$-5.$ You are a stock analyst who Furrently assigned to estimate the equity price of Periscope Adventures $($PA$).$ The firm will increase the dividend by $10$ percent for the next $3$ years and thereafter increase the dividend by a long$-$term growth rate annually. Your boss told you to estimate the long$-$term growth rate using a geometric average of last several dividend payments. More information on PA: $(1)$ The PA's most recent dividend is $$1\mathrm{.}46$ per share. $(2)$ PA has paid annual dividends of $$1\mathrm{.}20,$$$1\mathrm{.}36,$$$1\mathrm{.}40,$$$1\mathrm{.}42,$ and $$1\mathrm{.}46$ over the last $5$ years, respectively. $(3)$ Currently, T$-$bills pay $5\%$ per year annually, and the market risk premium of S&P $500$ Index stocks is $10\%$ per year. The stock beta of PA is $1\mathrm{.}0.$

a$.$ Find the long$-$term growth rate.

b$.$ Find the equity price using the dividend discount model. $($$$17\mathrm{.}46)$