Problem:

A firm has a project that costs $600 today and pays off next period $900 with probability .5 and $360 with probability .5. Assume that all investors are risk-neutral, the risk-free interest rate is 0, and there are no direct bankruptcy costs. The firm currently has 1000 shares outstanding and the firm has no cash on hand and no other assets except for this potential project. Assume risk-neutrality, a zero interest rate, no direct bankruptcy costs, and no taxes.

Requirement:

Question 1: Could the firm finance this project with a sale of new equity? If so, how many shares would need to be issued?

Question 2: Could the firm finance this project with a sale of bonds? If so, what would be the necessary promised repayment to bondholders to fund the project?

Question 3: Suppose now that the firm has an alternative project that also costs $600 and pays off $1800 with probability .2 and $240 with probability .8. The firm cannot make a legally binding commitment to one of the two projects. Will the firm be able to raise money in the bond markets to fund one of their projects? Justify your answer with the appropriate computations.