Happy Face Corporation s about to launch a new product. Depending on the success of the new product, Happy Face may have one of five values next year: $200 million, $180million, $160miilion, $100million and $80million. These outcomes are all equally likely, and this risk is diversifiable. Suppose the risk-free interest rate is 5% and that, in the event of default, 20% of the value of Happy faces assets will be lost to bankruptcy costs. (Ignore all other market imperfections, such as taxes.)

1) What is the initial value of Happyfaces equity without leverage? Now suppose Happyface has zero-coupon debt with a $120million face value due next year.

2) What is the initial value of Happyfacess debt?

3) What is the initial value of Happyfaces equity? What is Happyfaces total value with leverage? Suppose Happyface has 5 million shares outstanding and no debt at the start of the year.

4) If Happyface does not issue debt, what is its share price?

5) If Happyface issues debt of $120 million due next year and uses the proceeds to repurchase shares, what is the number of shares outstanding after the repurchase?

Please show all the steps and reasoning