SAGE Ltd$.$ had earnings per share of $$5$ as of December $31,2022,$ but paid no dividends. Earnings were expected to grow at $14\mathrm{.}2$ percent per year for the following five years. SAGE Ltd$.$ will start paying dividends for the first time on December $31,2027,$ distributing $50$ percent of its earnings to shareholders. Earnings growth will be $6$ percent per year for the next six years $($that is$,$ from January $1,2028,$ through to December $31,2033).$ Starting on December $31,2033,$ SAGE Ltd$.$ will begin to pay out $80$ percent of its earnings in dividends and earnings growth will stabilize at $2$ percent per year in perpetuity.The required rate of return on SAGE stock is $10$ percent. What should be the current share price of SAGE?