Start$-$Up Industries is a new firm that has raised $$200$ million by selling shares of stock. Management plans to earn a $24\%$ rate of return on equity, which is more than the $15\%$ rate of return available on comparable$-$risk investments. Half of all earnings will be reinvested in the firm.

a$.$ What will be Start$-$Up's ratio of market value to book value? $($Do not round intermediate calculations.$)$

Market$-$to$-$book ratio

b$.$ What will be Start$-$Up's ratio of market value to book value if the firm can earn only a rate of return of $10\%$ on its investments? $($Do not round intermediate calculations. Round your answer to $1$ decimal place.$)$

Market$-$to$-$book ratio