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Valuing Common Stocks Fundamentals of Corporate Finance Chapter 7 BMM Finansiell ekonomi LiU 2012
Valuing Common Stocks
Fundamentals of Corporate Finance Chapter 7 BMM
Finansiell ekonomi LiU2012
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Kom ihåg
• Nuvärde concepts can be applied to the valuation of common stocks
• Förhållande mellan aktie kurs, avkastning per aktie (earnings per share EPS) och tillväxt (growth rate) g
• Räkna ut kapitalkostnader på eget kapital r, diskonterings ränta
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Learning objectives
1. Market Values, Book Values, and Liquidation Values
2. How to value Common Stocks3. Simplifying the Dividend Discount Model (the
discounted cash flow model)4. Growth Stocks and Income Stocks5. There Are No Free Lunches on Wall Street
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Concepts and definitionsPrimary Market - Market for the sale of new securities
by corporations.
Secondary Market - Market in which previously issued securities are traded among investors.
Common Stock - Ownership shares in a publicly held corporation.
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Some conceptsBook Value: Net worth of the firm according to the balance
sheet.Dividend: Periodic cash distribution from the firm to the
shareholders.P/E Ratio: Price per share divided by earnings per share.Earnings per share: EPS = Earnings/ number of sharesROE: RE
return on equity= Earnings /Book value of equityObs: earnings =net income= årsresultat= vinst
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Going concern value • The difference between a firm’s actual market
value and its’ liquidation value is the so called “going concern value.”
Market value-Liquidation Value = Going concern value
Liquidation Value Net proceeds that could be realized by selling
the firm’s assets and paying off its creditors.
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Valuation of common stocksSingle period investment case• The (present) value of a common stock equals
the present value of dividends expected during the period plus the present value of the expected end-of-period price.
rPDivP
1
Price 110
The present value of future cash flows from a stock is also called the Intrinsic value of the stock.
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The DCF model: discounted cash flow method (Dividend Discount Model)
The value of any stock is the present value of its future cash flows. Dividends represent the future cash flows of the firm.
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How Common Stocks Are Valued
Expected Return rThe percentage yield that an investor forecasts from a
specific investment over a set period of time.
Expected Return r Div P PP
1 1 0
0
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Valuing Common Stocks
For a stock with no growth, and assuming the stock will exist indefinitely, we can value the stock as a PERPETUITY.
1 10
Div EPSPerpetuity Pr r
No growth means all earnings are paid to shareholders.
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How Common Stocks Are Valued
Example: If Blue Sky is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5.00?
15.0100
1001105Return Expected
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How Common Stocks Are Valued
Example - continued: Blue Sky price can be thought of as follows.
10015.11105Price 0
P
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Valuing Common Stocks
Constant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model).
P Divr g0
1
Given any combination of variables in the equation, you can solve for the unknown variable.
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What is the value of the stock that expects to pay a $3.00 dividend next year, and then increase the dividend at a rate of 8% per year, indefinitely? Assume a 12% expected return. (note: suppose that Blue Sky invested 40% back to the company, the dividend becomes 5*60%=3.)
00.75$08.012.0
00.3$10
grDivP
Example: valuing stocks
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Estimating the Cost of Equity Capital
Dividend Growth Rate can also be derived from applying the return on equity to the percentage of earnings plowed back into operations.
g = return on equity X plowback ratio
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Valuing Common Stocks
Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends.
P Divr
Divr
Div Pr
H HH0
11
221 1 1
( ) ( )...
( )
H - Time horizon for your investment.
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How Common Stocks Are ValuedFormula
P Divr
Divr
Div Pr
H HH0
11
221 1 1
( ) ( )...
( )
HH
H
tt
t
rP
rDivP
)1()1(10
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How Common Stocks Are Valued
ExampleBlue Sky is forecasted to pay a $5.00 dividend at the end of year one and a $5.50 dividend at the end of year two. At the end of the second year the stock will be sold for $121. If the discount rate is 15%, what is the price of the stock?
00.100$)15.01(
12150.5)15.01(
00.521
PV
PV
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How Common Stocks Are Valued
ExampleCurrent forecasts are for Blue Sky to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of 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?
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How Common Stocks Are ValuedExample
Current forecasts are for Blue Sky to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?
00.75$)12.01(48.9450.3
)12.01(24.3
)12.01(00.3
321
PV
PV
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How Common Stocks Are Valued
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Estimating the Cost of Equity CapitalExample – A stock was selling for $42.45 per
share at the start of 2012. Dividend payments for the next year were expected to be $1.68 a share. What is the dividend yield?
04.045.42
68.1Yield Dividend
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Estimating the Cost of Equity Capital
Example - continued - Northwest Natural Gas stock was selling for $42.45 per share at the start of 2009. Dividend payments for the next year were expected to be $1.68 a share. What is the expected return, assuming a growth rate of 6.1%?
101.0
061.045.42
68.1
r
r
Estimating the Cost of Equity Capital
Required Return Measurements
0
1
PDiv YieldDividend
gP
Divr
grDivP
0
1
10 Restated
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Estimating the Cost of Equity Capital• Valuing Non-Constant Growth
HH
HH
rP
rDiv
rDiv
rDivPV
)1()1(...
)1()1( 22
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grDivP H
H 1
The H period has a share value PH
it is evaluated as a growing perpetuity
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Estimating the Cost of Equity Capital
Example – Phoenix produces dividends in three consecutive years of 0, 0.31, and 0.65, respectively. The dividend in year four is estimated to be .67 and should grow in perpetuity at 4%. Given a discount rate of 10%, what is the price of the stock?
13.9)04.010.0(
67.0)1.01(
1)1.01(
65.0)1.01(
31.0)1.01(
03321
PV
Note here the discount factor is
1/(1+0,1)3
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Stock Price and Earnings Per Share
• If a firm chooses to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.
Payout Ratio: Fraction of earnings paid out as dividends
Plowback Ratio: Fraction of earnings retained by the firm
The payout ratio= 1-Plowback ratio
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Stock Price and Earnings Per ShareExample
Our company forecasts to pay a $8.33 dividend next year, which represents 100% of its earnings. This will provide investors with a 15% expected return. Instead, we decide to retain 40% of the earnings at the firm’s current return on equity of 25%. What is the value of the stock before and after the earnings distribution decision?
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Example• Pay a $8.33 dividend next year, which represents 100% of its
earnings. a 15% expected return. • plowback 40% of the earnings at the firm’s current return
on equity of 25%. the value of the stock with and without growth:
56.55$15.033.8
0 P
No Growth With Growth
00.100$10.015.0
00.510.040.025.0
0
P
g
With growth of the equity, the price of the share worth more than before! 100-55,56=44,44
Stock Price and Earnings Per Share
Example - continuedIf the company did not plowback some earnings, the stock price would remain at $55.56. With the plowback, the price rose to $100.00.
The difference between these two numbers is called the Present Value of Growth Opportunities (PVGO).
44.44$56.5500.100 PVGORemain critical! The growth rate of dividend 10% would amount to huge payment after 10 year! Especially when it is close to the discount rate. (r-g should be larger than 0). The stock price will explode!
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Stock Price and Earnings Per Share
Present Value of Growth Opportunities (PVGO): Net present value of a firm’s future investments.
Sustainable Growth Rate is the steady rate at which a firm can grow:
g = plowback ratio X return on equity.
1 1div divPVGOr g r
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Valuing a BusinessValuing a Business or Project
The value of a business or Project is usually computed as the discounted value of FCF out to a valuation horizon (H).
The valuation horizon is sometimes called the terminal value.
HH
HH
rPV
rFCF
rFCF
rFCFPV
)1()1(...
)1()1( 22
11
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Valuing a BusinessValuing a Business or Project
HH
HH
rPV
rFCF
rFCF
rFCFPV
)1()1(...
)1()1( 22
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PV (free cash flows) PV (horizon value)
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Sustainable growthHållbar tillväxt
• Long-term growth rate in dividends is a function of Plowback ratio and return on equity.
• Growth rate of equity=g• ROE= Earning/equity= (1+g)Earnings/(1+g)equityAt year 2, the company will have (1+g) Earnings to
distribute to the shareholders. Keeping the payout ratio constant, we will have an dividend growth (1+g).
g = RE *plowback ratio
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Effektiva MarknaderÄr prisförändringar predikterbara (effektivamarknadshypotesen, EMH)?Vad talar för och emot marknadseffektivitet?
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Effektiva Marknader
En marknad är effektiv om priset återspeglar alltillgänglig ”information”.Tre nivåer (typer) av information:• historisk information• publik information• insiderinformation
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Effektiva Marknader
Till dessa tre nivåer av information hör tre typerav effektivitet.Tre nivåer (typer) av marknadseffektivitet:• Svag effektivitet: priset återspeglar all hist. info.• Halvstark effektivitet: priset återspeglar all publikinformation.• Stark effektivitet: priset återspeglar även all insiderinformation.
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Är Marknaden Effektiv?
Svar: det vanligaste svaret är att”marknaden” åtminstone ärhalvstarkt effektiv.
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Svag effektivitet
Svag effektivitet: • ”Aktie”priserna följer en ”random walk”• Det går ej att prediktera ”aktie”priserna.Det betyder:• tidsserieanalys funkar ej• teknisk analys funkar ej• timing omöjlig
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Halvstark Effektivitet
Halvstark Effektivitet• Fundamental analys fungerar ej(inte heller teknisk analys fungerar, förstås)
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Stark Effektivitet
Stark Effektivitet• inte ens insiders erhåller överavkastning
Marknader är inte stark form effektivt. Därför insider erhåller faktiskt information som kan ge överavkastning. De vet mer än andra.
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EMH: Effektiva Marknadshypotesen
• Varken teknisk eller fundamental analys fungerar.
• Aktiva portföljvalsstrategier (stock picking) fungerar ej.
• Passiv (indexing) strategi är bäst.
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EMH motbevis
Regelbundenheter (anomalier) på aktiemarknaden• småföretagseffekten• januarieffekten• veckodagseffekten• P/E effekten
Obs: Alla dessa anomalier är själv-destruktiva. De tenderar försvinna när tillräckliga många aktörer agerar på det. ”fri lunchen försvinner”
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Småföretagseffekten
-- små företag har onormalt hög avkastning(även när risken tagits hänsyn till).
Men den här har varit avtagande sedan 90 talet.
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Januarieffekten
-- onormalt höga avkastningar i januari. Eller andra månad: februari, mars, april, …förklaring:--Aktier med realisationsförlust idecember månad (placerare söker efterorealiserade kursförluster för att minskaskatten?)
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Veckodagseffekten
-- de olika veckodagarna har olika storgenomsnittsavkastning (oftast måndag och tisdag har negativ avkastning och fredag har störst positiv avkastning).
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P/E effekten
-- företag med låga P/E tal ger en för högavkastning när man tagit hänsyn till risk.
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Kan anomalierna utnyttjas för att enkelttjäna pengar (är marknaden ineffektiv)?
• ofta är anomalierna så små att om man tar hänsyn tilltransaktionskostnaderna och analyskostnaderna så försvinnervinsterna (marknaden är alltså i praktiken effektiv).• när anomalierna blir kända har de en tendens att försvinna(marknaden blir effektiv).• Överavkastning kan vara kompensation för någon annan faktor än risken (marknaden är effektiv).• Kan vi lita på de akademiska studierna om anomalier (barasignifikanta resultat publiceras…)
effektiv marknad trots anomalierna
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Behavioral Finans
• Attityd mot risk och sättet att estimera sannolikhet är orationella!
Vi ogillar förluster på ett orationellt sätt. Vi är dålig förlorare. Vi tar mer risk när vi hade vunnit stort nyss. Precis som spel spelare.Sådana beteende leder till Prisbubbla. Många tjänade pengar i IT bubblan men förlorade sedan på högrisk aktier!
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Psykologiska påverkan
Fel bedömning på sannolikhet! • Vi har svårt att bedöma rätt när det gäller
marknads tendenser att gå upp eller gå ner. Detta uppfattning påverkas av vad hänt senaste. Marknads volatilitet förstärkas av våra tro!
• Vi har för mycket självförtroende. Den andra måste vara ”the bigger fool”.
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No Free LunchesTechnical Analysts
Investors who attempt to identify undervalued stocks by searching for patterns in past stock prices.
Forecast stock prices based on the watching the fluctuations in historical prices
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No Free Lunches
Scatter Plot of NYSE Composite Index over two successive weeks.
Where’s the pattern?
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Random Walk Theory
• Security prices change randomly, with no predictable trends or patterns.
• Statistically speaking, the movement of stock prices is random (skewed positive over the long term).
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Random Walk Theory
$103.00
$100.00
$106.09
$100.43
$97.50
$100.43
$95.06
Coin Toss Game
Heads
Heads
Heads
Tails
Tails
Tails
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Random Walk TheoryS&P 500 Five Year Trend?
or5 yrs of the Coin Toss Game?
80
130
180
Month
Leve
l
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Random Walk TheoryS&P 500 Five Year Trend?
or5 yrs of the Coin Toss Game?
80
130
180
230
Month
Leve
l
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Random Walk Theory
Last Month
This Month
Next Month
1,300
1,200
1,100
Market Index
Cycles disappear
once identified
Actual price as soon as upswing is recongnized.
upswingThe market immediately moves to the perceived new price incorporating the new information of a upswing/good news.
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Another ToolFundamental Analysts
Investors who attempt to find mispriced securities by analyzing fundamental information, such as accounting data and business prospects.
Research the value of stocks using NPV and other measurements of cash flow
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Efficient Market Theory
Efficient Market - Market in which prices reflect all 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 and private
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Efficient Market Theory
-16-11-6-149141924293439
Days Relative to annoncement date
Cum
ulat
ive
Abn
orm
al R
etur
n (%
)Announcement Date
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Market AnomaliesExisting Anomalies•The Earnings Announcement Puzzle•The New-Issue Puzzle
Old Anomalies•The Small Firm Effect•The January Effect•The PE Effect•The Neglected Firm Effect•The Value Line Effect
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Behavioral Finance
• Attitudes towards risk• Beliefs about probabilities
