Problem:
Your client is a regional savings and loan institution. You have been hired to assess the client's exposure to interest rate risk and advise on possible ways to reduce it. You have the following information on the S&L's balance sheet: The assets are 30-year, fixed-rate mortgages with an interest rate of 7%, issued 5 years ago. At that time, the total amount outstanding (i.e., lent out) was $3.6 billion. For simplicity, assume that payments on these mortgages are annual, that this year's payment has just been made, and that all future payments will be made exactly as scheduled (i.e., ignore the possibility that borrowers might default or choose to pay off their loans prior to maturity). Assume also that the mortgage payments your client has already received have been used to pay employee salaries, so that you can ignore these payments in all that follows. The liabilities are 5-year Certificates of Deposit (CDs) with a coupon rate of 8%, which we assume is paid annually (CDs are coupon bonds, so all coupon bond formulas apply to them). The total face value of the CDs that have been issued by your client is $2.5 billion. The yield curve is flat at 8%.
Required:
Question 1: Compute the (net) market value of your client's bank (i.e., the value of the assets minus the value of the liabilities).
Question 2: Compute the duration of the assets and of the liabilities.
Question 3: Compute the duration of the (net) market value of the bank.
Question 4: Your recommendation to the client is to sell some of the mortgage portfolio and buy 1-year CDs (which pay an annual coupon rate of 8%) with the proceeds. How many dollars worth of the assets does your client have to sell to reduce the duration of the (net) market value of the bank to 0 (i.e., to achieve immunization)?
Note: Please provide reasons to support your answer.