Suppose a firm needs $100 to invest in a project. The firm can choose between two

projects: S (safe) or R (risky). The bank cannot directly control the choice of project. If

it is S, then it will yield a cash ow of $300 with probability 0.8 and zero with probability

0.2. If it is R, the project will yield a cash flow of $423 with probability 0.5 and zero with

probability 0.5. Everybody is risk neutral. The riskless interest rate is 20%. The bank

would like to induce the choice of project S. Assume that collateral worth $1 to the rm

is worth $0.9 to the bank. The banking sector is perfectly competitive.

a. Demonstrate that when the bank offers an unsecured loan, project S will never be

chosen.

b. Calculate the interest rate when the bank offers an unsecured loan.

c. What kind of secured contract would the bank offer to induce the choice of project S?

d. Calculate the collateral and interest rate associated with this secured contract.