Download MBAC 6060 Chapter 9

MBAC 6060
Chapter 9
Stock Valuation
1
Concepts and Skills:
• Stock prices depend on:
1. Future dividends
2. The growth rate of those dividends
• Use the Dividend Growth Model to compute stock
prices
• Understand how expected growth opportunities
affect prices
• PE Ratios
• Stock markets work
2
Chapter Outline:
9.1 The Value of Common Stock
• The Three Dividend Models
9.2
9.3
9.4
9.5
Parameters in the Stock Valuation Equation
Growth
The Price-Earnings Ratio
Stock Markets
3
9.1 Common Stock Valuation
Share of Ownership entitles you to:
1.
Share of Profits
– Either paid (dividends) or retained (and paid later)
Share of Equity (Equity = Assets – Liabilities)
2.
–
–
–
–
–
3.
If the company is liquidated
Which means the assets are sold
Creditors (including bond holders) are paid
What is left (the residual) goes to the shareholders
So shares of stock are sometimes called residual claims
Share of vote for Board of Directors
Stock is worth the PV the money that is received:
1.
2.
Dividends paid to shareholders while the stock is held
Cash from the sale of the stock at the end of the holding
period
4
So What is a Share of Stock Worth?
• It is worth the present value of the cash flows you
get from owning the stock
1. Dividends paid to share holders
2. The price from selling the stock
• So what will the dividends be?
–
We’ll talk about this in a minute
• What will the sale price be?
–
We’ll talk about this now…
5
What will the sale price of a Stock be?
• You get the dividends while you hold the stock
• Whomever you sell the stock to gets the dividends
while they hold the stock
• And whomever they sell it to gets the dividends
while they hold it
• And when that owner sells, the new owner gets the
next dividends…
• So the Sale Price at any point in time is equal to the
present value of the dividends that come after
• We can substitute for any sale price
– It equals the PV of all the subsequent dividends
– Because that is what the next owner is buying
6
The Price of a Stock
D3
D1
D2
D4
P0 




2
3
4
1  R  1  R  1  R  1  R 
• The price of a stock at any time equals:
–
The present value of all future cash flows (dividends)
• Its as if we just keep pushing back the sale time to
include the next dividend and then the next dividend
and so on…
• So instead of estimating a future sale price…
all we have to do is Estimate All Future Dividends
7
How can we estimate All Future Dividends?
• To calculate the current price (P0), we need to
know the sale price at some future time…
OR
• Since a future sale price is a function of
all the dividends that come after that time
• We can push back the sale price forever!
• We just need to estimate all future dividends
8
So all we need is an estimate of all dividends…
• How can we estimate all future dividends?
– We can’t!
• But we can make some simplifying
assumptions
• We’ll look at Three Assumptions about
dividends
– And these will be our “Base Cases”
• Then we will develop formulas to calculate a stock’s
price for the each of these three assumption…
9
Three Dividend Assumptions
• Our “Base Cases”
1. Dividends are Constant forever
–
Dividends are $0.50 each year forever
2. Dividends have Constant Growth forever
–
The first dividend is $0.50, which grows by 5% per year
forever
3. Dividends Grow at a High Rate for a few years
then slow to Constant Growth forever
– The first dividend is $0.50, which grows by 15% for 3
years, then growth decreases to 5% per year forever
10
Dividend Assumption One:
• Dividends are the constant forever:
D 0 = D 1 = D2 = …
– So all dividends are $1.00 forever
– Since all the D’s are the same,
we don’t need a subscript:
D0 = D1 = D2 = D = $1.00
Call this “Constant Dividends”
or “Zero Growth”
11
Dividend Assumption Two:
• Dividends grow at a constant rate (g):
•
D1 = D0(1 + g)
D2 = D1(1 + g)
D3 = D2(1 + g)
• In general: Dt +1 = Dt(1 + g)
• If the dividend at time 0 is $1.00 (D0 = 1.00)
• And dividends grow at 5% forever:
D1 = 1.00(1.05) = $1.05
D2 = 1.05(1.05) = 1.00(1.05)2 = $1.1025
D3 = 1.1025(1.05) = 1.00(1.05)3 = 1.331
Call this “Constant Dividend Growth”
12
Dividend Assumption Three:
•
•
•
•
Dividends grow at a high rate for a few years (g1)
Then slow to a Constant Growth Rate (g2) forever
Dividends start at $1, grow at 20% for 2 years and
then grow at 5% forever:
g1 = 20% and g2 = 5%
D1 = D0(1 + g1) = $1.00(1.20) = $1.20
D2 = D1(1 + g1) = $1.20(1.20) = $1.44
D3 = D2(1 + g2) = $1.44(1.05) = $1.512
D4 = D3(1 + g2) = $1.512(1.05) = $1.5876
Call this “Super-Normal Growth”
(20% growth can’t last for very long!)
13
Calculating P0 under Assumption 1:
• Dividends are Constant Forever:
D0 = D1 = D2 = D3 = D
(So D with no subscript)
D
D
D
D
P0 




2
3
4
1  R  1  R  1  R  1  R 
•
•
This is just the Present Value of a Perpetuity:
So the value of a stock with CONSTANT DIVIDENDS is:
D
P0 
R
14
The Constant Dividend Model:
• Dividends are constant forever
– Zero Dividend Growth
• Does this seem silly?
– Maybe not. If dividends grow just at the rate of inflation
– then in real terms, dividends are constant:
Let Nominal Dividend Growth = g = 3%
Let Expected Inflation = h = 3%
D 0 1  g  D 0 1.03
D1 

 D0
1 h
1.03
Real Dividends: D0 = D1 = D2 = D
15
Constant Dividends (Zero Growth) Example 1
• A stock will pay a dividend of $1.50 per year forever
• The required annual discount is 8%
P0 = D/R = $1.50/.08 = $18.75
• Note that we could also has written:
– The Inflation-Adjusted Dividend is $1.50 per year
– The Real Discount Rate is 8%
16
Constant Dividends Example 2
• A stock will pay a no dividends until time 4
• Then it will pay a constant dividend of $2 per year forever
• The required annual discount is 5%
0
1
2
3
4
5
…
$2
$2
1. Calc the price at t = 3 (P3) using the first dividend (D4):
P3 = D/R = $2/0.05 = $40.00
2. Then take the present value of P3 back to P0:
P0 = P3/(1+R)3 = $40/(1.05)3 = $34.55
• Why do we value at time 3 first? Because the dividends start
17
at time 4, and we have an easy formula to value at time 3
Review Question:
• A stock will pay no dividends until 10 years from now
– It’s first dividend will be at time 10
• It will then pay an annual dividend of $3 per year forever
• Calculate the current price (P0) of the stock assuming a
required return of 10%
18
Review Answer:
First Part:
• Value the stock at time 9 (P9)
• Using the time dividend at time 10 (D10) :
P9 = D10/R = $3/0.10 = $30
Second Part:
• Value the stock at time 0 (P0)
• By taking the PV the P9
P0 = P9/(1 + R)9 = $30/(1.10)9 = $12.72
OR: nper = 9, rate = 0.10, fv = 30
=pv(rate, nper, pmt, [fv], type]) = = -12.72
Why do we value at time 9?
• Because the CFs start at time 10 and we have an easy formula
to value the stock at time 9
19
Constant Dividends Example 3
Quarterly Dividends:
• Starting next quarter, a stock will pay a $0.30
dividend per quarter forever.
• The required return is 10% APR-Quarterly
– So we need to use the periodic rate = 0.10/4 = 0.025
• Calculate the current price:
P0 = D/R
D = $0.30
R = 0.10/4 = 0.025
P0 = D/R = 0.30/0.025 = $12.00
20
Review Question:
• Starting next quarter, a stock will pay a dividend of $0.50 per
quarter forever
• Calculate the current price of the stock assuming a required
return of 16% APR Quarterly
21
Review Answer:
R = 0.16/4 = 0.04
P0 = D/R = $0.50/0.04 = $12.50
Note that the question could have read:
• A stock will pay an annual dividend of $2.00 in equal
quarterly installments forever…
Instead of:
• A stock will pay a dividend of $0.50 per quarter
forever…
22
Now to Dividend Assumption Two:
• Dividends grow at a constant rate (g) forever:
• D1 = D0(1 + g)
D2 = D1(1 + g)
D3 = D2(1 + g)
• In general: Dt +1 = Dt(1 + g)
• We need a good formula for calculating the price (P0)
under this assumption:
• Here’s the Constant Dividend Growth Rate Formula
– Using with the dividend just paid (D0 ) or the next (D1):
D0 1  g 
P0 
R -g
D1
P0 
R -g
23
Derivation of the Constant Dividend Growth Rate Formula:
• Start with the general price formula:
D3
D1
D2
D4
P0 




2
3
4
1  r  1  r  1  r  1  r 
• Since D1 is a function of D0
and D2 is a function of D1 and so on…
• We can substitute D0 for all the future dividends:
D1 = D0(1 + g)
D2 = D1(1 + g) = D0(1 + g)2
D3 = D2(1 + g) = D0(1 + g)3
24
Derivation of the Constant Dividend Growth Rate Formula:
• Substitute D0 for all of the future dividends…
P0 
D3
D1
D2
D4




1  r  1  r 2 1  r 3 1  r 4
D 1  g  D 0 1  g  D 0 1  g  D 0 1  g 
P0  0




1  R 
1  R 2
1  R 3
1  R 4
2
3
4
• Factor out the D0:
 1  g  1  g 2 1  g 3 1  g 4

P0  D0 






2
3
4


1

R






1

R
1

R
1

R


• Rewrite the ratios with a single exponent
 1  g   1  g 2  1  g 3  1  g 4

P0  D0 





 
 
 


1

R
1

R
1

R
1

R










25
Derivation of the Constant Dividend Growth Rate Formula:
• It must be the case that g is less then R. Why?
– A company that grows faster than its discount rate will
have infinite value! We’ll talk more about this later…
• If g < R then (1 + g)/(1 + R) < 1
• Increasing the exponent decreases the value:
– If g = 0.05 and R = 0.10
– then (1.05)/(1.10) = 0.9545
(0.9545)2 = 0.91
(0.9545)3 = 0.87
(0.9545)4 = 0.83 …
26
Derivation of the Constant Dividend Growth Rate Formula:
• Increasing the exponent decreases the value:
– If g = 0.05 and R = 0.10 then (1.05)/(1.10) = 0.9545
(0.9545)2 = 0.91
(0.9545)3 = 0.87
(0.9545)4 = 0.83 …
• Adding more terms of decreasing value means the sum of the
terms in in the brackets “converges” to a finite value:
 1  g   1  g  2  1  g 3  1  g  4

 1  g 

P0  D0 

 
 
    D0 
 1  R   1  R   1  R   1  R 

 R  g 
 1  g  D0 1  g  D1
P0  D0 



R -g
R -g
R - g
27
Constant Dividend Growth Model
Also called the Gordon Growth Model or the Dividend Growth Model (DGM)
We have two versions:
1. The price at time 0 (P0) as a function of the current dividend (D0)
•
Which was just paid an instant ago, so we don’t get that dividend!
2. The price at time 0 (P0) as a function of the dividend in 1 period (D1)
D0 1  g 
P0 
R -g
•
•
D1
P0 
R -g
We can also value the stock at any time t in the future (Pt)
Either as a function of the dividend at time t (Dt) or time t+1 (Dt+1):
D t 1  g 
Pt 
R -g
D t 1
Pt 
R -g
28
Constant Dividend Growth Model
• Is constant growth at g a silly assumption?
– Maybe not.
• If the company is in a mature industry, growth maybe
at the rate of population growth
• Think about the Sustainable Growth Rate:
(ROE x b)/(1 – ROE x b)
• If a firm has constant ROE and plowback ratio, then
growth will be constant.
29
Example: Constant Dividend Growth
•
•
•
•
A company just paid an annual dividend of $0.50
The dividend will increase by 2% per year (forever)
The required return on this stock is 15%
Calculate the price:
– Note that the question states the dividend was “just paid”
– This means we are given D0
D0 = $0.50
g = 2%
R = 15%
P0 = D0(1+g)/(R-g) = 0.50(1.02)/(0.15 - 0.02)= $3.92
30
Example 2: Constant Dividend Growth
•
•
•
•
A company will pay a dividend of $0.40 in one year
The dividend will increase by 3% per year (forever)
The required return on this stock is 13%
Calculate the price:
– Note that the question states “will pay”
– This means we are given D1
D1 = $0.40
g = 3%
R = 13%
P0 = D1/(R - g) = 0.40/(0.13 - 0.03) = $4.00
31
Review Question:
• A company just paid a dividend of $1.00 and it will
pay its next dividend in exactly one year
• The dividends will increase by 4% per year (forever)
• The required return on this stock is 10%
• Calculate the price.
32
Review Answer:
D0 = $1.00
g = 4%
R = 10%
D1 = D0(1 + g) = $1.00(1.04) = $1.04
P0 = D1/(R - g) = 1.04/(0.10 - 0.4) = $17.33
33
Example 3:
• A company will pay a dividend of $4 next
period
• Dividends will to grow at 6% per year
• The required return is 16%.
• What is the current price?
P0 = D1/(R - g) = 4/(0.16 - 0.06) = $40
34
Example Continued:
• What is the price expected to be in year 4?
(Use D4 to calculate P4)
D4 = D1(1 + g)3 = $4(1+.06)3 = $4.76
P4 = D4(1 + g) /(R – g)
P4 = $4.76(1.06) /(0.16 – 0.06) = $50.50
• You can also use D5 to calculate P4
D5 = D1(1 + g)4 = $4(1+.06)4 = $5.05
P4 = D5/(R – g)
P4 = $5.05/(0.16 – 0.06) = $50.50
35
Example Continued:
• What is the 4 yr return on the price of the stock?
P0 = $40 and P4 = $50.50
FV = PV(1 + R)t
Return = (FV/PV)(1/t) – 1 = (P4/P0)(1/t) – 1
= ($50.50/$40)1/4 – 1 = 0.06 =6%
OR: nper = 4; pv = -40; fv = 50.50
=rate(nper, pmt, pv, [fv], [type])
=rate(4,0,-40,50.50) = 0.06 = 6.00%
• Recall g = 6%
• The price grows at the same rate as dividend growth36
Example Continued:
What is the Return from t = 4 to t = 5?
First we need to calculate P5:
P5 = D6/(R – g) = $5.05(1.06)/(0.16 – 0.06)
= $5.353/0.1 = $53.53
Return = P5/P4 – 1
Return = $53.53/$50.50 – 1 = 0.06 = 6%
Let’s see why 
37
Example Continued:
At what rate do prices grow?
In other words: What is the Capital Gain Rate in any year?
(some algebra):
D1
P0 
R -g
and
D1 1  g 
P1 
R -g
D1 1  g 
P1
R -g
Return   1 
 1  (1  g )  1  g
D
P0
1
R -g
• So the dividend growth rate (g) is both:
1. The Dividend Growth Rate
2. The Capital Gain Rate
38
More about the Constant Dividend Growth Model:
P0 = D1/(R – g)
• If g > R in the above equation, then P0 is negative
• So for the model to work, it must be the case that R > g
• Note: If g > R, then (1+g)/(1+R) > 1
• And then we couldn’t have simplified the equation on slide 29
• But what if growth does exceed the discount rate?
– At least for a short period of time…
– Then we will have to use another model (Assumption 3)
• Eventually growth will have to slow…
– Because if g > R forever, the stock has infinite value:
– If dividends (and therefore prices) grow faster than the discount rate
– Then the PV of each successive term is larger than the last
– The 100th dividend is worth more in PV terms than the 1st dividend
39
Dividend Assumption 3: High Growth
• Dividend Growth will be high for a while
– Maybe even higher than R
• Then growth will decrease and become constant
forever
• Calculate the price in pieces:
1. Growing Annuity
2. The PV of a growing perpetuity
40
Example:
• A stock just paid a dividend of $2.00
• Dividend Growth will be 8% for 3 years
• After that, Dividend Growth will be 4% forever
• The required return in 12%
• Calculate the current price
The price at time zero is:
1. A 3 year, 8% Growing Annuity discounted at 12%
2. A 4% Growing Perpetuity, discounted at 12% first to time
three, then to time zero.
g 1 =8%
0
1
2
g 2 = 4%
3
4
5
6
…
$2.000
$2.160
$2.333
$2.519
$2.620
$2.725
$2.834
41
Part 1: Growing Annuity
• A 3 year, 8% Growing Annuity discounted at 12%
D0 (1  g1 )  (1  g1 )T 
P0 
1 
T 
R  g1  (1  R ) 
D0 = 2.00; R = .12; g1 = 0.08; T = 3
2.00(1.08)  (1.08) 3 
P0 
 5.58
1 
3
0.12  0.08  (1.12) 
42
Growing Annuity in Excel:
A 3 year, 8% Growing Annuity discounted at 12%
PV of a Growing Annuity in Excel:
=pv((1+R)/(1+g)-1, nper, -pmt)
R = 0.12; g = 0.08; nper = 3; pmt = D0 = 2.00
=pv(1.12/1.08-1,3,2) = 5.58
43
Part 2: Growing Perpetuity
• A 4% Growing Perpetuity discounted at 12%
• Starting in year 3
D4
P3 
R  g2
• D4 = 2.00(1 + g1)3(1 + g2) = 2.00(1.08)3(1.04) = 2.62
• R = 0.12; g2 = 0.04
2.62
P3 
 32.75
0.12  0.04
P3
32.75
P0 

 23.31
3
3
(1  R )
(1.12)
44
Example Continued:
• A stock just paid a dividend of $2.00
• Dividend Growth will be 8% for 3 years
• After that, Dividend Growth will be 4% forever
• The required return in 12%
The price at time zero is:
1. A 3 year, 8% Growing Annuity discounted at 12%
2. A 4% Growing Perpetuity, discounted at 12% first
to time three, then to time zero.
P0 = $5.58 + $23.31 = $28.89
45
Review Question:
•
•
•
•
•
A stock’s just paid a dividend of $1.
The dividend will grow at 20% for 5 years
Then grow at 5% forever.
The required discount rate is 10%.
Calculate the price of the stock.
• Given: g1 = 20%, g2 = 5%, R = 10%, D0 = $1.00
46
Review Answer:
• Part 1: 5 year, 20% Growing Annuity discounted at
10%
=pv((1+R)/(1+g)-1, nper, -pmt)
g = 20%; R = 10%; nper = 5; pmt = 1
=pv(1.1/1.2-1,5,-1) = 6.54
• Part 2: 5% Growing Perpetuity discounted at 10%, starting
in year 5, discounted to time 0
PV = D6/(R – g2) x 1/(1 + R)5
D6 = (1 + g1)5 x (1 + g2) = 1.00(1.20)5 x (1.05) = 2.6127
PV = 2.6127/(0.10 – 0.05) x 1/(1.10)5 = 32.45
P0 = 6.54 + 32.45 = 38.99
47
9.2 The Parameters (“g” and “R”)
Look at a Stock’s Growth Rate
• How fast will a company grow?
• Without a change financial policy or an expansion
into new business
• The firm will grow from Retained Earnings
• Multiplied by the Return on Equity (ROE)
– Also assume constant ROA and D/E
• g = Retention Ratio x ROE
• g = b x ROE
48
Derivation of g = b x ROE
• Earnings next year (NI1) equals
• Earnings this year (NI0)
• Plus the Income on the Retained Earnings (RE0 x ROE)
NI1 = NI0 + RE0 x ROE
NI1/NI0 = NI0/NI0 + (RE0 x ROE)/ NI0
NI1/NI0 = 1 + g
NI0/NI0 = 1
RE0/NI0 x ROE = Retention Ratio x ROE = b x ROE
1 + g = 1 + b x ROE
g = b x ROE
49
Compare “g” to Sustainable Growth Rate
g = b x ROE
SGR = b x ROE/(1 – b x ROE)
The “g” formula assumes Beginning Equity
The “SGR” formula assumes Ending Equity
• If you use Ending Equity for the SGR ROE,
• As we did in the Chipotle Case
• Then SGR = g
• See page 74 of the text
50
Look at a Stock’s Required Return
• The required return is also called the discount rate
• So solve for R and see what the components are:
P0 = D1/(R – g)
R = D1/P0 + g = Dividend Yield + Growth Rate
D1/P0 = Dividend Yield
g = Growth Rate
• So the Required Return is the sum of the Dividend Yield and
the Growth Rate
– Note that if D is quarterly, then g is quarterly and R is
quarterly
51
Look at a Stock’s Required Return (Cont)
• Recall the growth rate (g) is also the rate at which prices
increase
• So g is also the Capital Gain Rate
R = D1/P0 + g = Dividend Yield + Capital Gain Rate
• So the Required Return is also the sum of the Dividend Yield
and the Capital Gain Rate
52
Required Return Example:
•
•
•
•
`
The market price for a stock is $40 (P0 = $40)
The next (annual) dividend will be $1.40 (D1 = $1.40)
You expect the dividends to grow by 7% forever (g = 0.07)
Calculate the Required Rate of Return:
R = D1/P0 + g = $1.40/$40 + 0.07 = 0.105 = 10.50%
R is also the return from holding the stock.
• Verify this:
• Calculating the price in one year :
P1 = D1(1 + g)/(R – g) = $1.40(1.07)/(0.105 – 0.07) = $42.80
• The Total Return Cap Gain plus the Dividend
Total Return = (P1 + D1)/P0 – 1 = ($42.80 + 1.40)/$40 – 1 = 10.50% = R
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Required Return Example 2:
•
•
•
•
`
Same stock but now the market price for the stock is $35 (P0 = $35)
The next (annual) dividend will still be $1.40 (D1 = $1.40)
You still expect the dividends to grow by 7% forever (g = 0.07)
What has happened to the return from holding the stock?
Calculate the Required Rate of Return:
R = D1/P0 + g = $1.40/$35 + 0.07 = 0.11 = 11.00%
– Price decreased, the return from holding the stock increased
• Now you are only paying $35 for the same $1.40 dividend.
• Dividend yield was $1.40/$40 = 3.5%
• Dividend yield is now $1.40/$35 = 4.0%
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Review Question:
• A stock’s dividend yield is 6%
• Its dividend growth rate is 4% forever.
• Calculate the required return of the stock.
55
Review Answer:
• Dividend Yield = D1/P0 = 0.06
• Growth Rate = g = 0.04
• R = D1/P0 + g = 0.06 + 0.04 = 0.10 = 10%
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9.3 Growth Opportunities
• Opportunities to invest in positive NPV projects
• The value of a firm can be thought of as the sum of:
1. The value of a firm that pays out 100% of its
earnings as dividends
PLUS
2. The net present value of the growth opportunities
EPS
P
 NPVGO
R
(A firm that pays out 100% is called a cash cow)
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Growth Opportunities
• Recall: P0 = D1/(R – g)
• g = ROE x b
• If b = 0 then g = 0 and D1 = EPS1
• For b = 0  P0 = D1/(R – g) = EPS1/R
• If the observed Price is greater than EPS/R
• Then the market must believe NPVGO > 0
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NPV of Growth Opportunities
𝐸𝑃𝑆
𝑃=
+ 𝑁𝑃𝑉𝐺𝑂
𝑅
𝐸𝑃𝑆
𝑁𝑃𝑉𝐺𝑂 = 𝑃 −
𝑅
Example:
• The market price of a stock (P) is $20.
• Its forecast EPS is 1.50
• Its required rate = 10%
NPVGO = P – EPS/R = $20 – 1.50/.10 = $20 – $15 = $5
– If the firm never does anything new
– It will generate $1.50 in cash forever
– The PV of that Cash Cow is $15
– The difference between $20 and $15 must be the NPVGO
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Growth Opportunities
𝐸𝑃𝑆
𝑃=
+ 𝑁𝑃𝑉𝐺𝑂
𝑅
EPS = what the company is currently earning
EPS/R = PV of a perpetuity of current earnings
Price = PV of Current Earnings + NPV of Opportunities
• So should the company differ dividend payments and
invest in new projects?
Pay Dividends or Retain Earnings? 
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Pay Dividends or Retain Earnings?
• Example: Assume EPS = $5 and R = 10%
• So without RE  P = 5/.1 = $50
First Assume b = 40% and ROE = 15%
Then g = .4 x .15 = 6%
• D1 = EPS(1 – b) = $5(1 – 0.40) = $3
• P0 = D1/(R – g) = 3/(.1 – 0.06) = $75
• Retaining 40% to invest in 15% ROE projects increases value
• Price increases from $50 to $75
So retain earnings if ROE > R
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Pay Dividends or Retain Earnings?
• Example: Assume EPS = $5 and R = 10%
• So without RE  P = 5/.1 = $50
Now Assume b = 40% and ROE = 10%
Then g = .4 x .10 = 4%
• D1 = EPS(1 – b) = $5(1 – 0.40) = $3
• P0 = D1/(R – g) = 3/(.1 – 0.04) = $50
• Retaining 40% to invest in 10% ROE projects DOES NOT
increase value
• Price stays at $50
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Pay Dividends or Retain Earnings?
• Example: Assume EPS = $5 and R = 10%
• So without RE  P = 5/.1 = $50
Now Assume b = 40% and ROE = 5%
Then g = .4 x .05 = 2%
• D1 = EPS(1 – b) = $5(1 – 0.40) = $3
• P0 = D1/(R – g) = 3/(.1 – 0.02) = $37.50
• Retaining 40% to invest in 5% ROE projects lowers value
• Price drops to $37.50
So do not retain earnings if ROE < R
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Pay Dividends or Retain Earnings?
• If the firm can invest in projects that earn more than
the required rate of return
• If ROE > R
• Then Retain Earnings
• (But we already new that)
What should the plowback ratio be?
• If it is too big, then ROE will decrease
• Why?
• Scale?
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9.4 Price-Earnings Ratio
• Price/EPS = PE Ratio
EPS
P
 NPVGO
R
P
1 NPVGO
PE 
 
EPS R
EPS
PE is:
• Increasing in NPVGO (Growth Opportunities)
• Decreasing in R (a function of risk)
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PE Ratio
– Commonly used as a relative price measure
– S&P500 PE ratio from Robert Shiller’s website:
45
18
16
1929
35
Price-Earnings Ratio (CAPE)
2000
1981
40
30
25
20
14
1901
23.77
1966
Price-Earnings Ratio
12
10
20
8
1921
15
6
10
4
Long-Term Interest Rates
5
0
1860
2
1880
1900
1920
1940
Year
1960
1980
2000
0
2020
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Long-Term Interest Rates
50
PE Ratio
Another common usage: Calculate Expected Price
Given a company’s PE ratio (say 20x)
1. Estimate futures earnings:
Expected Earnings = Expected Mkt Size x Mkt Share x PM
2. Expected Stock Price = Expected Earnings x PE
67
Review Question:
• A company is in a growth industry
• The Market size is $200m and growing at 10% per
year
• Company’s Market share is 15% but will be 20%
• PM is 30%
• Current PE Ratio is 20x
• Number of Shares is 10 million
Calculate the Expected Price
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Review Answer:
Market size = $200; Market Growth = 10%
Market Share = 20%; PM = 30%; PE = 20x
•
•
•
•
•
Expected Market Size = $200(1.1) = $220m
Expected Sales = Mkt Size x Mkt Share = $220 x .20 = $44m
Expected NI = Expected Sales x PM = $44 x 30% = $13.2m
Expected EPS = $1.32
Expected Price = PE x Expected EPS = 20 x $1.32 = $26.4
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Common Stock versus Preferred Stock
Preferred Stock (usually) has:
• No Voting Rights
• Preference over common stock in Receiving Dividends
• Preference over common in Distribution of Assets in the Event of
Liquidation
– Preferred stock holders are after bond holders and other creditors but ahead of
common stock holders
Common Stock (usually) has:
• The Right to Vote for Board of Directors (one share, one vote)
– Recall the Board Hires the Management
• No Preference in Receiving Dividends
• No Preference in Distribution of Assets in the Event of Liquidation
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Common Stock Voting Rights
• Proxy Voting: Giving someone else your vote
– If Management is Bad:
•
•
•
•
•
•
A group of shareholders may try to remove them
But first must replace the board
Either buy enough shares to vote in a new board
Or try to get other shareholders to vote with them
This is called giving your proxy
This is called a “Proxy Fight”
– If management is doing a really bad job, share price drops
– Cheaper to buy enough shares to vote out board and fire managers
• Sometimes common stocks have different voting rights
–
–
–
–
–
Original owners don’t want to give up voting rights
Issue shares with less voting rights
And keep shares with higher voting rights
Google “Class A” owned by founders: 10 votes per share
Google “Class B” owned by the public: 1 vote per share
71
Common Stock Dividends
• Dividends are allocated proportionally to share
ownership
• Dividends are distributed Profits
• Must be paid from current or past (retained) earnings
– If a dividend is paid that exceeds current or retained
earnings, then it is not a dividend
– It is a return of capital to owners
• Dividends do not need to be paid
– Interest and debt payments do need to be paid
– Although after dividends are declared by the board,
dividend become a short term liability (Divs Payable)
72
Preferred Stock
• Preferred stock is usually issued at $100 par value
• Dividends are fixed and expressed as a percent of par
– 5% preferred pays $5 per year (really $1.25 quarterly)
• Preferred Dividends are paid from profits first
– If anything is left, common stock holders get theirs
• Preferred Dividends are (usually) cumulative
– If dividends are missed, they must be paid before common
dividends are paid
• Sometimes Preferred can be converted to common
– Convert-Preferred often used in new-venture financing
– How is this different from convertible debt?
73
9.5 The Stock Markets
• Dealers vs. Brokers
– Dealers take possession of the stocks (car dealer)
– Brokers link buyers and sellers (real estate broker)
• New York Stock Exchange (NYSE)
–
–
–
–
Members: Brokers and Specialists
Operations: Brokers receive orders, bring them to the Specialist’s post
Specialists act as Brokers or Dealers
NYSE Listing Requirements
• NASDAQ
–
–
–
–
Not a physical exchange, but a computer-based quotation system
Network of Dealers connected by computers and phones
Tech-heavy NASDAQ (Why?)
NASDAQ Listing requirements
Descriptions of NYSE and NASDAQ pages 288-290
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The Bid-Ask Spread
• Bid Price
– The price someone will pay for a stock
– What you will get from selling the stock
– Example $40.50
• Ask Price (aka Offer Price)
– The price someone wants to get for the stock
– What you will pay to buy the stock
– Example $40.60
• The difference between them is the Bid-Ask Spread
– $40.60 – $40.50 = $0.10
– It is a measure of trading costs
75