + 0.1072
𝑃𝑟𝑖𝑐𝑒0 = × 1− +
(0.14 − 0.1072) 1 + 0.14 (1 + 0.14)7

= $42.1951 × 0.184829 + 34.3968 = $42.20

(d) Constant growth dividend model
Method Two
with a finite horizon
– Gordon growth model, i.e., since the growth rate
(g) is constant, forever, and the required rates of
return for both investors are the same
𝐷𝑖𝑣0 × (1 + g)
𝑃𝑟𝑖𝑐𝑒0 =
(𝑟 − g)
$1.25 × (1.1072)
𝑃𝑟𝑖𝑐𝑒0 = = $42.20
(0.14 − 0.1072)
(e) Non-constant growth dividends
• The four models just discussed can only be used in cases
where a firm is expected to either:
– pay a constant dividend amount, indefinitely, or
– have its dividends grow at a constant rate for long periods of
time.
• But, in reality, the dividend growth patterns of most firms
tend to be variable, making the valuation process
complicated.
• However, if we can assume that at some point in the
future, the dividend growth rate will become constant,
then to calculate the price of the stock, we can use a
combination of:
– the Gordon growth model, and
– present value equations
(e) Non-constant growth dividends
Blue Star Airlines is expected to pay a
dividend of $1.00 at the end of this year.
Thereafter, the dividends are expected to
grow at the rate of 25% per year for 2 years,
and then drop to 18% for 1 year, before
settling at the industry average growth rate
of 10%, indefinitely. If Chelsea requires a
return of 16% to invest in a stock of this risk
level, how much would she be justified in
paying for this stock?
(e) Non-constant growth dividends
Step 1:
• Calculate the annual dividends expected in Years 1-
4, using the appropriate growth rates
𝐷𝑖𝑣1 = $1.00
𝐷𝑖𝑣2 = 𝐷𝑖𝑣1 × 1 + g1 = $1.00 × 1.25 = $1.25
𝐷𝑖𝑣3 = 𝐷𝑖𝑣2 × 1 + g2 = $1.25 × 1.25 = $1.56
𝐷𝑖𝑣4 = 𝐷𝑖𝑣3 × 1 + g3 = $1.56 × 1.18 = $1.84
Step 2:
• Calculate the price at the start of the constant
growth phase, using the Gordon growth model
𝐷𝑖𝑣4 × (1 + g) $1.84 × (1.10)
𝑃𝑟𝑖𝑐𝑒4 = = = $33.80
(𝑟 − g) (0.16 − 0.10)
(e) Non-constant growth dividends
Step 3:
• Calculate the PV of all cash flows by
discounting back to T0:
(1) each annual dividend, and
(2) the price at the end of Year 4
– Use Chelsea’s required rate of return as the
discount rate
$1.00 $1.25 $1.56 $1.84 $33.80
𝑃𝑉 = + + + +
(1.16)1 (1.16)2 (1.16)3 (1.16)4 (1.16)4

𝑃𝑉 = $22.47
(e) Non-constant growth dividends

Alternatively, we can calculate price using the

Cash Flow (CF) and NPV function keys on our
calculator, by entering the respective cash flows:

𝐶𝐹0 = $0; 𝐶𝐹1 = $1.00; 𝐶𝐹2 = $1.25; 𝐶𝐹3 = $1.56;

𝐶𝐹4 = ($1.84 + $33.80)

• Compute the NPV, using 𝑖 = 16%

< 𝐶𝑃𝑇 > 𝑁𝑃𝑉 = $22.47

Class Exercise