Village Fool stock is currently priced at $$78\mathrm{.}13$ per share and is expected to pay its next dividend, which is expected to be $$5\mathrm{.}03,$ in $1$ year. The stock has a beta of $1\mathrm{.}16.$ The market has an expected return of $15\mathrm{.}16\%,$ the risk$-$free rate is $3\mathrm{.}02\%,$ and the inflation rate is $2\mathrm{.}82\%.$ What is the stock price of Village Fool expected to be in $1$ year?

$$86\mathrm{.}46($plus or minus $10$ cents$)$

$$91\mathrm{.}49($plus or minus $10$ cents$)$

$$87\mathrm{.}77($plus or minus $10$ cents$)$

$$95\mathrm{.}77($plus or minus $10$ cents$)$

None of the above is within $10$ cents of the correct answer