1) Let the given 2 banks:
Bank 1 has assets composed only of ten-year, 12% coupon, $1 million loan with 12% yield to maturity. It is financed with the 10-year, 10 percent coupon, $1 million CD with the 10% yield to maturity.
Bank 2 has assets composed only of 7-year, 12%, zero-coupon bond with present value of $894,006.20 and maturity value of $1,976,362.88. It is financed by 10-year, 8.275% coupon, $1,000,000 face value CD with yield to maturity of 10%.
All securities except zero-coupon bond pay interest annually
i) If interest rates increase by 1% (100 basis points), how do values of assets and liabilities of each bank change?
ii) What accounts for differences between two banks’ accounts?
2) What is the duration of the 5-year, $1,000 Treasury bond with 10% semi-annual coupon selling at par? Selling with yield to maturity of 12%? 14%? What can you conclude about relationship between duration and yield to maturity? Plan the relationship. Explain why does this relationship exist?
3) By using a Spreadsheet to compute Yield to Maturity. Determine the yield to maturity on given bonds; all have maturity of 10 years, face value of $1,000, and coupon rate of 9% (paid semi-annually). The bond’s present market values are $945.50, $987.50, $1,090.00, and $1,225.875, respectively.
Market Value Total Payments Periodic coupon payment Face Value
945.500 20 451,000 9.87%
987.500 20 451,000 9.19
1,090.000 20 451,000 7.69
1,225.875 20 451,000 5.97
The Yield to Maturity will be?