The Good Prospects company has $$60$ million in cash and in one year its assets in place $($separate from the $$60$ million in cash$)$ will be worth $$300$ million with probability $0\mathrm{.}6,$ or $$80$ million with probability $0\mathrm{.}4.$

Next year, the firm also has to repay a loan of $$150$ million.

Today, the firm can either pay out the cash as a dividend or invest it in a project that will pay $$90$ million in the good state or $$70$ million in the bad state. The appropriate discount rate is zero.

i$)$ What is the project's NPV$?$ Should the project be undertaken?

ii$)$ When are shareholders better off, with or without the project? Why? Would lenders want the project to be undertaken?

iii$)$ How can the shareholders finance the project so as to make sure they undertake it rather than not?