Transcript Common Stock Valuation

Theory of Stock Valuation
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Same theory as bond valuation
Find PV of future cash flows
Use investor’s required rate of return as
the discount rate in finding PV
Cash Flows from Owning Stock
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Dividends
Capital gain (loss) from selling at a
higher (lower) price than you paid for
the stock
Difficulties in Valuing Stock
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1) Future cash flows not known
2) Stock has no maturity - infinite life of
corporation
3) No way to easily observe the rate of
return that the market requires
Stock Valuation Symbols
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D = dividend
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Subscript tells when dividend is expected to
be paid/received
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P = price
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Subscript tells when price is expected to be
paid/received
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Kc = investor’s required rate of return
Example 1
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D1 = $1.00
D2 = $1.25
D3 = $1.50
P3 = $50
If you require a 10% rate of return, what
is the most you will pay for this stock?
Using Financial Calculator
P/Y
C/Y
N
I/Y
PV
PMT
FV
1
1
1
10
-.9090 0
1.00
1
1
2
10
-1.033 0
1.25
1
1
3
10
-1.127 0
1.50
1
1
3
10
-37.57 0
50.00
Sum PVs to get -40.63
$40.63 is max price you are willing to pay for
this stock if you require a 10% rate of return.
Pay more than $40.63 → Return < 10%
Pay less than $40.63 → Return > 10%
BUT…future stock cash flows
are not known with certainty
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Future dividends aren’t known with
certainty
Dividends may be estimated, but it will
only be an estimate
Future selling price isn’t known with
certainty
How to overcome these problems?
Future Selling Price
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Can prove mathematically that it
doesn’t matter that we don’t know what
we can sell a stock for in the future
Need to use mathematical formula for
finding PV to prove this point
Mathematical Formula for
Finding PV
PV = FV x (1+i)-n
 PV = 1.00(1.10)-1 + 1.25(1.10)-2 +
1.50(1.10)-3 + 50(1.10)-3
 P0 = $40.63 (same answer as we got
using a financial calculator)
Theoretical Determination of
Future Selling Price
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The future selling price (Pn) is based on what
the next investor will pay for the stock.
The next investor is valuing the stock based
on the present value of his/her expected
future dividends and future selling price.
The next investor follows the same process,
etc., etc., etc.
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Since stock never matures, the actual
determination of the next selling price
can be put off indefinitely.
If the actual determination of the future
selling price is pushed far enough out
into the future, its present value will
eventually approach zero.
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With PV of future selling price dropping off to
zero, value of stock becomes the PV of its
dividend stream.
The question now becomes, how can you find
the PV of an unending stream of dividends?
Can do it if you make assumptions about how
dividends grow from year to year.
Constant Dividend (No Growth)
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P0 = Dp/Kp
P0 = Intrinsic value = Price today
Dp = Preferred Dividend (fixed amount,
doesn’t change)
Kp = Required rate of return on P/S
Preferred stock is an example where
the dividend is constant
Example 2
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If you require a 12% rate of return, what
is the maximum price you will pay for a
share of preferred stock that pays a
$1.25 annual dividend?
P0 = $1.25/.12 = $10.42
Dividends Growing at a Constant
Growth Rate
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P0 = D1/(Kc - g)
P0 = Intrinsic value = Price today
D1 = Dividend expected 1 year from
now
D1 = Last dividend paid x (1 + g)
Kc = Required rate of return
g = Constant annual dividend growth
rate
Example 3
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How much would you pay for a share of
common stock if the last dividend paid
was $2.00 per share, dividends are
expected to grow at a constant annual
rate of 5%, and you require a 10% rate
of return?
P0 = ($2 x 1.05)/(.10 - .05) = $42
What if a company isn’t paying
dividends?
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Just because a company is not currently
paying dividends doesn’t mean that they
never plan to.
Estimate when first dividend will be paid
and at what rate dividends will grow.
Find price for year prior to first dividend.
Discount future price back to present.
Example 4
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You estimate that a company that is not
currently paying dividends will pay a $5
dividend per share at the end of 5 years
and that dividends will grow at a
constant annual rate of 8% thereafter. If
you require a 12% rate of return, what is
the maximum price you will pay for the
stock today?
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P4 = D5/Kc-g
P4 = $5/(.12-.08) = $125
P0 = P4(1 + Kc)-4
P0 = $125(1+.12)-4 = $79.44 maximum
price you are willing to pay today
Valuing Non-public Corporations
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Twitter article
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Estimate total revenue
# users = 250 M by 2013
Revenue per user = $2 by 2013
250 M * $2 = $500 M total rev by 2013
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Borrow ratios from comparable firm
Google’s profit margin = .27 and
Google’s PE = 20
.27 * $500 M = $135 M profit
$135 * 20 = $2.7 B total value (as
measured by price * # shares)
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Discount future value back to present
Use 20% as appropriate rate for small,
risky, high growth company
N = 4; I/Y = 20; PMT = 0; FV = $2.7B
PV = $1.3 Billion estimated value for
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