XYZ Inc. has 2 million shares outstanding. The company currently pays out all its earnings as dividends and just paid a dividend of $5 per share. Its annual earnings are expected to be in perpetuity. It is considering a new project that requires retaining $1 million on year from now as an initial investment. The same opportunity will continue to exist indefinitely. Suppose in each subsequent year the company will retain and invest the same percentage of annual earnings as the first year. The return on new investments will remain 50% in perpetuity. The required rate of return for the company is 10%.

1. What is the per share stock price if the company undertakes no new investment? What are the annual earnings of the company without new investment?

2. What is the return on the new investment? Would undertaking the infinite series of new investment opportunities increase the firm's value? Explain intuitively without calculating the NPVs of the new investments.

3. What is the growth rate of the firm if the new investment opportunities are undertaken?

4. What is (per share) stock price if the company announces to undertake the infinite series of the investment opportunities?

5. Does the P/E (where E is the current earnings per share) increase, stay constant, or decrease after the announcement? Why?