Question $5$

ABC Corp has two projects, each costing $$100$ million today. The project payoffs in one year are given below:

$\backslash$table$[[\backslash$table$[[$Possible$],[$State$]],$Probability,Project $x$ Payoff,Project $Y$ Payoff$],[$Good$,70\%,121$ million,$143$ million$],[$Bad$,30\%,121$ million,$0]]$

Assume that the manager of the firm works in the best interest of shareholders. The state of the project is uncorrelated with the market. The riskfree rate equals $10\%.$

a$)$ Suppose that the firm has $$100$ million in hand$-$i$.$e$.,$ no external capital is necessary. Find the NPV of each project and determine which project the firm $($shareholders$)$ should choose.

b$)$ Suppose now the firm has no cash and must borrow $$100$ million $($i$.$e$.,$ one$-$year loan$).$ Assume that the lenders will charge the same discount rate as the one used in Part $($a$)$ for both projects. Determine the NPV of each project and which project the firm $($shareholders$)$ should choose.