Beepy Medical Devices Inc. has $3$ million outstanding shares and no debt. It currently has $$9$ million in excess cash it is planning to pay out to shareholders. Investors expect Beepy to continue as an ongoing business forever, with future cash flows of $$30$ million per year. Beepy's business is considered riskless, so its equity cost of capital is given by the risk$-$free rate of $5\%$ per year. a$)$ Suppose Beepy pays out the $$9$ million as a dividend, and will also pay out the future cash flows as an annual dividend. What is the company's stock price before the ex$-$dividend date? Denote this price by P$^(+).$ b$)$ By how much does the stock price change on the ex$-$dividend date? Denote the price change by $/\_\backslash$P$,$ express it in dollars $($but do not use the $ sign$),$ and use a plus sign to indicate a price increase and a minus sign to indicate a price decrease. c$)$ Suppose that before paying out the $$9$ million as a dividend, Beepy issues additional shares to raise extra $$21$ million, so that they can pay out the same amount $($ $$30$ million$)$ as in the subsequent years. What will be the annual dividend per share? d$)$ Now suppose that instead of paying a dividend, Beepy uses the $$9$ million to repurchase shares. How many shares will remain outstanding after the repurchase? e$)$ What will be the stock price after the repurchase? f$)$ Suppose again Beepy will pay out the $$9$ million as a dividend $($without issuing additional shares$),$ but now add taxes. In particular, assume that dividend income is taxed at $40\%$ and capital gains are taxed at $20\%.$ What will be the change in the firm's stock price, $/\_\backslash$P$^("$taxes $"),$ on the ex$-$dividend date in this case? Again, use a plus sign to indicate a price increase and a minus sign to indicate a price decrease. please answer all parts, thank you!