Assume a bank is in the process of restructuring a $1 million loan. The following information is provided. The current interest rate of the loan is 8% annually and matures at the end of this year. The cost of funds for this category of loan is 8%. There is a 20% probability that the loan will be defaulted and the recovery rate is 0.

Here are the restructuring terms:

Loan payments will be stretched to 5 years.

Interest rate will be reduced by 4% for the next 5 years.

Principal payment of $500, 000 in years 4 to 5.

No upfront fee.

The cost of funds for the bank increases to 10% since the risk of the loan increases after restructuring.

a. Is the present value of the new loan greater than the present value of the old loan?

b. What up-front fee will equate the present of the old and new loans?