Question $1$

a$.$You are a stock analyst in charge of valuing high$-$technology firms, and you are expected to come out with buy$-$sell recommendations for your clients. You are currently analyzing a firm called eTalk.com that specializes in Internet business communication. You are expecting explosive growth in this area. However, the company is not currently profitable even though you believe it will be in the future. Your projections are that the firm will pay no dividends for the next $10$ years. Eleven years from now, you expect the stock to pay its first dividend of $$2$ per share. You expect dividends to increase at a rate of $25$ percent per year for the nine years after that. At that point, the industry will start to mature and slow down; dividends will continue to grow but only at a rate of $9$ percent per year.

The stock is priced in the market at $$15$ per share. If you believe that a fair rate of return on a stock of this type is $14$ percent, what is your estimate of the value of the stock, and should you issue a recommendation to buy or to sell? $($make sure to show all work$)$

b$.$The day after you make your estimate in part $($a$)$ news indicates that things are not going as smoothly as predicted for this business. Your estimates of the initial dividend and the growth rates remain the same, but the timing has changed. You now decide that the firm will pay its first dividend $($$$2)$ in $16$ years. The high growth period $(25$ percent per year$)$ will last for only four years before slowing to a growth of $9$ percent per year.

Given a rate of return of $14$ percent, what is your new estimate of the value of the stock, and should you change your recommendation? $($make sure to show all work$)$