$1.$ Manufactured Earnings is a "darling" of Wall Street analysts. Its current market price is $$15$ per share, and its book value is $$5$ per share. Analysts forecast that the firm's book value will grow by $10$ percent per year indefinitely, and the cost of equity is $15$ percent. Given these facts, what is the market's expectation of the firm's long$-$term average ROE?

$2.$ Given the information in the question above, what will be Manufactured Earnings$$ stock price if the market revises its expectations of long$-$term average ROE to $20$ percent?$$

$3.$ Analysts reassess Manufactured Earnings' future performance as follows: growth in book value increases to $12$ percent per year, but the ROE of the incremental book value is only $15$ percent. What is the impact on the market$-$to$-$book ratio?

$$

$4.$ What types of companies have

$$a high PE and a low market$-$to$-$book ratio?

$$a high PE ratio and a high market$-$to$-$book ratio? a low PE and a high market$-$to$-$book ratio? a low PE and a low market$-$to$-$book ratio?

Please show all calculations on Excel, thanks!