Fundamentals of Corporate Finance
Chapter 7 BMM
Finansiell ekonomi LiU
2012

• 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
2

1. Market Values, Book Values, and Liquidation
Values
2. How to value Common Stocks
3. Simplifying the Dividend Discount Model (the discounted cash flow model)
4. Growth Stocks and Income Stocks
5. There Are No Free Lunches on Wall Street
3

Primary 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.
4

Book 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 shares
ROE: R
E return on equity= Earnings /Book value of equity
Obs: earnings =net income= årsresultat= vinst
5

• The difference between a firm’s actual market value and its’ liquidation value is the so called
“going concern value.”
Market valueLiquidation Value = Going concern value
Net proceeds that could be realized by selling the firm’s assets and paying off its creditors.
6

Single 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.
Price

P
0

Div
1
1

 r
P
1
The present value of future cash flows from a stock is also called the Intrinsic value of the stock.
7

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.
8

Expected Return r
The percentage yield that an investor forecasts from a specific investment over a set period of time.
 
Div
 
P
1 1 0
P
0
9

For a stock with no growth, and assuming the stock will exist indefinitely, we can value the stock as a
PERPETUITY.

0

1

1
No growth means all earnings are paid to shareholders.
10

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?
Expected Return

5

110

100

0 .
15
100
11

Example - continued: Blue Sky price can be thought of as follows.
Price

P
0

5

110
1 .
15

100
12

Constant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate ( Gordon Growth
Model ).
P
0

Div
1 r
 g
Given any combination of variables in the equation, you can solve for the unknown variable.
13

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.)
P
0
 r
Div
1
 g

$ 3 .
00
0 .
12

0 .
08

$ 75 .
00
14

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
15

Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends.
P
0

( 1
Div
 r
1
)
1

( 1
Div
 r
2
)
2
Div
H

P
H
( 1
 r )
H
H - Time horizon for your investment.
16

Formula
P
0

( 1
Div
 r
1
) 1

( 1
Div
 r
2
) 2
Div
H

P
H
( 1
 r ) H
P
0
 t
H 

1
( 1
Div t
 r ) t

( 1
P
H
 r )
H
17

Example
Blue 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?
PV
PV

5 .
00
( 1

0 .
15 )
1

$ 100 .
00

5 .
50

121
( 1

0 .
15 )
2
18

Example
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?
19

Example
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?
PV
PV

3 .
00
( 1

0 .
12 )
1

$ 75 .
00

3 .
24
( 1

0 .
12 )
2

3 .
50

94 .
48
( 1

0 .
12 )
3
20

21

Estimating the Cost of Equity Capital
Example – 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?
Dividend Yield

1 .
68
42 .
45

0 .
04
22

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%?
r r

1 .
68
42 .
45

0 .
101

0 .
061
23

Estimating the Cost of Equity Capital
Required Return Measurements
Dividend Yield

Div
1
P
0
Restated P
0

Div
1 r
 g r

Div
1
P
0
 g

Estimating the Cost of Equity Capital
• Valuing Non-Constant Growth
PV

( 1
Div
1
 r )
1

( 1
Div
2
 r )
2

...

( 1
Div
H
 r )
H

( 1
P
H
 r )
H
The H period has a share value P
H it is evaluated as a growing perpetuity
P
H

Div r

H g

1
25

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?
PV

0
( 1

0 .
1 )
1

0 .
31
( 1

0 .
1 )
2

9 .
13

0 .
65
( 1

0 .
1 )
3



( 1

1
0 .
1 )
3

( 0 .
0
10
.
67

0 .
04 )


Note here the discount factor is
1/(1+0,1) 3
26

• 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
27

Example
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?
28

• 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:
No Growth With Growth
P
0

8 .
33
0 .
15

$ 55 .
56
With growth of the equity, the price of the share worth more than before! 100-55,56=44,44 g

0 .
25

0 .
40

0 .
10
P
0

5 .
00
0 .
15

0 .
10

$ 100 .
00
29

Stock Price and Earnings Per Share
Example - continued
If 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).
PVGO

100 .
00

55 .
56

$ 44 .
44
Remain 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!

Present Value of Growth Opportunities (PVGO):
Net present value of a firm’s future investments.
PVGO
 div
1 r
 g
 div
1 r
Sustainable Growth Rate is the steady rate at which a firm can grow: g = plowback ratio X return on equity.
31

Valuing 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.
PV

(
FCF
1
1
 r )
1

(
FCF
2
1
 r )
2

...

(
FCF
H
1
 r )
H

( 1
PV
H
 r )
H
32

Valuing a Business or Project
PV

(
FCF
1
1
 r )
1

(
FCF
2
1
 r )
2

...

(
FCF
H
1
 r )
H

( 1
PV
H
 r )
H
PV (free cash flows) PV (horizon value)
33

• 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)equity
At 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 = R
E
*plowback ratio
34

Är prisförändringar predikterbara (effektiva marknadshypotesen, EMH)?
Vad talar för och emot marknadseffektivitet?
35

En marknad är effektiv om priset återspeglar all tillgänglig ”information”.
Tre nivåer (typer) av information:
• historisk information
• publik information
• insiderinformation
36

Till dessa tre nivåer av information hör tre typer av effektivitet .
Tre nivåer (typer) av marknadseffektivitet:
• Svag effektivitet: priset återspeglar all hist. info.
• Halvstark effektivitet: priset återspeglar all publik information.
• Stark effektivitet: priset återspeglar även all insiderinformation.
37

Svar: det vanligaste svaret är att
”marknaden” åtminstone är halvstarkt effektiv.
38

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
39

Halvstark Effektivitet
• Fundamental analys fungerar ej
(inte heller teknisk analys fungerar, förstås)
40

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.
41

• Varken teknisk eller fundamental analys fungerar.
• Aktiva portföljvalsstrategier ( stock picking ) fungerar ej.
• Passiv (indexing) strategi är bäst.
42

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”
43

-- små företag har onormalt hög avkastning
(även när risken tagits hänsyn till).
Men den här har varit avtagande sedan 90 talet.
44

-- onormalt höga avkastningar i januari. Eller andra månad: februari, mars, april, … förklaring:
--Aktier med realisationsförlust i december månad (placerare söker efter orealiserade kursförluster för att minska skatten?)
45

-- de olika veckodagarna har olika stor genomsnittsavkastning (oftast måndag och tisdag har negativ avkastning och fredag har störst positiv avkastning).
46

-- företag med låga P/E tal ger en för hög avkastning när man tagit hänsyn till risk.
47

Kan anomalierna utnyttjas för att enkelt tjäna pengar (är marknaden ineffektiv)?
• ofta är anomalierna så små att om man tar hänsyn till transaktionskostnaderna och analyskostnaderna så försvinner vinsterna (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 (bara signifikanta resultat publiceras…) effektiv marknad trots anomalierna
48

• 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!
49

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”.
50

 Technical 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
51

Scatter Plot of NYSE Composite Index over two successive weeks.
Where’s the pattern?
52

• 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).
53

Coin Toss Game
Heads
$106.09
Heads
$103.00
$100.43
Tails
$100.00
Heads
$100.43
$97.50
Tails
$95.06
Tails
54

130
80
180
S&P 500 Five Year Trend?
or
5 yrs of the Coin Toss Game?
Month
55

130
80
230
S&P 500 Five Year Trend?
or
5 yrs of the Coin Toss Game?
180
Month
56

Market
Index
1,300
Actual price as soon as upswing is recongnized.
1,200
The market immediately moves to the perceived new price incorporating the new information of a upswing/good news. upswing
1,100
Cycles disappear once identified
Last
Month
This
Month
Next
Month
57

 Fundamental 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
58

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
59

Announcement Date
-6
-11
-16
19
14
9
4
-1
39
34
29
24
Days Relative to annoncement date
60

Existing 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
61

• Attitudes towards risk
• Beliefs about probabilities
62

63