Zain Inc. is about to launch a new product. There are three possible outcomes for next year, depending on the success of the launch: $$270$ million, $$120$ million or $$90$ million. These outcomes are all equally likely. The interest rate is $6\%.($Ignore all other market imperfections, such as taxes.$).$ Zain has $$130$ million in debt due next year.

a$.$ What is Zain$$s total value with leverage?

b$.$ Now suppose that in the event of default, $40\%$ of the value of Zain$$s assets will be lost to bankruptcy costs. What is Zain$$s total value with leverage and distress costs?