08model
10/6/2009 8:16
12/2/2002
Chapter 8.
Model for Valuing Common Stock
This model is similar to the bond valuation models developed in Chapter 7 in that we employ discounted cash
flow analysis to find the value of a firm's stock.
Stocks can be evaluated in two ways:
(1) by finding the present value of the expected future dividends, or (2)
by finding the present value of the firm's expected future operating income, subtracting the value of the debt
and preferred stock to find the total value of the common equity, and then dividing that total value by the
number of shares outstanding to find the value per share.
Both approaches are examined in this spreadsheet.
THE DISCOUNTED DIVIDEND APPROACH
The value of any financial asset is equal to the present value of future cash flows provided by the asset. When
an investor buys a share of stock, he or she typically expects to receive cash in the form of dividends and then,
eventually, to sell the stock and to receive cash from the sale.
Moreover, the price any investor receives is
dependent upon the dividends the next investor expects to earn, and so on for different generations of
investors.
Thus, the stock's value ultimately depends on the cash dividends the company is expected to
provide and the discount rate used to find the present value of those dividends.
Here is the basic dividend valuation equation:
+
+
.
.
.
.
The dividend stream theoretically extends on out forever, i.e., n = infinity.
Obviously, it would not be feasible
to deal with an infinite stream of dividends, but fortunately, an equation has been developed that can be used to
find the PV of the dividend stream, provided it is growing at a constant rate.
Naturally, trying to estimate an infinite series of dividends and interest rates forever would be a
tremendously difficult task.
Now, we are charged with the purpose of finding a valuation model that is easier
to predict and construct.
That simplification comes in the form of valuing stocks on the premise that they
have a constant growth rate.
VALUING STOCKS WITH A CONSTANT GROWTH RATE
In this stock valuation model, we first assume that the dividend and stock will grow forever at a constant
growth rate. Naturally, assuming a constant growth rate for the rest of eternity is a rather bold statement.
However, considering the implications of imperfect information, information asymmetry, and general
uncertainty, perhaps our assumption of constant growth is reasonable.
It is reasonable to guess that a given
firm will experience ups and downs throughout its life. By assuming constant growth, we are trying to find the
average of the good times and the bad times, and we assume that we will see both scenarios over the firm's
life.
In addition to assuming a constant growth rate, we will be estimating a long-term required return for
the stock.
By assuming these variables are constant, our price equation for common stock simplifies to the
following expression:
In this equation, the long-run growth rate (g) can be approximated by multiplying the firm's return on assets