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 1.5, 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 5% 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 = P1/P0-1) and how much is attributable to dividend yield (D1/P0)?

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 10%

i. What is the implied growth rate?

ii. What is the value of the stock?

iii. What is the present value of growth opportunities?