Yesterday, Initech paid out $$0\mathrm{.}86$B in dividends and repurchased $$4\mathrm{.}475$B worth of shares. Initech has $1\mathrm{.}22$B shares

outstanding and pays all of its dividends and makes its repurchases at the end of each year. Because of the slow down in

the economy, analysts expect that next year Initech will hold dividend payments constant at yesterday's level and cancel

its stock repurchase program. Two years from now, analysts forecast that total payouts will return to the level of yesterday.

After that date analysts expect that total payouts will grow at an annual rate of $2\mathrm{.}5\%$ in perpetuity. Assume that investors

require a $9\mathrm{.}5\%$ rate of return on Initech shares. What is the Total Payout model estimate of the stock price today?

$$

A$.$ $$69\mathrm{.}60$

B$.$ $$57\mathrm{.}69$

C$.$ $$70\mathrm{.}39$

D$.$ $$63\mathrm{.}18$

E$.$ $$77\mathrm{.}07$

Answer is apparently $57\mathrm{.}69$ according to my professor, please explain how this makes sense and how to solve it$.$ Thanks!