A mutual fund manager has a $$80$ million portfolio with a beta of $2\mathrm{.}0.$ The risk$-$free rate is $5\mathrm{.}1\%,$ and the market risk premium is $5\mathrm{.}5\%.$ The manager expects to receive an additional $$20$ million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be $14\%.$ What should be the average beta of the new stocks added to the portfolio?

$0\mathrm{.}1000$

$0\mathrm{.}0818$

$0\mathrm{.}0955$

$0\mathrm{.}0909$

$0\mathrm{.}0864$