A company must pay its bank a 1020 "old debt" at time 1. The firm does not notify the bank, but it knows that the value of its assets will only be 1,000 at time 1 and that it cannot, therefore, reimburse the bank in full. The firm finds an investment project that requires an investment of 100 days which will give payment at time 1 of 50 or 148 with equal probability.

A 10% discount rate should be used for this project. It must be assumed that all agents present no risk.

1. It must be shown that this project is not profitable. The company wishes to obtain financing for the project and therefore goes to the bank. The only information the bank learns is that the project will have a value of 148 at time 1, not that there is a 50% chance that it will have a value of 50. The bank agrees to lend 100 to the company for one year at 10% interest.

2. Show that pursuing the non-profitable project has an advantage for the owners of the firm.

3. What is the highest amount of old debt the firm could have if this over-investment problem were to disappear?

(Hint: To calculate the debt level we can assume that the shareholders do not receive any cash flow in the State where the project is worth 50. We can wonder when the cash flow towards the shareholders is greater than the uncertain cash flow expected?)