# Money and Banking

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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 Dividend-Discount 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:
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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 re-written 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 =
i-g
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
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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
\$80-160
8-16%
12%
4%
50%
50%
\$50
\$30-110
6-22%
14%
8%
30%
70%
\$70
\$10-90
3.3-30%
16.67%
13.3%
20%
80%
\$80
\$0-80
0-40%
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
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