Mr$.$ Altman has an idea for a new project, and he is considering starting a new business. The investment cost for the new project is $$42$ million today. After one year, the project will either succeed or fail, the value of the project becoming $$100$ million or $$20$ million, respectively. Since Mr$.$ Altman has no money today, he wants to finance the project either through equity or debt.

Mr$.$ Altman knows that after the investment, he has opportunities to take private benefits from the project. If he gives up the private benefits, the project will succeed with $80\%$ probability and fail with $20\%$ probability. If he pursues the private benefits, he can get $$30$ million into his pocket, but the project$$s probability of success reduces to $20\%$ and the probability of failure increases to $80\%.$

Assume all potential investors are risk$-$neural and the risk$-$free rate is $0.$

$($a$)(4$ points$)$ What is the minimum fraction of total shares for potential equity holders to break even? Can this project be equity financed?

$($b$)(4$ points$)$ What is the minimum face value of debt for potential debt holders to break even? Can this project be financed by debt?