Suppose the First National Bank of Duluth has $500.00 million in total assets with an average asset duration of five years. Assume that the bank’s liabilities are comprised of $86.75 million of demand deposits and $163.75 million in bonds with a 4.00% coupon rate (which pays annually) and a five year time-to-maturity. Further assume that current market interest rates are at 9.00% per annum. Show work.
(a) Calculate the duration of the bank’s bonds.
(b) What is this bank’s duration gap? Is the bank asset- or liability-sensitive?
(c) If interest rates are expected to decrease to 8.00%, approximate the bank’s change in net worth in millions.