Assume all risks involved in this question are idiosyncratic $($firm$-$specific$)$ so investors discount rate is always the risk$-$free rate, $10\%.$ A firm currently has two assets: $$60$ million cash and a risky investment project A that lasts for one year. It also has $$121$ million debt payment due next year. The firm faces an additional risky investment B that also lasts one year, which requires initial investment of $$60$ million today.$$Scenario $1(50\%)$Scenario $2(50\%)$Assume all risks involved in this question are idiosyncratic $($firm$-$specific$)$ so investors' discount rate is always the risk$-$free rate, $10\%.$ A firm currently has two assets: $$60$ million cash and a risky investment project A that lasts for one year. It also has $$121$ million debt payment due next year. The firm faces an additional risky investment $B$ that also lasts one year, which requires initial investment of $$60$ million today.

$\backslash$table$[[$Scenario $1(50\%),$Scenario $2(50\%)$cash flow of Project A$$$$110$ mil$$ $$44$ milcash flow of Project B$$$$77$mil$$ $$33$ milIf the managers objective is to maximize firm value, will they invest in project B$?$If the managers objective is to maximize shareholder value, will they invest in project B$?$ Please explain.