1. a. A zero-coupon bond pays $1000 in five years. i) What is the value of the bond today? The nominal interest rate is 1% ii) Price the bond if the interest rate is now 10% iii) Describe the relationship between the interest rate and the bond price. b. A zero-coupon bond pays $1000 in one year and sells for $924 now. Calculate the yield to maturity of the bond. c. A zero-coupon bond pays $1000 in six years and sells for $770 now. Calculate the yield to maturity of the bond to the nearest basis point (one hundredth of one percent). d. A consol pays $20 each year forever. The consol is currently selling for $160. The consol begins payments next year. What is the yield to maturity of the consol? c. A one-period coupon bond has a face value of SFV and pays an annual coupon amount C. Show that if the bond is priced at par (that is, the bond price equals its face value), then the yield of the bond is the coupon rate c. f. An annual coupon bond has a maturity of twelve years, a face value of $1000, and a coupon rate of 4%. The current market price of the bond is $780. Use a grid search to find the yield to maturity of the bond to the nearest basis point one hundredth of a percent). Other methods will not receive full credit. Use a spreadsheet program and print a copy of your work. gA U.S. Treasury note with a face value of S1000 pays interest semiannually at matures in three years. If the coupon rate is 4% and the bond equivalent yield is 5%, find the price of the note. Obey all pricing conventions h 1) At the grocery store, apples cost 96 cents and bananas cost 92 cents. If a shopper buys twenty apples and ten bananas, what is the total cost at checkout? ii) A one year zero coupon bond with a face value of S100 has a yield of 4.1667% A similar bond with a maturity of two years has a yield of 4.2572%. If a bond manager holds a bond portfolio with twenty zero coupon bonds that mature in one year and ten zero coupon bonds that mature in two years, what is the value of the bond portfolio? iii) Compare part (i) to part() in a sentence or two. i. Consider the prices for the following zero-coupon bonds: Bond Bond A Bond B Bond Maturity 1 year 2 year 3 year Face Value SI SI 525 Price 0.98 094 23 Calculate the price of an annual coupon bond that matures in 3 years with a coupon rate of 5% on a face value of $100 (Problem 1. continued) j. At the grocery store, you buy a ten apples and a hundred bananas. The price of an apple is 98 cents, while your total bill is $103.80. What is the price of a banana? Explain your solution procedure using an equation. k. Suppose three bonds that pay annual coupons have a face value of 100 and are priced according to the following table: Bond A Coupon Rate 0% 2.5% 5% Maturity 1 year 2 years 3 years Price S96.89922 596 25466 $95.25892 Three zero coupon bonds with maturities of 1 year, 2 years, and 3 years have a face value of $1 each. Find the price of each zero coupon bond. Compare parts (1) and (k)
