

Money
& Banking MGT411
VU
Lesson
19
VALUING
STOCKS
Valuing
Stocks
Fundamental
Value and Dividend Discount
Model
Risk
and Value of Stocks
Valuing
Stocks
People
differ in their opinions of
how stocks should be
valued
Chartists
believe that they can
predict changes in a stock's
price by looking at patterns in
its
past
price movements
Behavioralists
estimate the value of stocks
based on their perceptions of investor
psychology
and
behavior
Others
estimate stock values based on a detailed
study of the fundamentals, which can
be
analyzed
by examining the firm's financial
statements.
In
this view the value of a
firm's stock depends both on
its current assets and
estimates of its
future
profitability
The
fundamental value of stocks
can be found by using the
present value formula to
assess how
much
the promised payments are worth, and
then adjusting to allow for
risk
Chartists
and Behavioralists focus instead on estimates of the
deviation of stock prices
from
those
fundamental values
Fundamental
Value and the DividendDiscount
Model
As
with all financial instruments, a stock
represents a promise to make monetary
payments on
future
dates, under certain
circumstances
With
stocks the payments are in the
form of dividends, or distributions of
the firm's profits
The
price of a stock today is equal to the
present value of the payments the
investor will receive
from
holding the stock
This
is equal to
The
selling price of the stock in one
year's time plus
The
dividend payment received in the
interim
Thus
the current price is the present
value of next year's price
plus the dividend
If
Ptoday is the purchase price of stock,
Pnext year
is the sales
price one year later
and Dnext
year is
the
size
of the dividend payment, we can
say:
D
P
Next
year
+
next
year
=
P
today
(1
+
i
)
(1
+
i
)
What
if investor plans to hold stock for
two years?
D
D
nex
P
+
In
two
P
toda =
+
yea
In
two
(1
+
i)2
(1
+
i
)
(1
+
i)2
Generalizing
for n years:
62
Money
& Banking MGT411
VU
D
D
=
+
+
.....
+
_
year
in
_
two
_
years
next
P
today
(1
+
i
)
(1
+
i
)
2
D
Pn
+
n
_
years
_
_
now
_
years
_
_
now
from
from
(1
+
i
)
(1
+
i
)
n
n
If
a stock does not pay
dividends the calculation can
still be performed; a value of
zero is used
for
the dividend payments
Future
dividend payments can be estimated
assuming that current
dividends will grow at
a
constant
rate of g per year.
D
next
_
year
=
D
today (1 +
g
)
For
multiple periods:
(1
+
g
)n
D
years from now
=
D
n
today
Price
equation can now be
rewritten as:
(1
+
g
)
(1
+
g
)
2
D
D
today
today
=
+
+
.....
+
P
today
(1
+
i
)
(1
+
i
)
2
(1
+
g
)
n
D
Pn _
years
_
from
_
now
today
+
(1
+
i
)
n
(1
+
i
)
n
Assuming
that the firm pays dividends
forever solves the problem of
knowing the selling
price
of
the stock; the assumption allows us to treat the stock as we
did a consol
D
today
Ptoday =
ig
This
relationship is the dividend discount
model
The
model tells us that stock
price should be high
when
Dividends
are high
Dividend
growth is rapid, or
Interest
rate is low
Why
stocks are risky?
Stockholders
receive profits only after the
firm has paid everyone
else, including
bondholders
It
is as if the stockholders bought the firm by
putting up some of their own
wealth and
borrowing
the rest
This
borrowing creates leverage,
and leverage creates
risk
Imagine
a software business that
needs only one computer
costing $1,000 and purchase
can be
financed
by any combination of stocks
(equity) and bonds (debt).
Interest rate on bonds is
10%.
Company
earns $160 in good years and
$80 in bad years with equal
probability
63
Money
& Banking MGT411
VU
Table:
Returns distributed to debt and equity
holders under different financing
assumptions
Percent
Percent
Required
Payment
to Equity
Expected
St.
Dev. of
Equity
(%) Debt (%) payments on
equity
Return
Equity
Equity
Return
10%
bonds
holders
(%)
Return
(%)
100%
0
0
$80160
816%
12%
4%
50%
50%
$50
$30110
622%
14%
8%
30%
70%
$70
$1090
3.330%
16.67%
13.3%
20%
80%
$80
$080
040%
20%
20%
If
the firm were only 10%
equity financed, shareholders' liability
could come into
play.
Issuing
$900 worth of bonds means
$90 for interest payments.
If
the business turned out to be bad, the
$80 revenue would not be
enough to pay the interest
Without
their limited liability, stockholders
will be liable for $10
shortfall. But actually,
they
will
lose only $100 investment
and not more and the firm goes
bankrupt.
Stocks
are risky because the
shareholders are residual claimants.
Since they are paid last,
they
never
know for sure how
much their return will
be.
Any
variation in the firm's revenue flows
through to stockholders dollar for
dollar, making their
returns
highly volatile
64
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