A firm has $100$m in cash on hand and a debt obligation of $100$m due next period. With this cash, it can take one of two projects $($A and B$)$ which cost $100$m each. Assume that the firm cannot raise any additional funds. If the economy is favourable, project A will pay $120$m and project B will pay $101$m$.$ If the economy is unfavourable, project A will pay $60$m and project B will pay $101$m$.$ Assume

that investors are risk$-$neutral, there are no taxes or direct costs of bankruptcy, the risk$-$free rate of interest is nil, and the probability of each state of nature obtaining is equal.

a$.$ What is the NPV of each project?

b$.$ Which project will equity$-$holders want the firm$$s manager to take?

c$.$ Show that debt$-$holders would find it incentive$-$compatible to cut the face value of their claim to $82$m$.$