Hazel Morrison, a mutual fund manager, has a $$40$ million portfolio with a beta of $1\mathrm{.}00.$ The risk$-$free rate is $4\mathrm{.}25\%,$ and the market risk premium is $6\mathrm{.}00\%.$ Hazel expects to receive an additional $$5\mathrm{.}50$ million, which she plans to invest in additional stocks. After investing the additional funds, she wants the fund's required and expected return to be $13\mathrm{.}00\%.$ What must the average beta of the new stocks be to achieve the target required rate of return?

Select the correct answer.

a$.4\mathrm{.}73$

b$.4\mathrm{.}79$

c$.4\mathrm{.}75$

d$.4\mathrm{.}77$

e$.4\mathrm{.}81$