Consider a firm with $25 in cash and assets in place that will pay a certain $20 at date 1. Assume the discount rate and risk-free rate are 0%. The firm's manager, acting in the interest of the equity holders, can choose between two projects:

Project L:

o Invest $25 (using the cash) at date 0.

o Receive certain $30 at date 1.

Project C:

o Invest $25 (using the cash) at date 0.

o Receive $50 if in good state at date 1 (40% probability)

o Receive $0 if in bad state at date 1 (60% probability)

1. Suppose the firm is all-equity financed.

a. Which project will the manager choose?

b. What is the value of the firm? Discuss whether and why/why not the manager made the decision to maximize firm value.

2. Suppose the firm has $40 in debt that matures at date 1

a. Which project will the manager choose?

b. What is the value of the firm? Discuss whether and why/why not the manager made the decision to maximize firm value.

3. Suppose the firm has convertible debt with a face value of $20 that matures at date 1. The debt holders have the option to convert their debt into 60% of the value of the firm at date 1.

a. What must the minimum value of the firm for which debt holders will choose to convert their debt to equity?

b. What are the original equity holders' payoffs in each state (good and bad) for each project (L and C)?

c. Which project will the manager choose?

d. What is the value of the firm? Discuss whether and why/why not the manager made the decision to maximize firm value.