Assume the current Price$-$to$-$Earnings $($P$/$E$)$ ratio for Firm A is $20,$ which is the same as the S&P $500$ index. If Firm A is an average firm, what is the required rate of return? Additionally, if Firm A is not an average firm, and its current stock price is $$100,$ with forward earnings per share of $$5,$ a required rate of return of $10\%,$ and a plowback ratio of $50\%,$ what is the expected Return on Equity $($ROE$)$ for Firm A$?$