Consider a firm that is expected to earn $5 per share next year. EPS will continue at this level in perpetuity assuming none of the earnings are reinvested.

a. Suppose, at the end of each of the next five years the firm can reinvest $3 per share and those funds will earn a level 20% annual return in perpetuity starting the year after being reinvested. What is the price per share and P/E ratio if investors require a 12% return on investment?

b. Show that the P/E ratio is the reciprocal of the interest rate (investors required rate of return) if the reinvestment rate falls from 20% to 12%.

c. What is the relation between the P/E ratio and investors required rate of return when the latter is greater, smaller, or equal to the firms reinvestment rate of return?