The XiaXia Corporation is a company whose sole assets are $$$$100$ comma $000100,000$ in cash and three projects that it will undertake. The projects are$$ risk$-$free and have the following cash$$ flows: LOADING... $.$

XiaXia plans to invest any unused cash today at the$$ risk$-$free interest rate of $10\%10\%.$ In one$$ year, all cash will be paid to investors and the company will be shut down.

a$.$ What is the NPV of each$$ project? Which projects should XiaXia undertake and how much cash should it$$ retain?

b$.$ What is the total value of XiaXia$\text{'}$s assets$($projects and$$ cash$)$ today?

c$.$ What cash flows will the investors in XiaXia $$receive$?$ Based on these cash$$ flows, what is the value of XiaXia $$today$?$

d$.$ Suppose XiaXia pays any unused cash to investors$$ today, rather than investing it$.$ What are the cash flows to investors in this$$ case? Based on these cash$$ flows, what is the value of XiaXia $$today$?$

e$.$ Explain the relationship in your answers to parts $($b$),($c$),$ and $($d$).$