For the next year, Swiss Reinsurance Co$.($Swiss Re$)$ will pay a dividend of CHF$0\mathrm{.}1$ per share. You expect that over the next few years Swiss Re will gradually increase its dividend to $1\mathrm{.}60$ francs per share. Specifically, you expect that D$1=0\mathrm{.}10,$ D$2=0\mathrm{.}40,$ and D$3=0\mathrm{.}80,$ and D$4=1\mathrm{.}60$ francs per share. After year $4$ you expect the dividends to grow in perpetuity at the rate of g $=5\%$ per year, so that for example D$5=1\mathrm{.}05\backslash$times D$4,$ D$6=1\mathrm{.}05\backslash$times D$5,$ etc. You have estimated that the expected rate of return on other stocks of equivalent risk to Swiss Re is $10\%$ per year.

a$)$ Based on the dividend forecasts above, what is your estimate of the current $($time $0)$ value of a share of Swiss Re common stock? $(1$ pt$)$

b$)$ If the perpetual growth rate is $4\mathrm{.}5\%$ rather than $5\%$ what is your new estimate for the value of a share of common stock? $(0\mathrm{.}5$ pts$)$

c$)$ If the next few years are more difficult for Swiss Re than predicted and D$1=0\mathrm{.}10$ but dividends only grow at $5\%$ in year $2$ and in perpetuity. What is the value of a share of common stock in this scenario? $(0\mathrm{.}5$ pts$)$