$1.$ Suppose that if investors purchase a share of Firm A$\text{'}$s stock today, there is a $50\%$

probability that they will receive a $$150$ per share dividend payment one year later, and

a $50\%$ probability that they will receive a $$50$ per share dividend payment. After this

payment, the firm will be liquidated, and the shares will have no further claims on the

firm's liquidation value. If stock investors require a $9\%$ return to invest in this firm, what

should be the price per share today? If the discount rate increases to $11\%$ today, what

would be the new price per share? At the new price, what is the investors' expected

return during the year?

$2.$ A firm is expected to earn $$10$ per share in one year and plans to invest $60\%$ of its

earnings in new investment opportunities, paying out the remaining $40\%$ as dividends

each year. Once an investment is made, it will generate a fixed rate of return annually.

Investors believe the firm's new investments can yield a $12\%$ return per year and

require a $12\%$ expected return to invest in the firm due to the risk associated with these

cash flows. What should be the current price per share? Additionally, suppose the firm

announces that it expects its new investments to generate a $15\%$ return per year, while

the plowback ratio and required rate of return remain unchanged. By what percentage

will the stock price increase upon this announcement? Will this news alter the stock's

expected return going forward $($after the price adjusts to the news$)?$