Stocks and Stock Markets
Common Stock - Ownership shares in a publicly heldcorporation.
Primary Market - Market for the sale of new securities bycorporations. (vs. secondary market)
Initial Public Offering (IPO) - First offering of stock to thegeneral public.
Seasoned Issue - Sale of new shares by a firm that hasalready been through an IPO 1
Common Stock Valuation
Professor: Burcu Esmer
2
Primary vs. Secondary Markets: Example
Shannon sells 100 shares of Google stock from her portfolioto Mike for $500 per share to help pay for her son Domenic’scollege education.
How much does Google receive from the sale of its shares?
Does this transaction occur on the primary or secondary market?
3
Bid Price/Ask PriceBid Price: The prices at which investors are willing to buy shares.
Ask Price: The prices at which current shareholders are willing tosell their shares.
Example:
If an investor wishes to purchase 100 shares of Apple with a bidprice of $253.40 and an ask price of $253.48, how much couldthe investor expect to pay for the shares? What is the bid-askspread?
Answer: $253.48 4
Stocks & Stock Market
Dividend - Periodic cash distribution from the firm to theshareholders.
P/E Ratio - Price per share divided by earnings per share.
www.finance.yahoo.com
5
http://www.finance.yahoo.com/
Basic Terminology: Example
You are considering investing in a firm whose shares arecurrently selling for $50 per share with 1,000,000 sharesoutstanding. Expected dividends are $2/share and earnings are$6/share.
What is the firm’s Market Cap? P/E Ratio? Dividend Yield?
Market Capitalization $50 1,000,000 $50,000,000
$50P/E Ratio 8.33
$6
$2Dividend Yield .04 4%
$50
6
Stocks & Stock Market
• Book Value - Net worth of the firm according to the balance sheet.
• Does the stock price equal to book value?
No!!!
http://finapps.forbes.com/finapps/jsp/finance/compinfo/FinancialIndustrial.jsp?tkr=FDX
• Liquidation Value - Net proceeds that could be realized by selling thefirm’s assets and paying off its creditors.
• Does the stock price equal to liquidation value?
No!!!
• Market Value -The value of the firm as determined by investors whowould be willing to purchase the company.
7
http://finapps.forbes.com/finapps/jsp/finance/compinfo/FinancialIndustrial.jsp?tkr=FDX
Stocks & Stock Market
The difference between a firm’s actual market value and its’liquidation or book value is attributable to its “going concernvalue.”
• Factors of “Going Concern Value”• Extra earning power
• Intangible assets (R&D)
• Value of future investments (growth companies)
• What determines firms’ future profits? The earnings that canbe generated by the firm’s current tangible and intangibleassets and the future growth opportunities. 8
Valuing Common Stocks
• Stock Valuation Methods
• Valuation by comparables
• Ratios and multiples
• Price and Intrinsic Value
• Dividend Discount Model
9
Valuing Common Stocks Valuation Using Multiples
Source: MSN money
10
For industry financials: http://biz.yahoo.com/p/s_peeu.html
http://biz.yahoo.com/p/s_peeu.html
Price-to-earnings ratio:Method: using your company's EPS and a comparable company's P/E ratio (or the industry or
market average):
Market-to-book ratio:Method: using your company's book value of equity, the number of shares outstanding and a
comparable company's market-to-book ratio (or the industry or market average):
EBITDA (cash flow) Multiples: Investment bankers’ shortcut to valuationMethod: using your company's income statement and value of equity, the number of shares
outstanding and a comparable company's Capital/EBITDA ratio (or the industry or market average)
11
High PE and high MB generally mean investors are expecting high growth.
Note.. Undervalued stocks generaly have low PE ratios
Valuing Common StocksPrice and Intrinsic Value• Remember:
Price of any security = PV of future cash flows
If you hold a stock forever, cash flows = all future dividends
• If you sell the stock eventually, what are the cash flows?
• = dividends received + future sale price of the stock
value of all dividends thereafter
Price = the PV of all future dividends! 12
Valuing Common Stocks
Suppose you buy a stock and sell it next year, then;
Div: Dividend Payment
r
PDivV
1Value Intrinsic
11
13
You can think of intrinstic value as the ‘fair’ price of the stock.
Example
• Suppose that an investor buys a share of Besmer Corp. Todayand plans to sell it in 1 year. Suppose investors expect a cashdividend of $3 over the next year and expect the stock to sellfor $81 a year. If the discount rate is 12%, then instrintic valueis :
r
PDivV
1Value Intrinsic
11
75$12.1
813Value Intrinsic
V
14
Valuing Common Stocks
Expected Return - The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the holding period return (HPR).
Suppose you buy a stock and sell it next year, then;
0
011Return ExpectedP
PPDivr
Div: Dividend Payment
15
Valuing Common Stocks
The formula can be broken into two parts.
Dividend Yield + Capital Appreciation
0
01
0
1Return ExpectedP
PP
P
Divr
16If investors buy the stock at intrinsic value then their expected return will equal the discount rate.
Example (Cont.)
• Calculate the expected return if the price of the stock is $75and you expect the stock to sell for $81 next yext year. You willget $3 dividend payment next year.
0
01
0
1Return ExpectedP
PP
P
Divr
%1275
7581
75
3 ReturnExpected
%1275
75813Return Expected
17
Dividend yield Capital appreciation
What happens if price is above $75?
What happens if price is below $75?
Valuing Common StocksDividend Dicount Model
Computation of today’s stock price which statesthat share value equals the present value of allexpected future dividends.
t
tt
r
PDiv
r
Div
r
DivP
)1(...
)1()1( 22
1
10
18
Valuing Common Stocks
Example
Current forecasts are for Besmer Company to pay dividends of $3,$3.24, and $3.50 over the next three years, respectively. At the endof three years you anticipate selling your stock at a market price of$94.48. What is the price of the stock given a 12% expected return?
PV
PV
3 00
1 12
3 24
1 12
350 94 48
1 12
00
1 2 3
.
( . )
.
( . )
. .
( . )
$75.19
Value of Besmer Corp for different horizons• Do investors with different horizons will come to
different conclusions about the value of the stock?
• Estimate the price of the Besmer Stock for each of theinvestor.
Year 1 Year 2 Year 3
Basak Div=3P=81
Zeynep Div=3 Div=3.24P=87.48
Aslihan Div=3 Div=3.24 Div=3.5P=94.48
20
Value of Besmer Corp for different horizons
0
10
20
30
40
50
60
70
80
1 2 3 10 20 30 50 100
Valu
e p
er
sh
are
, d
oll
ars
Investment Horizon, Years
PV (Terminal Price)
PV (Dividends)
21
Dividend Discount ModelSpecial Cases
• Zero Dividend Growth
• Constant Growth
• Non-Constant Growth
22
1. Zero Dividend Growth
• If we forecast no growth, and plan to hold out stockindefinitely, we will then value the stock as aPERPETUITY. (D1 = D2 = D3 = … = D∞ (a perpetuity))
Perpetuity PDiv
ror
EPS
r 0
1 1
Assumes all earnings are paid to shareholders. Remember there is no
growth!
23
Example
• Stock XYZ has an expected growth rate of 0%. Each share ofstock just received an annual $3.24 dividend per share. If therequired return on the stock is 12% what is the value of thecommon stock?
27$12.0
24.30 PPerpetuity
24
2. Constant Growth
• A version of the dividend growth model in which dividendsgrow at a constant rate (Gordon Growth Model).
• The constant growth model assumes that dividends will growforever at the rate g.
gr
DivP
10
Given any combination of variables in the
equation, you can solve for the unknown variable.
Note: This formula only works when g is less
than r!
25
2. Constant Growth
D0 = current (most recently paid) dividend
D1 = D0(1+g)
D2 = D1(1+g) = D0(1+g)(1+g) = D0(1+g)2
…
…
Dn = D0(1+g)n
26
Example
What is the value of a stock that expects to pay a $3.00dividend next year, and then increase the dividend at arate of 8% per year, indefinitely? Assume a 12% expectedreturn.
• What is the value of a stock which just paid a dividend of$3.00, the expected growth rate is 8% per year. Assume a 12%expected return?
• Calculate next year’s dividend first! Div1 = Div0 x (1+g)= 3x1.08 =$3.24
00.75$08.12.
00.3$10
gr
DivP
00.81$08.12.
24.3$10
gr
DivP 27
Required Rates of Return (using constant growth)
Estimating Expected Required Rates of Return:
Example: What rate of return should an investor expect on a
share of stock with a $2 expected dividend and 8% growth rate
that sells today for $60?
Expected rate of return offered by other, equally risky stocks
28
3. Nonconstant Growth
• Set the investment horizon (year H) at the future year bywhich you expect the company’s growth to settle down.
H
H
H
H
r
P
r
Div
r
Div
r
DivPV
)1()1(...
)1()1( 22
1
1
29
Changing Growth (steps)
1) Calculate dividends at end of each period of non-constantgrowth.
2) Calculate price at end of non-constant growth window.
3) Compute PVs of steps (1) and (2). This is your stock price.
30
Example
Stock GP has an expected growth rate of 16% for the first 3 yearsand 8% thereafter. Each share of stock just received an annual$3.24 dividend per share. If the required return on the stock is 15%what is the value of the common stock under this scenario?
31
Stock GP has two phases of growth. The first, 16%, starts at timet=0 for 3 years and is followed by 8% thereafter starting at timet=3. We should view the time line as two separate time lines inthe valuation.
0 1 2 3 4 5 6
D1 D2 D3 D4 D5 D6
Growth of 16% for 3 years Growth of 8% to infinity!
32
Determine the annual dividends.
D0 = $3.24 (this has been paid already)D1 = D0(1+g1)
1 = $3.24(1.16)1 =$3.76
D2 = D0(1+g1)2 = $3.24(1.16)2 =$4.36
D3 = D0(1+g1)3 = $3.24(1.16)3 =$5.06
D4 = D3(1+g2)1 = $5.06(1.08)1 =$5.46
Example (cont.)
33
We determine the PV of cash flows.
PV(D1) = D1(PVIF15%, 1) = $3.76 (.870) = $3.27
PV(D2) = D2(PVIF15%, 2) = $4.36 (.756) = $3.30
PV(D3) = D3(PVIF15%, 3) = $5.06 (.658) = $3.33
P3 = $5.46 / (.15 - .08) = $78 [CG Model]
PV(P3) = P3(PVIF15%, 3) = $78 (.658) = $51.32
34
Finally, we calculate the intrinsic value by summing all the cash flowpresent values.
V = $3.27 + $3.30 + $3.33 + $51.32 = $61.22
35
Preferred Stock
• Preferred Stock = debt/equity “hybrid” security
• debt-like features:• often lack voting rights
• dividend payments usually fixed and paid before common stockdividends
• sometimes convertible to common stock
• similarity to common stock:• preferred dividends have lower priority than debt interest
payments
• preferred dividends usu. not tax-deductible to corp.
• Preferred Stock Valuation:• use perpetuity PV formula when appropriate 36
Preferred Stock Example
• Stock PS has an 8%, $100 par value issue
outstanding. The appropriate discount rate is 10%.
What is the value of the preferred stock?
DivP = $100 ( 8% ) = $8.00.
P0 = Div1 / r = $8.00 / 10% = $80
37
Valuing common stocksWhere does growth come from?
Firm invests in projects
… which is
paid out as
divs, or
reinvested
in the firm.
…which produces cash flow
38
Valuing Common Stocks
What determines the growth rate (g)?
Growth can be derived from applying the return on equity to thepercentage of earnings plowed back into operations.
g = return on equity X plowback ratio
(sustainable growth rate)
Payout Ratio - Fraction of earnings paid out as dividends
Plowback Ratio - Fraction of earnings retained by the firm
Sustainable Growth Rate - Steady rate at which firm cangrow; return on equity x plowback ratio
39
Valuing Common Stocks
• If a firm elects to pay a lower dividend, andreinvest the funds, the stock price may increasebecause future dividends may be higher.
40
What determines the growth rate (g)?• Suppose that BlueSkies starts the year with book equity (book
value of equity) of $25 a share and earns return on equity of20% per year. (remember roe: net income/book value ofequity).
• EPS= book value of equity per share x ROE = 25 x .2= $5
• İf BlueSkies pays $3 dividend next year then• Payout ratio = 3/ 5 = .60 and Plowback ratio=2/5= .40
• After reinvesting 40% of earnings, BlueSkies will start the next year with additional equity per share of • Earnings per share in the first year x plowback ratio=
= book equity per share x ROE year x plowback ratio = 25 x .2 x .4 = $2
• The growth rate of BlueSkies’s equity = $2 / $25 = 8%
• g = return on equity X plowback ratio = .2 x .4 = 8%41
Valuing Common Stocks
Example
BlueSkies forecasts to pay a $5.00 dividend nextyear, which represents 100% of its earnings. Thiswill provide investors with a 12% expected return.Instead, we decide to plowback 40% of theearnings at the firm’s current return on equity of20%. What is the value of the stock before andafter the plowback decision?
42
Valuing Common Stocks
Example
BlueSkies forecasts to pay a $5.00 dividend next year, whichrepresents 100% of its earnings. This will provide investors with a12% expected return. Instead, we decide to plowback 40% of theearnings at the firm’s current return on equity of 20%. What is thevalue of the stock before and after the plowback decision?
P05
1267
.$41.
No Growth With Growth
g
P
. . .
. .$75.
20 40 08
3
12 08000The value of earnings from
assets that are already in place.
43
Valuing Common Stocks
Example - continued
If the company did not plowback some earnings, thestock price would remain at $41.67. With the plowback,the price rose to $75.00.
The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of GrowthOpportunities (PVGO).
• Present Value of Growth Opportunities (PVGO).• Net present value of a firm’s future investments. 44
Valuing Common Stocks
Value of assets in place $41.67
+ Present Value of growth opportunities (PVGO)
$33.33
Total Value of the stock $75
Note that if return on equity was 12% (=discount rate) –keeping the plowback ratio as 40%, then the price of the stock would still be $41.67.
Plowing earnings back does increase stock price ifinvestors believe that the reinvested earnings will earna higher rate of return than the rate investors require(the discount rate).
45
Valuing Common Stocks
Note with growth opportunities, P/E is 15 (=75/5).
without growth opportunities, P/E is 8.33 (=41.67/5).
Example
Suppose that instead of plowing money back into lucrativeventures, BlueSkies’s management is investing at an expectedreturn on equity of 10%, which is below the return of 12% thatinvestors could expect to get from comparable securities.
A. Find the sustainable growth rate of dividends and earnings.Assume a 60% payout ratio.
B. Find the new value of its investment opportunities. Explainwhy this value is negative despite the positive growth rate ofearnings and dividends.
C. İf you were a corporate raider, would BlueSkies be a goodcandidate for an attempted takeover?
46
Example cont.
• A. Sustainable growth rate= g = roe x plowback ratio = .1 x .4 =4%
• B. No growth case: P= 5/.12 = $41.67
with 4% growth: P= 3 / .12-0.04 = $ 37.50
The difference (41.67 – 37.50 = $4.17) is the money BlueSkies iswasting by investing in bad projects.
• C. Sure! Buy the company for 37.50 (less than the pv of assetsin place)
47
Valuing Common Stocks
• If return on equity= r then NPV of funds plowed back intofirm is zero. (does not matter if invest EPS or pay as dividend).
• If return on equity > r then NPV>0 and shareholder value isincreased.
• If return on equity < r then NPV return on equity the stock price will grow eachyear, but by less than shareholders could have earned investingthe $ themselves!
48
Valuing Growth Stocks
Present Value of Growth Opportunities (PVGO) –
where:
EPS = Earnings per share
PVGO = Present Value of Growth Opportunities49
Valuing Growth Stocks: Example
Suppose a stock is selling today for $55/share and there are10,000,000 shares outstanding. If earnings are projected to be$20,000,000, how much value are investors assigning to growthper share? Assume a discount rate of 10%.
50
51
Growing Annuity
We could discount each cash flow individually and then sum them, or we
could rewrite the above as the difference between two growing
perpetuities.
CF1 CF1(1+g) CF1(1+g)2 CF1(1+g)
N-1
0 1 2 3 Nr
CF0(1+g) CF0(1+g)2 CF0(1+g)
3 CF0(1+g)N
0 1 2 3 Nr where
CF0=CF1/(1+g)
Growing annuities are written one of two ways. Either in terms of the first
cash flow (CF1) or in terms of a growth rate on a previous cash flow
(CF0(1+g)).
51
Subtracting the 2) from 1) leaves the first N Cash Flows
r
1)
Growing perpetuity
CF0(1+g) CF0(1+g)2
0 1 2
N+1
CF0(1+g)N+1
N
CF0(1+g)N
2)
0 0
0 1 2 3r
N+1
CF0(1+g)N+1
Growing perpetuity that starts in N+1 years
N
00
1) - 2) =CF0(1+g) CF0(1+g)
2
0 1 2 N
CF0(1+g)N
52
gr
)g1(CF)1(PV 0
Find the PV of timeline 1) and 2)
N
1N0
)r1(
1
gr
)g1(CF)2(PV
N
N0
N
1N00
0
)r1(
)g1(1
gr
)g1(CF
)r1(
1
gr
)g1(CF
gr
)g1(CF
)2(PV)1(PVPV
(PVIFr,N)Discounts
to time N
54
N
N1
N
N0
0)r1(
)g1(1
gr
CF
)r1(
)g1(1
gr
)g1(CFPV
CF1 CF1(1+g) CF1(1+g)2 CF1(1+g)
N-1
0 1 2 3 Nr
CF0(1+g) CF0(1+g)2 CF0(1+g)
3 CF0(1+g)N
0 1 2 3 Nr
Notice that if CF1 = CF0(1+g) the above two timelines are identical
A very common mistake is to put (N-1) into the formula when you
see the top timeline. To avoid this mistake remember N in the
formula is the number of cash flows and NOT NECESSARILY the
exponent on the last cash flow.
55
Growing Annuity Example:
You are asked to value an existing security that makes a series of
cash flows that grow by 5% each year. There are 8 cash flows left.
The previous cash flow was just paid and was $3. What is the value
of the security if the discount rate is 10%?
3(1.05) 3(1.05)2 3(1.05)3 3(1.05)8
0 1 2 3 8r
58.19$)10.1(
)05.1(1
05.10.
)05.1(3
)r1(
)g1(1
gr
)g1(CFPV
8
8
N
N0
0
56
Growing Annuity Example (Cont’d):
Identical problem asked another way:You are asked to value an
existing security that pays a series of cash flows that grow by 5%
each year. There are 8 cash flows left. The NEXT cash flow will be
$3.15. What is the value of the security if the discount rate is 10%?
3.15 3.15(1.05) 3.15(1.05)2 3.15(1.05)7
0 1 2 3 8r
58.19$)10.1(
)05.1(1
05.10.
15.3
)r1(
)g1(1
gr
CFPV
8
8
N
N1
0
N is # of CFs not
the exponent on
last CF!
57
TVM Formula Summary
))1(),...,1((
)1(
)1(1
...),)1(),1((
)1(
1)1()...(
)1(
111
...)(
)1(
001
10
2
0201
100
021
0
21
0
0
N
N
N
N
N
N
N
N
N
gCFCFgCFCF
r
g
gr
CFPVAnnuityGrowing
gCFCFgCFCF
gr
CF
gr
gCFPVPerpetuityGrowing
r
rCFFVCFCFCFCF
rrrCFPVAnnuity
CFCFCF
r
CFPVPerpetuity
r
CFCFFlowCashSingle
Finding mispriced stocks
58
Mutual Fund Performance
-40
-30
-20
-10
0
10
20
30
40
1962
1977
1992
Retu
rn (
%)
Funds
Market
Source: Brealey, Myers, & Allen
Carhart (1997) study of 1,493 US mutual funds and the market index
59
Mutual Fund Performance Relative to the Market from 1970 to 2001
1311
28
34
29
21
17
31 1
0
5
10
15
20
25
30
35
-4%
or
less
-3% -2% -1% 0 to -
1%
0 to
+1%
1% 2% 3% 4% or
more
Note: These are only surviving mutual funds, so it isprobably biased upwards. Many of the poorest performingfunds likely shut down during this time period.
Source: Malkiel, A Random Walk Down Wall Street
60
Finding mispriced stocks (cont.)
Method I: Technical Analysis
Investors who attempt to identifyundervalued stocks by searching for patternsin past stock prices.
Forecast stock prices based on the watchingthe fluctuations in historical prices (thus“wiggle watchers”)
61
Any predictability here?
62
Random Walk Theory
• Security prices change randomly, with nopredictable trends or patterns.
• Statistically speaking, the movement of stockprices is random
• They are equally likely to offer a high or lowreturn on any particular day, regardless of whathas occurred on previous days.
63
Random Walk Theory
Last
Month
This
Month
Next
Month
1,300
1,200
1,100
Market
Index
Cycles
disappear
once
identified
64
Actual price as soon as upswing is recognized
S&P 500 and random draw… which is which?
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Months
Valu
e o
f $1 I
nvestm
en
t
65
Finding mispriced stocks
Method II: Fundamental Analysts
Investors who attempt to find mispricedsecurities by analyzing fundamentalinformation, such as accounting data andbusiness prospects.
Research the value of stocks using NPV andother measurements of cash flow
66
Fundamental Analysis
Fundamental analysts are paid to uncover stocks for which price does not equal intrinsic value.
What happens in a market with many talented
and competitive fundamental analysts?
67
Efficient Market Theory
Efficient Market - Market in which prices reflectall available information.
• Weak Form Efficiency
• Market prices reflect all historical information
• Semi-Strong Form Efficiency
• Market prices reflect all publicly available information
• Strong Form Efficiency
• Market prices reflect all information, both public andprivate
68
Degree of Market Efficiency
Weak
Semi-strong
Strong
69
Efficient Market Theory
-16
-11
-6
-1
4
9
14
19
24
29
34
39
Days Relative to annoncement date
Cu
mu
lati
ve A
bn
orm
al
Retu
rn
(%)
Announcement Date
70
Weak form efficiency• Prices contain all information from past prices• Stock prices are not predictable returns follow a
random walkHighly recommend: A Random Walk Down Wall Street
by Burton G. Malkiel
t
1t
tt turnReExpected1
P
Pr
Random Error
71
Weak form market efficiency
• Weak form market efficiency states that the currentstock price reflects all past price information
• Implications
• Patterns in prices don’t exist
• Prices follow a random walk
• “Technical” trading strategies that just try to findpatterns in stock prices don’t earn excess returns
72
Semi-strong form efficiency:
• Prices contain all publicly available information(past and current)• Accounting statements• News• Everything publicly available: “No stone left
unturned”
• Implications• Prices adjust immediately to new public information
• “News”• “Fundamental” trading strategies that pick stocks
based on financial characteristics don’t earn excessreturns
73
Strong form efficiency
• Price reflects all information
• All public information
• All private information, including inside information
• Implications• Prices would immediately adjust to reflect any new
event that occurs in the firm, industry, and economy
• It would be impossible for any investor (even the firmCEO) to consistently gain excess returns
74
Market AnomaliesThere are a number of market anomalies that seem to puzzle
efficient market theorists, including:
The Earnings Announcement Puzzle
The New-Issue Puzzle
Bubbles
75
Behavioral Finance
Some believe that deviations in prices from intrinsic value can be explained by behavioral psychology, in two broad areas:
Attitudes toward risk--People generally dislike incurring losses, yet they aremore apt to take bigger risks if they are experiencing a period of substantialgains.
e.g. In the dot-com boom, it is theorized that investors experienced such great consistentgains that they stopped worrying about the risk of loss; thus driving prices artificially higherthan their fundamental values.
Beliefs about probabilities--Individuals commonly look back to what hashappened in recent periods and assume this is representative of futureoutcomes.
e.g. Most investors believe they are better-than-average investors, but not everyspeculator can consistently profit at the other’s expense. «Overconfidence»
76
