Stock Valuation

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STOCK VALUATION 1. Common stock valuation A share of common stock is more difficult to value in practice than a bond, for at least three reasons. First, with common stock, not even the promised cash flows are known in a advance. Second, the life of the investment is essentially forever, since common stock has no maturity. Third, there is no way to easily observe the rate of return that the market requires. Nonetheless, as we will see, there are cases in which we can come up with the present value of the future cash flows for a share of stock and thus determine its value. Cash Flows Imagine that you are considering buying a share of stock today. You plan to sell the stock in one year. You somehow know that the
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From Chapter 6 (Example 6.7), we know that the dividend on a share of preferred stock has zero growth and thus is constant through time. For a zero growth share of common stock, this implies that: D1 = D2 = D3 = D = constant So, the value of the stock is:
|P0= |

If the dividend grows at a steady rate, then we have replaced the problem of forecasting an infinite number of future dividends with the problem of coming up with a single growth rate, a considerable simplification. In this case, if we take D0 to be the dividend just paid and g to be the constant growth rate, the value of a share of stock can be written as:
|P0= |D1 |+ |D2 |+ |D3 |+… | |
| |(1+R)1 | |(1+R)2 | |(1+R)3 | | |

|= |D0(1+g)1 |+ |D0(1+g)2 |+ |D0(1+g)3 |+… | |
| |(1+R)1 | |(1+R)2 | |(1+R)3 | | |

As long as the growth rate, g, is less than the discount rate, r, the present value of this series of cash flows can be written very simply as:
|P0= |D0(1+g) |= |D1

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