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 $1(50\%)$

cash flow of Project A mil

cash flow of Project B mil

$$110$mil

$$77$ mil

Scenario $2(50\%)$

$$44$

$$33$

If the manager's objective is to maximize firm value, will they invest in project $B?$ If the manager's objective is to maximize shareholder value, will they invest in project B$?$ Please explain.