1. XYZ Inc. has expected earnings over the next year of $2/share (E[E1] = 2). The company is expected to maintain an earnings retention rate of 40% (b = 0.4), i.e., 60% of earnings are expected to be paid out as dividends every year. The company has a beta of 2, the risk-free rate is 4% (rf = 4%), and the market risk premium is also 4% (E[rM]-rf = 4%).

1. If the growth rate in earnings is expected to be 4% in perpetuity
   1. What is the value of the stock?
   2. What is the expected price a year from now?
   3. Whatistheexpectedholdingperiodreturnoverthenextyear?
   4. whatisROEjustifiesthisgrowthrate?
   5. whatisthepresentvalueofgrowthopportunityforthisstock?
2. Ifthecurrentpriceofthestockis$18/share,whatistheimpliedgrowthrate?
   1. whatistheimpliedgrowthrate?
   2. whatistheimpliedROE?
   3. whatisthepresentvalueofgrowthopportunityforthisstock?

If the ROE is expected to be 15% in perpetuity

1. whatistheimpliedgrowthrate?
2. whatistheimpliedROE?
3. whatisthepresentvalueofgrowthopportunityforthisstock?

2.XYZ Inc. is expected to pay no dividends for the next 5 years. However, at the end of the sixth year (at time 6), the company is expected to pay a dividend of $1/share. Dividends are expected to grow at 10% per year for the following 9 years (through the end of the 15th year, i.e., time 15), then to grow at 5% every year thereafter (forever). Assume the appropriate discount rate (required return) is 10%.

1. What is the expected value of the stock at time 15?
2. What is the expected value of the stock at time 5?
3. What is the value of the stock today?