Sahara Co. pays a dividend of one dollar for every share (before valuation, time t). The expected growth rate of dividend is 25% per year for the next 4 years and then will level off to 5% per year forever. Jimmy believes that stockholders of Sahara Co. has a required rate of return of 20% per year.

1. Estimate the intrinsic value of a share of Sahara Co.'s stock

2. Suppose Jimmy believes that Sahara Co.'s expected growth rate of 25% will decline linearly over the next 4 years to the stable growth rate of 5%. Estimate the intrinsic value of a share of Sahara Co.'s stock.

3. Show that assumption of linearly declining extraordinary growth rate leads to a lower estimate of the value of Sahara Co.'s extraordinary growth opportunities.