If ROE $>$ rS$,$ then a company will increase shareholder value $($stock price will go up$)$ when retaining earnings and reinvesting them within the company.

Assume a firm has ROE $=20\%$ and rS$=15\%.$ Next period's earnings $($E$1)$ will be $$8$ per share.

Calculate the share price if the firm retains $25\%$ of its earnings $($and pays out $75\%$ as a dividend$).$

Calculate the share price if the firm retains $50\%$ of its earnings $($and pays out $50\%$ as a dividend$).$

What is the difference in price?

A$.)$ $$7\mathrm{.}50$

B$.)$ $$2$

C$.)$ $$11\mathrm{.}25$

D$.)$ $$20$

E$.)$ $$15$