Lily owns shares in Patina Constructions Pty Ltd$.$ Currently, the market price of the share is $$30\mathrm{.}31.$ The company expects to grow at a constant rate of $4$ per cent for the foreseeable future. Its last dividend was worth $$3\mathrm{.}125.$ Kaitlin$$s required rate of return for such shares is $13\mathrm{.}35$ per cent. She wants to find out whether she should sell her shares or add to her holdings.

a$.$ What is the maximum price that you would be willing to pay for this share? $($round to $2$ d$.$p$)$

b$.$ Based on your answer to part a$,$ should Lily buy additional shares in Patina Constructions? Why or why not?

c$.$ What is the share price in $4$ years if the growth rate increases to $5\%$ after $4$ years? $($round to $2$ d$.$p$)$