XYZ Inc. has expected earnings over the next year of $2/share (E1 = 2). The company is expected to maintain an earnings retention rate of 40%, 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%, and the market risk premium is also 4%.

a. If the growth rate in earnings is expected to be 4% in perpetuity

i. What is the value of the stock?

ii. What is the expected price a year from now?

iii. What is the expected holding period return over the next year? How much of this return is due to capital gains (price appreciation) and how much is attributable to dividend yield?

iv. What ROE justifies this growth rate?

v. What is the present value of growth opportunities for this stock?

b. If the ROE is expected to be 15% in perpetuity

i. What is the implied growth rate?

ii. What is the value of the stock?

iii. What is the present value of growth opportunities?

c. If the current price of the stock is $18/share

i. What is the implied growth rate?

ii. What is the implied ROE?

iii. What is the present value of growth opportunities?