An investment of $500$ will generate one of two outcomes: $400$ in one year and $500$ in two years OR $350$ in one year and $300$ in two years. Each outcome has a $50\%$ probability. The discount rate is $15\%.$

i$.$

What is the expected NPV of the investment?

ii$.$

Assume that you have an option to abandon in one year for $300.$ If you abandon, you keep that as the year one cash flow and give up the year two cash flow. Is the abandonment rational for either outcome? What is the NPV of the investment assuming rational abandonment and the value of the abandonment option?