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

$\backslash$table$[[\backslash$table$[[$Project$]],\backslash$table$[[$Cash Flow$],[$Today $($$$)]],\backslash$table$[[$Cash Flow$],[$in One Year $($$$)]]],[$A$,-20,000,30,000],[$B$,-10,000,25,000],[$C$,-60,000,80,000]]$

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

Interest rate $$

a$.$

What is the NPV of each project? Which projects should Xia undertake?

$\backslash$table$[[$Project$,\backslash$table$[[$Cash flow$],[$today$]],\backslash$table$[[$Cash flow in$],[$one year$]],$NPV$],[$A$,(20000\mathrm{.}00),30000\mathrm{.}00,],[$B$,(10000\mathrm{.}00),25000\mathrm{.}00,],[$C$,(60000\mathrm{.}00),80000\mathrm{.}00,]]$

Accept no projects

and

b$.$ What is the total value of Xia's assets $($projects and cash$)$ today?

Value of company is the sum of its projects' NPVs

Plus its cash

Total value of the company