A bank is in the process of renegotiating an $$100$ million loan

payments. If liquidated, it expects to receive $$96$ million. The new

loan will lower interest rates to $6\mathrm{.}5\%$ and extend the maturity to six

years. A grace period of three years is offered during which time only

interest will be paid. Principal payments of $$50$ million each year are

expected at the end of the last two years. An up$-$front fee of $1\%$ will

be collected as part of the renegotiation.

a$)$ If the cost of funds to the bank is $8\%$ after rescheduling, is the

bank better of with the new terms? Explain.

b$)$ What should the minimum up$-$front fee in percent be for the bank

to reschedule the loan?