$5.$ YYY Company$$s current EPS is $$5.$ It was $$3$ five years ago. The company pays out $50\%$ of its earnings as dividends, and the stock sells for $$50.$

a$.$ Calculate the historical growth rate in earnings. $[$Hint: this is a $5-$year growth period.$]$

b$.$ Calculate the next expected dividend per share, D$1.$ Assume that past growth will continue.

c$.$ What is YYY Company$$s cost of equity, rs$?$