Business has been good for Keystone Control Systems, as indicated by the thirteen$-$year growth in earnings per share. The earnings have grown from $$1\mathrm{.}00$ to $$2\mathrm{.}41.$

a$.$ Determine the compound annual rate of growth in earnings $($n $=13).($Do not round intermediate calculations. Input your answer as a percent rounded to $2$ decimal places.$)$

b$.$ Based on the growth rate determined in part a$,$ project earnings for next year $($E$1).($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

c$.$ Assume the dividend payout ratio is $45$ percent. Compute D$1.($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

d$.$ The current price of the stock is $$20.$ Using the growth rate $($g$)$ from part a and D$1$ from part c$,$ compute Ke$.($Do not round intermediate calculations. Input your answer as a percent rounded to $2$ decimal places..$)$

e$.$ If the flotation cost is $$1\mathrm{.}50,$ compute the cost of new common stock $($Kn$)$ using growth rate $($g$)$ from part a and dividend $($D$1)$ from part c$.($Do not round intermediate calculations. Input your answer as a percent rounded to $2$ decimal places.$)$