Chapter 11.3, Problem 99AYU

Stock Price One method of pricing a stock is to discount the stream of future dividends of the stock. Suppose that a stock pays $\$P$ per year in dividends, and historically, the dividend has been increased $i\%$ per year. If you desire an annual rate of return of $r\%$, this method of pricing a stock states that the price that you should pay is the present value of an infinite stream of payments: Price = $P+P\cdot \frac{1+i}{1+r}+P\cdot {\left(\frac{1+i}{1+r}\right)}^2+P\cdot {\left(\frac{1+i}{1+r}\right)}^3+\mathrm{........}$

The price of the stock is the sum of an infinite geometric series. Suppose that a stock pays anannual dividend of $\$4.00$, and historically, the dividend has been increased $3\%$ per year. You desire an annual rate of return of $9\%$. What is the most you should pay for the stock?