Beckman Engineering and Associates $($BEA$)$ is considering a change in its capital structure.BEA

currently has $$20$ million in debt carrying a rate of $8$ percent, and its stock price is $$40$ per

share with $2$ million shares outstanding.BEA is a zero growth firm and pays out all of its

earnings as dividends.EBIT is $$14\mathrm{.}933$ million, and BEA faces a $40$ percent federal$-$plus$-$state

tax rate.The market risk premium is $4$ percent, and the risk free rate is $6$ percent.BEA is considering

increasing its debt level to a capital structure with $40$ percent debt, based on market values,

and repurchasing shares with the extra money that it borrows.BEA will have to retire the

old debt in order to issue new debt, and the rate on the new debt will be $9$ percent.BEA has a

beta of $1\mathrm{.}0.$

a$.$ What is BEA$$s unlevered beta? Use market value D$/$S when unlevering.

b$.$ What are BEA$$s new beta and cost of equity if it has $40$ percent debt?

c$.$ What are BEA's WACC and total value of the firm with $40$ percent debt?