Transcript FI3300 Corporation Finance

FINC3131
Business Finance
Chapter 9:
Stocks and Their Valuation
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Learning objectives
1. Compute the price of a preferred stock.
2. Compute the price of common stock under
various assumptions about dividend growth.
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Preferred stock
1. Hybrid security.
2. Like bonds, preferred stockholders
receive a fixed dividend that must be
paid before dividends are paid to
common stockholders.
3. However, companies can omit
preferred dividend payments without
fear of pushing the firm into
bankruptcy.
Common Stock
1.
2.
3.
4.
5.
Represents ownership
Ownership implies control
Stockholders elect directors
Directors elect management
Management’s goal: Maximize the
stock price
Dividend growth model
Value of a stock is the present value of the
future dividends expected to be generated
by the stock.
D3
D1
D2
D
P0 


 ...
1
2
3
(1  rs )
(1  rs )
(1  rs )
(1  rs )
^
Preferred stock
Pays a fixed dividend forever.
Price of preferred stock is simply the present value
of a perpetuity.
Preferred stock
Price of
preferred stock
Pps
D

rp
Required rate of return on preferred stock.
dividend
Required rate of
return on preferred
stock/ cost of
capital for preferred
stock
D
rp 
Pps
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Common stock
For common stock, the future cash flows are:
 Dividends
 Selling price
These cash flows are highly uncertain.
 To find the value of common stock, we make
assumptions about how dividends evolve in
the future. We look at 3 set of assumptions:
1. Constant dividend stream
2. Dividends grow at constant rate (constant
dividend growth model)
3. Non-constant dividend growth
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Constant dividend stream





Same amount of dividend is paid for ever.
Cash flow stream resembles a perpetuity.
Thus, we value the common stock in the same way as
we value the preferred stock.
Common
Common stock price, Pe
stock
D
Pe 
re
Cost of equity capital, re
D
re 
Pe
dividend
Cost of equity
capital or
required rate
of return on
equity
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Dividends grow at constant rate 1
1. Assume that dividends grow at a
constant rate, g, per period forever.
2. Given this assumption, the price of
common stock equals
D0 = Dividend
that the firm just
paid
D0 1  g 
D1
Pe 

re  g
re  g
Required rate
of return on
equity
Don’t panic.
D1 = D0(1 + g)
Dividend
growth rate
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Dividends grow at constant rate 2
Useful properties.
1. All other things unchanged,
•
•
•
If D0 increases (decreases), Pe increases
(decreases).
If g increases (decreases), Pe increases
(decreases).
If re increases (decreases), Pe decreases
(increases).
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Dividends grow at constant rate 2
1. By rearranging the above equation, we
can find the required rate of return on
equity
D1
Capital gains
re 
g
Required rate
yield
of return on
Pe
equity
Dividend yield
2. For the constant growth model to work,
re > g.
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Constant growth problems 1
 Jarrow Company will pay an annual dividend
of $3 per share one year from today. The
dividend is expected to grow at a constant rate
of 7% permanently. The market requires 15%
What is the current price of the stock (to 2
decimal places)?
In this question D1 is already given to you.
Verify that Price = $37.5
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Constant growth problems 2
 Johnson Foods Inc. just paid a dividend of $10
(i.e., D0 = 10.00). Its dividends are expected to
grow at a 4% annual rate forever. If you
require a 15% rate of return on investments of
this risk level, what is Johnson Foods’s current
stock price? (to 2 decimal places)
Straightforward application of price formula.
Verify that price = $94.55
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Constant growth problems 3
 The price of a stock in the market is $62. You
know that the firm has just paid a dividend of
$5 per share (i.e., D0 = 5). The dividend growth
rate is expected to be 6 percent forever. What
is the investors’ required rate of return for this
stock (to 2 decimal places)?
Use re = (D1/P) + g.
Verify that re = 14.55%
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Constant growth problems 4
 A firm is expected to pay a dividend of
$5.00 on its stock next year. The price of
this stock is $40 and the investor’s
required rate of return is 20%. The firm’s
dividends grow at a constant rate. What
is this constant dividend growth rate (g)?
use re = (D1/P) + g
Verify that g = 7.5%
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Constant growth problems 5
 In order to use the constant dividend growth
model to value a stock it must be true that:
a. The required rate of return is less than the expected
dividend growth rate.
b. The expected dividend growth rate is greater than zero.
c. The next dividend (D1) is expected to be greater than
$1.00.
d. The expected dividend growth rate is less than the
required rate of return.
Which statement is correct?
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Non-constant dividend growth 1
1. With this assumption, dividends grow at
different rates for different periods of
time. Eventually, dividends will grow at a
constant rate forever.
2. Time line is very useful for valuing this
type of stocks.
3. To value such stocks, also need the
constant growth formula.
4. Best way to learn is through an example.
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Non-constant dividend growth 2

ABC Co. is expected to pay dividends at the end of the
next three years of $2, $3, $3.50, respectively. After
three years, the dividend is expected to grow at 5%
constant annual rate forever. If the required rate of
return on this stock is 15%, what is the current stock
price?
$2.00
T=0
T =1
Dividends grow
at 5% forever
$3.00 $3.50
T=2
T=3
T=4
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What to do?
1. Use constant growth formula to find
stock price at the end of year 3. Call this
stock price P3.
2. Add P3 to dividend received at t=3. This
sum is the cash flow for t=3. Find PV of
this cash flow.
3. Find PV of dividends at t=1, t=2.
4. Current stock price = sum of 2 and 3.
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Apply the method to
find ABC’s stock price
1. P3 = (3.5 x (1.05))/(0.15 – 0.05) = 36.75
2. At t=3, cash flow is 36.75 + 3.50 = 40.25
Current stock price, P0
2
3
40.25
P0 


 $30.47
2
3
1.15 1.15
1.15
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If D0 = $2 , r=13% and g = 30% for 3
years before achieving long-run growth
of 6%, what is the PV?
1. Can no longer use just the constant
growth model to find stock value.
2. However, the growth does become
constant after 3 years.
0 r = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
P$ 3 
46.114
54.107
^
= P0
4.658
0.13  0.06
 $66.54
Another type of non-constant
growth problem
Malcolm Manufacturing, Inc. just paid a $2.00
annual dividend (that is, D0 = 2.00). Investors
believe that the firm will grow at 10% annually for
the next 2 years and 6% annually forever
thereafter. Assuming a required return of 15%,
what is the current price of the stock (to 2 decimal
places)?
Use timeline to ‘see’ the problem better.
Verify that stock price = $25.29
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Summary
1. Find the price/ present value of equity
securities
2. Consols, preferred stock are valued using the
same techniques.
3. Common stocks are valued under 3 different
assumptions about dividends
•
•
•
Constant dividends
Dividends grow at constant rate
Dividends grow at different rates
4. Assignment:
problems: 9-1 9-2 9-3 9-6 9-7 9-8 9-11 9-13 9-14
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