Ex7-1: A government bond is currently selling for $1,195 and pays $75 per year in interest for 14 years when it matures. If the redemption value of this bond is $1,000, what is its yield to maturity? Ex7-2: Suppose the government bond described in example 1 above is held for five years and then the savings institution acquiring the bond decides to sell it at a price of $940. Can you figure out the average annual yield the savings institution will have earned for its five-year investment in the bond? Ex7-3: A bank holds a 6%, semiannual coupon bond with a current market price of $988. The bond has a par value of $1,000 and matures in 10 years. What is the yield to maturity? Ex7-4: A bank holds two bonds: A and B. A is a 6%, semiannual coupon bond with a current market price of $975. B is a 6.3% coupon bond that pays interest annually and has a current market price of $990. Both bonds have a face value $1,000 and mature in 6 years. Which bond has the higher YTM? Ex7-5: Using following information, calculate the impact of one percent increase in market interest rate on the bond price. Financial Term Today One year later Market interest rate 3% 4% Coupon rate (semi-annual payment) 3% 3% Face value $1,000 $1,000 Maturity 10 years ? Price ? ? YTM 3% ? Ex7-6: U.S. Treasury bills are available for purchase this week at the following prices (based upon $100 par value) and with the indicated maturities: a. b. c. $97.25, 182 days. $95.75, 270 days. $98.75, 91 days. Calculate the bank discount rate (DR) on each bill if it is held to maturity. What is the equivalent yield to maturity (sometimes called the bond-equivalent or couponequivalent yield) on each of these Treasury Bills? Ex7-7: First National Bank of Bannerville has posted interest revenues of $63 million and interest costs from all of its borrowings of $42 million. If this bank possesses $700 million in total earning assets, what is First National’s net interest margin? Suppose the bank’s interest revenues and interest costs double, while its earning assets increase by 50 percent. What will happen to its net interest margin? Ex7-8: Farmville Financial reports a net interest margin of 2.75 percent in its most recent financial report, with total interest revenue of $95 million and total interest costs of $82 million. What volume of earning assets must the bank hold? Suppose the bank’s interest revenues rise by 5 percent and its interest costs and earnings assets increase by 9 percent. What will happen to Farmville’s net interest margin? Ex7-9: Suppose Carroll Bank and Trust reports interest-sensitive assets of $570 million and interestsensitive liabilities of $685 million. What is the bank’s dollar interest-sensitive gap? Its relative interestsensitive gap and interest-sensitivity ratio? Ex7-10: Peoples’ Savings Bank has a cumulative gap for the coming year of + $135 million, and interest rates are expected to fall by two and a half percentage points. Can you calculate the expected change in net interest income that this thrift institution might experience? What change will occur in net interest income if interest rates rise by one and a quarter percentage points? Ex7-11: The cumulative interest rate gap of Poquoson Savings Bank increases 60 percent from an initial figure of $25 million. If market interest rates rise by 25 percent from an initial level of 3 percent, what changes will occur in this thrift’s net interest income? Ex7-12: Sunset Savings Bank currently has the following interestsensitive assets and liabilities on its balance sheet with the interest-rate sensitivity weights noted. Interest-Sensitive Assets $ Amount Rate Sensitivity Index Federal fund loans $ 50.00 1.00 Security holdings 50.00 1.20 Loans and leases 350.00 1.45 Interest-Sensitive Liabilities $ Amount Rate Sensitivity Index Interest-bearing deposits $ 250.00 0.75 Money-market borrowings 90.00 0.95 What is the bank’s current interest-sensitive gap? Adjusting for these various interest rate sensitivity weights what is the bank’s weighted interest-sensitive gap? Suppose the federal funds interest rate increases or decreases 50 basis points. How will the bank’s net interest income be affected (a) given its current balance sheet makeup and (b) reflecting its weighted balance sheet adjusted for the foregoing ratesensitivity indexes? Ex7-13: Snowman Bank, N.A., has a portfolio of loans and securities expected to generate cash inflows for the bank as follows: Expected Cash Inflows of Principal and Interest Payments Annual Period in Which Cash Receipts Are Expected $1,275,600 746,872 341,555 62,482 9,871 Current year Two years from today Three years from today Four years from today Five years from today Deposits and money market borrowings are expected to require the following cash outflows: Expected Cash Outflows of Annual Period during Which Cash Principal and Interest Payments Payments Must Be Made $1,295,500 831,454 123,897 1,005 ----- Current year Two years from today Three years from today Four years from today Five years from today If the discount rate applicable to the previous cash flows is 4.25 percent, what is the duration of the Snowman’s portfolio of earning assets and of its deposits and money market borrowings? What will happen to the bank's total returns, assuming all other factors are held constant, if interest rates rise? If interest rates fall? Given the size of the duration gap you have calculated, in what type of hedging should Snowman engage? Ex7-14: A government bond currently carries a yield to maturity of 6 percent and a market price of $1,168.49. If the bond promises to pay $100 in interest annually for five years, what is its current duration? Ex7-15: Suppose that a savings institution has an average asset duration of 2.5 years and an average liability duration of 3.0 years. If the savings institution holds total assets of $560 million and total liabilities of $467 million, does it have a significant leverageadjusted duration gap? If interest rates rise, what will happen to the value of its net worth? Ex7-16: Stilwater Bank and Trust Company has an average asset duration of 3.25 years and an average liability duration of 1.75 years. Its liabilities amount to $485 million, while its assets total $512 million. Suppose that interest rates were 7 percent and then rise to 8 percent. What will happen to the value of the Stilwater bank's net worth as a result of a decline in interest rates? Ex7-17: Given the cash inflow and outflow figures in Problem 7-15 for Snowman Bank, N.A., suppose that interest rates began at a level of 4.25 percent and then suddenly rise to 4.75 percent. If the bank has total assets of $20 billion and total liabilities of $18 billion, by how much would the value of Snowman’s net worth change as a result of this movement in interest rates? Suppose, on the other hand, that interest rates decline from 4.25 percent to 3.5 percent. What happens to the value of Snowman’s net worth in this case and by how much in dollars does it change? What is the size of its duration gap? Ex7-18: Carter National Bank holds $15 million in government bonds having a duration of 12 years. If interest rates suddenly rise from 6 percent to 7 percent, what percentage change should occur in the bonds’ market price?
