Stock Valuation. Numb Corp. will pay a dividend of $3.75 next year.
The company has stated that it will maintain a constant growth rate of
5 percent a year forever. If you want a 15 percent rate of return, how
much will you pay for the stock? What if you want a 10 percent rate of
return? What does this tell you about the relationship between the
required return and the stock price?

The formula for valuing any asset can be expressed as Price= Next
Period Dividend (D1)/R-g, where R is the discount rate and g is the
growth rate.  Plug in the information:

(a) P=3.75/(.15-.05)-->You would be willing to pay $37.50 for this stock

(b) At a discount rate of only 10%, we get P=3.75/(.10-.05), or $75.

The above calculations indicate that there is an inverse relationship
between stock price and required return.  Comparing (a) and (b), the
lower the required return, the MORE you are willing to pay for an
investment.  Conversely, (and also a fundamental idea in finance), the
higher the required return, the LESS you will be willing to pay for
that investment.

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