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Problem Walk$-$Through

You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $$2\mathrm{.}25$ a share at the end of the year $(D_1=$$$2\mathrm{.}25)$ and has a beta of $0,9.$ The risk$-$free rate is $4\mathrm{.}5\%,$ and the market risk premium is $4\%.$ Justus currently sells for $$31\mathrm{.}00$ a share, and its dividend is expected to grow at some constant rate, g$.$ Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of $3$ years? $($That is$,$ what is widehat$(P{)}_3?)$ Do not round intermediate calculations. Round your answer to the nearest cent.