A firm with a book value of $$15\mathrm{.}60$ per share and $100$ percent dividend payout is expected to have a return on common equity of $15$ percent per year indefinitely in the future. Its cost of equity capital is $10$ percent.a$.$ Calculate the intrinsic price$-$to$-$book ratio.b$.$ Suppose this firm announced that it was reducing its payout to $50$ percent of earnings in the future. Consider two scenarios $1).$ the dividend that is not paid out is invested at the same ROCE of $15\%$; $2).$ the dividend that is not paid out is invested at the required rate of return $10\%.$ What is the new intrinsic price$-$to$-$book ratio in these two scenarios?