#$15$ The stock of Nogro Corporation is currently selling for $$10$ per share. Earnings per share in the coming year are expected to be $$2.$ The company has a policy of paying out $50\%$ of its earnings each year in dividends. The rest is retained and invested in projects that earn a $20\%$ rate of return per year. This situation is expected to continue indefinitely.

a$.$ Assuming the current market price of the stock reflects its intrinsic value as computed using the constant$-$growth DDM$,$ what rate of return do Nogro's investors require?

b$.$ By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested?

c$.$ If Nogro were to cut its dividend payout ratio to $25\%,$ what would happen to its stock price?